A substrate comprising an electrode and an optical modulator having reduced diffraction

Abstract

A substrate for use in a light modulator is disclosed. The substrate may comprise at least one drive electrode applied to the substrate. The drive electrode is arranged in a pattern across the substrate. The pattern of drive electrodes across the substrate comprises a plurality of repeating building blocks. The electrodes in the building blocks form the at least one drive electrode.

Description

Technical Field

[0001] The subject matter of the present disclosure relates to optical modulators, substrates, optical modulator methods, and computer-readable media.

Background Art

[0002] Optically active glazing is known in the art. Typically, an optically active glazing system comprises two parallel plates made of a transparent dielectric material such as glass or plastic material. The internal volume defined between the plates may be subdivided into a plurality of small, independent volumes or individual cells filled with a dielectric fluid. The fluid contains a suspension of particles of a dielectric, charged or chargeable material. The opposing faces of the two plates carry electrodes facing each other. The electrodes are connected to a power source associated with control means.

[0003] The electrodes of each plate are formed by combs that are arranged alternately in pairs within each other. The electrodes of the two alternately arranged combs can take voltages of the same or opposite polarities. By an appropriate voltage on the electrodes, the particles can be concentrated at different locations between the electrodes, giving the system either a transparent or an opaque appearance.

[0004] There are various drawbacks associated with known systems. When the known glazing is in its transparent configuration, the electrodes applied to the plates cause a diffraction effect. The diffraction effect is undesirable for the glazing. In some situations, the presence of the diffraction effect can also be harmful to safety. For example, when optically active glazing is applied in a vehicle such as a car, the presence of diffraction can cause confusion or distraction to the vehicle operator.

Prior Art Documents

Patent Documents

[0005]

Patent Document 1

[0006] [Non-Patent Document 1] Leutenegger, M., Rao, R., Leitgeb, R. A. and Lasser, T. Fast focus field calculations. Opt. Express 14, 11277 - 11291 (2006) [Non-Patent Document 2] Hu, Y. et al. Efficient full - path optical calculation of scalar and vector diffraction using the Bluestein method. Light Sci. Appl. 9, 1 - 11 (2020) [Non-Patent Document 3] Murray, Ian B., Densmore, V., Bora, V., Pieratt, W. M., Hibbard, D. L., and Milster T. D. Numerical comparison of grid pattern diffraction effects through measurement and modeling with OptiScan software. Proc. SPIE 8016, Window and Dome Technologies and Materials XII, 80160U (2011) [Non-Patent Document 4] Yonghe, L. et al. (2013). "A Simple Sweep-line Delaunay Triangulation Algorithm". In: Journal of Algorithms and Optimization (JAO) 1.1, pp. 30 - 38 [Non-Patent Document 5] Alan Mathison Turing, "The chemical basis of morphogenesis" [Summary of the Invention] [Problems to be Solved by the Invention]

[0007] It would be advantageous to provide an improved substrate with electrodes and an optical modulator comprising such an improved substrate to address these and other problems. The inventors have found that electrode designs in known systems result in diffraction. Addressing this concern results in a substrate that can be applied with less diffraction. [Means for Solving the Problems]

[0008] A substrate for use in an optical modulator may comprise a plurality of interdigitated drive electrodes applied to the substrate, each of the plurality of drive electrodes being arranged in a pattern across the substrate, and the plurality of interdigitated drive electrodes being arranged alternately with respect to each other on the substrate. The drive electrodes are electrically insulated from each other such that the voltages on the drive electrodes can be independently controlled.

[0009] When such a substrate is used in an optical modulator, the varying voltages applied to the electrodes may cause electrophoretic movement of particles within the optical layer between two such substrates. The movement then causes modulation of the light shining through the substrate. At least two such substrates, each having at least two drive electrodes, are typically used, although additional substrates and / or drive electrodes may be used. The optical modulator is preferably electrophoretic, although it may be dielectrophoretic. Substrates according to embodiments may also be used in other technologies, such as OLED or electrowetting. Substrates according to embodiments may be combined with another substrate according to embodiments, although this is not necessary; one or both of the substrates may be transparent. In glazing applications, typically both substrates are transparent.

[0010] Optically active glazing, particularly so-called smart glazing, is an important application of optical modulators, for example, of embodiments of substrates on which a plurality of interdigitated electrodes are applied. Typically, all substrates within the optical modulator are transparent; this is particularly so in glazing applications. In embodiments, one or more substrates may be translucent. In embodiments, one substrate may be opaque while the opposing substrate is transparent or translucent. Such an optical modulator will change the appearance of the incident light. The substrate may be reflective.

[0011] An important issue for applications such as grazing is diffraction. Preferably, the diffraction is reduced to a small number. Diffraction can be calculated with a number called the pixelated noise metric, which is the ratio of the maximum intensity among all non-zero order peaks from the magnitude spectrum to the maximum intensity of the zero order peak. See, for example, the paper Murray, Ian B., Densmore, V., Bora, V., Pieratt, W.M., Hibbard, D.L., and Milster T.D. "Numerical comparison of grid pattern diffraction effects through measurement and modeling with OptiScan software." Proc. SPIE 8016, Window and Dome Technologies and Materials XII, 80160U (2011), which is incorporated herein by reference. It has been found that it is difficult to further reduce the pixelated diffraction value using the conventional patterning of electrode lines. However, the inventors have found a way to overcome this obstacle and create a design that breaks existing barriers. In an embodiment, the calculated pixelated noise metric of the drive electrode pattern of the substrate is less than 6.05% or less than 5% or less than 4%. In particular, the pixelated noise metric of the building block may be less than these thresholds.

[0012] In an embodiment, the pattern of the drive electrodes is formed by a plurality of repeating building blocks. The building blocks comprise electrodes that interfit. By repeating the building blocks adjacent to each other, the electrodes on the building blocks are formed into drive electrodes. For example, the building blocks may be fused to be patterned with a mask lay outing tool before depositing the entire pattern on the substrate. The building blocks may partially overlap. For example, if the electrode lines of a first building block coincide with the electrode lines of a neighboring building block and they both belong to the same drive electrode, these electrode lines of the two building blocks may be fused. In an embodiment, the building blocks are surrounded by drive buses, and the drive buses are preferably merged with the buses for the same drive electrodes of neighboring building blocks.

[0013] In an embodiment, for driving the drive electrodes, the drive buses are disposed at the sides of the substrate for each drive electrode. The drive buses may otherwise connect the insulated electrodes to the drive electrodes. The drive buses may then be connected to a controller.

[0014] The drive buses may be placed only at the sides of the substrate, but may also extend across the substrate, for example, between the building blocks or as part of a building block. For example, a plurality of straight drive buses may extend across the building blocks, and arms may extend from the drive buses to further connect the electrodes to the drive electrodes. Preferably, it is avoided that two drive buses extend adjacent to each other across the substrate. This is because a narrow furrow may be formed that may adversely affect diffraction. When two drive electrodes are used, the drive buses are preferably alternated between the building blocks.

[0015] In an embodiment, the building block may comprise a plurality of mutually mating electrodes extending in at least two directions across the building block. The inventors have found that using electrodes of a relatively long length compared to the size of the building block is advantageous for reducing diffraction. For example, for at least one of the plurality of mutually mating electrodes within the building block, the maximum length between any two points on the electrode, measured along the electrode within the building block, is at least twice the length of the diagonal of the building block unit.

[0016] In an embodiment, the building block may comprise a plurality of branch nodes where the electrodes branch. For example, at least three electrode lines may be connected to a branch node. Introducing a cluster of branch nodes increases the local variability of the electrodes and increases the electrode length compared to the building block diagonal. For example, the cluster of branch nodes may comprise at least a first branch node, and the first node is directly connected to a second branch node and a third branch node through electrode lines. In an embodiment, the cluster may be larger. For example, the first branch node is directly connected to two further branch nodes, and the two further branch nodes are then directly connected to four branch nodes.

[0017] A cluster of nodes together with the electrode lines connecting the nodes may form a tree. More generally, the drive electrodes may be a tree.

[0018] Such clusters of branching nodes may be introduced into the electrode pattern manually, but the inventors have found an algorithm that can create patterns with a large number of branching nodes. For example, the drive electrodes may be found by calculating the spanning tree of a Voronoi pattern. The complementary electrode pattern may be formed by placing edges that extend across the edges removed from the Voronoi pattern. Instead of the Voronoi pattern, other tessellations may be used. For example, a regular tessellation may be used, perhaps using one or more polygon shapes. The tessellation may be randomized by randomly shifting the edges of the tessellation. The spanning tree of the randomized tessellation may be used as the electrodes; the complementary electrodes may be formed from the dual graph.

[0019] Building blocks may be repeated across a substrate by copying and translating the blocks without mirroring or rotating. However, in embodiments, isometries, such as mirroring, rotation, and / or point reflection, are applied to the building blocks. Although multiple building blocks may be used, using isometries has the advantage that the arrangement of the building blocks can be improved without the need to optimize multiple blocks. For example, if a drive bus runs across the substrate and is used between building blocks, for example, isometries can be used to avoid the drive buses being placed adjacent to each other on the substrate. For example, an entire row or column of building blocks may be mirrored about its longitudinal axis to form the next row or column of building blocks, etc. Mirroring the building blocks in this way has the advantage that the drive buses can be merged between different building blocks and thus avoid grooves between the building blocks. Mirroring the building blocks has the advantage that a symmetric electrode design for the substrate may be established, which is advantageous when manufacturing an optical modulator.

[0020] In embodiments, the tiles are arranged in a checkerboard and individual tiles may be mirrored or point reflected. In embodiments, the tiles are not in a checkerboard and the edges of the tiles are parallel or orthogonal to each other.

[0021] The substrate according to the embodiment may be used in a light modulator, also known as an optical modulator. For example, two such substrates may be arranged opposite to each other such that charged particles suspended in the fluid between the substrates can move by applying a voltage to the electrodes. Typically, the electrode designs for the lower and upper substrates are the same, but this is not necessary. Similarly, the two designs are typically aligned with each other, but this is not necessary. The particles may absorb or reflect light. The reflection may be specular or diffuse or intermediate between both. The particles may emit light having, for example, phosphorescence or fluorescence.

[0022] The light modulator provides a panel whose transparency or reflectivity can be modified. In an embodiment, the color or color intensity etc. may be changed. The light modulator may be used as a cover for a container such as a closet, cabinet, and the like. Depending on the particular application, the light modulator is also called an ambient light modulator, a dynamic light modulator, a light modulator, a color modulator, an IR modulator, a UV modulator, an IR active filter, a UV active filter, or a dynamic color filter.

[0023] A particularly advantageous application is in optically active glazing, which in the art is also called smart glazing, smart window, controllable glazing, optical panel, electronic signage, dynamic light panel, dynamic color panel, active color panel, active light panel, active light surface, active color surface, dynamic light surface, or dynamic color surface.

[0024] In an embodiment, the controller is configured to apply a potential to electrodes on a substrate of the optical modulator to obtain an electromagnetic field between the electrodes. The electromagnetic field causes electrophoretic movement of particles towards or from the electrodes. As the particles change position, the optical properties of the panel, such as transparency or reflectivity, change. If the particles are colored, the color of the panel can also change. By changing the pairs of electrodes between which the electromagnetic field is established, the particles can be moved in a desired direction. The inventors have found that the control of the optical modulator need not be limited to changing which electrodes the electromagnetic field is applied between, but can also include changing the maximum amplitude. Advantageously, it should be noted that an alternating current is used. For example, by driving at a lower maximum amplitude, the change rate of the optical modulator changes. This can be advantageous, for example, when the maximum amplitude is reduced to avoid overshoot while driving towards a desired target transparency or reflectivity. The maximum amplitude may also or instead be increased when starting to drive towards the target transparency or reflectivity. For example, the controller may be configured to obtain one of a plurality of levels of transparency or reflectivity of the optical modulator by using an alternating current or voltage of one of a plurality of maximum amplitudes. The relationship may be indicated by an algorithm or the like. The relationship between the level of transparency or reflectivity and the maximum amplitude may be governed, for example, by a look-up table showing a sequence of maximum amplitudes for driving towards the transparency or reflectivity. It should be noted that an alternating voltage is also possible.

[0025] In addition to changing the electrodes between which the signal is applied, changing the maximum amplitude of the drive signal may also be used to improve balanced driving. For example, the power applied to some electrodes, such as the maximum amplitude, may be different from that applied to other electrodes. For example, the controller may be configured to apply a potential difference between successive electrodes on the same substrate and simultaneously apply a potential difference between opposing electrodes on an opposing substrate.

[0026] In an embodiment, at least one of the two substrates conforms to the embodiment. The other substrate may or may not have one or more electrodes. In an embodiment, the superposition of the electrodes on the substrate meets the limits regarding the ratio of the electrode length to its diameter within the building block, or the limits regarding the pixelation noise ratio, for example, such limits are shown herein. Instead of the diameter, other measures regarding the size of the building block may generally be used. For example, in the case of a rectangular building block, the average of the building block sides such as the harmonic mean of the building block sides may be used.

[0027] In an embodiment, there are at least two electrodes on each substrate, but there may be three or more electrodes. For example, at least three electrodes may be applied to at least one of the first substrate and the second substrate. For example, in an embodiment, two electrodes may be applied to the first substrate and three electrodes may be applied to the second substrate. Typically, the opposing substrates are mirrored such that the electrode lines face each other; this is not necessary and different effects are possible when the electrodes are not arranged in such a way.

[0028] A further aspect of the present invention is a structure comprising an optical modulator according to an embodiment. A further aspect of the present invention is a vehicle comprising an optical modulator according to an embodiment. For example, the vehicle and / or the structure may comprise an optical modulator and a controller configured to control the transparency or reflectivity of the optical modulator by controlling the voltage applied to the electrodes of the optical modulator, and the controller is electrically connected or connectable to the optical modulator.

[0029] The optical modulator is, for example, an electronic device that may be driven by a power source under the control of the controller. For example, the controller may instruct the power source to apply a specific waveform to a specific electrode in order to achieve various transparency or reflectivity effects or the lack thereof.

[0030] Embodiments of the method may be implemented on a computer as a computer-implemented method, or in dedicated hardware, or a combination of both. Executable code for embodiments of the method may be stored on a computer program product. Examples of computer program products include memory devices, optical storage devices, integrated circuits, servers, online software, etc. Preferably, the computer program product includes non-transitory program code stored on a computer-readable medium for performing embodiments of the method when the program product is executed on a computer.

[0031] In an embodiment, the computer program includes computer program code adapted to perform all or part of the steps of an embodiment of the method when the computer program is executed on a computer. Preferably, the computer program is embodied on a computer-readable medium.

[0032] Further details, aspects, and embodiments are described by way of example only with reference to the drawings. The elements of the figures are shown for simplicity and clarity and are not necessarily drawn to scale. In the figures, elements corresponding to elements already described may have the same reference numerals.

Brief Description of the Drawings

[0033]

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Embodiments for Carrying Out the Invention

[0034] List of reference signs The following list of references and abbreviations is provided to facilitate the interpretation of the drawings and shall not be construed as limiting the claims. 10 Optical modulator 11 First substrate 12 Second substrate 13, 13a, 13b Electrodes 14, 14a, 14b Electrodes 15 Fluid 16 Controller 30 Particles 20 Vehicle 21 Optical modulator 40 Optical modulator 41 First substrate 42 Second substrate 43 Third substrate 46 Controller 100 - 102 Substrates 111 - 114 Main lines 121 - 124 Main lines 131 - 134 Interlocking electrodes 140 Building block 141 - 144 Building blocks 110, 120 Drive buses 110’ and 120’ drive buses 119 and 129 connection zones Points on the sides of building blocks 151 - 157 Building block 160 Partial building blocks 161 and 162 Building blocks 171 and 172 Directions 191 and 192 Nodes 201 - 207 Nodes 210 - 218 Angles α1 - α7 Electrode lines 221 - 222 Substrate 180 Point on the substrate 181 First shortest distance 182 Second shortest distance 183 First drive electrode 188 Second drive electrode 189 Building block 601 Substrates 602 - 604 Groove 640 Building blocks 611 - 622 Building blocks 651 - 662 First electrode 720 Second electrode 730 Edge seal 740 Spacer 750 Semiconductor ink 760 Substrates 772 and 774 First drive bus 812 Second drive bus 814 Building block 820 Drive bus parts 902 - 906 Drive electrode 912 Computer - readable media 1000 and 1001 Writable part 1010 Computer program 1020 Integrated circuit(s) 1110 Processing unit 1120 Memory 1122 Application - specific integrated circuit 1124 1126 Communication element 1130 Interconnect 1140 Processor system

[0035] While the subject matter of this disclosure may be embodied in many different forms, it is understood that this disclosure is not intended to be limited to the specific embodiments shown, illustrated, and described herein as examples of the principles of the subject matter of this disclosure. One or more specific embodiments will be shown in the drawings and described in detail herein.

[0036] In the following, for the sake of understanding, the elements of the embodiments are described in terms of operation. However, it will be apparent that each element is configured to perform the functions described as being performed by each element. Further, the subject matter of this disclosure is not limited to the embodiments only, but also includes all other combinations of features described herein or recited in the different dependent claims that are different from each other.

[0037] For example, a substrate for use in an optical modulator is disclosed. The substrate may comprise a plurality of interlocking drive electrodes applied to the substrate, each of the plurality of drive electrodes being arranged in a pattern across the substrate, and the plurality of interlocking drive electrodes being arranged alternately with respect to each other on the substrate. The pattern of the plurality of drive electrodes across the substrate comprises a plurality of repeating building blocks.

[0038] FIG. 1b schematically shows an example of an embodiment of a substrate. The substrate is particularly useful, for example, for use in an optical modulator of the type described herein. Across the substrate, a plurality of interlocking drive electrodes are applied to the substrate.

[0039] An exemplary use of the substrate is in an electrophoretic light modulator. Typically, an electrophoretic light modulator comprises at least two substrates, each having at least two drive electrodes, although this is not necessary; for example, an electrophoretic light modulator may comprise a single substrate having two electrodes and a counter substrate having one electrode. In either case, preferably, at least one of the substrates in the light modulator conforms to the embodiment.

[0040] An embodiment of a light modulator comprises a first substrate according to the embodiment and a second substrate. The first and second substrates are arranged with their inner sides facing each other. At least one drive electrode is applied to the inner side of the first substrate. The optical layer is arranged between the first substrate and the second substrate. The controller is configured to apply a potential to at least one drive electrode that causes modulation of the optical properties of the light modulator. One or both of the first and second substrates are transparent and / or translucent.

[0041] There are many different types of light modulators that use at least one drive electrode applied to a substrate. Since light passes through the substrate, interference is a common problem in the field of light modulators. The optical layer and the controller may be arranged to modulate the optical properties using effects that depend on the potential on the drive electrode; examples include the dielectrophoretic effect and the electrophoretic effect. For example, optical modulation may include modulation of particles arranged within the optical layer. The number of drive electrodes may range from one on a single substrate to multiple drive electrodes on one or both substrates.

[0042] The optical layer arranged between the first substrate and the second substrate may, for example, contain particles suspended in a fluid. The controller may be configured to apply a potential to the drive electrode and move the particles, thus modulating the optical properties of the light modulator.

[0043] In an embodiment, the particles include electrically charged or chargeable particles, and the controller is configured to apply a potential to the drive electrodes to obtain an electromagnetic field that causes electrophoretic movement of the particles. In an embodiment, the electromagnetic field is configured between at least two drive electrodes disposed on the same substrate or on different substrates.

[0044] In an embodiment, the particles include dielectric particles, and the controller is configured to apply a potential to the drive electrodes to apply an electric field gradient to the particles, enabling the particles to move under the action of dielectrophoretic forces.

[0045] The controller may apply an electrical signal to one or more of the drive electrodes. Embodiments for controlling dielectrophoretic forces may use signals including DC signals and / or AC signals. Embodiments for controlling electrophoretic forces may use signals including DC signals and / or AC signals.

[0046] Below, some known optical modulators are reviewed and some options in the technology and electrodes are shown.

[0047] U.S. Patent No. 10,921,678, which is incorporated herein by reference and has the title "Electrophoretic device", shows an electrophoretic device having only one patterned electrode on one of two substrates. For example, one substrate having an electrode according to U.S. Patent No. 10,921,678 may be replaced by a substrate according to an embodiment comprising one single electrode. U.S. Patent No. 8,054,535 B2 (incorporated herein by reference) and U.S. Patent No. 8,384,659 B2 (incorporated herein by reference) show alternative examples of electrophoretic optical modulators in which one of two substrates has two patterned electrodes.

[0048] The patterned electrodes are also used in dielectrophoretic light modulators. For example, U.S. Patent Application No. 2005185104A1 (incorporated herein by reference) and U.S. Patent Application No. 20180239211A1 (incorporated herein by reference) show dielectrophoretic light modulators having a substrate with patterned electrodes. Any of these cited electrophoretic or dielectrophoretic light modulators may be adapted by patterning the electrodes on a substrate according to an embodiment.

[0049] In an embodiment, the light modulator includes a first substrate and a second substrate. At least one of the first and second substrates may be obtained according to an embodiment. For example, the first and second substrates may be arranged with their inner sides facing each other. Using a substrate according to an embodiment has, for example, the effect of reducing optical interference. The optical layer is disposed between the first substrate and the second substrate. The drive electrodes are arranged to modulate the electric field within the optical layer. The optical layer includes a fluid containing particles, and the particles are electrically chargeable or charged. The particles may move under the control of an electric field. For example, the controller may be configured to apply a potential to the drive electrodes to obtain an electromagnetic field at the drive electrodes, causing the electrophoretic movement of particles towards or from one of at least one of the drive electrodes that causes modulation of the optical properties of the light modulator.

[0050] The paper "Reversible Metal Electrodeposition Devices: An Emerging Approach to Effective Light Modulation and Thermal Management", which is incorporated by reference, also shows a substrate on which patterned electrodes are applied. The patterned electrodes may be advantageously configured according to an embodiment, for example, to reduce interference.

[0051] Embodiments of the substrate may be used in an electrochromic device (ECD). An electrochromic device (ECD) controls optical properties such as optical transmission, absorption, reflection, and / or emittance in a continuous but reversible manner (electrochromism) by the application of a voltage. This property enables the electrochromic device to be used for applications such as smart glass, electrochromic mirrors, and electrochromic display devices.

[0052] Electrochromic devices are described, for example, in the paper "Silver grid electrodes for faster switching ITO free electrochromic devices" by Antonio California et al., which is hereby incorporated by reference. That paper describes the fabrication of electrochromic devices, in this case electrochromic devices without ITO.

[0053] Electrochromic devices use electrically conductive electrodes applied to a substrate. The cited paper uses silver grids made using silver ink as the electrically conductive electrodes. Electrochromic devices may include an electrochromic material. The cited paper uses poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS). In an electrochromic device, at least one drive electrode, e.g., an electrically conductive electrode, is applied to the substrate. The drive electrodes are arranged in a pattern across the substrate. The cited paper discloses two different grid patterns, the regular hive and the regular ladder designs. See Table 1 and Figure 3 of the cited paper.

[0054] In the case of the cited paper, the electrodes may be applied to a substrate by screen printing polyethylene terephthalate (PET) onto the substrate. The electrodes are typically an electrically conductive material, such as a metal or a metal oxide. In the cited paper, silver ink was used to screen print a grid onto PET using a RokuPrint RP 2.2 device and an 180-wire mesh. The samples were dried in an oven at 130 °C for 15 minutes. One or two layers of PEDOT:PSS SV3 were later printed by screen printing on top of these silver grids.

[0055] By a regular pattern, such as the hibe or ladder pattern and the combination of transmitted light in the cited paper, the electrochromic device is subject to interference. One way to avoid interference is to use a pattern according to an embodiment, for example, where the electrodes have a long pattern compared to other repeating elements, such as building blocks.

[0056] For example, the metal grids used in the cited paper may be replaced by drive electrodes applied to the substrate, the drive electrodes are arranged in a pattern across the substrate, the pattern of drive electrodes across the substrate comprises a plurality of repeating building blocks, the building blocks comprise one or more electrodes extending in at least two directions across the building block, the electrodes within the building block form at least one drive electrode, and for at least one electrode within the electrodes within the building block, the maximum length between any two points on the electrode measured along the electrode within the building block is at least twice the length of the diagonal of the building block unit. Instead of requiring a minimum length of the electrode, the pattern may use other features to reduce interference, such as a high degree of branching, for example, branching of the electrode into two or more paths, the branching repeating a plurality of times, for example, at least 2, 3, 4, or more times, resulting in a branching of the initial electrode into at least 4, 8, 16, or more electrodes.

[0057] Another example of an electrochromic device is given in U.S. Patent No. 5,161,048, having the title "Electrochromic window with metal grid counter electrode and acidic polyelectrolyte", which is incorporated herein by reference. For example, an electrochromic device may comprise a transparent electrochromic film and an ion-conductive layer disposed between a pair of electrodes. A metal grid electrode is provided for the electrodes. Figure 1 of the patent shows the metal grid according to the cited patent. To form the counter electrode, the metal grid is disposed adjacent to a second glass substrate.

[0058] For example, in an embodiment of an electrochromic device, the electrochromic device may comprise a transparent substrate, an electrically conductive electrode member, a transparent electrochromic film in contact with the electrically conductive electrode member, an ion-conductive polymer in contact with the electrochromic film; and a patterned conductive electrode in contact with the ion-conductive polymer. The patterned conductive electrode may be obtained according to the embodiment.

[0059] The substrate according to the embodiment can be advantageously applied in several other technologies. For example, an optical modulator may be an electrowetting optical modulator, as shown in U.S. Patent Application Publication No. 2005 / 0185104 (A1), which is incorporated herein by reference. A substrate as in the embodiment may also be used in other electro-wetting and OLED applications.

[0060] In OLEDs and electro-wetting, electrodes are required on only one of the plurality of substrates. The substrate having the electrodes may conform to the embodiment.

[0061] In the application of the optical modulator for grazing, both substrates are typically transparent. In other applications, such as in televisions, e - book readers, etc., only one substrate may be transparent.

[0062] Figure 1b shows two drive electrodes on the same surface. The two drive electrodes are shown in two different dashed - line styles in Figure 1b. For example, to facilitate finer control of the voltage difference across the substrate, there may be three or more electrodes on the same side of the substrate. The drive electrodes are applied on the same side of the substrate. Applying electrodes to the substrate may be done by lithography, for example, using a mask representing the electrode pattern. The electrodes may also be applied by embedding the electrodes in the substrate.

[0063] The drive electrodes are electrically connected and, for example, have the same potential everywhere. The drive electrodes may comprise drive buses and main lines. At least, the main lines interfit with the main lines of further drive electrodes. Typically, the drive electrodes extend in a substantially straight line across the substrate, while the main lines are intertwined.

[0064] In an embodiment, the two substrates of the optical modulator each have two electrodes disposed on their inner surfaces. However, as described, a plurality of electrodes on one or both substrates may not be required. For example, an embodiment of the optical modulator comprises a first substrate and a second substrate. For example, the first substrate may comprise one drive electrode, and the second substrate may not comprise a drive electrode. For example, the first substrate may comprise two drive electrodes, and the second substrate may comprise one drive electrode. For example, the first substrate may comprise two drive electrodes, and the second substrate may comprise two drive electrodes. For example, the first substrate may comprise three or more drive electrodes, and the second substrate may comprise two or more drive electrodes.

[0065] However, a modulator in which each substrate includes two drive electrodes is used as an illustrative example. The design of the substrate featuring two drive electrodes may be adapted to have a single drive electrode, for example, by connecting the two drive electrodes or by removing one of the plurality of drive electrodes. Adapting the substrate in such a way can make the substrate suitable for use in different technologies.

[0066] Each of the plurality of drive electrodes is arranged in a pattern across the substrate. The plurality of drive electrodes are arranged alternately with respect to each other on the substrate. Typically, a drive electrode includes a plurality of main lines each extending across the substrate. The main lines of the drive electrodes are alternating, for example, interlocking. For example, in FIG. 1b, the first drive electrode includes main lines 111-114, and the second drive electrode includes main lines 121-124. Each drive electrode is driven by its drive bus. FIG. 1b shows two drive buses: drive bus 110 and drive bus 120. The drive electrodes also serve to connect the main lines together. For example, in FIG. 1b, drive bus 110 drives and connects main lines 111-114; drive bus 120 drives and connects main lines 121-124. More than four main lines as shown in this example can be present. The use of main lines is advantageous for reducing the length of the electrodes, but it is not necessary. A design using only one main line for one drive electrode is not impossible, but it is advantageous to have a plurality of main lines.

[0067] The plurality of main lines of the first and second electrodes are arranged alternately with respect to each other on the substrate.

[0068] The motivating applications for substrates such as substrate 100 may be applicable in smart glazing, such as in light modulators, in residential homes, offices, greenhouses, vehicles, and the like. The transparency or reflectivity level of the smart glazing may be electrically adapted. For example, in smart glazing, two substrates such as substrate 100 are stacked such that the surfaces on which two electrodes are applied face each other. A fluid having particles is confined between the two substrates. Embodiments of the smart glazing are further discussed below. In an embodiment, electrodes, for example, two or more electrodes, are applied to one surface of each substrate. For example, to facilitate the stacking of three or more substrates, there may be one, two, or more electrodes on the other surface of substrate 100.

[0069] Some of the following embodiments show examples of modulating the transparency or reflectivity level. The light modulator may be adapted for other optical effects. For example, if desired, the embodiments may be modified for different levels of translucency instead of different levels of transparency. If desired, the type of particles used in the embodiments can be changed for different particles, for example, in terms of at which wavelengths the particles absorb or reflect and how specular or diffusive the reflection is. For example, in an embodiment, the light modulator can modulate different levels of reflection. The particles can also emit light. Stacking multiple optical layers further increases the possibilities.

[0070] Having two sets of alternating main lines is sufficient to provide electrically adaptable glazing; with the two alternating sets, the electric field at any part of the substrate can be controlled because two opposing electrodes bound that part from two opposing sides.

[0071] Interestingly, the pattern in which the drive electrodes extend across the substrate is created by a plurality of repeating building blocks. As shown in FIG. 1b, the drive electrodes on substrate 100 are shown as four blocks: blocks 141, 142, 143, and 144, all of which are substantially the same. The number of building blocks may be more than four. The building blocks repeat in both directions across the substrate, e.g., in a first direction 191, e.g., the x direction shown horizontally in the figure, and in a second direction 192, e.g., the y direction shown vertically in the figure.

[0072] For example, FIG. 1a schematically shows an example of an embodiment of building block 140. Building block 140 includes a plurality of interlocking electrodes that extend in at least two directions across the building block. In FIG. 1a, four electrodes: electrodes 131 - 134 are shown. When the building block is repeated across the substrate in two directions, the electrodes within the building block will form the drive electrodes, e.g., will form a plurality of main lines of the drive electrodes. Note that the building block is typically connected in a substrate electrode design tool. Typically, the building block includes five or more electrode lines. For example, within the scope of the embodiment, between eight and twelve main lines are used. However, the number of electrode lines can be much larger. For example, the building block may include many short electrode lines near the edges that connect to the lines of other building blocks when the block is repeated. Considering such short derivatives, the number of lines can increase to, e.g., 50. Clearly, using larger building blocks may also increase the number of electrode lines. In an embodiment, the number of electrode lines within the building block is between eight and fifty, or between eight and twenty-five, etc.

[0073] The drive electrodes formed by the repeating building blocks are connected to the drive buses. Typically, the electrode lines within a building block are connected to the electrode lines in neighboring blocks by merging corresponding electrode lines; although this is not necessary, connection zones can be inserted between the repeating building blocks to connect the corresponding electrode lines.

[0074] This step can connect multiple main lines together, thus forming a single drive electrode. FIG. 1b shows two connection zones 119 and 129 where the main lines belonging to the same drive electrode are connected to drive bus 110 and drive bus 120, respectively.

[0075] The electrodes shown in FIG. 1a are alternately dashed with the same dashed style as in FIG. 1b. In reality, it just happens to be the case in this example that a particular electrode of the building block in FIG. 1a always ends within the first drive electrode or within the second electrode, as indicated by the dashed style. However, this is not necessarily the case. The electrodes within a building block may end as part of the first drive electrode or as part of the second drive electrode. This can change, for example, the pattern of the repeating building blocks as a result of the parity of the number of electrodes within the building block.

[0076] For example, a particular pattern of repeating building blocks may be used for a modulator having two drive electrodes, in which case alternating main lines may be assigned to the two drive electrodes. However, the same pattern of repeating building blocks may be used for a modulator having three drive electrodes, in which case all adjacent sets of three main lines may be assigned to the three drive electrodes.

[0077] Furthermore, although the building block shown in FIG. 1a is square, this is also not necessary. For example, the building block may be rectangular. In an embodiment, the building block shape(s) may form a so-called tessellation. For example, the building block may be triangular, hexagonal, or even a combination of plane-filling shapes.

[0078] As described above, FIGS. 1a and 1b are schematic. This is especially true for the depiction of the electrodes. The electrodes shown in FIG. 1a are straight and their length is equal to the length of the side of the building block. However, in an embodiment, the electrodes on the building block are more intricate for at least one of the plurality of interlocking electrodes within the building block, and the maximum length between any two points on the electrode, measured along the electrode within the building block, is at least twice the length of the diagonal of the building block unit.

[0079] For example, considering the electrode of FIG. 1a shown schematically, the maximum length possible along the same electrode is the length of the side of the building block. The ratio of the maximum length to the diagonal of FIG. 1a (shown schematically) is

Number

[0080] Typically, two or more electrode lines within a building block meet this condition. For example, in an embodiment, the building block comprises a plurality of electrode lines that are not electrically connected within the building block, and the longest path on each electrode of the plurality of electrodes is longer than twice the diagonal length of the building block. The number of the plurality may be at least 2, at least 4, at least 10, etc.

[0081] By adapting the shape of the electrodes, unwanted diffraction effects can be altered. Reducing the diffraction effect is particularly important for transparent substrates, since in applications such as in e-book readers, for example in the case of diffusive reflection displays, the effect will be less noticeable. However, specular reflection displays such as dimmable mirrors will be affected by the diffraction effect. The inventors have found that optical diffraction in a light modulator can be reduced by orienting the line shape of the electrodes at a plurality of different angles, spreading the diffraction in space, and thus reducing the intensity of the strongest diffraction spots. For example, in the case of a dimmable mirror, it is important to reduce diffraction.

[0082] In an embodiment, the dimmable mirror comprises a light modulator according to an embodiment. For example, the dimmable mirror comprises a transparent substrate, an optical layer, and a reflective substrate. One or both of the substrates are according to the embodiment. The dimmable mirror may be electrophoretic. Typically, each substrate has two electrodes, but this is not necessary.

[0083] FIG. 1c schematically shows an example of an embodiment of substrate 101. Substrate 101 is similar to substrate 100 except for how the main lines formed from the electrodes on the building block are connected to the drive buses. In FIG. 1a, connection zones are inserted between the repeating building blocks and drive buses 110 and 120. In the connection zones, the main lines belonging to the same drive electrode are connected to the same drive bus. In FIG. 1c, the drive buses are directly adjacent to the building blocks. A part of the building block is modified to avoid the drive buses connecting to the main lines of different drive electrodes.

[0084] For example, building block 141 may be a copy of building block 140, but electrode 134 is shortened so that main line 122, of which line 134 is a part, does not connect to bus 110. In FIG. 1c, the building blocks are substantially the same except that disconnection is introduced at some of the electrodes of the building block adjacent to the drive bus in order to avoid connecting the main line to the drive bus. All the building blocks shown in FIG. 1c are thus modified, but in an embodiment, most of the building blocks, for example, the building blocks not adjacent to drive buses 110, 120 are not modified.

[0085] FIG. 1d schematically shows an example of an embodiment of substrate 102.

[0086] In an embodiment, the electrodes within a building block each connect to the same opposing sides of the building block. This results in the main lines formed by the electrodes on the building block connecting the opposing sides of the substrate. In such a situation, having only two drive buses, for example, each extending along an opposing side of the substrate, is sufficient to connect and drive the drive electrodes.

[0087] However, it is not necessary for the electrodes within a building block to connect the opposing sides of the building block. Typically, all the electrodes within a building block will connect two sides of the building block, but these two sides do not need to be opposing. The reason for this is that the electrodes may be continued by the next building block. In such a situation, most of the main lines will still connect the same two opposing sides, but at the edge of the substrate, this may not happen. This is because there is no further building block to carry the electrodes forward. To allow for a more complex electrode design for the building block, the main line may be connected to the drive bus from two sides, for example, two sides of the substrate adjacent to the same corner of the substrate.

[0088] In FIG. 1d, drive buses 110' extending along two sides of the substrate and drive buses 120' extending along the other two sides of the substrate are shown.

[0089] An advantage of this configuration is that the drive buses can be made in the same plane. This, however, is not necessary. The drive buses can, if desired, connect from all three or four sides, for example, to further increase the design freedom for the building blocks. Various examples are shown herein.

[0090] It should be noted that drive electrodes, such as drive buses and / or main lines, can overlap. This is possible, for example, by creating a portion of dielectric material between the electrodes. For example, such overlapping electrodes can be partially or completely in different planes of the substrate.

[0091] For example, in an embodiment, a first drive electrode may be deposited. Then, the dielectric is locally deposited, and finally, a second drive electrode is deposited. The dielectric is arranged to cover at least the point where the first and second electrodes cross. Vias may be used for the lower first drive electrode, for example, to connect to the lower first drive electrode. Depositing the drive electrodes may include depositing the drive buses.

[0092] FIG. 1e schematically shows an example of an embodiment of a building block. In FIG. 1e, two electrodes are schematically shown. In an actual implementation, the tracks of the electrodes shown will typically be much more intricate.

[0093] The building block of FIG. 1e shows four electrode lines respectively connected to at least two sides of the building block. In this case, the electrode lines are not directly connected to the opposing sides of the building block. Since it is only necessary for the driving electrode to be driven from one side, the connection of the opposing sides of the building block is not required. However, for covering the substrate, it is convenient if at least one or more of the electrodes reach the opposing side from the location where the electrode is driven. This is not necessary; there are main line electrodes that reach only a part of the substrate, and they may be driven from two sides.

[0094] Figure 1e shows that the main electrode into which a specific electrode line of a building block is incorporated can reach across the substrate even though it does not connect the sides facing the electrode line. For example, the electrode line starting at 151 on the left side connects to the non-opposing upper side of the building block at 157. When the same building block is repeated on the building block shown, the main line formed by this line continues at point 154 of the repeating building block and reaches the opposing side of the repeating building block at 152. Similarly, at 155 on the left side of the building block, an electrode line that will be part of the second drive electrode starts. This electrode line connects to the upper side at 153 and continues in the repeating block at 154. Therefore, an electrode line starting on the left side of a building block may not connect to the opposing side of that building block, but that electrode line nevertheless advances that distance in the x direction and reaches the right side of a building block, but a different building block, for example, a building block above or below the shown building block. The same is possible in the reverse for the y direction. In an embodiment, the main line connects the opposing sides of the substrate in a first direction 191, for example, the x direction, while extending through a plurality of blocks, and in a cross-sectional direction, for example, the y direction, while extending through at least two or more blocks. Typically, the first direction 191 and the second direction 192 are orthogonal; this is not strictly necessary, and the two directions may be inclined with respect to each other.

[0095] Figure 1f shows that two electrode lines within a building block do not need to be connected within the building block, but can still be connected within the substrate through connections in neighboring building blocks. For example, consider the electrode starting at the left side at point 151. The electrode goes out on the upper side of the building block. Different from the example in Figure 1e, the main line into which the electrode line starting at 151 is incorporated connects to the opposing part of the building block shown in Figure 1f.

[0096] The electrode line starting at the left side of the building block at 151 is connected to the upper side of the building block at 157. If the same building block is repeated at the top of the building block shown, the electrode line will connect to the bottom side at point 156 and connect to the same side as the point on the bottom side at point 154. Returning to the building block shown in Figure 1f, the electrode line continues on its upper side at point 153 and connects to the right side at point 152, i.e., the opposite side of the side at point 151.

[0097] In an embodiment, a drive electrode, e.g., the main line of a drive electrode, connects a first point on a first side of a first building block to a second point on the opposite side of the same building block, and between the first point and the second point, the main line intersects at least the next second building block of the first building block.

[0098] In this example, the longest path between two points on the same electrode line is formed by the path starting at 155. According to an embodiment, the length of the longest path is a multiple of the size of the building block, e.g., the side or diagonal; for example, the longest path may be at least twice the length of the diagonal. In this example, only one path of its length exists, but there may be multiple such long paths.

[0099] An alternative requirement may be to consider a path extending through neighboring building blocks. For example, the longest path starting at a side, e.g., the left side, and connecting to the opposite side of the same building block may be a multiple of the diagonal of the building block, and this path may extend through neighboring building blocks. Using this definition, a somewhat higher threshold, e.g., 2, may be used, but a higher threshold, e.g., 3, is also possible.

[0100] In an embodiment, the electrode line on the building block connects two points on the same side.

[0101] In an embodiment, the electrode line on the building block connects two points on different non-opposite sides of the building block.

[0102] Figure 1f also shows an electrode line connecting two opposite sides of the building block. In an embodiment, all the electrode lines on the building block connect the opposite sides of the building block. However, as shown, this is not necessary. Typically, the drive bus is straight, while the main lines are intricate.

[0103] Figure 1g schematically shows an example of an embodiment of the substrate. Figure 1g shows a variant method of tiling the substrate using building blocks. In Figure 1g, the building blocks are staggered. For example, in a first direction 191, for example, in the x direction, the building blocks 160 are aligned in rows. At the top of the building blocks, the building blocks are similarly aligned in rows, but the building blocks are offset with respect to the lower rows. The offset is shown as half of the block, but this could also be another fraction of the building block width, for example, 1 / 3 of the building block width.

[0104] If a rectangular substrate is desired, partial building blocks can be added to the rows to fill the substrate. Figure 1g shows two half-width building blocks: building block 161 and building block 162. Building blocks 161 and 162 can be identical to half of the substrate 160, but more typically, both are designed for connecting drive electrodes and for coverage of the substrate. As shown, each row has partial building blocks, for example, building block 161 in odd rows and building block 162 in even rows. However, having a staggered design, it is possible to have both partial building blocks, for example, at the beginning and end of even rows, and use full building blocks in alternating, for example, odd rows only.

[0105] Other tessellations, such as substrate filling tile laying, can be used to create the electrode pattern. For example, in an embodiment, the building blocks are parallelograms, rhombuses, or the like. In an embodiment, the building blocks may be aligned in rows, and in odd rows, the blocks are mirrored, for example, flipped; sometimes called glide reflection symmetry. In addition to mirroring, the building blocks may also be point reflected or inverted.

[0106] FIG. 1h schematically shows an example of an embodiment of the substrate. As in FIG. 1b or FIG. 1c, the building blocks repeat across the substrate in at least two directions. However, in FIG. 1h, a plurality of different building blocks are used; FIG. 1h shows two building blocks 171 and 172. Both blocks 171 and 172 repeat in two directions, for example, a first direction 191 and a second direction 192. In FIG. 1h, building block 171 does not directly adjoin building block 171; for example, the two building blocks form a checkerboard filling. This is not necessary, but for example, the first building block may connect to a copy of the first building block at two opposite sides, but may connect to the second building block at the other two opposite sides. There may be more than three different building blocks.

[0107] For example, using different tiles adjacent to each other in different directions increases design flexibility, which may be used, for example, to ensure the continuity of the supply to the tiles inside the substrate, while at the edge of the substrate, a connection to the controller(s) can be made.

[0108] Note that in an electrode scheme, a tile may be powered by an adjacent tile. For example, in a checkerboard stitching of building blocks, one building block can power the next building block. This may include different tile layouts. For example, vertically adjacent and / or horizontally adjacent tiles may be different. In an embodiment, a portion of the checkerboard is repeated while a portion comprises different tiles. For example, consider five adjacent tiles, e.g., center, left, right, top, and bottom; such tiles may be different or repeated, but preferably the electrode lines are configured to connect to either the electrode lines in adjacent tiles and / or the entire drive bus.

[0109] FIG. 2a schematically shows an example of an electrode embodiment; within a substrate, the electrode is part of a single drive electrode. For example, the electrode shown in FIG. 2a may be part of an electrode line within a single building block. The electrodes shown may also be formed from a plurality of adjacent building blocks. For example, the clusters shown in FIGS. 2a or 2b may be part of main lines 111-114, 121-124 or electrode lines 131-134.

[0110] The electrode comprises a plurality of nodes at which the electrode branches. Branch nodes 201, 202, and 203 are shown. The nodes are electrically directly connected through the electrode lines. One such electrode line between branch node 201 and branch node 203 is indicated by reference numeral 221.

[0111] Having a plurality of branch nodes within the electrode has been found to be advantageous for increasing the ratio of the electrode length to the building block diagonal, which in turn is advantageous for reducing diffraction. Having a cluster of branch nodes causes the electrode to be at various angles, which contributes to reducing diffraction.

[0112] In an embodiment, the main line or further drive electrodes form a tree, for example, an undirected and acyclic graph. Preferably, the tree comprises many branch nodes. The branch nodes have the advantage of allowing the introduction of angles between electrode lines. For example, FIG. 1a shows a branch node 201 directly connected to two further branch nodes: node 202 and node 203. At all three nodes 201 - 203, the electrodes branch.

[0113] FIG. 2b schematically shows an example of an electrode embodiment. This example elaborates on the example of FIG. 2a. Seven branch nodes of the electrodes are shown. Branch node 201 is directly connected to branch node 202 and branch node 203. Branch nodes 202 and 203 are each similarly connected to two further branch nodes. Branch node 202 is connected to branch node 204 and branch node 205. Branch node 203 is connected to branch node 206 and 207. The direct connection between branch node 203 and 206 is indicated by reference numeral 222.

[0114] The branching pattern of FIG. 2a or FIG. 2b increases the ratio of the electrode length to the building block diameter or diagonal. These branching patterns similarly increase the variety of directions of the electrode lines and reduce the long elongation of parallel electrode lines. Such improvements are similarly valuable without contribution to the ratio. For example, in an embodiment, a substrate for use in an optical modulator is provided, the substrate is - Comprising a plurality of interlocking drive electrodes (111 - 114, 121 - 124) applied to a substrate, each of the plurality of drive electrodes is arranged in a pattern across the substrate, the plurality of interlocking drive electrodes are alternately arranged relative to each other on the substrate, the electrodes on the substrate comprise a plurality of nodes where the electrodes branch, the nodes are electrically connected through electrode lines, the plurality of nodes and the connecting electrode lines form a tree, the electrodes comprise at least a first node (201) where the electrode branches into at least three electrode lines, the first node (201) is directly connected through an electrode line to a second node (202) and a third node (203), and the electrodes branch into at least three electrode lines at the second node and at the third node.

[0115] Figure 2c schematically shows an example of an electrode embodiment; within the substrate, the electrode is part of a single drive electrode. For example, the electrode shown in Figure 2c could be part of an electrode line within a single building block. The electrodes shown could similarly be formed from a plurality of adjacent building blocks.

[0116] Eight nodes directly connected to the electrode line: Nodes 210 - 218 are shown. Figure 2c does not show branches for all of these nodes. In reality, not all nodes need to be branch nodes. For example, a node may connect two electrode lines at an angle.

[0117] For example, the path from 210 to 218 could be the maximum length path between any two points on the electrode, e.g., from point 210 to 218. Along the path from node 210 to node 218, the subsequent electrode lines form an angle. These angles are shown as α1 to α7. For example, α1 is the angle between the electrode line from node 210 to 211 and the electrode line from node 211 to node 212.

[0118] To reduce diffraction, the angles in the design are preferably non-uniform. For example, the angles along a path, e.g., the longest path, may be randomly selected or may be selected to uniformly sample the range of possible angles within 0 to 360 degrees. For example, in an embodiment, the angles are selected such that at least all blocks of 30 degrees have one angle selected. For example, the angles may be selected from each range of ranges 1 - 30, 31 - 60, ···, 331 - 360. Long paths affect diffraction; having many angles within a long path makes the path less uniform and thus may reduce diffraction. Measurements may likewise be made by first reducing all angles modulo 180.

[0119] Instead of limiting to the angles along a path, all angles may be included at the nodes within a building block. For example, a node connecting n electrode lines defines n - 1 angles between consecutive electrode lines. Similarly, for these angles, it is preferred that these angles are uniform and cover the full range of angles. For example, these may be randomly selected or may be selected to sample the full range of angles, e.g., from 0 - 180 degrees.

[0120] Nodes are preferably selected to cover a building block and thus the substrate. For example, nodes may be randomly selected across a building block.

[0121] Note that the electrode lines between nodes may be straight or curved. Having straight lines makes the calculations for the design easier, but a curved design provides more flexibility that can be used to combat diffraction. For curved designs such as Figure 3 below, the consideration of angles may be limited to branch nodes. In an embodiment, the substrate is curved and the plurality of repeating building blocks comprises at least two different shapes.

[0122] FIG. 3 schematically shows an example of an embodiment of the substrate 180. Details of two drive electrodes: electrode 188 and electrode 189 are shown. The details shown may be, for example, part of a building block. The details may also occur when two building blocks are aligned adjacent to each other.

[0123] FIG. 3 shows an example of an electrode with a curved electrode line. The following considerations are similarly applicable to designs using straight electrode lines.

[0124] FIG. 3 shows a point 181 on the substrate that is not on the electrode. At such a point, control of the electric field is desired so that the electrophoretic movement of particles in the optical layer adjacent to the substrate 180 can be controlled. Point 181 is shown as a small disk for clarity.

[0125] For a point such as point 181, the distance to the two nearest electrodes can be calculated. The nearest distance between the electrode and point 181 can be considered the minimum distance between any point on the electrode and point 181. For example, for point 181 and electrode 189, the nearest distance is obtained at 183. For example, for point 181 and electrode 188, the nearest distance is obtained at 182. The distance is calculated as the Euclidean distance.

[0126] For example, the desired objectives when forming the electrode pattern are as follows.

[0127] From any point within the substrate, for example point 181, the closest distance to the first drive electrode and the closest distance to the second drive electrode should both be less than the threshold value. For example, both distance 183 and distance 182 should be less than the threshold value. Such a threshold value is preferably effective across the entire substrate, for example, across the entire portion where particle motion is controlled. Imposing a limit on the distance at which a point can be removed from an electrode imposes a limit on the attenuation of the electric field at that point from that electrode. The value for the threshold depends on the intensity of the electric field and on the desired uniformity, such as the optical effects, speed, and uniformity of the transition between different optical states. As an example, the threshold value could be set to 50 micrometers.

[0128] Another way to limit the electrodes from being too far apart from each other is to limit the sum of the closest distances to the first and second drive electrodes, for example, by requiring that they be less than a first threshold value. For example, the sum of distance 182 and 183 is less than the first threshold value. If the two electrodes are too far apart from each other, there may be a slow region between the two electrodes where neither electrode has much effect, for example, where both electric fields are extremely attenuated. The appropriate threshold value also depends on the specific application, but as an example, 100 micrometers could be taken as the first threshold value.

[0129] At the same time, there may be a case where it is desired to avoid the electrodes getting too close to each other. For example, if the electrodes on the substrate are too close to each other, the chance of accidental short circuits increases. For example, it may be required that the sum of distance 182 and 183 be at least a second threshold value. The appropriate value for the second threshold depends on the application. As an example, the second threshold value could be taken as 10 micrometers.

[0130] The upper and lower limits for the distance between electrodes can be calculated for any point on the substrate, and appropriate limits can be set for them as shown. To simplify the calculation, it may be required that the distance from a point on the first drive electrode to a point on the second drive electrode is at least a second threshold value. For example, this distance may similarly be taken as 10 micrometers.

[0131] In the case of an electrode pattern where the electrode line is a line, the calculation can be further simplified by limiting the calculation to nodes including the endpoints of the electrode line.

[0132] In an embodiment, the horizontal size of a building block, for example in a first direction 191, for example the x - direction, is at least 10 times the sum of the electrode line width and the electrode distance, also called the line gap. For example, the electrode distance may be taken as the sum of the maximum closest distances to the two closest electrodes, for example the sum of distances 183 and 182. The electrode line width and the electrode distance depend on the application. As an example, the electrode line width may be considered to be 5 micrometers. The electrode line width may be 1 micrometer or 10 micrometers or a value in between. Other values are possible. For example, in the case of the vertical size of the building block in a second direction 192, for example the y - direction, the same lower limit as in the x - direction may be taken. For example, the building block is rectangular or square, and the dimension of its side is at least 500 micrometers, for example at least 1000 micrometers, etc.

[0133] In an embodiment, the electrode line width is not constant when measured along the electrode line. For example, the electrode line width may be measured perpendicular to the side of the electrode line. A constant electrode line width has a tendency for the line-to-line distance to be (more) constant, which in turn has the drawback of contributing to diffraction. In an actual design, the width of the electrode is typically maintained below a maximum value. As an example value, the maximum value may be taken as the maximum line-to-line distance of the electrode so that the electrode line is nowhere thicker than the space between the electrodes.

[0134] The line gap, e.g., the electrode pitch, need not be constant. For example, in a spiraled design such as the spiral design of FIG. 5b, it is possible to have a low-diffraction design with a substantially constant line gap, but in a more randomized design, e.g., a Waal design, the line gap is typically not constant and can vary, for example, within a certain range.

[0135] Making the building blocks too small may cause diffraction by the repetition of similar building blocks. Making the building blocks too large may cause problems regarding optimization and evaluation in production. As examples, the sides of the building blocks may be 0.5 mm, 1 mm, 1 cm, and 10 cm, but may extend, for example, up to 100 cm or larger values. For example, one or both sides of the building block may be between 0.5 mm and 10 cm.

[0136] In an embodiment, the building block is square, but a rectangle is possible. In an embodiment, the building block sides have the same ratio as the substrate. In an embodiment, the building block is not square and may be any one or more plane-filling shapes. For the diameter, e.g., the maximum distance between two points of the building block, the same lower limit may be taken as in the x-direction.

[0137] The electrode pattern may be optimized for various constraints. For example, the length of the electrode is preferably short to maintain low electrical resistance. In an embodiment, for a point on the substrate, the lengths of the two closest electrodes to that point are approximately equal, for example, having a ratio within a threshold of 1.

[0138] Preferably, optical diffraction below a threshold is particularly important. Further information regarding diffraction for various example designs is provided herein.

[0139] Optical diffraction The following method was used to estimate optical diffraction.

[0140] 1. Preparing a design drawing: - Crop to 1024×1024 microns (unit cell size); - Normalize the pixel values to 255 (black = 0; white = 255);

[0141] 2. Use the Bluestein method [1, 2] to calculate the magnitude and angle without scaling.

[0142] Since optical diffraction can be formulated as a Fourier transform, conventional methods are to use the fast Fourier transform (FFT) algorithm. However, the use of FFT requires a fixed sampling relationship between the discretization of the input field and the discretization of the output field. The Bluestein method is efficient and flexible in the selection of the sampling grid and uses the chirp z-transform (CZT) algorithm instead of the FFT algorithm.

[0143] 3. Find the maximum intensity of the zero-order (main) peak (I main ) from the magnitude spectrum;

[0144] 4. I within the magnitude spectrum mainIgnore pixels having signals from peaks;

[0145] 5. Find the maximum intensity among all other higher-order peaks (I higher );

[0146] 6. The resulting diffraction metric value is calculated in the same way as in the case of reference [3]: [Number]

[0147] The experiment confirmed that the calculated pixelated noise metric matched the obvious actual diffraction in the test setup.

[0148] Multiple designs were used to test the noise metric parameters. Table 1 summarizes these tests. In column 1, the unofficial design names are listed. Column 2 shows the figure number where the design is shown. Columns 7 and 8 present the estimated intensity values for the zero-order and higher-order peaks from the magnitude spectrum. Column 9 shows the resulting pixelated metric value in % for all designs. The lower this value, the better the diffraction level of the corresponding design.

[0149] Column 3 gives the longest length of the electrodes within the building block. Columns 4 and 5 give the building block width (x direction) and height (y direction). Column 6 gives the ratio of the longest electrode length to the diameter length within the building block.

[0150] The references cited above are as follows. The references are incorporated by reference.

[0151] [1] Leutenegger, M., Rao, R., Leitgeb, R. A. and Lasser, T. Fast focus field calculations. Opt. Express 14, 11277 - 11291 (2006) [2]Hu, Y. et al. Efficient full-path optical calculation of scalar and vector diffraction using the Bluestein method. Light Sci. Appl. 9, 1 - 11 (2020) [3]Murray, Ian B., Densmore, V., Bora, V., Pieratt, W. M., Hibbard, D. L., and Milster T. D. Numerical comparison of grid pattern diffraction effects through measurement and modeling with OptiScan software. Proc. SPIE 8016, Window and Dome Technologies and Materials XII, 80160U (2011)

[0152] Therefore, the pixelated noise metric can be calculated as follows.

[0153] First, black and white design patterns are generated for a specific dimension, where the electrode lines are black and the substrate background is white. The results in this specification are calculated using the common 8 - bit byte to represent one pixel. In this case, 255 is used to represent white and 0 is used to represent black. The Bluestein method is then used to calculate the magnitude and angle for the chirp z - transform (CZT) without scaling. The Bluestein method is a Fourier - like transform that gives computational characteristics. Finally, the pixelated noise metric can be calculated as the ratio of the higher peak value to the main peak value. The main peak value is determined as the maximum intensity within the magnitude spectrum of the chirp z - transform (CZT) of the design pattern, while the higher peak value is determined as the second - maximum intensity within the magnitude spectrum chirp z - transform (CZT) excluding the main peak.

[0154]

Table 1

[0155] Figures 4a - 4i schematically show examples of substrates having a low ratio. Figures 5a and 5b schematically show examples of embodiments of substrates having a high ratio. Note that the high - ratio design has low diffraction. The ratio is calculated as the quotient of the longest length of a rectangle having the dimensions shown in columns 4 and 5 and the length of the diagonal. Column 9 is calculated as the quotient of column 8 and column 7. Columns 3, 4, and 5 are in micrometers.

[0156] In the past, it has been shown that it is difficult to obtain a low pixelation noise metric by experimental design. However, it has been found that it is possible to obtain a lower pixelation noise metric by the design according to the embodiments.

[0157] In an embodiment, the ratio is at least 2, at least 3, at least 5, or at least 10. In an embodiment, the pixelation noise metric is less than 6.10, less than 6.07, less than 6.05, less than 6, less than 5, or less than 4. In an embodiment, the ratio is at least 2 and the pixelation noise metric is less than 6.07. In an embodiment, the ratio is at least 3 and the pixelation noise metric is less than 6.07. In an embodiment, the ratio is at least 10 and the pixelation noise metric is less than 4. A design having a high ratio can be generated quickly and thus can be easily tested and selected for any other requirements.

[0158] Figures 5a and 5b show a design having two drive electrodes on the surface of the substrate. Any of the designs can be modified to have only a single drive electrode on the surface of the substrate, for example, by removing one of the two drive electrodes. For example, such a modified design can be used in a modulator that uses a substrate with a single electrode.

[0159] The designs shown in FIGS. 4a - 4i and FIGS. 5a - 5b can be realized in a single plane without having intersecting electrodes. In particular, when these designs are connected to two drive buses, intersecting electrodes are not required. When three or more drive electrodes are used, or when a more complex electrode pattern is used, electrode intersections may or may be necessary. However, such intersections are possible, for example, where two electrode lines cross, and a dielectric material may be placed between the electrodes. For example, such an insulator may be deposited at the intersection location. For example, the first drive electrode is in the first plane of the substrate, and the second drive electrode is in the second plane of the substrate.

[0160] FIG. 6a schematically shows an example of an embodiment of building block 601. FIG. 1d shows an L - shaped drive bus for a substrate, and building block 601 is similar in that regard except that the drive bus is applied to building blocks that are repeated across the substrate. This provides further advantages.

[0161] In FIG. 6a, drive buses for each of two drive electrodes are shown. Schematically, the configuration of the drive electrodes is shown inside building block 601. The two drive buses are patterned to indicate driving different drive electrodes. Each of the two drive buses has two arms; the two arms extend along two sides of the building block, and the two sides meet at a corner of the building block. In this example, the building block is square, but this is not necessary. One of the two arms extends along the full length of the side, while the other arm is shortened to avoid electrical contact with the other drive bus. For example, the gap remaining between the two drive buses may be the same size as between the drive electrodes, for example, 50 micrometers. Note that the drive electrodes are partially connected through the drive buses. A part of the drive electrode is connected to the drive bus in the x - direction, while the other part is connected to the side in the y - direction.

[0162] The building blocks 601 formed in this way can be repeated across the substrate in various ways.

[0163] FIG. 6b schematically shows an example of an embodiment of the substrate 602. In FIG. 6b, the building blocks of FIG. 6a are copied a plurality of times. To obtain the substrate 602, the building blocks are copied by repeated translations in the x and y directions. Each of the building blocks shown in FIG. 6b can be obtained by a direct translation of any other building block.

[0164] A drawback of this configuration is that the drive buses of different drive electrodes finally face each other. To avoid short circuits, a small amount of space, for example, a width comparable to that between the drive electrodes, for example, 50 micrometers, is left. Although not shown in FIG. 6b, various portions of the translated drive buses need to be connected together, for example, by electrode lines.

[0165] For example, as shown by the arrow 640, a vertical groove is formed; that is, two electrode lines extending in parallel are approaching each other. Similar grooves exist in the horizontal direction. Such grooves have been found to have an adverse effect on diffraction. If the building blocks have low diffraction, the design may still be better than a pattern using inferior building blocks, but it is desirable to avoid these grooves.

[0166] FIG. 6c schematically shows an example of an embodiment of the substrate 603. In the substrate 603, the building blocks are repeated across the substrate but are arranged to avoid grooves as in the case of FIG. 6b. In this embodiment, the building blocks are translated and mirrored in two directions in this case.

[0167] Building block 611 is mirrored in the y direction to form building block 621. Building block 621 is placed directly below building block 611. Building block 611 is mirrored in the x direction to form building block 612. Building block 612 is placed directly to the right of building block 611. Building block 611 is mirrored in both the x direction and the y direction to form building block 622. For example, the mirroring may have the side of the building block as the mirror axis.

[0168] By mirroring the building blocks, it is ensured that the drive buses of the same drive electrodes end adjacent to each other on the substrate. By merging these drive buses, grooves are avoided and diffraction is reduced.

[0169] In an embodiment, at least the drive electrodes on the substrate have mirror symmetry; in an embodiment, the drive electrodes and the drive buses have mirror symmetry. For example, the substrate is symmetric with respect to the x-axis and / or the y-axis. This is an important advantage during manufacturing. Because this allows the upper and lower substrates to be equal. Eliminating the need to produce separate substrates for the upper and lower parts of the optical modulator also eliminates the need to monitor separate types of substrates. Furthermore, having symmetry in the substrate allows a broken upper substrate to be replaced by the lower substrate, and vice versa. Because they are the same. A straight line along the mirror symmetry axis, for example, a drive bus, is useful because the design can be mirrored around that axis. Using the building blocks in a mirrored or non-mirrored form helps to create a mirror-symmetric design.

[0170] This is particularly advantageous when manufactured using a photolithography step for patterning the electrodes. This is because the same substrate patterning can be used for both substrates of the modulator, limiting production costs. The presence of straight busbars attached to a building block or a part of each building block facilitates this effect. Having a symmetric design in one direction to use the same electrode pattern for all substrates is possible without a straight busbar, for example, by local modification of the electrode design at the edges of the symmetric lines. In embodiments, the drive electrode pattern has at least one symmetry in one direction, using, for example, tiling of the building blocks with mirror rings across the substrate and / or a rotatable electrode pattern design.

[0171] FIG. 6d schematically shows an example of an embodiment of substrate 604. In substrate 604, the building blocks repeat across the substrate but are arranged to avoid grooves as in the case of FIG. 6b. In this embodiment, the building blocks are translated and mirror-ringed and rotated over 180 degrees.

[0172] Building block 651 is mirror-ringed in the y direction to form building block 661. Building block 661 is placed directly below building block 651. Building block 651 is point-reflected, for example, rotated over 180 degrees, to form building block 652. Building block 652 is placed directly to the right of building block 651. Building block 651 is mirror-ringed in the x direction to form building block 662.

[0173] Note that the odd-numbered columns of substrate 604 are the same as the odd-numbered columns of substrate 603. The even-numbered columns of substrate 604 are the same as the even-numbered columns of substrate 603 except that they are translated in the y direction across the building blocks.

[0174] By mirroring the building blocks, it is ensured that the drive buses of the same drive electrodes end adjacent to each other on the substrate. By merging these drive buses, grooves are avoided and diffraction is reduced.

[0175] The advantage of the patterns in FIGS. 6c and 6d is that both reduce diffraction. The disadvantage of the pattern in FIG. 6c is that one of the connection points of the drive electrodes in the upper and lower parts of the substrate is much smaller than the connection points of the other electrodes. Since such electrical connections can be easily made, this is not necessarily a problem. However, this problem is avoided in FIG. 6d where both electrodes can be easily connected in the upper and lower parts of the substrate 604. Note that the drive bus far to the right of the substrate 604 may extend to the right in the upper and / or lower parts if so desired.

[0176] Another way to obtain the drive bus pattern of FIG. 6d is to translate the building block 651 one block to the right and invert its electrodes. For example, the drive bus that previously drove the first electrode now drives the second electrode, and vice versa. The next row starting with block 661 may be obtained by mirroring row 651. This transformation pattern will give the same pattern for the drive buses, but will result in a difference when applied to the main line. If the pattern of the main line is inverted rather than point-reflected, it will probably look quite different.

[0177] However, it should be noted that while the pattern of the drive electrodes may follow the same mirroring and translation patterns as the drive buses, this is not necessary. The drive electrodes may follow different patterns, such as a translation similar to that in FIG. 6b, or something similar. It means that the drive buses may look, for example, like those in FIGS. 6c or 6d, but the main line is the same from block to block.

[0178] The advantage of the drive bus extending across the substrate is that the length along the drive electrodes to a point on the substrate is shorter. Further, the lengths are more uniform, i.e., there is less difference between the length of a first electrode close to a point and the length of a second electrode close to the same point.

[0179] A drive bus is not necessary. One or more or all of the drive electrodes on the substrate may be powered from a source other than the drive bus applied on the same side of the substrate. For example, the drive electrodes may be connected through vias from one surface of the substrate, e.g., the inner surface, to a second surface of the substrate, e.g., the outer surface. The vias may be connected on the outer surface to the same or a similar power source as may be used for a drive bus, for example. For example, the drive bus may be applied on the outer surface from the edge of the substrate to the vias; other configurations are possible. The connection to the power source may pass through a controller.

[0180] For example, the drive electrodes may be insulated from the edge of the substrate; for example, an insulated drive electrode may be surrounded on all sides by other drive electrodes. Using insulated electrodes significantly simplifies the pattern design because it is no longer necessary to ensure that each drive electrode can reach the drive bus. For example, an insulated drive electrode may be connected from the inside to the outside using a via, and the via may be connected to a controller.

[0181] Vias may also be used to connect one part of a drive electrode to another part of the same drive electrode. For example, a drive electrode may comprise two parts insulated from each other; for example, the two parts may be insulated from each other because another drive electrode extends between them. Connecting the two parts across the inner surface may cause an electrical short. In an embodiment, the two parts or multiple parts are each connected from the inside to the outside by vias. On the outside, the vias are electrically connected to each other; thus, forming the drive electrode from that portion.

[0182] Returning to Fig. 5a, this type of electrode design can be constructed from tessellations. Specific useful sources for electrode designs are Delaunay Triangulations and their corresponding Voronoi duals. These triangulations are, for example, a straightforward way to quickly generate a large number of tessellations in order to optimize the design. However, other plane fillings, such as randomizations of regular tilings, or even non-periodic tilings such as Penrose tilings, can be used instead.

[0183] The inventors refer to Yonghe, L. et al. (2013). "A Simple Sweep-line Delaunay Triangulation Algorithm" In: Journal of Algorithms and Optimization (JAO) 1.1, pp. 30 - 38. The paper is incorporated by reference.

[0184] For example, it may be possible to follow the following algorithm. The embodiments are described for covering a substrate, but may be used similarly for covering building blocks.

[0185] I: Generate a semi-randomized point distribution within a specific area Obtain a first set of points that cover the substrate. For example, the following may be done to obtain a semi-randomized distribution of points across the substrate.

[0186] Step 1 - All points are initially evenly distributed within the area.

[0187] Step 2 - Then, for each point, create a small random variation in the x and y coordinates. For example, the random variation range may be set and taken such that it is not greater than 30% of the initial distance between the evenly spaced points. Another way to obtain such a pattern is to pick points from an appropriate distribution.

[0188] II: Calculate the first network and the second network

[0189] Step 3 - Calculate the triangulation. For example, points may be triangulated and each point is connected to six neighboring points: probably excluding the edges and corners of the substrate. It has been found that Delaunay triangulation works well for this step. Delaunay triangulation is an example of tiling.

[0190] The Voronoi pattern or Voronoi-like pattern is then calculated from the triangulation, for example, as follows: Step 4 - Create a second set of points corresponding to the centers of the triangles.

[0191] Step 5 - Optionally, for each triangle center point, create a small random variation in the x and y coordinates. For example, the random variation may be the same as in the case of the first set of points, and for example, the variation is not greater than 30% of the initial distance between points.

[0192] Step 6 - Connect together the second set of points that cross the boundaries of the triangles; for example, calculate the dual graph for the triangulation. For example, the center points are connected to their direct neighbors.

[0193] If the tiling used is Delaunay triangulation and the optional shifting of the second set of points is skipped, the second network obtained in this way is a Voronoi network. If a different type of tiling or triangulation is used, or if the center points are shifted, the resulting grid of polygons will not be exactly a Voronoi network, but it will be similar to such a network and will be suitable for use in an optical modulator.

[0194] III: Creation of the first and second electrode patterns At this point, two networks are created, a second network, a Voronoi-like pattern of polygons, and a first network, for example, a Delaunay triangulation. The two patterns are each other's duals or approximately so, depending on the randomization.

[0195] From the second network, for example, the Voronoi network, the pattern for the second electrode can be obtained by breaking selected edges of the Voronoi polygons, for example, breaking the walls. From the first network, for example, the triangulation, the electrodes for the first electrode can be obtained.

[0196] Step 7 - Remove the edges in the second network (e.g., Voronoi-like network) until the network reduces to a tree. This can be done by a path-finding search algorithm for the first network, for example, triangulation, starting from a point in a first set of points, for example, the center within a Voronoi polygon. The path-finding algorithm attempts to find a path for each node of the first network. Such an algorithm is also known as one that finds a spanning tree in a graph.

[0197] Such a search algorithm can be a depth-first search or a breadth-first search. The breadth-first search provides a long but very straight pattern, while the depth-first search provides a short and not very straight pattern. The best results were obtained by following a mixture between the "depth-first search" algorithm and the "breadth-first search" algorithm. For example, the depth-first search step or the breadth-first search step can be selected according to a probability distribution, for example, depending on the depth of the search. A suitable distribution is the gamma distribution.

[0198] When an edge in the first network is included in the spanning tree, the dual edge in the second network that intersects the added edge in the first network is removed. Therefore, the resulting spanning tree of the first network may create a tree or a forest within the second network, for example, a Voronoi network. If the second network does not completely reduce to a tree or a forest, this can be achieved by removing further edges within the second network.

[0199] In this way, two trees are created that cover the substrate and interfit as required for the optical modulator. The pattern of Figure 5a was obtained using the above algorithm.

[0200] Once an appropriate graph is obtained, the graph can be converted into an actual electrode design by giving thickness to all path segments. As an example, a thickness of 10 micrometers may be used. For example, a mask layout tool may be used.

[0201] Further adaptations that may be made to the design include: - Screening design units to eliminate shortcuts between electrode 1 and electrode 2. An increase in thickness may introduce shortcuts. These can be avoided by repeating the process, moving edges or nodes, and repeating the generation process. - Including that a drive bus may be added. - Including integrating the second electrode. It may happen that the second electrode is a forest rather than a tree. This can be solved by adding edges, typically connecting to the drive bus and thus integrating the forest into a tree. - Correcting the point coordinates of the electrodes to maintain a minimum line gap between electrodes of, for example, 20 μm and / or to maintain an average line gap between electrodes of, for example, 50 μm. - In particular, when no driving bus for covering is used, it includes shifting the electrodes to enable stitching the design and ensure the continuity of the electrodes from one unit to another. - It includes shifting the electrodes to reduce optical diffraction, refraction, scattering, or moiré. - It includes improving or optimizing the randomization of short segment orientations to reduce optical diffraction, refraction, scattering, or moiré effects. This makes it possible to reduce the confusion in viewing through the display. - Further randomization can include converting the straight segments between points into curved segments. For example, splines may be used between points.

[0202] It has been found that further optimizing the design can be advantageously carried out in several optimization loops. For example, after generating the first electrode segment and the second electrode segment using the above procedure based on tessellation or a procedure based on a tuning pattern or the like, the segments can be converted into paths that give width to the segments. For example, the segments may represent the center lines of polygons of a specific width. Although this procedure will mostly work well, further optimization may be possible because it may give unfavorable effects.

[0203] For example (A), it can be verified that the first path does not contact the second path. If this condition is violated, one or both of those paths, for example, the first path, may be modified so that the first path no longer contacts the second path.

[0204] For example (B), it can be verified that all the first paths are connected at a single first electrode. If this condition is violated, the paths can be created and / or deleted to connect all the first paths to the first electrode.

[0205] For example (C), it can be verified that all the second paths are connected at a single second electrode. If this condition is violated, the paths can be created and / or deleted in order to connect all the first paths to the first electrode.

[0206] Parts B and C can be repeated in a loop until both electrodes are fully connected. For example, it should be noted that, as described herein, the addition of a drive bus to the design may help in the integration of the electrodes. If necessary, part A may also be repeated in this loop.

[0207] Once the first and second electrodes are fully connected and no longer short - circuited, the next loop of optimization can be performed.

[0208] For example (D), it can be verified that the distance between the first electrode and the second electrode is always within a predetermined range. If this condition is violated, the paths of the first and / or second electrodes can be modified to maintain the distance within that range.

[0209] Part D may be repeated until no points are found where the electrodes are too close or too far apart.

[0210] These optimizations may be performed in a computer - implemented method for optimizing the electrode pattern. Further or alternative optimizations may be added herein, for example, as proposed above. For example, the design may be repeated for optical performance, for length ratios, and the like. For example, because the initial pattern of the first and second paths can be generated at low cost using tessellation or the like, the optimization process has the option to end the optimization and start from a new pattern if insufficient progress is made. In an embodiment, rather than the paths themselves being modified, the first set of points and the second set of points are modified and the generation is repeated from that point onwards.

[0211] The electrodes obtained through this procedure have a large number of branch nodes and typically have many different angles. These factors are advantageous for low diffraction. For example, an advantageous substrate for use in an optical modulator comprises a plurality of interlocking drive electrodes applied to the substrate, each of the plurality of drive electrodes being arranged in a pattern across the substrate, the plurality of interlocking drive electrodes being arranged alternately with respect to each other on the substrate, and at least one of the first and second drive electrodes being a spanning tree of the tessellation.

[0212] A computer-implemented method for obtaining a first electrode design and a second electrode design for use in a substrate of an optical modulator, wherein the first and second electrodes together cover the substrate to provide an electric field configurable within the optical modulator, the method - obtaining a tessellation (100) of the substrate, the tessellation comprising a plurality of cells (101; 102; 103) that cover the substrate without overlapping, - obtaining a center point (111) within each cell of the tessellation, - calculating a spanning tree (Figure 1c) for the center points, the edges of the spanning tree representing two neighboring cells of the tessellation, - deriving a first electrode design (121) from the spanning tree, - deriving a second electrode design (122) from the tessellation, the deriving including removing portions of the tessellation where the edges of the spanning tree intersect the boundaries of the cells of the tessellation, including.

[0213] Some modified embodiments are contemplated. For example, in the above embodiments, any of the following modifications may be added.

[0214] 1. Tessellation a. The tessellation is aperiodic and / or randomized, b. The tessellation is a Voronoi diagram and / or a perturbed Voronoi diagram. c. An initial set of randomized points covering the substrate is selected, a triangulation of the set of points is calculated, and the tessellation is obtained as the dual of the triangulation. i. The triangulation may be a Delaunay triangulation. ii. The set of points may be obtained by perturbation of a uniform set of points taken from a distribution, e.g., a Poisson distribution. iii. The dual may be calculated from selected points within the triangles, such as circumcenters. d. The maximum diameter of each cell is smaller than a threshold value, e.g., smaller than 50 μm.

[0215] 2. Spanning tree a. The spanning tree calculation iteratively constructs a spanning tree by selecting cells from a tessellation that are visited by a partial spanning tree but have unvisited neighbors, and the spanning tree is extended by visiting one of the multiple unvisited neighbors. i. The selection of visited cells may be a combination of depth-first and breadth-first, e.g., a gamma distribution.

[0216] 3. Correct electrodes a. Integrating the electrodes i. Determine the components and connect them. 1. For example, through a connecting subplane or by assigning a separate subplane for each electrode and connecting within the subplane. The components can be similarly connected along the sides of the plane, or by tiling the design, or by drive buses between building blocks. 2. Select two neighboring components, reinsert the removed part of the tessellation, remove the corresponding edge of the spanning tree, and / or vice versa, to connect them. b. Break the circular part of the second electrode. c. Modify the shortcut between the first electrode and the second electrode caused by giving a width to the electrodes by moving parts of the first and / or second electrodes. d. Verify and correct the optical properties. i. From any point in the plane, the distances to the first electrode and to the second electrode should both be less than a threshold value (e.g., 50 μm), or their sum should be less than the threshold value (50 μm). ii. The distance from a point on the first electrode to the second electrode should be at least a second threshold value (20 μm), and vice versa.

[0217] 4. Optimal modulator a. An optical modulator according to a normal claim, wherein the first and second electrode designs are according to the design method of any one of the preceding claims.

[0218] It should be emphasized that the above method is not the only way to obtain a design with a low pixelation noise metric or a high ratio of electrode length to diagonal. For example, instead of using a Voronoi network, a network based on a Turing pattern may be used; for example, see the paper "The chemical basis of morphogenesis" by Alan Mathison Turing, which is incorporated herein by reference.

[0219] The design of FIG. 5b was not obtained from tessellation, but still gives good values. For example, in the design according to FIG. 5b, it includes a spiral. In the spiral, a first electrode line and a second electrode line belonging to the first drive electrode and the second drive electrode respectively are spiral on the substrate. In the area between the spirals, even when some electrical lines are substantially parallel, the pattern gives good values overall. The pattern may be further improved by causing the spirally configured lines to undulate, particularly in other several turns of the spiral, for example, 1-3 turns. Such undulation may be, for example, by adding protrusions that disrupt the pattern to the electrode lines, as shown in FIG. 4e or FIG. 4f. For example, all the lines within the spiral may undulate, for example, having the amplitude of the undulation of protrusions that decrease towards the center of the spiral.

[0220] Two substrates according to an embodiment may be combined to form an optical modulator. The optical modulator is particularly suitable for glazing. Exemplary embodiments of the optical modulator are shown below.

[0221] FIG. 7a schematically shows an embodiment of an optical modulator 10 that may be applied in smart glazing.

[0222] Reference is made to patent application PCT / EP2020 / 052379, which is hereby incorporated by reference herein; this application includes advantageous designs for optical modulators that may be further improved, for example, by including electrodes, buildable blocks, and / or substrates as described herein.

[0223] The optical modulator 10 can be electronically switched between a transparent state and a non-transparent state, and vice versa, or between a reflective state and a non-reflective state, and vice versa. The optical modulator 10 includes a first substrate 11 and a second substrate 12 arranged opposite to each other. At least two electrodes are applied inside the first substrate 11: electrodes 13a and 13b are shown. These at least two electrodes are collectively referred to as electrode 13. At least two electrodes are applied inside the second substrate 12: electrodes 14a and 14b are shown. These at least two electrodes are collectively referred to as electrode 14.

[0224] The fluid 15 is provided between the substrates. The fluid contains particles 30, such as nanoparticles and / or microparticles, and the particles are electrically charged or chargeable. For example, the particles may inherently have a charge on the surface of the particles. For example, the particles may be surrounded by charged molecules.

[0225] The electrodes are arranged to drive the particles 30 to move towards or away from the electrodes in response to the applied electric field. The optical properties of the optical modulator, particularly transparency or reflectivity, depend on the location of the particles 30 in the fluid. For example, there may be provided a connection for applying an electromagnetic field to the electrodes.

[0226] At least one electrode, but preferably both electrodes 13 and 14, are shown schematically in the figure according to the embodiment.

[0227] In an embodiment, at least one of the electrode patterns on the first substrate and the electrode patterns on the second substrate has a calculated low pixelation noise metric that contributes to diffraction. Interestingly, the electrode patterns on the substrate may not individually meet the limits regarding their pixelation noise metrics, but their combination, i.e., their superposition, may meet the limits. Since this is the pattern that will be visible to the eye when looking through the optical modulator, the low pixelation noise metric in the superposition will similarly contribute to low diffraction. Appropriate limits for the patterns on the first and / or second substrate or for the superposition are: less than 6.05% or including 5% or 4%.

[0228] In an example, substrates 11 and 12 may be optically transparent outside the electrodes, typically >95% transparent at the relevant wavelengths, for example, >99% transparent, etc. Considering the electrodes, the transparency can be much lower, for example, 70%. The term "optical" may relate to wavelengths visible to the human eye (about 380 nm - about 750 nm) when applicable, and may relate to a broader range of wavelengths including infrared (about 750 nm - 1 μm) and ultraviolet (about 10 nm - 380 nm) and sub - selections thereof when applicable. In an exemplary embodiment of the optical modulator, the substrate material is selected from glass and polymers.

[0229] In another example, one substrate, such as the lower substrate 12, may be reflective or partially reflective, while the upper substrate 11 is transparent. The optical properties of the optical modulator, particularly the reflectivity, depend on the location of the particles 30 in the fluid. When the panel is in the open state (vertical drive), the particles will be approximately positioned between the opposing electrodes of the two substrates, whereby the incident light can pass through the transparent upper substrate and the optical layer with relatively little interference and be reflected or partially reflected on the lower substrate.

[0230] The distance between the first substrate and the second substrate is typically less than 30 μm, for example 15 μm or the like. In an exemplary embodiment of the optical modulator, the distance between the first substrate and the second substrate is less than 500 μm, preferably less than 200 μm, preferably less than 100 μm, even more preferably less than 50 μm, for example, less than 30 μm.

[0231] In an example, the modulator may be provided with a flexible polymer, and the rest of the device may be provided with glass. The glass may be hard glass or flexible glass. If required, a protective layer may be provided on the substrate. If two or more colors are provided, two or more layers of flexible polymer may be provided. The polymer may be polyethylene naphthalate (PEN), polyethylene terephthalate (PET) (optionally with a SiN layer), polyethylene (PE), etc. In a further example, the device may be provided with at least one flexible polymer. Thus, the modulator may be attached to any surface, such as by using an adhesive.

[0232] The particles 30 may be adapted to absorb light, thereby preventing a particular wavelength from passing through. The particles 30 may reflect light; for example, the reflection may be specular, diffuse, or intermediate between the two. The particles may absorb some wavelengths and reflect other wavelengths. The particles may also or instead emit light, for example, using phosphorescence, fluorescence, or the like. Even a fluid may emit light whose emission is modulated by changing the location of the particles.

[0233] In an exemplary embodiment of the optical modulator, the size of the nanoparticles ranges from 20 - 1000 nm, preferably from 20 - 300 nm, more preferably less than 200 nm. In an exemplary embodiment of the optical modulator, the nanoparticles / microparticles may include a coating on a pigment, and preferably may include a core. In an exemplary embodiment of the optical modulator, the coating of the particles is made of a material selected from conductive and semiconductive materials.

[0234] In an exemplary embodiment of the optical modulator, the particles are adapted to absorb light having wavelengths from 10 nm - 1 mm, such as, for example, from 400 - 800 nm, from 700 nm - 1 μm, and from 10 - 400 nm, and / or are adapted to absorb a portion of the light having a wavelength range falling within 10 nm - 1 mm (filter), and combinations thereof.

[0235] In an exemplary embodiment of the optical modulator, the particles are electrically charged or chargeable. For example, the charge on the particles may be from 0.1 e to 10 e (5 * 10 -7 -0.1 C / m2) per particle.

[0236] In an exemplary embodiment of the optical modulator, the fluid is present in an amount of 1 - 1000 g / m2, preferably 2 - 75 g / m2, more preferably 20 - 50 g / m2, such as, for example, 30 - 40 g / m2. It is a great advantage that much less fluid and similar particles can be used according to this layout.

[0237] In an exemplary embodiment of the optical modulator, the particles are present in an amount of 0.01 - 70 g / m2, preferably 0.02 - 10 g / m2, such as, for example, 0.1 - 3 g / m2.

[0238] In an exemplary embodiment of the optical modulator, the particles have colors selected from cyan, magenta, and yellow, and from black and white, and combinations thereof.

[0239] In an exemplary embodiment of the optical modulator, the fluid comprises one or more of a surfactant, an emulsifier, a polar compound, and a compound capable of forming a hydrogen bond.

[0240] Fluid 15 may be a nonpolar fluid having a dielectric constant smaller than 15. In an exemplary embodiment of the optical modulator, the fluid has a relative dielectric constant εr smaller than 100, preferably smaller than 10, for example smaller than 5. In an exemplary embodiment of the optical modulator, fluid 15 has a dynamic viscosity exceeding 10 mPa·s.

[0241] Electrodes 13a, 13b and electrodes 14a, 14b are in fluid contact with the fluid. The fluid is in direct contact with the electrodes or, indirectly, for example, the fluid may contact a second medium having the electrodes through a porous layer or the like. In an embodiment, the electrodes cover about 1-30% of the substrate surface. In an embodiment, the electrodes have an electrical conductivity > 1 * 10 7 S / m, similar to 100 nΩm (at 273K: for comparison, typically used ITO has 105 nΩm) and comprises an electrically conductive material having a resistivity smaller than that. In an embodiment of the optical modulator, the electrodes comprise copper, silver, gold, aluminum, graphene, titanium, indium, and combinations thereof, preferably copper. The electrodes may be in the form of micro-wires embedded in a polymer-based substrate; for example, in the form of copper micro-wires.

[0242] Connections for applying an electromagnetic field to electrodes, where the applied electromagnetic field to the electrodes causes the movement of nanoparticles and microparticles from a first electrode to a second electrode and vice versa. There may be provided connections for applying an electromagnetic field to the electrodes. For example, in an exemplary embodiment of an optical modulator, the current is between -100 - +100 μA, preferably between -30 - +30 μA, more preferably between -25 - +25 μA. For example, the power supply may be electrically connected to at least two electrodes. The power supply may be adapted to provide waveform power. At least one of the amplitude, frequency, and phase may be adaptable to provide different states within the optical modulator. For example, the mode of power may be adapted by a controller.

[0243] The optical modulator 10 may comprise one or more segments, where a segment is a single optically switchable entity that may vary in size. The substrate may at least partially confine a volume that is a segment.

[0244] The device may comprise a driver circuit for changing the appearance of (individual) segments by applying an electromagnetic field. Thus, similarly, the appearance of the optical modulator or one or more of its parts may change. For example, a segment may have an area of at least 1 mm 2 The design allows for stacking to enable more colors; for example, in the case of full-color applications, the stacking of two or three modulators may provide most or all of the colors respectively.

[0245] Having one or more segments enables local control of the optical modulator; this is advantageous for some applications but not necessary. In the case of smart glazing, the optical modulator may be used with or without segments. For example, when applied in smart glazing, transparency or reflectivity can be locally controlled, e.g., to block a sun-patch without reducing the transparency or reflectivity of the entire window. The segments can be relatively large, e.g., having a diameter of at least 1 mm or at least 1 cm.

[0246] In an exemplary embodiment of the optical modulator, the substrates (11, 12) are aligned and / or the electrodes (13, 14) are aligned. For example, electrodes 13a, 13b and electrodes 14a, 14b may be aligned to face each other. In an aligned substrate, the electrodes on different substrates are behind each other when viewed in a direction orthogonal to the substrate. When the optical modulator is disassembled and the substrates are placed together with the electrodes facing up, the electrode patterns are mirror images of each other.

[0247] Aligning the substrates may increase the maximum transparency or reflectivity of the optical modulator, while when selecting the optical modulator for more criteria such as the range of transparency or reflectivity, it may be better not to align or not fully align the two substrates. The optical modulators can be stacked. For example, two stacked optical modulators can be made from three substrates, with the central substrate having electrodes on both of its surfaces. In an embodiment of the optical modulator, optionally, at least one of the substrates 11, 12 of the first optical modulator is the same as the substrates 11, 12 of at least one second optical modulator. In the case of stacked modulators, alignment can increase the maximum transparency or reflectivity, but may be detrimental to other considerations, e.g., diffraction.

[0248] FIG. 7b schematically shows an example of an embodiment of the optical modulator 40. The optical modulator 40 is similar to the optical modulator 10, except that it includes a plurality of optical layers; in the example, two optical layers are shown. There may be three or more optical layers. Each optical layer is disposed between two substrates. The optical modulator 40 can be regarded as a stack of two-substrate optical modulators as in FIG. 7a. As shown, the optical modulator 40 includes three substrates: a first substrate 41, a second substrate 42, and a third substrate 43. There is an optical layer between substrates 41 and 42, and there is an optical layer between substrates 42 and 43. The optical layers may be the same as the optical layers of the optical modulator 10. The controller 46 is configured to control the current on the electrodes of the substrates. For example, in FIG. 7b, the controller 46 may be electrically connected to at least 4×2 = 8 electrodes.

[0249] Interestingly, the particles in the plurality of optical layers may be different so that multiple layers can be used to control more optical properties of the optical modulator. For example, the particles in different optical layers may absorb or reflect at different wavelengths, for example, may have different colors. This can be used by the controller 46 to create different colors and / or different color intensities on the panel. For example, a four-substrate panel may have three optical layers each having different color particles, for example, cyan, yellow, and magenta. By controlling the transparency or reflectivity of different colors, a wide color spectrum can be created.

[0250] The surface of the substrate facing another substrate may be supplied with two or more patterns, for example, as in the case of the embodiment. For example, the outer substrates 41 and 43 may receive electrodes only on the inner side, while the inner substrate, for example, substrate 42, may have electrodes on both sides.

[0251] Substrates 41 and 42 together may be regarded as an embodiment of the optical modulator. Similarly, substrates 42 and 43 together may be regarded as an embodiment of the optical modulator.

[0252] FIG. 7c schematically shows an example of an embodiment of a vehicle 20 with smart glazing for a window 21. This is a particularly advantageous embodiment because during driving, the level of incident light can be changed frequently and rapidly. Using smart glazing in a vehicle has the advantage that the light level can be maintained at a constant level by adjusting the transparency of the vehicle's windows. Furthermore, the reduced diffraction effect improves safety by reducing the driver's distraction. The vehicle 20 may include a controller configured to control the transparency or reflectivity of the window 21.

[0253] Smart glazing can be used similarly in other glazing applications where the amount of incident light is variable, such as in buildings, offices, homes, greenhouses, and skylights. A skylight is a window placed on the ceiling to allow sunlight to enter the room.

[0254] The light modulator may have two optical states, for example, a transparent state and an opaque state or a reflective state and a non-reflective state. The light modulator, such as light modulator 10 or light modulator 40, - Create an alternating voltage on at least one of the first and second substrates and apply an alternating current between at least the first electrode and the second electrode on the first substrate and / or between the first electrode and the second electrode on the second substrate to switch to a second optical state, for example, an opaque state or a non-reflective state, - Create an alternating voltage between the first substrate and the second substrate and apply an alternating current between the first electrode on the first substrate and the first electrode on the second substrate and / or between the second electrode on the first substrate and the second electrode on the second substrate to switch to a first optical state, for example, a transparent state or a reflective state may be configured as follows.

[0255] The electrode pattern on the first substrate is at least partially arranged in the same pattern as the second electrode on the second substrate. Typically, the electrodes face each other, but the patterns of the first and second electrodes may be shifted relative to each other.

[0256] A protective coating may be provided on at least a part of the inner surface area of at least one of the first substrate and the second substrate.

[0257] The drive signal applied to the drive electrode typically has a varying voltage. For example, the power supply may operate at an AC frequency to switch to a transparent or non-transparent state. Such a signal may have a frequency, for example, between 1 - 1000 Hz. A balanced electrolytic current may be obtained by continuously switching the polarities of the oppositely charged electrodes on the first and second substrates and / or between the first and second substrates.

[0258] Figures 8a - 8b schematically show side views of an embodiment of the optical modulator in use. Applying an electric field to the electrodes on the substrate causes an electric force on the particles. Using this effect, the particles can move around, so different transparency or reflective states can be induced within the optical modulator. The controller may control the electric field, for example, its amplitude, frequency, and phase. In an embodiment, the controller is connected to at least four electrodes: two electrodes for each substrate. However, more electrodes may be used and connected to the controller; for example, three or more electrodes may be used for the substrate to better fine-tune the grayscale and drive it into a non-transparent or non-reflective state. Multiple electrodes may also be used to support multiple segments on the substrate.

[0259] Figure 8a shows the optical modulator in a state where no electric field is applied. In Figure 8a, no electric force is yet applied to the particles 30 suspended in the fluid 15.

[0260] In the configuration shown in FIG. 8a, the conductive electrode pattern disposed on the upper substrate is completely or substantially aligned with the conductive electrode pattern on the lower substrate. The conductive electrode pattern may be deposited on a transparent or (partially) reflective glass substrate, or may be embedded in a plastic substrate or the like.

[0261] The alignment between the upper electrode pattern and the lower electrode pattern contributes to a wider achievable level of transparency or reflectivity. However, alignment is not required because a similar effect can be obtained without alignment. Without alignment, a certain range of transparency or reflectivity can be obtained as well.

[0262] Note that in these examples, reference is made to the upper and lower substrates to refer to the higher or lower substrate on the page. The same substrate may also be referred to, for example, as the front substrate and the rear substrate. This is because in glazing applications, the substrates will be aligned vertically rather than horizontally.

[0263] FIG. 8b shows an optical modulator. For example, in instance P1, a potential +V1 is applied to each micro-wire electrode on the upper substrate, while a negative voltage, for example, -V1, is applied to each micro-wire electrode on the lower substrate. Thus, in this case, the same positive potential is applied to all electrodes 13, and the same negative potential is applied to electrodes 14. The potential difference causes negatively charged particles to flow near the electrodes on the upper substrate, and the particles align substantially with the upper electrodes. As a result, when both the upper and lower substrates are transparent, the transparency of the optical modulator 10 will increase. Similarly, for example, when the upper substrate is transparent and the lower substrate is reflective, the solution contains positively charged particles and they will flow near the electrodes on the lower substrate, where they will align substantially with the lower electrodes, the reflectivity of the optical modulator 10 will increase.

[0264] Similar transparency or reflectivity can be achieved when the voltages of the upper and lower electrodes are reversed in a second instance P2 of the on state, as opposed to the instance of P1. In instance P2, the voltage of each electrode on the upper substrate is supplied with a negative potential -V1 here, while the voltage of the aligned electrodes of the lower substrate is supplied with a positive potential. This state is similar to the state shown in FIG. 8b, but the upper and lower substrates are in a reversed state. Similarly, in this configuration, the transparency or reflectivity of the optical modulator 10 is high.

[0265] Interestingly, for example, by switching between the positive potential of the electrode on the upper substrate (and the negative potential on electrode 14), as shown as electrode 13 in FIG. 8b, and the positive potential of the electrode on the lower substrate, as shown as electrode 14 in FIG. 8b, the transparency or reflectivity can be maintained while reducing corrosion damage to the electrodes. This alternating electric field can be achieved by applying an alternating potential to the upper and lower electrodes.

[0266] Applying a waveform is optional but a useful measure to increase the lifespan of the optical modulator by reducing corrosion. Corrosion can occur, for example, when using copper electrodes because copper ions dissolve into the ionic fluid on one substrate and flow to the electrode on the opposing substrate where they deposit. By applying a waveform, the direction of copper ion transport is frequently reversed, thus reducing corrosion damage. Between the two instances P1 and P2, the corrosion current between the two substrates balances or is substantially balanced, for example, >95% balanced. For example, when the corrosion rate of the electrode on the upper plate occurs, between each time instance P1 and vice versa, in instance P2, there is a balanced deposition of copper onto the lower electrode. Thus, particles continuously migrate or move between the upper and lower electrodes, and the optical modulator or smart window is always in the on state, while the dynamic electrolytic current between the upper and lower electrodes is constant, and thus there is no or negligible net loss of electrode material on the upper and lower electrodes.

[0267] Figure 8c shows how a state of reduced transparency or reflectivity can be obtained. An alternating voltage is applied on the same substrate. For example, in an embodiment, as shown in Figure 8c, a potential +V2 is applied to the first electrode, and the next adjacent electrode has an opposite potential -V2, etc. This can be obtained by applying the potential +V2 to electrode 13a and the opposite potential -V2 to electrode 13b. On the opposing substrate, the potential +V2 may be applied to electrode 14a and the opposite potential -V2 may be applied to electrode 14b. For example, the electrodes may be arranged such that the electrodes on the substrates are aligned; the electrodes on the upper substrate have the opposing electrodes on the lower substrate, and vice versa. For example, in order to reduce transparency or reflectivity, the opposing electrodes may receive the same potential, while the neighboring electrodes receive opposite potentials. The embodiment is shown in Figure 8c, the four electrodes are denoted by reference numerals 13a, 13b, 14a, and 14b, and the rest of the electrodes follow in an alternating manner.

[0268] By using an AC driving cycle between the upper substrate and the lower substrate, oblique and horizontal electric fields are generated between the two substrates, thereby causing random diffusion of the particles, thereby creating a closed state of the optical modulator. As a result of this configuration, the particles move obliquely and horizontally between the upper substrate and the lower substrate, and the diffusion of the particles into the visible aperture of the optical modulator contributes to the closed opaque state of the optical modulator.

[0269] For the transparent state shown in Figure 8b, the waveform may be applied to the electrodes such that, for example, the electrodes shown in Figure 8b in a state having a positive potential become negative, and vice versa. Similar to the case of Figure 8b, for example, applying a waveform between electrodes 13a and 13b and between 14a and 14b reduces corrosion damage to the electrodes.

[0270] The AC driving cycle may be implemented by using an interlocking line configuration that combines upper and lower electrode configurations shown in plan view in Figures 5, 6a - 6d, etc.

[0271] The degree to which transparency or reflectivity increases or decreases in FIGS. 8b and 8c depends on the voltage and the frequency difference. By changing the voltage difference, the amount by which transparency or reflectivity increases or decreases respectively is controlled. For example, a curve representing light transmittance versus voltage may be determined, for example, measured. A corresponding voltage, for example an AC voltage, may be applied to obtain a particular level of light transmittance, for example a particular transparency, for example a particular grayscale level. Levels between transparent and non-transparent may be obtained by interpolating the signal for the transparent state or for the non-transparent state. Similarly, a curve representing light reflectivity versus voltage may be determined, for example, measured. A corresponding voltage, for example an AC voltage, may be applied to obtain a particular level of reflectivity. Levels between reflective and non-reflective may be obtained by interpolating the signal for the reflective state or for the non-reflective state.

[0272] Different electrode patterns may be used for the optical modulator. Each electrode pattern may provide a range of grayscale, for example levels of transparency or reflectivity, that the optical modulator is capable of achieving. However, the particular range of grayscale for any given electrode pattern may differ from another electrode pattern. In other words, different patterns give an increase in transparency or reflectivity or an increase in opacity, but the exact response to the drive signal depends on many factors including the particular pattern used. Variations in the optical properties of the optical modulator may have, for example, a fine resolution of less than 1 mm. Note that pixilation of the optical modulator is not required to achieve different visible optical patterns in the optical modulator, for example a logo.

[0273] This effect may be used to embed a visible image into the light modulator by locally changing the electrode pattern on the substrate of the light modulator. For example, different electrode patterns may locally have different greyscales with a permanent offset relative to each other. For example, by locally changing the electrode pattern or its pitch, the maximum transparency or reflectivity may be changed.

[0274] The result is an area on the light modulator having different intensities of greyscale, for example, different greyscales, or different intensities of coloring. The areas may, however, have the same color point. In embodiments, they may switch together with the rest of the window, although at different speeds. For example, even when the same voltage is applied to the electrodes in two different areas, they may cause different transparency states, for example, different transmission levels, due to different electrode patterns. For example, the curve representing transmittance versus voltage may be shifted. For example, when the voltage control is changed in the same way in both areas, the light transmittance may change in both areas, but with different amounts. Areas may also be made less responsive to drive signals by reducing the density of the electrodes; in particular, areas may be made not to switch at all, for example, by not applying electrodes within the area.

[0275] For example, the electrode material may be copper, aluminum, gold, indium-tin oxide (ITO), etc. ITO is transparent, while Cu / Al is reflective, so different electrode materials may result in different appearances regardless of the drive voltage. Similarly, different materials with different resistances will result in different electric fields. For example, ITO will have a smaller electric field even when driven by the same voltage.

[0276] Embodiments of a method of modulating light include obtaining an electromagnetic field between a plurality of drive electrodes, applying a potential to one of the plurality of drive electrodes applied to two opposing substrates to cause modulation of light shining through the substrates, and causing electrophoretic movement of particles towards or from one of the plurality of drive electrodes, where the two opposing substrates are as in the case of the embodiment.

[0277] Many different ways of performing the method are possible, as will be apparent to those skilled in the art. For example, the order of the steps may be performed in the order shown, but the order of the steps can vary, or some steps may be performed in parallel. Additionally, other method steps may be inserted between the steps. The inserted steps may represent improvements to the method as described herein, or may be unrelated to the method. For example, some steps may be performed at least partially in parallel. Further, a given step may not be fully completed before the next step begins.

[0278] Driving the electrodes may involve using a signal having a selected maximum amplitude corresponding to one of a plurality of levels of transparency or reflectivity of the light modulator. The signal may be an alternating current or an alternating voltage.

[0279] Embodiments of the method may be implemented using software that includes instructions for causing a processor system to perform the method. The software may only include steps taken by a particular sub - entity of the system. The software may be stored on a suitable storage medium such as a hard disk, floppy disk, memory, optical disk, etc. The software may be sent as a signal along a wired or wireless path or using a data network, e.g., the Internet. The software may be made available for download onto a server and / or for remote use on a server. Embodiments of the method may be implemented using programmable logic, e.g., a bitstream configured to configure a field programmable gate array (FPGA), to perform the method.

[0280] It will be recognized that the subject matter of the present disclosure extends equally to a computer program, particularly a computer program on or in a carrier wave, adapted to implement the subject matter of the present disclosure. The program may be in the form of object code, such as source code, object code, intermediate source code in the code, and partially compiled forms, or in any other form suitable for use in implementing embodiments of the method. Embodiments related to computer program products include computer - executable instructions corresponding to each step of at least one of the processing steps of the described method. These instructions may be subdivided into sub - routines and / or stored in one or more files that may be statically or dynamically linked. Another embodiment related to computer program products includes computer - executable instructions corresponding to each of the devices, units, and / or parts of at least one of the described systems and / or products.

[0281] FIG. 9a shows a computer-readable medium 1000 having a writable portion 1010 that includes a computer program 1020, and also a computer-readable medium 1001 having a writable portion that includes a computer program. The computer program 1020 includes instructions for causing a processor system to perform an optical modulator method according to an embodiment. For example, the processor system may be connected to an optical modulator panel. The computer program 1020 may be embodied as a physical mark on the computer-readable medium 1000 or by magnetization of the computer-readable medium 1000. However, any other suitable embodiment is also conceivable. Further, although the computer-readable medium 1000 is shown here as an optical disk, it will be recognized that the computer-readable medium 1000 may be any suitable computer-readable medium such as a hard disk, solid state memory, flash memory, etc., and may be non-recordable or recordable. The computer program 1020 includes instructions for causing the processor system to perform the optical modulator method.

[0282] FIG. 9b shows a schematic diagram of a processor system 1140 according to an embodiment of a controller for an optical modulator. The processor system includes one or more integrated circuits 1110. The architecture of the one or more integrated circuits 1110 is schematically shown in FIG. 9b. Circuit 1110 includes a processing unit 1120, such as a CPU, to execute computer program components to perform the method according to an embodiment and / or implement its modules or units. Circuit 1110 includes a memory 1122 for storing programming code, data, etc. A part of the memory 1122 may be read-only. Circuit 1110 may include a communication element 1126, such as an antenna, a connector, or both, and the like. Circuit 1110 may include an application specific integrated circuit 1124 for performing some or all of the processing defined in the method. The processor 1120, the memory 1122, the application specific IC 1124, and the communication element 1126 may be connected to each other via an interconnect 1130, such as a bus. The processor system 1110 may be configured for contact and / or non-contact communication using an antenna and / or a connector, respectively.

[0283] For example, in an embodiment, the processor system 1140, such as a device, may include a processor circuit and a memory circuit, and the processor may be configured to execute software stored in the memory circuit. For example, the processor circuit may be an Intel Core i7 processor, an ARM Cortex-R8, etc. In an embodiment, the processor circuit may be an ARM Cortex M0. The memory circuit may be a ROM circuit or a non-volatile memory, such as a flash memory. The memory circuit may be a volatile memory, such as an SRAM memory. In the latter case, the device may include a non-volatile software interface, such as a hard drive, a network interface, etc., configured to provide software.

[0284] For example, a controller for an optical modulator for controlling the voltage applied to an electrode may include a processor circuit, or alternatively or in addition, may include a state machine.

[0285] Figures 10a - 10d schematically illustrate aspects of an embodiment of an optical modulator. The modulator is exemplary and non - limiting. Figures 10a - 10d correspond to the same embodiment of the optical modulator. The modulator may advantageously be combined with other features described herein. Portions of the modulator may be advantageous in an insulating state, with or without combinations with other features described herein. In particular, Figures 10a - 10d provide advantageous examples of building blocks, drive electrodes, drive buses, bus electrode connections, etc., each of which may be considered in an insulating state.

[0286] In an embodiment of a building block where the building block 820 of Figure 10a is an example, the building block comprises a pattern of a plurality of electrodes arranged in an interlocking pattern. When the building block is repeated across a substrate, the electrodes terminating at the left and right sides of the building block, and the drive electrodes terminating at the top and bottom sides of the building block, match up to form a plurality of drive electrodes for the optical modulator in this case. The drive electrodes are arranged in an interlocking pattern. It may or may not be necessary to connect the electrodes at the ends of the repeating building blocks in order to couple the electrodes to the drive electrodes. In building block 820, the number of drive electrodes is two, for example, a first drive electrode and a second drive electrode. However, more than two drive electrodes are possible.

[0287] The building block 820 shown has several advantageous properties that help reduce interference in the optical modulator in which the building block is included, as shown, for example, in Figures 10b - 10d.

[0288] For example, a first characteristic satisfied by building block 820 is that, for at least one of a plurality of mutually engaging electrodes within building block 820, the maximum length between any two points on the electrode, measured along the electrode within building block 820, is at least twice the length of the diagonal of the building block. In practice, in this example, this characteristic is valid for a plurality of electrodes of building block 820.

[0289] For example, a second characteristic satisfied by building block 820 is that building block 820 includes electrodes that branch at nodes to form a tree. Building block 820 shows a highly branched tree. For example, there is a first node at which the electrode branches into at least three lines, each of which is connected to at least three second nodes that similarly branch into at least three lines. In practice, there may further be three second nodes connected to a third node at which the electrodes similarly branch.

[0290] For example, a third characteristic satisfied by the electrodes within a building block is that the angles at the nodes of the electrodes are sufficiently distributed over the range from 0 to 360. For example, the building block shows at least some angles within the range of 0 - 30, up to the range of 330 - 360, and some angles within the range of 30 - 60. In practice, any range from x to x + 30 is shown by the angles of FIG. 10a. In practice, this characteristic is valid for a plurality of electrodes within building block 820.

[0291] In building block 820, the electrode lines are constructed from connected straight line segments. The line segments may similarly or alternatively be curved. In this example, the electrode line width within building block 820 is constant along the electrode line; this is not necessary.

[0292] For example, a fourth characteristic satisfied by the building block is that the building block has a calculated low pixelation noise metric; in this case, less than 4%.

[0293] Any one of the above characteristics may be used to address interference, and they need not be combined as is done in building block 820. For example, only characteristic 1, or only characteristic 2, or only characteristic 3, or only characteristic 4, or combinations, such as 1 and 2, or 2 and 3, 2 and 4, 3 and 4, 1 and 2 and 3 and 4, 2 and 4 and 4, or any other combination, possibly in combination with other features described herein, may be had.

[0294] Building block 820 also satisfies that the distance between two adjacent lines is constrained, e.g., longer than a minimum and shorter than a maximum. Building block 820 is an example of a building block where electrodes are in the same plane and do not cross. Note that if crossing electrodes are desired, that is not an obstacle. For example, two electrodes may cross by having an insulator between the two electrodes at the crossing. The insulator may be the substrate itself. For example, one of the electrodes may be redirected via two vias to extend on the back of the substrate.

[0295] FIG. 10b.1 schematically shows substrate 810 and drive buses. Drive bus 812 and drive bus 814 are shown. To create a substrate for an optical modulator, building block 820 repeats within an area bounded by the drive buses. The drive buses are arranged to drive drive electrodes. In this example, a first drive electrode 812 is arranged on two adjacent sides of the substrate, while a second drive electrode 814 is arranged on two adjacent opposite sides of the substrate. Electrodes 812 and 814 do not contact. In use, a varying voltage is applied to electrodes 812 and 814 to create a voltage distribution that causes an optical effect between substrate 810 and an opposing substrate (not shown in FIG. 10b.1).

[0296] In particular, the drive bus 812 or the side electrode extends along the left side and the upper side. At one point, the connection point shown here at the upper left is provided for connecting the bus 812 to the controller. In particular, the drive bus 814 or the side electrode extends along the right side and the bottom side. At one point, a connection point is provided for connecting the bus 814 to the controller. The bus 814 extends along the upper side outside the bus 812. The advantage of extending one electrode, such as the bus 814, along three sides is that both electrodes can be connected to form the same side. That is, the entire optical modulator can potentially be powered from a single side of the substrate. The bus 814 extends here over a limited portion, for example, less than 1 / 4 of the side. The bus 814 may also extend further to approximately the connection portion of the bus 812.

[0297] The substrate thus formed may be combined, for example, with a mirror image of the substrate (e.g., flipping the design with respect to the horizontal axis or flipping the design with respect to the vertical axis).

[0298] FIG. 10b.2 schematically shows a deformation of the substrate 810 and the drive bus. The drive bus 812 and the drive bus 814 are shown. As in FIG. 10b.1, the building block 820 repeats within the area bounded by the drive buses 812 and 814.

[0299] In addition to the drive bus along the edge of the substrate 810, additional drive buses extending within and across the substrate 810 are shown.

[0300] Figure 10b.2 shows additional drive buses 815 - 819 extending across the substrate. A portion of the additional drive buses, in this example buses 815 and 816, are connected to drive bus 814. A portion of the additional drive buses, in this example buses 817 and 819, are connected to drive bus 812. From the additional drive buses, optional protrusions extend along the sides of the copy of the building block. Thus, all building blocks may have drive buses extending along each of their respective edges, for example, a first drive bus for two sides connected at a vertex of the building block and a second drive bus for the other two sides connected at an opposite vertex. The substrate of Figure 10b.2 may also be combined with a mirror image.

[0301] An advantage of the arrangement shown in Figure 10b.2 is that power is distributed more evenly across the device. As a result, the transition is more uniform and finishes more quickly.

[0302] The building blocks shown in Figures 10b.1 and 10b.2 have square building blocks, but generally speaking, the building blocks can have any shape. In particular, any one or more shapes for tiling a plane, for example, repeatable shapes, can be used. In particular, the building blocks can have a rectangular shape, for example, a non - square shape. For example, one side can be at least 1.5 times the length of the other side. The shape of the building block is the same as the shape of the optical modulator and may have, for example, the same relative dimensions.

[0303] Building blocks may be patterned using one or more building block stepper masks. Additional steppers may be used for drive buses. Steppers may also be used where connections are made by overlapping metal depositions. For example, when a stepper is processing the metal of drive bus 812, there may be an overlap with where the arrangement of 820 exists. Connections from the outside to the electrodes, e.g., to 812, may use conventional foil bolding or clips.

[0304] Note that while one type of building block may be repeated, multiple types of building blocks may also be used. For example, the shape may be triangular. The shape of the building blocks may affect the shape of the overall device. This may be advantageous, for example, to conform the form factor of an optical modulator. Further, building blocks of various shapes may be combined within a single substrate. For example, it may have a square or rectangular shape at the center of the substrate and a triangular shape at the edges.

[0305] Using different shapes and / or dimensions can be useful for substrates without straight edges, as further discussed herein. Using different shapes and / or dimensions can also be useful for curved substrates, such as non-flat substrates. Although not strictly necessary, using different shapes for the building blocks allows the building blocks to better conform to the shape of the substrate. Curved substrates may be combined with another curved substrate to form a curved optical modulator. For example, in an embodiment, the drive bus is arranged along a triangular segmentation of the curved substrate, the drive bus follows the triangular segmentation, and the building block shape is arranged between the drive buses. For example, in an embodiment, the building blocks surrounding the center of the substrate are square or rectangular, while the edge building blocks are triangular. The latter configuration can be done using two shapes or more than three shapes. Note that although a curved substrate may be supported by a single form of building block, it is advantageous to use multiple shapes. In general, building blocks of different shapes can similarly be applied to curved substrates without long electrodes. An example of such a substrate is a substrate for use in an optical modulator, the substrate comprising a plurality of interlocking drive electrodes applied to the substrate, each of the plurality of drive electrodes being arranged in a pattern across the substrate, the plurality of interlocking drive electrodes being arranged alternately with respect to each other on the substrate, the pattern of the plurality of drive electrodes across the substrate comprising a plurality of repeating building blocks, the building blocks comprising a plurality of interlocking electrodes extending in at least two directions across the building block, the interlocking electrodes within the building block forming the drive electrodes, the substrate being curved, and the plurality of repeating building blocks including at least two different shapes.

[0306] Figure 10c schematically shows the details of the corner of Figure 10d discussed below. In Figure 10c, a corner of the building block 820 and a part of the drive buses 812 and 814 are shown. Figures 10d-10d schematically show the building blocks 820 repeating across the substrate. Figure 10d corresponds to the lower left corner of Figure 8b. Figure 10d corresponds to the lower right corner of Figure 8b. The building blocks 820 repeat across the substrate in two directions by translation. The repetition may be a glide translation, for example, a translation followed by a reflection.

[0307] Figure 10c shows how the electrodes formed by the repetition of the building blocks may be connected to the drive buses. For example, the electrode lines may extend from the drive buses to the electrodes within the building blocks.

[0308] Figure 10d schematically shows the details of the repetition of the building blocks 820 between the buses 812 and 814. In Figure 10d, parts of four copies of the building blocks are shown. The edges between the building blocks are denoted by the capital letters A, B, C, and D. The electrodes on one side of the building block are connected to the electrodes on the opposite side of the building block; note that the electrodes in the design match so that aligning the building blocks is sufficient to create continuous electrodes.

[0309] In this example, as can be seen in FIG. 10d, when repeated across the substrate, the blocks are depicted such that they slightly overlap. Having an overlap can, if desired, be avoided, but this is convenient. The overlap in this example is 3%. That is, 3% of the x - dimension of the building block overlaps with 3% of the next block in the x - direction. The amount of overlap is preferably small, for example, between 1% and 5%. Larger or smaller overlaps are possible. It is also possible to have no overlap at all, in which case the building blocks will be aligned directly adjacent to each other. The same is valid for the y - direction, for example, in embodiments where overlaps such as 3%, between 1% and 5% etc. are considered.

[0310] In this example, the building block 820 repeats across the substrate in two orthogonal directions by translation. The repetition can be a glide translation, for example, a translation followed by a reflection.

[0311] FIG. 11 schematically shows a cross - section of an embodiment of the optical modulator 700. In FIG. 11, two substrates: substrate 772 and substrate 774 are shown. Inter - mating drive electrodes and drive buses are applied to their surfaces, for example, according to the embodiment. A spacer 750 is placed between substrates 772 and 774 to maintain the substrates at a predetermined distance. The space between the two substrates is filled with semiconductor ink 760, for example, as described herein, while an edge seal is applied around the edges of the two substrates. By selecting different types of ink, the panel can be configured to modulate, for example, from transparent to opaque, or between reflective and non - reflective.

[0312] FIG. 12a schematically shows an embodiment of an optical modulator. In FIG. 12a, a corner of a substrate according to the embodiment is shown. A drive bus or edge connector is disposed along the upper and right edges of the substrate. Drive electrodes corresponding to the drive bus are connected to the drive bus at a plurality of points, for example, at a first point and a second point. For some portions of the electrodes, two connections may be required to integrate the electrodes, for example, to ensure that the entire electrode is connected. However, it may be arranged for the electrode to connect to the drive bus multiple times, even when it is not required to connect to the first electrode. For example, the first point and the second point may be connected along the drive bus but also through an electrode that crosses the substrate. In that case, a portion of the drive bus between the first point and the second point may be removed. Removing this portion of the drive bus does not disconnect the drive bus from the power source because the drive bus remains connected through the electrode. FIG. 12b shows an example where a portion of the drive bus is removed. FIG. 12c shows the same portion of the substrate but emphasizes the electrodes connecting portions 902, 904, and 906.

[0313] Interrupting long electrode lines, especially straight lines, is beneficial for reducing diffraction. If the edge connector is only located at the edge of the device, as shown in the embodiments of FIGS. 10a - 10d, this will only make a slight difference. However, in the case of embodiments having a drive bus surrounding a building block, the impact is significant. There, the straight lines around the building block will significantly increase diffraction and optical artifacts. Here, these straight lines are interrupted at multiple locations and thus diffraction or optical artifacts can be reduced. For example, a drive bus as shown in FIGS. 6a - 6d benefits from removing a portion of the drive bus.

[0314] Figure 13a schematically shows an example of an embodiment of a building block. Figure 13b schematically shows an example of an embodiment of a substrate for use in an optical modulator. The building block of Figure 13a is repeated in two directions, in this case parallel to the edges of the substrate, across the substrate of Figure 13b. The interlocking electrodes within the building block of Figure 13a are connected in Figure 13b to form two interlocking drive electrodes that extend in at least two directions across the building block.

[0315] Note that the electrodes shown in FIGS. 13 and 13b are very intricate. This can be seen, for example, from their high degree of branching or from the high ratio between the maximum length between any two points on the electrodes within the building block and the diagonal of the building block (the ratio is greater than 2).

[0316] The drive electrodes within the substrate of Figure 13b are in the same plane and do not cross. Note that this design completely connects the electrodes without floating electrodes on the edges. Note that some of the electrodes on the edges of the building block are connected through the electrodes within adjacent building blocks.

[0317] The building block is based on a so-called Turing pattern. The Turing pattern has been found to be advantageous for generating a small number of but longer branches. As a result, the design is less likely to form floating electrodes that may have to be processed separately. The Turing pattern is also known as a reaction-diffusion system - in this particular example, the Gray-Scott equation was used.

[0318] Figures 14a - 14h schematically show embodiments of a substrate in which the pattern of a plurality of drive electrodes across the substrate comprises a plurality of repeating building blocks. The repeating building blocks form a plurality of interlocking electrodes extending in at least two directions across the substrate. The electrodes within the building blocks may have various advantageous properties, for example, having a high ratio between the electrode length and the diagonal; however, this is not necessary. One type of building block or multiple types of building blocks may be used. The blocks may be rotated, mirrored, and / or translated in order to fill the substrate. Drive buses may be placed between the building blocks in order to distribute power; alternatively or additionally, the building blocks may be connected to each other in order to distribute power. The building blocks may have the same shape, but again, their electrode patterns may be different or may not be different.

[0319] Figure 14a schematically shows an embodiment of a substrate in which the building block is rectangular, in this case, square.

[0320] Figures 14b and 14c schematically show embodiments of a substrate in which the building block is triangular, in this case, a right triangle. Any other triangular shape is also possible.

[0321] The advantage of having building blocks of different shapes is that substrates of different shapes can be more easily supported. For example, a square-shaped substrate can be supported by square building blocks or by triangular building blocks as shown in FIGS. 14a and 14b. However, with triangular building blocks, a triangular substrate can be easily tiled, for example, at the edges, without the need to support partial building blocks or different types of building blocks.

[0322] Figure 14d schematically shows an embodiment of a substrate in which the building block is hexagonal, in this case, regular hexagonal.

[0323] FIG. 14e schematically shows an embodiment of a substrate in which the building block is trapezoidal.

[0324] FIG. 14f schematically shows an embodiment of a substrate in which the building block is a polygon, in this case, for example, a rectangular polygon having right angles. It should be noted that the polygon need not be convex as shown in FIG. 14f. The polygon may be a polyomino; for example, a polygon constructed from integral squares. In the example shown, a tromino is used. Other examples of polyominoes include tetrominoes and pentominoes. The polygon may be an isothetic polygon, for example, a rectilinear polygon.

[0325] FIG. 14g schematically shows an embodiment of a substrate in which the building block is square. FIG. 14h schematically shows an embodiment of a substrate in which the building block is triangular. It should be noted that substrates of various shapes can be supported by combining the building blocks. It should also be noted that different shapes are possible for the substrate with triangular building blocks.

[0326] The shape of the substrate of FIG. 14h may also be supported by rectangular building blocks, but partial building blocks or edge type building blocks may be used to support sloped edges of the substrate, etc.

[0327] Supporting substrates of different shapes is advantageous for supporting different applications. For example, in a vehicle, windows are often not rectangular. Having building blocks of various shapes makes it easier to support the desired shape.

[0328] Supporting substrates of different shapes is also advantageous for supporting non-planar substrates.

[0329] The following numbered clauses are the intended embodiments.

[0330] Clause 1. A substrate for use in an optical modulator, - comprising a plurality of mutually engaging drive electrodes (111-114, 121-124) applied to the substrate, each of the plurality of drive electrodes being arranged in a pattern across the substrate, the plurality of mutually engaging drive electrodes being alternately arranged relative to each other on the substrate, the pattern of the plurality of drive electrodes across the substrate comprising a plurality of repeating building blocks, the building blocks comprising - a plurality of mutually engaging electrodes extending in at least two directions across the building block, the mutually engaging electrodes within the building block forming drive electrodes, and for at least one electrode within the plurality of mutually engaging electrodes within the building block, the maximum length between any two points on the electrode measured along the electrode within the building block being at least twice the length of the diagonal of the building block unit, the substrate.

[0331] Clause 2. The substrate according to Clause 1, wherein the calculated pixelation noise metric of the drive electrode pattern of the substrate is less than 6.05% or less than 5% or less than 4%.

[0332] Clause 3. The substrate according to Clause 1 or 2, wherein the electrodes on the substrate comprise a plurality of nodes at which the electrodes branch, the nodes being electrically connected through electrode lines, the plurality of nodes and the connecting electrode lines forming a tree, the electrodes comprising at least a first node (201) at which the electrode branches into at least three electrode lines, the first node (201) being directly connected through an electrode line to a second node (202) and to a third node (203), and the electrodes branching into at least three electrode lines at the second node and at the third node.

[0333] Clause 4. - the angle between two directly connected electrode lines being randomly selected, and / or, - The directly connected electrode lines within the building block form a plurality of angles that cover an interval from 0 to 360 degrees. In particular, for each specific interval of at least 30 consecutive angles, there is at least one angle within the plurality of angles that falls within the specific interval, and / or - A plurality of nodes are randomly selected to cover the area of the building block, and / or - The electrode lines are straight or curved, and / or - The substrate according to clause 3, wherein the electrode line width is not constant along the electrode line.

[0334] Clause 5. - From any point within the substrate, the shortest distances to the first drive electrode and to the second drive electrode should both be less than a threshold value, and / or - From any point within the substrate, the sum of the shortest distances to the first drive electrode and to the second drive electrode is less than a first threshold value and / or exceeds a second threshold value, and / or - The distance from a point on the first drive electrode to a point on the second drive electrode is at least the second threshold value, and / or - The horizontal and / or vertical size of the building block is at least 10 times the sum of the electrode line width and the electrode distance. The substrate according to any one of clauses 1 to 4.

[0335] Clause 6. - The drive electrodes are in the same plane and do not intersect, or - The drive electrodes intersect within the substrate, and a dielectric separates the intersecting drive electrodes at least at the intersecting points. The substrate according to any one of clauses 1 to 5.

[0336] Clause 7. - The building block repeats across the substrate in at least two directions, and / or - A plurality of different building blocks repeat across the substrate in one or two directions, and / or - Two different building blocks repeat in a checkerboard pattern across the substrate, and / or, - The substrate according to any one of clauses 1 to 6, wherein the substrate comprises non-repeating electrode lines connected to the drive electrodes.

[0337] Clause 8. - Two electrodes within a building block that are not connected within the building block are connected within the substrate through connections in neighboring building blocks, and / or, - The substrate according to any one of clauses 1 to 7, wherein the electrodes within the building block are connected to at least two sides of the building block.

[0338] Clause 9. - The building block is translated with and without mirroring and / or point reflection, and / or, - The rows or columns of the building block are mirrored with respect to their longitudinal direction to form the next row or column of the building block. The substrate according to any one of clauses 1 to 8.

[0339] Clause 10. At least one drive bus is disposed on the substrate for each drive electrode to drive the drive electrodes, - At least one drive bus is disposed on the side of the substrate for each drive electrode to drive the drive electrodes, and / or, - The drive bus is only disposed on the side of the substrate, and / or, - The drive bus is disposed between the building blocks covering the substrate. The substrate according to any one of clauses 1 to 9.

[0340] Clause 11. At least one driving bus is arranged on the substrate for each driving electrode to drive the driving electrode, at least one driving bus is arranged on the side of the substrate and / or the side of the building block, the driving bus has a discontinuous part, and the discontinuous part is connected through the driving electrode driven by the driving bus. The substrate according to any one of Clauses 1 to 10.

[0341] Clause 12. The substrate according to any one of Clauses 1 to 11, wherein at least one of the first and second driving electrodes is a spanning tree of the tessellation.

[0342] Clause 13. The substrate according to any one of Clauses 1 to 12, wherein the driving electrode has mirror symmetry.

[0343] Clause 14. The substrate according to any one of Clauses 1 to 13, wherein the substrate is non-rectangular.

[0344] Clause 15. An optical modulator, - A first substrate and a second substrate, at least one of the first and second substrates being the one according to any one of Clauses 1-14, the first and second substrates being arranged with their inner sides facing each other, and a plurality of driving electrodes (111-114, 121-124) being applied to the inner side of at least one of the first and second substrates. The first substrate and the second substrate. - An optical layer between the first substrate and the second substrate comprising, the optical layer being - A fluid containing particles, the particles being electrically charged or chargeable. The fluid, - A controller configured to obtain an electromagnetic field between a plurality of driving electrodes to cause electrophoretic movement of particles towards or from one of the plurality of driving electrodes by applying a potential to the plurality of driving electrodes to cause modulation of the optical characteristics of the optical modulator. The optical modulator.

[0345] Clause 16. - The electrode pattern on the first substrate, the electrode pattern on the second substrate, and / or the overlay of the electrode patterns of the first and second substrates have a calculated pixelated noise metric of less than 6.05% or 5% or 4%, the optical modulator according to clause 15.

[0346] Clause 17. A method of modulating light, comprising: - Applying a potential to a plurality of drive electrodes applied to two opposing substrates to cause modulation of light shining through the substrates, resulting in electrophoretic movement of particles towards or from one of the plurality of drive electrodes, obtaining an electromagnetic field between the plurality of drive electrodes, wherein the two opposing substrates are the substrates according to any one of clauses 1 to 16.

[0347] Clause 18. A computer-implemented method for calculating a pixelated noise metric for an electrode pattern for an optical modulator, comprising: - Preparing black and white design drawings for specific dimensions, wherein the electrode lines are black and the substrate background is white; - Calculating the magnitude and angle for the chirp z-transform (CZT) without scaling using the Bluestein method; - Determining the main peak value as the maximum intensity within the magnitude spectrum of the chirp z-transform (CZT) of the design drawing; - Determining the higher peak value as the second maximum intensity within the magnitude spectrum chirp z-transform (CZT) excluding the main peak; - Calculating the pixelated noise metric as the ratio of the higher peak value to the main peak value and including the computer-implemented method.

[0348] Clause 19. A method for calculating the pixelated noise metric according to clause 18, wherein the design drawing is an 8-bit drawing, black is set to 0, and white is set to 255.

Claims

1. A substrate for use in an optical modulator, comprising: - At least one drive electrode (111-114, 121-124) applied to the substrate, the drive electrodes being arranged in a pattern across the substrate, the pattern of drive electrodes across the substrate comprising a plurality of repeating building blocks, the building blocks comprising: - One or more electrodes extending in at least two different directions across the building block, the electrodes within the building block forming at least one drive electrode, the electrodes within the building block comprising a plurality of nodes where the electrodes branch, the nodes being electrically connected through electrode lines, the plurality of nodes and the connecting electrode lines forming a tree graph, the electrodes comprising at least a first node (201) where the electrode branches into at least three electrode lines, the first node (201) being directly connected through an electrode line to a second node (202) and to a third node (203), the electrodes branching into at least three electrode lines at the second node and into at least three electrode lines at the third node, the substrate.

2. The substrate according to claim 1, wherein the at least two different directions are orthogonal or oblique to each other.

3. For at least one electrode within the electrodes in the building block, the maximum length between any two points on the electrode measured along the electrode within the building block is at least twice the length of the diameter of the building block unit, the diameter being defined as the maximum distance between two points of the building block, the substrate according to claim 1.

4. The substrate according to claim 3, wherein the building block is rectangular and the maximum distance between two corners of the building block is the diagonal of the building block.

5. The calculated pixelation noise metric of the drive electrode pattern of the substrate is less than 6.05%, the pixelation noise metric being defined as the ratio of the maximum intensity among all non-zero order peaks to the maximum intensity of the zero order peak from the magnitude of the Fourier spectrum, the substrate according to claim 1.

6. - The angle between two directly connected electrode lines is randomly selected, and / or - The directly connected electrode lines within the building block form a plurality of angles that cover an interval from 0 to 360 degrees. In particular, for each specific interval of at least 30 consecutive angles, there is at least one angle within the plurality of angles that falls within the specific interval, and / or - A plurality of nodes are randomly selected to cover the area of the building block, and / or - The electrode lines are straight or curved, and / or - The width of the electrode line is not constant along the electrode line, the substrate according to claim 1.

7. - The building block repeats across the substrate in at least two different directions, and / or - A plurality of different building blocks repeat across the substrate in one or two directions, and / or - Two different building blocks repeat in a checkerboard pattern across the substrate, and / or - The substrate comprises non-repeating electrode lines connected to drive electrodes, the substrate according to claim 1.

8. - Two electrodes within the building block that are not connected within the building block are connected within the substrate through connections within neighboring building blocks, and / or - The electrodes within the building block are connected to at least two sides of the building block, the substrate according to claim 1.

9. - The building block is translated without mirroring and with point reflection, and / or - The building block is mirrored and translated without point reflection, and / or - The building block is point reflected and translated without mirroring, and / or - A row or column of the building block is mirrored with respect to its longitudinal direction to form the next row or column of the building block, the substrate according to claim 1.

10. At least one drive bus is disposed on the substrate for each drive electrode of at least one drive electrode to drive the drive electrode. - At least one drive bus is disposed on the side of the substrate for each drive electrode to drive the drive electrode, and / or - The drive bus is only disposed on the side of the substrate, and / or - The substrate according to claim 1, wherein a drive bus is arranged between building blocks across the substrate.

11. - At least one drive electrode is insulated from an edge of the substrate, and vias are connected from a surface of the substrate facing the drive electrode to the insulated drive electrode to supply power to the insulated drive electrode and / or to connect the insulated drive electrode to another part of the drive electrode on the substrate. The substrate according to claim 1.

12. - At least one drive bus is arranged on the substrate for each drive electrode to drive the drive electrode, and at least one drive bus is arranged on a side of the substrate and / or a side of a building block. The drive bus has a discontinuous portion, and the discontinuous portion is connected through a drive electrode driven by the drive bus. The substrate according to claim 1.

13. - The substrate according to claim 1, wherein the drive electrode has mirror symmetry.

14. - The substrate according to claim 1, wherein the substrate is non-rectangular.

15. - At least one drive electrode is a plurality of drive electrodes, - A plurality of drive electrodes (111 - 114, 121 - 124) are interlocked with each other, each of the plurality of drive electrodes is arranged in a pattern across the substrate, the plurality of interlocked drive electrodes are arranged alternately with respect to each other on the substrate, and a plurality of patterns of drive electrodes across the substrate include a plurality of repeating building blocks. The building block has - A plurality of interlocked electrodes extending in at least two different directions across the building block, and the interlocked electrodes within the building block form drive electrodes. The substrate according to claim 1.

16. - The plurality of drive electrodes include a first drive electrode and a second drive electrode, - From any point within the substrate, the shortest distance to the first drive electrode and to the second drive electrode is less than a threshold value, and / or - From any point within the substrate, the sum of the shortest distances to the first drive electrode and to the second drive electrode is less than a first threshold value and / or exceeds a second threshold value, and / or - The distance from a point on the first drive electrode to a point on the second drive electrode is at least the second threshold value, and / or - The horizontal and / or vertical size of the building block is at least 10 times the sum of the electrode line width and the electrode distance. The substrate according to claim 15.

17. - The drive electrodes are present in the same plane and do not intersect, or - The drive electrodes intersect within the substrate, and the dielectric separates the intersecting drive electrodes at least at the intersection points, the substrate according to claim 15.

18. An optical modulator, comprising: - The first substrate and the second substrate according to any one of claims 1 to 17, wherein the first and second substrates are arranged with their inner sides facing each other, and at least one drive electrode (111-114, 121-124) is applied to the inner side of at least one of the first and second substrates, the first substrate and the second substrate; - An optical layer between the first substrate and the second substrate; - A controller configured to apply a potential to the drive electrodes to cause modulation of the optical characteristics of the optical modulator. An optical modulator comprising the above.

19. The optical layer contains particles, the particles are electrically charged or chargeable, and the controller is configured to apply a potential to the drive electrodes to obtain an electromagnetic field that causes electrophoretic movement of the particles towards or from the drive electrodes, which causes modulation of the optical characteristics of the optical modulator, the optical modulator according to claim 18.

20. An optical modulator, comprising: - The first substrate according to any one of claims 15 to 17 and the second substrate according to any one of claims 15 to 17, wherein the first and second substrates are arranged with their inner sides facing each other, and at least one drive electrode (111-114, 121-124) is applied to the inner side of at least one of the first and second substrates, the first substrate and the second substrate; - An optical layer between the first substrate and the second substrate; - A controller configured to apply a potential to the drive electrodes to cause modulation of the optical characteristics of the optical modulator, and configured to obtain an electromagnetic field between a plurality of drive electrodes that causes electrophoretic movement of the particles towards or from one of the plurality of drive electrodes, by applying a potential to the plurality of drive electrodes to cause modulation of the optical characteristics of the optical modulator. An optical modulator comprising the above.

21. - The electrode pattern on the first substrate, the electrode pattern on the second substrate, and / or the overlay of the electrode patterns of the first and second substrates has a calculated pixelated noise metric of less than 6.05%, and the pixelated noise metric is defined as the ratio of the maximum intensity among all non-zero order peaks from the magnitude of the Fourier spectrum to the maximum intensity of the zero order peak. The optical modulator according to claim 18.

22. A method of modulating light, comprising: - Applying a potential to a driving electrode applied to two opposing substrates to obtain an electromagnetic field between the driving electrodes that causes electrophoretic movement of particles towards or from one of the plurality of driving electrodes, which causes modulation of the light shining through the substrates, wherein at least one or both of the two opposing substrates are the substrates according to any one of claims 1 to 17. A method of modulating light.

23. A computer-implemented method for calculating a pixelated noise metric for an electrode pattern for an optical modulator, comprising: - Preparing a black and white design drawing, wherein the electrode lines are black and the substrate background is white; - Using the Bluestein method to calculate the magnitude and angle for the chirp z-transform (CZT) without scaling; - Determining the main peak value as the maximum intensity within the magnitude of the Fourier spectrum of the chirp z-transform (CZT) of the design drawing; - Determining the higher peak value as the second maximum intensity within the magnitude of the Fourier spectrum of the chirp z-transform (CZT) excluding the main peak; - Calculating the pixelated noise metric as the ratio of the higher peak value to the main peak value A computer-implemented method.

24. The method for calculating the pixelated noise metric according to claim 23, wherein the design drawing is an 8-bit drawing, black is set to 0, and white is set to 255.

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