Substrate comprising electrodes and light modulator with reduced diffraction

Abstract

To provide a substrate for use in a light modulator.SOLUTION: A substrate may comprise at least one driving electrode applied thereto. The driving electrode is arranged in a pattern across the substrate. The pattern of multiple driving electrodes across the substrate comprises multiple repeated building blocks. Electrodes in the building blocks form the at least one driving electrode.SELECTED DRAWING: Figure 12c

Description

[Technical Field]

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

[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 a plastic material. The internal volume defined between the plates may be subdivided into a plurality of small, independent volumes or individual cells that are filled with a dielectric fluid. The fluid contains a suspension of particles of a dielectric, charged, or chargeable material. Opposing surfaces of the two plates carry electrodes facing each other. The electrodes are connected to a power source associated with a control means.

[0003] The electrodes on each plate are formed by combs interleaved within each other in pairs. The electrodes of the two interleaved combs can be voltaged with the same or opposite polarity. Depending on the 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 diffraction effects. Diffraction effects are undesirable for glazing. In some situations, the presence of diffraction effects can be detrimental to safety. For example, when optically active glazing is applied in a vehicle such as a car, the presence of diffraction can be confusing or distracting to the vehicle operator. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] U.S. Patent No. 10921678 [Patent Document 2] U.S. Patent No. 8054535 [Patent Document 3] U.S. Patent No. 8384659 [Patent Document 4] U.S. Patent Application Publication No. 2005 / 185104 [Patent Document 5] U.S. Patent Application Publication No. 2018 / 0239211 [Patent Document 6] U.S. Patent No. 5161048 [Patent Document 7] U.S. Patent Application Publication No. 2005 / 0185104

Non-licensed literature

[0006]

Non-patent document 1

Non-patent document 2

Non-patent document 3

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

[0008] A substrate for use in an optical modulator may include a plurality of interdigitated drive electrodes applied to the substrate, each of the plurality of drive electrodes arranged in a pattern across the substrate, the plurality of interdigitated drive electrodes being interleaved with respect to one another on the substrate, the drive electrodes being electrically isolated from one another so that the voltages on the drive electrodes may be independently controlled.

[0009] When such substrates are used in light modulators, a varying voltage applied to the electrodes can cause electrophoretic movement of particles in the optical layer between two such substrates. The movement, in turn, causes modulation of light shining through the substrates. At least two such substrates, each with at least two drive electrodes, are typically used, although additional substrates and / or drive electrodes may be used. The light modulator is preferably electrophoretic, but could also 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, but this is not required; one or both of the substrates may be transparent. In glazing applications, typically both substrates are transparent.

[0010] Optically active glazing, especially so-called smart glazing, is an important application of light modulators, for example, in the embodiment of a substrate on which multiple interdigitated electrodes are applied. Typically, all substrates in a light modulator are transparent; this is particularly true 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 light modulators will change the appearance of incident light. The substrates may be reflective.

[0011] A key issue for applications such as glazing is diffraction. Preferably, diffraction is reduced to a small number. Diffraction can be calculated using a number called the pixelated noise metric, which is the ratio of the maximum intensity of all non-zero-order peaks from a magnitude spectrum to the maximum intensity of the zero-order peak. See, for example, Murray, Ian B., Densmore, V., Bora, V., Pieratt, W.M., Hibbard, DL, 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), incorporated herein by reference. Further reduction of pixelated diffraction values has proven difficult using conventional patterning of electrode lines. However, the present inventors have discovered a way to overcome this obstacle and create a design that breaks existing barriers. In embodiments, 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%. In particular, the pixelation noise metric of the building blocks may be below these thresholds.

[0012] In an embodiment, the pattern of drive electrodes is formed by a plurality of repeating building blocks. The building blocks comprise interdigitated electrodes. 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 merged into a pattern in a mask layout tool before depositing the entire pattern on the substrate. The building blocks may partially overlap. For example, if an electrode line of a first building block matches an electrode line of a neighboring building block and both belong to the same drive electrode, these electrode lines of the two building blocks may be merged. In an embodiment, the building blocks are surrounded by a drive bus, which advantageously merges with the bus for the same drive electrode of the neighboring building block.

[0013] In an embodiment, a drive bus is disposed on the edge of the substrate for each drive electrode to drive the drive electrode. The drive bus may connect otherwise isolated electrodes to the drive electrode. The drive bus may then be connected to a controller.

[0014] The drive buses may be located only on the edges of the substrate, but may also extend across the substrate, for example, between building blocks or as part of the building blocks. For example, multiple straight drive buses may extend across the building blocks, and arms may extend from the drive buses to connect the electrodes to further drive electrodes. Preferably, two drive buses extending across the substrate adjacent to each other are avoided, as this would result in the formation of narrow furrows that may adversely affect diffraction. If two drive electrodes are used, the drive buses are advantageously alternated between the building blocks.

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

[0016] In embodiments, a building block may include multiple branch nodes from which 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, a cluster of branch nodes may include at least a first branch node, where the first node is directly connected to a second branch node and a third branch node through electrode lines. In embodiments, the cluster may be larger, for example, where the first branch node is directly connected to two additional branch nodes, which in turn are directly connected to four branch nodes.

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

[0018] While such clusters of branching nodes may be manually introduced into an electrode pattern, the inventors have discovered an algorithm that can create patterns with a large number of branching nodes. For example, drive electrodes may be found by computing a spanning tree of a Voronoi pattern. A complementary electrode pattern may be formed by placing edges that extend across edges that are removed from the Voronoi pattern. Instead of a Voronoi pattern, other tessellations may be used. For example, a regular tessellation may be used, perhaps using one or more polygonal 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 an electrode; a complementary electrode may be formed from the dual graph.

[0019] Building blocks may be repeated across the substrate by copying and translating the blocks without mirroring or rotation. However, in embodiments, isometry, e.g., mirroring, rotation, and / or point reflection, is applied to the building blocks. While multiple building blocks could be used, using isometry has the advantage that the placement of the building blocks can be improved without having to optimize multiple blocks. For example, if drive buses that span the substrate are used, e.g., between building blocks, isometry can be used to avoid placing the drive buses adjacent to each other on the substrate. For example, an entire row or column of building blocks may be mirrored along its length to form the next row or column of building blocks, and so on. Mirroring building blocks in this manner has the advantage that drive buses can be merged between different building blocks, thus avoiding gaps between building blocks. Mirroring building blocks has the advantage that a symmetric electrode design for the substrate may be established, which is advantageous when fabricating light modulators.

[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 checkerboard, and the edges of the tiles are parallel or orthogonal to each other.

[0021] Substrates according to embodiments may be used in light modulators, also known as optical modulators. For example, two such substrates may be positioned opposite each other so that application of a voltage to the electrodes can move charged particles suspended in a fluid between the substrates. Typically, the electrode designs for the lower and upper substrates are identical, but this is not required. Similarly, the two designs are typically aligned with each other, but this is not required. The particles may absorb or reflect light. The reflection may be specular or diffuse, or something in between. The particles may emit light, for example, with phosphorescence or fluorescence.

[0022] Light modulators provide panels whose transparency or reflectivity can be modified. In embodiments, the color or color intensity may be changed. Light modulators may be used as covers, for example, for containers such as closets, cabinets, and the like. Light modulators may also be referred to as ambient light modulators, dynamic light modulators, light modulators, color modulators, IR modulators, UV modulators, IR active filters, UV active filters, or dynamic color filters, depending on the specific application.

[0023] A particularly advantageous application is in optically active glazing, also referred to in the art as smart glazing, smart windows, controllable glazing, optical panels, electronic signage, dynamic light panels, dynamic color panels, active color panels, active light panels, active light surfaces, active color surfaces, dynamic light surfaces, or dynamic color surfaces.

[0024] In an embodiment, the controller is configured to apply a potential to electrodes on the substrate of the light modulator to obtain an electromagnetic field between the electrodes. The electromagnetic field causes electrophoretic movement of particles toward or away 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 pair of electrodes between which the electromagnetic field is established, the particles can move in a desired direction. The inventors have found that control of the light modulator need not be limited to changing between which electrodes the electromagnetic field is applied, but can also include changing the maximum amplitude. Note that an alternating current is advantageously used. For example, driving with a lower maximum amplitude changes the rate of change of the light modulator. This is advantageous when, for example, the maximum amplitude may be reduced to avoid overshoot while driving toward a desired target transparency or reflectivity. The maximum amplitude may also or alternatively be increased when beginning to drive toward the target transparency or reflectivity. For example, the controller may be configured to obtain one of multiple levels of transmittance or reflectance of the light modulator by using an AC current or voltage of one of multiple maximum amplitudes. The relationship may be indicated by an algorithm or the like. The relationship between the level of transmittance or reflectance and the maximum amplitude may be governed, for example, by a lookup table indicating a sequence of maximum amplitudes for driving toward transmittance or reflectance. Note that AC voltages are also possible.

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

[0026] In an embodiment, at least one of the two substrates is according to the embodiment. The other substrate may have one or more electrodes or no electrodes. In an embodiment, the electrode overlay on the substrates satisfies a limit on the ratio of the electrode length to its diameter within a building block or a limit on the pixelation noise ratio, for example, such limits are set forth herein. Instead of the diameter, other measures of the size of the building blocks may generally be used. For example, in the case of rectangular building blocks, the average of the building block sides may be used, such as the harmonic mean of the building block sides.

[0027] In some embodiments, 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 some embodiments, two electrodes may be applied to the first substrate and three electrodes may be applied to the second substrate. Typically, opposing substrates are mirrored so that the electrode lines face each other; this is not necessary, and different effects are possible when the electrodes are not so arranged.

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

[0029] A light modulator is an electronic device that may be driven by a power source under the control of, for example, a controller, which may direct the power source to apply particular waveforms to particular electrodes to achieve various transparency or reflectivity effects, or lack thereof.

[0030] The method embodiments may be implemented on a computer as a computer-implemented method, or in dedicated hardware, or a combination of both. Executable code for the method embodiments 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 the method embodiments when said program product is run on a computer.

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

[0032] Further details, aspects, and embodiments will now be described, by way of example only, with reference to the drawings, in which elements are illustrated for simplicity and clarity and have not necessarily been drawn to scale. In the figures, elements corresponding to elements already described may have the same reference numerals. [Brief explanation of the drawings]

[0033] [Figure 1a] 1A and 1B are schematic diagrams illustrating examples of embodiments of building blocks; [Figure 1b] 1A-1C are diagrams illustrating examples of embodiments of a substrate. [Figure 1c] 1A-1C are diagrams illustrating examples of embodiments of a substrate. [Figure 1d] 1A-1C are diagrams illustrating examples of embodiments of a substrate. [Figure 1e] 1A and 1B are schematic diagrams illustrating examples of embodiments of building blocks; [Figure 1f] 1A and 1B are schematic diagrams illustrating examples of embodiments of building blocks; [Figure 1g]1A-1C are diagrams illustrating examples of embodiments of a substrate. [Figure 1h] 1A-1C are diagrams illustrating examples of embodiments of a substrate. [Figure 2a] 1A-1C are schematic diagrams illustrating examples of electrode embodiments. [Figure 2b] 1A-1C are schematic diagrams illustrating examples of electrode embodiments. [Figure 2c] 1A-1C are schematic diagrams illustrating examples of electrode embodiments. [Figure 3] 1A-1C are diagrams illustrating examples of embodiments of a substrate. [Figure 4a] 1A-1C are diagrams illustrating examples of embodiments of a substrate. [Figure 4b] 1A-1C are diagrams illustrating examples of embodiments of a substrate. [Figure 4c] 1A-1C are diagrams illustrating examples of embodiments of a substrate. [Figure 4d] 1A-1C are diagrams illustrating examples of embodiments of a substrate. [Figure 4e] 1A-1C are diagrams illustrating examples of embodiments of a substrate. [Figure 4f] 1A-1C are diagrams illustrating examples of embodiments of a substrate. [Figure 4g] 1A-1C are diagrams illustrating examples of embodiments of a substrate. [Figure 4h] 1A-1C are diagrams illustrating examples of embodiments of a substrate. [Figure 4i] 1A-1C are diagrams illustrating examples of embodiments of a substrate. [Figure 5a] 1A-1C are diagrams illustrating examples of embodiments of a substrate. [Figure 5b] 1A-1C are diagrams illustrating examples of embodiments of a substrate. [Figure 6a] 1A and 1B are schematic diagrams illustrating examples of embodiments of building blocks; [Figure 6b] 1A-1C are diagrams illustrating examples of embodiments of a substrate. [Figure 6c] 1A-1C are diagrams illustrating examples of embodiments of a substrate. [Figure 6d] 1A-1C are diagrams illustrating examples of embodiments of a substrate. [Figure 7a]1A and 1B are diagrams illustrating examples of embodiments of optical modulators. [Figure 7b] 1A and 1B are diagrams illustrating examples of embodiments of optical modulators. [Figure 7c] 1 is a diagram illustrating a schematic example of an embodiment of a vehicle; [Figure 8a] 1A and 1B are diagrams illustrating an embodiment of an optical modulator. [Figure 8b] 1A and 1B are diagrams illustrating an embodiment of an optical modulator. [Figure 8c] 1A and 1B are diagrams illustrating an embodiment of an optical modulator. [Figure 9a] 1 is a diagram illustrating a computer-readable medium having a writable portion containing a computer program according to an embodiment; [Figure 9b] FIG. 1 is a diagram that schematically illustrates a representation of a processor system according to an embodiment. [Figure 10a] 1A-1C are schematic diagrams illustrating aspects of an embodiment of an optical modulator. [Figure 10b.1] 1A-1C are schematic diagrams illustrating aspects of an embodiment of an optical modulator. [Figure 10b.2] 1A-1C are schematic diagrams illustrating aspects of an embodiment of an optical modulator. [Figure 10c] 1A-1C are schematic diagrams illustrating aspects of an embodiment of an optical modulator. [Figure 10d] 1A-1C are schematic diagrams illustrating aspects of an embodiment of an optical modulator. [Figure 11] 1A and 1B are schematic cross-sectional views of embodiments of optical modulators; [Figure 12a] 1A and 1B are diagrams illustrating an embodiment of an optical modulator. [Figure 12b] 1A and 1B are diagrams illustrating an embodiment of an optical modulator. [Figure 12c] 1A and 1B are diagrams illustrating an embodiment of an optical modulator. [Figure 13a] 1A and 1B are schematic diagrams illustrating examples of embodiments of building blocks; [Figure 13b] 1A-1C are diagrams illustrating examples of embodiments of a substrate. [Figure 14a] 1A and 1B are diagrams illustrating an embodiment of a substrate. [Figure 14b] 1A and 1B are diagrams illustrating an embodiment of a substrate. [Figure 14c] 1A and 1B are diagrams illustrating an embodiment of a substrate. [Figure 14d] 1A and 1B are diagrams illustrating an embodiment of a substrate. [Figure 14e] 1A and 1B are diagrams illustrating an embodiment of a substrate. [Figure 14f] 1A and 1B are diagrams illustrating an embodiment of a substrate. [Figure 14g] 1A and 1B are diagrams illustrating an embodiment of a substrate. [Figure 14h] 1A and 1B are diagrams illustrating an embodiment of a substrate. DETAILED DESCRIPTION OF THE INVENTION

[0034] List of Reference Numbers The following list of references and abbreviations is provided to facilitate interpretation of the drawings and shall not be construed as limiting the claims. 10 Optical Modulator 11 First substrate 12 Second board 13, 13a, 13b electrode 14, 14a, 14b electrode 15 Fluid 16 Controllers 30 particles 20 cars 21 Optical Modulator 40 Optical Modulator 41 First substrate 42 Second board 43 Third Board 46 Controller 100-102 PCB 111-114 Main Line 121-124 Main Line 131-134 Interdigitated electrodes 140 Building Blocks 141-144 Building Blocks 110, 120 Drive Bus 110', 120' drive bus 119, 129 Connection Zone 151-157 Points on the edges of building blocks 160 Building Blocks 161, 162 Partial building blocks 171, 172 Building Blocks 191, 192 direction Nodes 201-207 210-218 nodes α1-α7 angle 221-222 Electrode Line 180 boards 181 points on the board 182 First Shortest Distance 183 Second Shortest Distance 188 first drive electrode 189 Second driving electrode 601 Building Blocks 602-604 PCB 640 Groove 611-622 Building Blocks 651-662 Building Blocks 720 first electrode 730 Second electrode 740 Edge Seal 750 spacer 760 Semiconductor ink 772, 774 board 812 First Drive Bus 814 Second Drive Bus 820 Building Blocks 902-906 Drive bus part 912 Drive electrode 1000, 1001 Computer-readable medium 1010 Writable area 1020 Computer Program 1110 Integrated Circuit(s) 1120 Processing Unit 1122 memory 1124 dedicated integrated circuits 1126 Communication Elements 1130 Interconnect 1140 Processor System

[0035] While the subject matter of the present disclosure is susceptible to embodiment in many different forms, one or more specific embodiments have been shown in the drawings and will be described in detail herein, with the understanding that the disclosure is to be considered as an exemplification of the principles of the subject matter of the present disclosure and is not intended to limit the disclosure to the specific embodiments shown and described.

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

[0037] For example, a substrate for use in an optical modulator is disclosed. The substrate may include a plurality of interdigitated drive electrodes applied to the substrate, each of the plurality of drive electrodes arranged in a pattern across the substrate, the plurality of interdigitated drive electrodes being interleaved with respect to one another on the substrate. The pattern of the plurality of drive electrodes across the substrate comprises a plurality of repeating building blocks.

[0038] Figure 1b shows a schematic example of an embodiment of a substrate that is particularly useful for use in, for example, an optical modulator of the type described herein. Across the substrate, a plurality of interdigitated 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 required, for example, an electrophoretic light modulator may comprise a single substrate having two electrodes and an opposing substrate having one electrode. In either case, preferably, at least one of the substrates in the light modulator is in accordance with the embodiment.

[0040] The optical modulator includes a first substrate according to the embodiment and a second substrate. The first and second substrates are arranged with their interiors facing each other. At least one drive electrode is applied to the interior of the first substrate. An optical layer is disposed between the first and second substrates. The controller is configured to apply an electric potential to the at least one drive electrode, causing modulation of the optical properties of the optical modulator. One or both of the first and second substrates are transparent and / or semi-transparent.

[0041] There are many different types of optical modulators that use at least one drive electrode applied to a substrate. Because light is transmitted through the substrate, interference is a common problem in the field of optical modulators. An optical layer and controller may be arranged to modulate optical properties using effects that depend on the potential on the drive electrodes; examples include dielectrophoretic and electrophoretic effects. For example, optical modulation may include modulation of particles disposed 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 disposed between the first and second substrates may include, for example, particles suspended in a fluid, and the controller may be configured to apply an electric potential to the drive electrodes to move the particles and thus modulate the optical properties of the light modulator.

[0043] In embodiments, 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 effects electrophoretic movement of the particles. In embodiments, the electromagnetic field is configured between at least two drive electrodes disposed on the same substrate or disposed on different substrates.

[0044] In an embodiment, the particles comprise dielectric particles, and the controller is configured to apply a potential to the drive electrodes to apply an electric field gradient to the particles, allowing 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 that control the dielectrophoretic force may use signals that include DC and / or AC signals. Embodiments that control the electrophoretic force may use signals that include DC and / or AC signals.

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

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

[0048] 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 substrates with patterned electrodes. Any of these cited electrophoretic or dielectrophoretic light modulators may be adapted by patterning electrodes on the substrate according to embodiments.

[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 according to the embodiment. For example, the first and second substrates may be arranged with their interiors facing each other. Using substrates according to the embodiment has the effect of, for example, reducing optical interference. An optical layer is arranged between the first substrate and the second substrate. Drive electrodes are arranged to modulate an electric field in the optical layer. The optical layer includes a fluid containing particles, and the particles are electrically charged or chargeable. The particles may move under the control of the 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, resulting in electrophoretic movement of the particles toward or away from one of the at least one drive electrodes, causing modulation of the optical properties of the light modulator.

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

[0051] Embodiments of the substrate may be used in electrochromic devices (ECDs), which control optical properties such as optical transmission, absorption, reflection, and / or emittance in a continuous yet reversible manner by the application of voltage (electrochromism). This property allows electrochromic devices to be used for applications such as smart glass, electrochromic mirrors, and electrochromic display devices.

[0052] Electrochromic devices are described, for example, in the article "Silver grid electrodes for faster switching ITO-free electrochromic devices" by Antonio California et al., which is incorporated herein by reference, and which describes the fabrication of electrochromic devices, in this case, electrochromic devices that are free of ITO.

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

[0054] Electrodes may be applied to a substrate by screen printing polyethylene terephthalate (PET) onto the substrate, as in the cited paper. Electrodes are typically electrically conductive materials, such as metals or metal oxides. In the cited paper, silver ink was used to screen print grids onto the PET using a RokuPrint RP 2.2 instrument and a 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 subsequently printed on top of these silver grids by screen printing.

[0055] The combination of a regular pattern, such as the hive or ladder pattern in the cited paper, and light transmission causes interference in electrochromic devices. One way to avoid interference is to use a pattern in accordance with the embodiments, such as an electrode, that is long compared to other repeating elements, such as building blocks.

[0056] For example, the metal grid used in the cited paper may be replaced by drive electrodes applied to a substrate, the drive electrodes 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 directions across the building blocks, the electrodes within a building block forming at least one drive electrode, and for at least one electrode 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 a diagonal of a building block unit. Instead of requiring a minimum length of electrodes, the pattern may use other features that reduce interference, such as a high degree of branching, e.g., branching of the electrode into two or more paths, which branching repeats multiple times, e.g., at least 2, 3, 4, or more times, resulting in 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. Pat. No. 5,161,048, entitled "Electrochromic window with metal grid counter electrode and acidic polyelectrolyte," which is incorporated herein by reference. For example, an electrochromic device may include a transparent electrochromic film and an ion-conductive layer disposed between a pair of electrodes. A metal grid electrode is provided for the electrode. Figure 1 of the patent shows a metal grid according to the cited patent. To form a 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-conducting polymer in contact with the electrochromic film, and a patterned conductive electrode in contact with the ion-conducting polymer. The patterned conductive electrode may be in accordance with an embodiment.

[0059] The substrate according to the embodiment can be advantageously applied in several other technologies. For example, the light modulator can be a dielectrophoretic light modulator, as shown in, for example, U.S. Patent Application Publication No. 20050185104(A1), which is incorporated herein by reference. The substrate as in the embodiment can also be used in other electrowetting and OLED applications.

[0060] In OLEDs and electrowetting, electrodes are required on only one of the substrates. The substrate with electrodes may be according to the embodiment.

[0061] In light modulator applications for glazing, both substrates are typically transparent. In other applications, such as televisions and e-readers, only one substrate may be transparent.

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

[0063] The drive electrodes are electrically connected, e.g., have the same potential everywhere. The drive electrodes may comprise drive buses and main lines. At least the main lines are interdigitated with main lines of further drive electrodes. Typically, the drive electrodes extend in substantially straight lines across the substrate, while the main lines are convoluted.

[0064] In an embodiment, each of the two substrates of the optical modulator has two electrodes disposed on its inner surface. However, as noted, multiple electrodes on one or both substrates are not required. For example, an embodiment of the optical modulator includes a first substrate and a second substrate. For example, the first substrate may include one drive electrode and the second substrate may include no drive electrodes. For example, the first substrate may include two drive electrodes and the second substrate may include one drive electrode. For example, the first substrate may include two drive electrodes and the second substrate may include two drive electrodes. For example, the first substrate may include three or more drive electrodes and the second substrate may include two or more drive electrodes.

[0065] However, a light modulator in which each substrate includes two drive electrodes is used as a motivating example. A substrate design 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 drive electrodes. Adapting the substrate in this way may make it suitable for use in different technologies.

[0066] Each of the multiple drive electrodes is arranged in a pattern across the substrate. The multiple drive electrodes are arranged alternately with respect to one another on the substrate. Typically, the drive electrodes comprise multiple main lines, each extending across the substrate. The main lines of the drive electrodes are alternating, e.g., interdigitated. For example, in FIG. 1b, the first drive electrode comprises main lines 111-114, and the second drive electrode comprises main lines 121-124. Each drive electrode is driven by its own 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. There can be more main lines than the four shown in this example. The use of main lines is advantageous because it reduces the length of the electrodes, but it is not necessary. While it is not impossible to design one with only one main line per drive electrode, it is advantageous to have multiple main lines.

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

[0068] An inspiring application for substrates such as substrate 100 is in smart glazing, e.g., light modulators, which may be applied in homes, offices, greenhouses, cars, and the like. The transparency or reflectivity level of smart glazing can be electrically tailored. For example, in smart glazing, two substrates, such as substrate 100, are stacked with the surfaces on which two electrodes are applied facing each other. A fluid with particles is trapped between the two substrates. Smart glazing embodiments are discussed further below. In embodiments, an electrode, e.g., two or more electrodes, is applied to one surface of each substrate. For example, to facilitate stacking of three or more substrates, one, two, or more electrodes may be present on the other surface of substrate 100.

[0069] Some embodiments below show examples of modulating transparency or reflectivity levels. Light modulators may be adapted for other optical effects. For example, if desired, embodiments could be modified for different levels of translucency instead of different levels of transparency. If desired, the types of particles used in embodiments can be varied, for example, for particles that differ in which wavelengths the particles absorb or reflect and how specular or diffuse the reflection is. For example, in embodiments, light modulators can modulate different levels of reflection. 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 an electrically adaptable glazing; with two alternating sets the electric field in 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 exhibit four blocks: blocks 141, 142, 143, and 144, which are all substantially identical. The number of building blocks may be greater than four. The building blocks repeat in both directions across the substrate, for example, 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 illustrates an example embodiment of a building block 140. The building block 140 comprises multiple interdigitated electrodes extending across the building block in at least two directions. Four electrodes are shown in FIG. 1a: electrodes 131-134. When a building block is repeated across a substrate in two directions, the electrodes within the building block will form drive electrodes, e.g., multiple main lines of drive electrodes. Note that building blocks are typically connected in a substrate electrode design tool. Typically, a building block comprises five or more electrode lines. For example, within the scope of embodiments, between eight and twelve main lines are used. The number of electrode lines, however, can be much higher. For example, a building block may comprise many short electrode lines near its edges that connect to lines of other building blocks when the block is repeated. To account for such short offshoots, the number of lines could be increased, for example, to 50. Obviously, using larger building blocks may also increase the number of electrode lines. In embodiments, the number of electrode lines in a building block is between 8 and 50, or between 8 and 25, etc.

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

[0074] This step allows multiple main lines to be connected together, thus forming a single drive electrode. Figure 1b shows two connection zones 119 and 129 where 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 in the same dashed line style in FIG. 1b. In fact, it happens to be the case in this example that a particular electrode of a building block in FIG. 1a always ends up, for example, within a first drive electrode or within a second electrode, as indicated by the dashed line style in this case. This is not necessarily the case, however. An electrode within a building block may end up as part of a first drive electrode or as part of a second drive electrode. This may change the pattern in which the building blocks repeat, for example, 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 an optical modulator having two drive electrodes in which alternate main lines are assigned to two drive electrodes, however, the same pattern of repeating building blocks may be used for an optical modulator having three drive electrodes in which every adjacent set of three main lines is assigned to three drive electrodes.

[0077] Additionally, while the building blocks shown in FIG. 1a are square, this is not required. For example, the building blocks may be rectangular. In embodiments, the building block shape(s) may form a so-called tessellation. For example, the building blocks may be triangles, hexagons, or even combinations of plane-filling shapes.

[0078] As mentioned, Figures 1a and 1b are schematic. This is especially true for the depiction of the electrodes. The electrodes shown in Figure 1a are straight, and their lengths are equal to the side lengths of the building blocks. However, in embodiments, the electrodes on a building block are more convoluted, with at least one electrode in a plurality of interdigitated electrodes in the building block, and the maximum length between any two points on the electrode measured along the electrode in the building block is at least twice the length of the diagonal of the building block unit.

[0079] For example, if we consider the electrodes shown schematically in Figure 1a, the maximum possible length along the same electrode is the length of the side of the building block. The ratio of the maximum length to the diagonal of Figure 1a (shown schematically) is:

number

[0080] Typically, two or more electrode lines within a building block satisfy this condition. For example, in an embodiment, a building block includes 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 plurality may be at least 2, at least 4, at least 10, etc.

[0081] By adapting the electrode shape, undesirable diffraction effects can be modified. Reducing diffraction effects is particularly important for transparent substrates because the effects will be less noticeable in the case of, for example, diffusely reflective displays, such as those sometimes applied in e-readers. However, specular reflective displays, such as dimmable mirrors, will be affected by diffraction effects. The inventors have found that optical diffraction in light modulators can be reduced by orienting the electrode line shapes at multiple different angles, spreading the diffraction in space and thus reducing the intensity of the strongest diffraction spots. For example, in the case of dimmable mirrors, reducing diffraction is important.

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

[0083] FIG. 1c shows a schematic 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 blocks 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, 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. To avoid the drive buses having to connect to main lines of different drive electrodes, some of the building blocks are modified.

[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 Figure 1c, the building blocks are substantially the same except that a disconnect is introduced in some electrodes of the building block next to the drive bus to avoid connecting the main line to the drive bus. All building blocks shown in Figure 1c are modified in this way, but in embodiments, the majority of building blocks, e.g., building blocks that are not adjacent to drive buses 110, 120, are not modified.

[0085] FIG. 1d shows a schematic example of an embodiment of the substrate 102.

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

[0087] However, it is not required that electrodes within a building block connect opposite sides of the building block. Typically, all electrodes within a building block will connect two sides of the building block, but it is not required that these two sides be opposite. The reason for this is that electrodes may be continued by the next building block. In such a situation, most main lines will still connect the same two opposite sides, but at the edge of the substrate, this may not happen because there are no additional building blocks to carry the electrodes forward. To allow for more complex electrode designs for building blocks, main lines 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] FIG. 1d shows drive bus 110' extending along two edges of the substrate and drive bus 120' extending along the other two edges of the substrate.

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

[0090] It should be noted that drive electrodes, e.g., 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, a dielectric is locally deposited, and finally, a second drive electrode is deposited. The dielectric is disposed to cover at least the point where the first and second electrodes intersect. 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 a drive bus.

[0092] Figure 1e shows a schematic example of an embodiment of a building block, in which two electrodes are shown schematically, in a practical implementation the electrode tracks shown would typically be much more intricate.

[0093] The building block in FIG. 1e shows four electrode lines, each connected to at least two sides of the building block. In this case, the electrode lines do not directly connect to opposite sides of the building block. Because the drive electrodes only need to be driven from one side, connections to opposite sides of the building block are not required. However, to cover the substrate, it is advantageous if at least one of the electrodes reaches the opposite side from where the electrode is driven. This is not necessary; there may be main line electrodes that reach only a portion of the substrate and are driven from two sides.

[0094] FIG. 1e shows that the main electrodes incorporating a particular electrode line of a building block can still reach across the substrate, even though the electrode line does not connect opposing sides. For example, an electrode line beginning at 151 on the left side connects to the non-opposing top side of the building block at 157. If the same building block were repeated on the building block shown, the main line this line forms would continue at point 154 on the repeating building block and reach the opposing side of the repeating building block at 152. Similarly, an electrode line that will be part of a second drive electrode begins on the left side of the building block at 155. This electrode line connects to the top side at 153 and continues in the repeating block at 154. Thus, an electrode line that begins on the left side of a building block may not connect to the opposing side of that building block; the electrode line, however, travels that distance in the x-direction and reaches the right side of the building block, but a different building block, e.g., a building block above or below the building block shown. The same is possible for the y direction, and vice versa. In an embodiment, the main lines extend through the blocks in a first direction 191, e.g., the x direction, and extend through at least two or more blocks in a cross-sectional direction, e.g., the y direction, connecting edges of the substrate that are opposite in the first direction 191, e.g., the x direction. Typically, the first direction 191 and the second direction 192 are orthogonal; this is not strictly necessary, and the two directions can be inclined with respect to each other.

[0095] Figure 1f shows that two electrode lines within a building block do not have to be connected within the building block, but can still be connected within the substrate through connections in neighboring building blocks. For example, consider an electrode that starts on the left edge at point 151. The electrode exits on the top edge of the building block. Unlike the example in Figure 1e, the main line into which the electrode line starting at 151 is embedded connects to opposite parts of the building block shown in Figure 1f.

[0096] An electrode line beginning on the left side of the building block at 151 connects to the top side of the building block at 157. If the same building block were repeated on top of the building block shown, the electrode line would connect to the bottom side at point 156 and to the same side as the bottom side point at point 154. Returning to the building block shown in FIG. 1f, the electrode line continues on its top side at point 153 and connects to the right side at point 152, i.e., the side opposite the side at point 151.

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

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

[0099] An alternative requirement may be to consider paths that extend through neighboring building blocks. For example, the longest path that starts on an edge, e.g., the left edge, and connects to an opposite edge 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, some higher threshold, e.g., 2, may be used, although a higher threshold, e.g., 3, is also possible.

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

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

[0102] Also shown in Figure 1f are electrode lines connecting two opposite sides of the building block. In embodiments, all electrode lines on a building block connect opposite sides of the building block. However, as shown, this is not required. Typically, the drive buses are straight, while the main lines are convoluted.

[0103] FIG. 1g shows a schematic example of an embodiment of a substrate. FIG. 1g shows a variant of tiling a substrate with building blocks. In FIG. 1g, the building blocks are staggered. For example, in a first direction 191, e.g., the x-direction, the building blocks 160 are aligned in rows. At the top of the building blocks, the building blocks are also aligned in rows, but the building blocks are offset relative to the rows below. The offset is shown as half a block, but it could also be another fraction of the building block width, e.g., 1 / 3 of the building block width.

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

[0105] Other tessellations, such as substrate fill tiling, can be used to create the electrode pattern. For example, in embodiments, the building blocks are parallelograms, rhombuses, or the like. In embodiments, the building blocks may be aligned in rows, and in odd rows, the blocks are mirrored, e.g., flipped; sometimes referred to as glide reflection symmetry. In addition to mirroring, the building blocks may also be point-reflected or inverted.

[0106] FIG. 1h schematically illustrates an example embodiment of a substrate. As in FIG. 1b or 1c, building blocks are repeated across the substrate in at least two directions. However, in FIG. 1h, multiple different building blocks are used; FIG. 1h shows two building blocks 171 and 172. Both blocks 171 and 172 are repeated in two directions, e.g., a first direction 191 and a second direction 192. In FIG. 1h, building block 171 is not directly adjacent to building block 171; for example, the two building blocks form a checkerboard packing. While this is not required, for example, a first building block could connect to a copy of the first building block on two opposing sides but connect to a second building block on two other opposing sides. There may be more than two different building blocks.

[0107] For example, using different tiles that are adjacent and alternating in different directions increases design flexibility and may be used, for example, to ensure continuity of supply to tiles within the interior of the substrate, while connections to controller(s) can be made at the edge of the substrate.

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

[0109] FIG. 2a shows a schematic example of an electrode embodiment; within the substrate, the electrode is part of a single drive electrode. For example, the electrode shown in FIG. 2a could be part of an electrode line within a single building block. The electrodes shown could also be formed from multiple building blocks adjacent to each other. For example, the cluster shown in FIG. 2a or 2b could be part of a main line 111-114, 121-124, or electrode line 131-134.

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

[0111] It has been found that having multiple branch nodes within an electrode is advantageous for increasing the ratio between electrode length and building block diagonal, which in turn is advantageous for reducing diffraction. Having clusters of branch nodes causes the electrodes to be at various angles, which contributes to reducing diffraction.

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

[0113] Figure 2b shows a schematic example of an embodiment of an electrode. This example expands on the example of Figure 2a. Seven branch nodes of the electrode are shown. Branch node 201 is directly connected to branch node 202 and branch node 203. Branch nodes 202 and 203 are in turn connected to two further branch nodes, respectively. Branch node 202 is connected to branch node 204 and branch node 205. Branch node 203 is connected to branch nodes 206 and 207. The direct connection between branch nodes 203 and 206 is indicated by reference numeral 222.

[0114] The branching patterns of Figures 2a or 2b increase the ratio of electrode length to building block diameter or diagonal. These branching patterns also increase the variety of electrode line directions and reduce long stretches of parallel electrode lines. Such improvements are equally valuable without contributing to the ratio. For example, in an embodiment, a substrate for use in a light modulator is provided, the substrate comprising: - comprising a plurality of interdigitated drive electrodes (111-114, 121-124) applied to a substrate, each of the plurality of drive electrodes being arranged in a pattern across the substrate, the plurality of interdigitated drive electrodes being arranged in an alternating pattern with respect to one another on the substrate, the electrodes on the substrate comprising a plurality of nodes from which the electrodes branch, the nodes being electrically connected through electrode lines, the plurality of nodes and connecting electrode lines forming a tree, the electrodes comprising at least a first node (201) from which the electrode branches into at least three electrode lines, the first node (201) being directly connected through the electrode lines to a second node (202) and to a third node (203), the electrode branching into at least three electrode lines at the second node and at the third node.

[0115] 2c shows a schematic example of an electrode embodiment; within the substrate, the electrode is part of a single drive electrode. For example, the electrode shown in FIG. 2c could be part of an electrode line within a single building block. The electrode shown could also be formed from multiple building blocks next to each other.

[0116] Eight nodes are shown that are directly connected to electrode lines: nodes 210-218. Figure 2c does not show branches for all of these nodes. In fact, 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 may be the longest path between any two points on the electrodes, e.g., from points 210 to 218. Along the path from node 210 to node 218, successive electrode lines make angles. These angles are denoted as α1 through 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, it is preferable that angles in the design be non-uniform. For example, angles along a path, e.g., the longest path, may be selected randomly or may be selected to uniformly sample a range of possible angles within the range of 0 to 360 degrees. For example, in an embodiment, angles are selected such that one angle is selected from at least every block of 30 degrees. For example, angles may be selected from each of the ranges 1-30, 31-60, ..., 331-360. Long paths affect diffraction; having many angles within a long path may make the path less uniform, thus reducing diffraction. Measurements may similarly be made by first reducing all angles modulo 180.

[0119] Instead of being limited to angles along a path, nodes within a building block may include all angles. For example, a node connecting n electrode lines defines n-1 angles between consecutive electrode lines. Similarly, it is preferable for these angles to be uniform and represent the full range of angles. For example, they may be selected randomly or selected to sample the full range of angles, e.g., from 0-180 degrees.

[0120] The nodes are preferably selected to cover the building block and therefore the substrate, for example, the nodes may be selected randomly across the building block.

[0121] Note that the electrode lines between nodes can be straight or curved. Having straight lines makes the design easier to calculate, but curved designs offer greater flexibility that can be used to combat diffraction. For curved designs, such as Figure 3 below, angle considerations may be limited to branching nodes. In an embodiment, the substrate is curved and the multiple repeating building blocks comprise at least two different shapes.

[0122] 3 shows a schematic example of an embodiment of substrate 180. Details of two drive electrodes are shown: electrode 188 and electrode 189. The details shown may, for example, be part of a building block. The details may also arise because two building blocks are aligned next to each other.

[0123] Figure 3 shows an example of an electrode with curved electrode lines. The following considerations apply to designs using straight electrode lines as well.

[0124] 3 shows a point 181 on the substrate that is not on an 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 may be calculated. The nearest distance between an electrode and point 181 may be considered to be the smallest distance between any point on the electrode and point 181. For example, for point 181 and electrode 189, the nearest distance is given at 183. For example, for point 181 and electrode 188, the nearest distance is given at 182. The distances are calculated as Euclidean distances.

[0126] For example, desirable objectives for electrode patterns are as follows:

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

[0128] Another way to limit the distance between electrodes is to limit the sum of the closest distances to the first and second drive electrodes, e.g., require that they be less than a first threshold. For example, the sum of distances 182 and 183 is less than a first threshold. If the two electrodes are too far from each other, there may be a throw region between the two electrodes where neither electrode has much effect, e.g., both electric fields are severely attenuated. The appropriate threshold again depends on the particular application, but by way of example, 100 micrometers may be taken as the first threshold.

[0129] At the same time, one may want to avoid having the electrodes too close to each other. For example, if the electrodes on the substrate are too close to each other, the chance of accidental shorting increases. For example, the sum of distances 182 and 183 may be required to be at least the second threshold. The appropriate value for the second threshold depends on the application. As an example, the second threshold may be taken as 10 micrometers.

[0130] 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, the distance from a point on the first drive electrode to a point on the second drive electrode can be required to be at least a second threshold. For example, this distance can also be taken as 10 micrometers.

[0131] For electrode patterns where the electrode lines are lines, the calculations can be further simplified by limiting the calculations to the nodes that contain the endpoints of the electrode lines.

[0132] In an embodiment, the horizontal size of the building blocks, e.g., in a first direction 191, e.g., 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 largest nearest distances to the two nearest electrodes, e.g., the sum of distances 183 and 182. The electrode line width and electrode distance depend on the application. By way of 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 therebetween. Other values are possible. For the vertical size of the building blocks, e.g., in a second direction 192, e.g., the y-direction, the same lower limit as for the x-direction may be applied. For example, the building blocks may be rectangular or square, with side dimensions of at least 500 micrometers, e.g., at least 1000 micrometers.

[0133] In embodiments, the electrode line width is not constant as measured along the electrode line. For example, the electrode line width may be measured perpendicular to the sides of the electrode line. A constant electrode line width has the disadvantage that the line-to-line distance also tends to be constant, which in turn contributes to diffraction. In practical designs, the width of the electrodes is typically kept below a maximum value. As an example value, the maximum value may be taken as the maximum line-to-line distance of the electrodes, so that the electrode lines are nowhere thicker than the space between the electrodes.

[0134] The line gap, e.g., the distance between electrodes, does not need to be constant. For example, in a spiraled design such as the spiraling design of Figure 5b, it is possible to have a low diffraction design with a substantially constant line gap, whereas in a more randomized design, e.g., a Waal design, the line gap is typically not constant but can vary, e.g., within a range.

[0135] Making building blocks too small can lead to diffraction due to repetition of similar building blocks. Making building blocks too large can lead to problems with optimization and evaluation in production. For example, the sides of a building block can be 0.5 mm, 1 mm, 1 cm, and 10 cm, but can extend to, for example, 100 cm or more. For example, one or both sides of a building block can be between 0.5 mm and 10 cm.

[0136] In embodiments, the building blocks are square, but rectangular is possible. In embodiments, the building block sides have the same ratio as the substrate. In embodiments, the building blocks are not square, but may be any one or more plane-filling shapes. For diameter, e.g., the maximum distance between two points on a building block, the same lower bound as for the x-direction may be taken.

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

[0138] Of particular importance is optical diffraction, which is preferably below threshold. Further information regarding diffraction for various example designs is provided herein.

[0139] Optical Diffraction To estimate the optical diffraction, the following method was used.

[0140] 1. Prepare the design drawing: - Crop to 1024x1024 microns (unit cell size); - Normalize pixel values to 255 (black=0; white=255);

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

[0142] Because optical diffraction can be formulated as a Fourier transform, the conventional method is to use a fast Fourier transform (FFT) algorithm. However, using an 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 a chirp z-transform (CZT) algorithm instead of an FFT algorithm.

[0143] 3. Zero-order (main) peak (I main ) to find the maximum intensity;

[0144] 4. I in the Magnitude Spectrum mainIgnore pixels with signals from the peak;

[0145] 5. All other higher order peaks (I higher ) to find the maximum intensity;

[0146] 6. The resulting diffraction metric values are calculated as in reference [3]:

number

[0147] Experiments confirmed that the calculated pixelation noise metric matches the actual diffraction evident in the test setup.

[0148] Multiple designs were used to test noise metric parameters. Table 1 summarizes these tests. Column 1 lists the informal design names. Column 2 indicates the figure number in which the design appears. Columns 7 and 8 present estimated intensity values for the zero-order and higher-order peaks from the magnitude spectrum. Column 9 shows the resulting pixelation metric values 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 in 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 in the building block.

[0150] The above-referenced references are as follows: The references are incorporated by reference.

[0151] [1]Leutenegger, M., Rao, R., Leitgeb, RA 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, WM, Hibbard, DL, and Milster TD 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 pixelation noise metric can be calculated as follows:

[0153] First, a black and white design image is generated for a specific dimension, with the electrode lines in black and the substrate background in white. The results herein are calculated using a standard 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 of the CZT chirp z-transform without scaling. The Bluestein method is a Fourier-like transform, but with computational properties. Finally, the pixelation 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 in the magnitude spectrum of the CZT chirp z-transform of the design image, while the higher peak value is determined as the second maximum intensity in the magnitude spectrum of the CZT chirp z-transform, excluding the main peak.

[0154] [Table 1]

[0155] Figures 4a-4i schematically show examples of substrates with low ratios. Figures 5a and 5b schematically show examples of substrate embodiments with high ratios. Note that high ratio designs have low diffraction. The ratio is calculated as the quotient of the longest length and the diagonal length of a rectangle having the dimensions shown in columns 4 and 5. 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, experimental designs have shown that it is difficult to obtain low pixelation noise metrics. However, designs according to embodiments have shown that it is possible to obtain even lower pixelation noise metrics.

[0157] In embodiments, the ratio is at least 2, at least 3, at least 5, or at least 10. In embodiments, 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 embodiments, the ratio is at least 2 and the pixelation noise metric is less than 6.07. In embodiments, the ratio is at least 3 and the pixelation noise metric is less than 6.07. In embodiments, the ratio is at least 10 and the pixelation noise metric is less than 4. Designs with high ratios can be generated quickly and therefore easily tested and selected for any other requirements.

[0158] 5a and 5b show designs with two drive electrodes on the surface of the substrate. Either design may 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 may be used in an optical modulator that uses a substrate with a single electrode.

[0159] The designs shown in Figures 4a-4i and 5a-5b can be realized in a single plane without 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 more complex electrode patterns are used, electrode intersecting may be used or may be required. However, such intersecting may be possible, for example, where two electrode lines intersect, and a dielectric material may be disposed between the electrodes. For example, such an insulator may be deposited at the intersecting location. For example, a first drive electrode may be in a first plane of the substrate, and a second drive electrode may be in a second plane of the substrate.

[0160] Figure 6a shows a schematic example of an embodiment of building block 601. Figure 1d shows an L-shaped drive bus for a substrate, building block 601 is similar in that respect except that the drive bus is applied to building blocks that are repeated across the substrate, which provides additional advantages.

[0161] FIG. 6a shows the drive buses for each of the two drive electrodes. Schematically, the configuration of the drive electrodes is shown inside building block 601. The two drive buses are patterned to indicate that they drive different drive electrodes. Each of the two drive buses has two arms; the two arms extend along two sides of the building block, where the two sides meet at a corner of the building block. In this example, the building block is square, but this is not required. One of the two arms extends along the entire 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 can be the same size as between the drive electrodes, e.g., 50 micrometers. Note that the drive electrodes are partially connected through the drive buses. Part of the drive electrode connects to the drive bus in the x-direction, while the other part connects to the side in the y-direction.

[0162] The building blocks 601 so formed can be repeated across the substrate in a variety of ways.

[0163] Figure 6b shows a schematic example of an embodiment of a substrate 602. In Figure 6b, the building blocks of Figure 6a are copied multiple 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 Figure 6b can be obtained by direct translation of any other building block.

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

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

[0166] Figure 6c shows a schematic example of an embodiment of a substrate 603, in which the building blocks repeat across the substrate but are arranged to avoid grooves as in Figure 6b. In this embodiment, the building blocks are translated and mirrored, this time in two directions.

[0167] Building block 611 is mirrored in the y direction to form building block 621. Building block 621 is located directly below building block 611. Building block 611 is mirrored in the x direction to form building block 612. Building block 612 is located directly to the right of building block 611. Building block 611 is mirrored in the x direction as well as the y direction to form building block 622. For example, the mirroring may have an edge of the building block as the mirroring axis.

[0168] Mirroring the building blocks ensures that drive busses for the same drive electrode end up next to each other on the substrate. Merging these drive busses avoids grooves and reduces diffraction.

[0169] In embodiments, at least the drive electrodes on the substrate have mirror symmetry; in embodiments, the drive electrodes and drive bus have mirror symmetry. For example, the substrate is symmetrical about the x-axis and / or about the y-axis. This is an important advantage during manufacturing because it allows the top and bottom substrates to be identical. Eliminating the need to produce separate substrates for the top and bottom of the light modulator also eliminates the need to maintain separate types of substrates. Furthermore, having symmetry in the substrate allows a broken top substrate to be replaced by the bottom substrate, and vice versa, because they are identical. Straight lines along a mirror symmetry axis, such as a drive bus, are useful because the design can be mirrored around that axis. Using building blocks in mirrored or non-mirrored form is useful for creating mirror-symmetric designs.

[0170] This is particularly advantageous when fabricating using photolithography steps to pattern the electrodes, because the same substrate patterning can be used for both substrates of the light modulator, limiting production costs. The presence of straight bus bars attached to the building blocks or parts of each building block facilitates this effect. To use the same electrode pattern for all substrates, having a symmetrical design in one direction is possible without straight bus bars, for example, by local modification of the electrode design at the edges of the symmetry line. In embodiments, the drive electrode pattern has at least one symmetry in one direction, for example, by mirroring across the substrates and / or tiling the building blocks with a rotatable electrode pattern design.

[0171] Figure 6d shows a schematic example of an embodiment of a substrate 604, where the building blocks are repeated across the substrate but arranged to avoid grooves similar to that in Figure 6b. In this embodiment, the building blocks are translated, mirrored, and rotated through 180 degrees.

[0172] Building block 651 is mirrored in the y direction to form building block 661. Building block 661 is located directly below building block 651. Building block 651 is point-reflected, e.g., rotated through 180 degrees, to form building block 652. Building block 652 is located directly to the right of building block 651. Building block 651 is mirrored in the x direction to form building block 662.

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

[0174] Mirroring the building blocks ensures that drive busses for the same drive electrode end up next to each other on the substrate. Merging these drive busses avoids grooves and reduces diffraction.

[0175] An advantage of the patterns of Figures 6c and 6d is that they both reduce diffraction. A disadvantage of the pattern of Figure 6c is that the connection points of one of the drive electrodes at the top and bottom of the substrate are much smaller than the connection points of the other electrode. This is not necessarily a problem because such electrical connections can be easily made; however, this problem is avoided in Figure 6d, where both electrodes are easily connectable at the top and bottom of substrate 604. Note that the drive bus on the far right of substrate 604 could be extended toward the right at the top and / or bottom, if so desired.

[0176] Another way to obtain the drive bus pattern of Figure 6d is to translate building block 651 one block to the right and invert its electrodes, e.g., the drive bus that previously drove the first electrode now drives the second electrode, and vice versa. The next row, beginning with block 661, may be obtained by mirroring row 651. This transformation pattern will give the same pattern for the drive buses, but will produce differences when applied to the main lines. If the pattern of the main lines were inverted rather than point-reflected, it would likely look quite different.

[0177] However, it should be noted that while the pattern of the drive electrodes can follow the same pattern of mirroring and translation as the drive busses, this is not required. The drive electrodes could follow a different pattern, for example, a translation similar to that in Figure 6b, or something similar. That would mean that the drive busses could look like, for example, Figure 6c or 6d, but the main lines would be the same from block to block.

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

[0179] A drive bus is not required. One or more or all of the drive electrodes on the substrate may be powered from a source separate from the drive bus applied on the same edge 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 at the outer surface to a power source, e.g., the same or similar power source as may be used for the drive bus. 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 be through a controller.

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

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

[0182] Returning to FIG. 5a, this type of electrode design can be constructed from tessellations. A particularly useful source of electrode designs is the Delaunay triangulation and its corresponding Voronoi dual. These triangulations are a straightforward way to quickly generate a large number of tessellations, for example, to optimize a design. However, other planar tilings, such as randomized regular tilings, or even aperiodic tilings such as Penrose tiling, can be used instead.

[0183] The present 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, the following algorithm may be followed: Although the embodiment is described to cover a substrate, it may be used to cover a building block as well.

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

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

[0187] Step 2 - Then, for each point, create a small random variation of the x,y coordinates. For example, the random variation range can be taken between equally spaced points, set to be no larger than 30% of the initial distance between the points. Another way to obtain such a pattern is to draw points from an appropriate distribution.

[0188] II: Compute the first and second networks

[0189] Step 3 - Compute the triangulation. For example, the points may be triangulated such that each point is connected to six neighbors: possibly excluding the edges and corners of the substrate. The Delaunay triangulation has been found to work well for this step. The Delaunay triangulation is an example of a tiling.

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

[0191] Step 5 - Optionally, for each triangle center point, create a small random variation of the x,y coordinates. For example, the random variation may be similar to that for the first set of points, e.g., the variation is no greater than 30% of the initial distance between the points.

[0192] Step 6 - Connect together the second set of points that cross the boundary of the triangle; e.g., compute the dual graph for the triangulation. For example, the central point is connected to its direct neighbors.

[0193] If the tiling used is a Delaunay triangulation and the optional shifting of the second set of points is skipped, the second network thus obtained is a Voronoi network. If a different type of tiling or triangulation is used, or if the center point is shifted, the resulting grid of polygons will not strictly be a Voronoi network, but it will resemble 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 have been created: the second network, a Voronoi-like pattern of polygons, and the first network, e.g., a Delaunay triangulation. Each of the two patterns is, or nearly is, the dual of the other, depending on the randomization.

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

[0196] Step 7 - Eliminate edges in the second network (e.g., a Voronoi-like network) until the network is reduced to a tree. This can be done by a path-finding search algorithm on the first network (e.g., a triangulation), starting from a point in the first set of points, e.g., the center in a Voronoi polygon. The path-finding algorithm attempts to find a path to each node in the first network. Such algorithms are also known as finding spanning trees in a graph.

[0197] Such a search algorithm can be a depth-first search or a breadth-first search. A breadth-first search provides long but very straight patterns, while a depth-first search provides short, non-straight patterns. The best results have been obtained by following a mixture between a "depth-first search" and a "breadth-first search" algorithm. For example, the depth-first or breadth-first search step may be selected by a probability distribution, which may depend, for example, on the depth of the search. A suitable distribution is the gamma distribution.

[0198] When an edge in a 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. Thus, the resulting spanning tree of the first network may give rise to trees or forests in the second network, e.g., a Voronoi network. If the second network does not completely reduce to trees or forests, this can be achieved by removing additional edges in the second network.

[0199] This creates two trees that cover the substrate and interdigitate as needed for the light modulator. The pattern in Figure 5a was obtained using the above algorithm.

[0200] Once a suitable graph is obtained, it can be converted into an actual electrode design by assigning a thickness to every path segment. 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 are: - This involves screening the design units to eliminate shortcuts between electrode 1 and electrode 2. The increase in thickness may have introduced shortcuts. These can be avoided by repeating the process, moving edges or nodes, and repeating the generation process. - Including that driving buses can 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 an edge, typically connecting it to a driving bus, thus integrating the forest into a tree. - correcting the electrode point coordinates to maintain a minimum line gap between electrodes of e.g. 20 μm and / or to maintain an average line gap between electrodes of e.g. 50 μm. - Including shifting electrodes to allow stitching of the design and ensure continuity of electrodes from one unit to another, especially when a covering drive bus is not used. - Including shifting electrodes to reduce light diffraction, refraction, scattering, or moiré. - Improved or optimized randomization of short segment orientation to reduce light diffraction, refraction, scattering, or moiré effects, which allows for lower viewing confusion when viewing through the display. Further randomization can be achieved by converting straight segments between the points into curved shaped segments, for example splines may be used between the points.

[0202] It has been found that further optimization of the design can be advantageously performed in several optimization loops. For example, after generating the first and second electrode segments using the above-mentioned tessellation-based procedure or a Turing pattern-based procedure or similar, the segments can be converted into paths that give the segments widths. For example, a segment may represent the centerline of a polygon of a particular width. While this procedure will work well most of the time, there are cases where it can have undesirable effects, so further optimization is possible.

[0203] For example, (A) it may be verified that the first path does not touch the second path, and if this condition is violated, one or both of the paths, e.g., the first path, may be modified so that the first path no longer touches the second path.

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

[0205] For example, (C) it can be verified that all secondary pathways are connected at a single secondary electrode, and if this condition is violated, pathways can be created and / or deleted to connect all primary pathways to the primary electrode.

[0206] Parts B and C may be repeated in a loop until both electrodes are fully connected. Note that the addition of a drive bus to the design, for example, as described herein, may aid in electrode integration. If necessary, Part A may be repeated in this loop as well.

[0207] Once the first and second electrodes are fully connected and not shorted, the next loop of optimization can occur.

[0208] For example, (D) it can be verified that the distance between the first and second electrodes is always within a predetermined range. If this condition is violated, the path 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 electrode patterns. Further or alternative optimizations may be added as suggested herein, for example, above. For example, the design may be iterated for optical performance, for length ratio, and the like. Because the cost of generating the initial patterns of the first and second paths, for example, using tessellation or the like, is low, the optimization process has the option of terminating the optimization and starting with a new pattern if insufficient progress is made. In an embodiment, the paths themselves are not modified, but rather 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 many branching 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 interdigitated drive electrodes applied to the substrate, each of the plurality of drive electrodes being arranged in a pattern across the substrate, the plurality of interdigitated drive electrodes being alternately arranged with respect to each other on the substrate, and at least one of the first and second drive electrodes being a spanning tree of tessellation.

[0212] 1. A computer-implemented method for obtaining a first electrode design and a second electrode design for use in a substrate of an optical modulator, the first and second electrodes together covering the substrate to provide a configurable electric field within the optical modulator, the method comprising: - obtaining a tessellation (100) of a substrate, the tessellation comprising a plurality of cells (101; 102; 103) covering the substrate without overlapping, - obtaining a center point (111) in each cell of the tessellation; - Computing a spanning tree (Fig. 1c) for a central point, 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, said deriving including removing portions of the tessellation where edges of the spanning tree cross boundaries of cells of the tessellation; Includes.

[0213] Several modified embodiments are conceivable. For example, any of the following modifications may be added to the above embodiment.

[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 computed, and a 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 perturbing a uniform set of points drawn from a distribution, e.g., a Poisson distribution iii. The dual may be calculated from a selected point within the triangle, such as the circumcenter. d. The maximum diameter of each cell is less than a threshold value, for example, 50 μm.

[0215] 2. Spanning Tree a. The spanning tree computation iteratively builds a spanning tree by selecting cells from the tessellation that are visited by the 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, for example, a gamma distribution.

[0216] 3. Correct electrodes a.Integrate the electrodes i. Determine the components and combine them 1. For example, through connecting subplanes, or by allocating a separate subplane for each electrode and connecting within the subplanes. Components can similarly be coupled along the edges of the planes, or by tiling the design, or by drive buses between building blocks. 2. Select two neighboring components and connect them by reinserting the removed part of the tessellation and removing the corresponding edge in the spanning tree, and / or vice versa. b. Break the circular part of the second electrode c. Correcting a shortcut between the first and second electrodes caused by electrode width by moving portions of the first and / or second electrodes d. Verify and correct optical properties i. From any point in the plane, the distance to the first electrode and the distance to the second electrode should both be less than a threshold value (e.g., 50 μm), or their sum should be less than a 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 (20 μm), and vice versa.

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

[0218] It should be emphasized that the above method is not the only way to obtain designs with low pixelation noise metrics or high electrode length to diagonal ratios. For example, instead of using Voronoi networks, networks based on Turing patterns may be used; see, for example, 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 by tessellation, but still provides good results. For example, the design according to FIG. 5b includes a spiral. In the spiral, the first and second electrode lines belonging to the first and second drive electrodes, respectively, are spiral on the substrate. Even if some electrical lines are roughly parallel in the areas between the spirals, the pattern as a whole provides good results. The pattern can be further improved by undulating the spiral-structured lines, especially in the other few turns of the spiral, e.g., 1-3 turns. Such undulations can be, for example, as shown in FIG. 4e or 4f, by adding protrusions to the electrode lines that disrupt the pattern. For example, all lines in the spiral can be undulating, e.g., with a undulating amplitude of the protrusions decreasing toward the center of the spiral.

[0220] Two substrates according to the embodiments may be combined to form a light modulator, which is particularly suitable for glazing. Exemplary embodiments of the light modulator are shown below.

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

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

[0223] The light 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 light modulator 10 comprises a first substrate 11 and a second substrate 12 arranged opposite each other. On the inside of the first substrate 11, at least two electrodes are applied: electrodes 13a, 13b are shown. These at least two electrodes are collectively referred to as electrodes 13. On the inside of the second substrate 12, at least two electrodes are applied: electrodes 14a, 14b are shown. These at least two electrodes are collectively referred to as electrodes 14.

[0224] A fluid 15 is provided between the substrates. The fluid contains particles 30, e.g., nanoparticles and / or microparticles, which are electrically charged or chargeable. For example, the particles may have an inherent charge on their surface. For example, the particles may be surrounded by charged molecules.

[0225] The electrodes are positioned to drive the particles 30 to move towards or away from the electrodes in response to an applied electric field. The optical properties of the light modulator, in particular its transparency or reflectivity, depend on the location of the particles 30 within the fluid. For example, connections may be provided to apply an electromagnetic field to the electrodes.

[0226] At least one electrode, but preferably both electrodes 13 and 14, are according to an embodiment, which are shown diagrammatically in the figures.

[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 substrates may not individually meet the limit for their pixelation noise metric, but their combination, i.e., their superposition, may. Since this is the pattern that will be visible when viewed through the light modulator, a low pixelation noise metric in the superposition will also contribute to low diffraction. Suitable limits for the patterns on the first and / or second substrates or for the superposition include: less than 6.05%, 5%, or 4%.

[0228] In examples, substrate 11 and substrate 12 may be optically transparent outside the electrodes, typically >95% transparent, e.g., >99% transparent, at relevant wavelengths. Taking the electrodes into account, the transparency may be much lower, e.g., 70%. The term "optical" may relate to wavelengths visible to the human eye (approximately 380 nm-approximately 750 nm), where applicable, or to a broader range of wavelengths, including infrared (approximately 750 nm-1 μm) and ultraviolet (approximately 10 nm-380 nm) and subselections thereof. In exemplary embodiments of the optical modulator, the substrate material is selected from glass and polymer.

[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 light modulator, in particular its reflectivity, depend on the location of the particles 30 within the fluid. When the panel is in the open state (vertical actuation), the particles will be located approximately between the opposing electrodes of the two substrates, allowing incident light to pass relatively unimpeded through the transparent upper substrate and optical layer 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, such as 15 μm. In exemplary embodiments 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, such as less than 30 μm.

[0231] In an example, the modulator may be made of a flexible polymer, and the rest of the device may be made of glass. The glass may be hard glass or flexible glass. If required, a protective layer may be provided on the substrate. If more than one color is provided, more than one layer 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 made of 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 certain wavelengths from passing through. The particles 30 may reflect light; for example, the reflection may be specular, diffuse, or somewhere in between. The particles may absorb some wavelengths and reflect others. The particles may also or instead emit light, for example, using phosphorescence, fluorescence, or the like. Even fluids may emit light whose emittance is modulated by changing the location of the particles.

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

[0234] In exemplary embodiments of the light modulator, the particles are adapted to absorb light having wavelengths of 10 nm-1 mm, e.g., 400-800 nm, 700 nm-1 μm, and 10-400 nm, and / or are adapted to absorb (filter) a portion of light having a wavelength range falling within 10 nm-1 mm, and combinations thereof.

[0235] In an exemplary embodiment of the light modulator, the particles are electrically charged or chargeable. For example, the charge on the particles is between 0.1e and 10e (5 * 10 -7 -0.1C / m2).

[0236] In an exemplary embodiment of the light modulator, the fluid is present in an amount of 1-1000 g / m, preferably 2-75 g / m, more preferably 20-50 g / m, such as 30-40 g / m, etc. A major advantage is that with this layout, much less fluid and like particles can be used.

[0237] In an exemplary embodiment of the light modulator, the particles are present in an amount of 0.01-70 g / m 2 , preferably 0.02-10 g / m 2 , such as 0.1-3 g / m 2 .

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

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

[0240] Fluid 15 may be a non-polar fluid having a dielectric constant less than 15. In an exemplary embodiment of the light modulator, the fluid has a relative dielectric constant εr less than 100, preferably less than 10, such as less than 5. In an exemplary embodiment of the light modulator, fluid 15 has a dynamic viscosity greater than 10 mPa.s.

[0241] Electrodes 13a, 13b and electrodes 14a, 14b are in fluid contact with the fluid. The fluid may be in direct contact with the electrodes or indirectly, e.g., the fluid may contact the second medium with the electrodes, such as through a porous layer. In embodiments, the electrodes cover about 1-30% of the substrate surface. In embodiments, the electrodes have an electrical conductivity (at 20°C) > 1 * 10 7 The electrodes include electrically conductive materials having a resistivity of less than 100 nΩm (at 273 K; for comparison, typically used ITO has 105 nΩm), which is similar to S / m. In light modulator embodiments, the electrodes include copper, silver, gold, aluminum, graphene, titanium, indium, and combinations thereof, preferably copper. The electrodes may be in the form of microwires embedded in a polymer-based substrate; for example, copper microwires.

[0242] Connections for applying an electromagnetic field to the electrodes may be provided, wherein the applied electromagnetic field to the electrodes results in the movement of nanoparticles and microparticles from the first electrode to the second electrode and vice versa. Connections for applying an electromagnetic field to the electrodes may be provided. For example, in an exemplary embodiment of the light modulator, the current is between -100 and +100 μA, preferably between -30 and +30 μA, and more preferably between -25 and +25 μA. For example, a power supply may be in electrical communication with 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 light modulator. For example, the power aspect may be adapted by a controller.

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

[0244] The device may include a driver circuit for changing the appearance of the (individual) segments by applying an electromagnetic field, which in turn may change the appearance of the light modulator or one or more portions thereof. For example, the segments may be at least 1 mm 2 The design allows for stacking to allow for more colors; for example, for a full-color application, a stack of two or three modulators may provide most or all of the colors, respectively.

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

[0246] In an exemplary embodiment of the light 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 aligned substrates, the electrodes on different substrates are behind each other when viewed perpendicular to the substrates. When the light 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 light modulator. On the other hand, when selecting a light modulator based on more criteria, such as the range of transparency or reflectivity, it may be better not to align the two substrates or to align them completely. Light modulators may be stacked. For example, two stacked light modulators may be made from three substrates, with the middle substrate having electrodes on both surfaces. In light modulator embodiments, optionally, at least one substrate 11, 12 of a first light modulator is the same as the substrate 11, 12 of at least one second light modulator. In the case of stacked modulators, alignment may increase the maximum transparency or reflectivity, but may be detrimental to other considerations, such as diffraction.

[0248] FIG. 7b schematically illustrates an example embodiment of a light modulator 40. The light modulator 40 is similar to the light modulator 10, except that it includes multiple optical layers; two optical layers are shown in the example. There may be more than two optical layers. Each optical layer is disposed between two substrates. The light modulator 40 may be considered a stack of two-substrate light modulators, as in FIG. 7a. As shown, the light modulator 40 includes three substrates: a first substrate 41, a second substrate 42, and a third substrate 43. An optical layer is located between the substrates 41 and 42, and an optical layer is located between the substrates 42 and 43. The optical layers may be similar to those of the light modulator 10. A controller 46 is configured to control 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 multiple optical layers may be different, allowing multiple layers to be used to control more optical properties of the light modulator. For example, particles in different optical layers may absorb or reflect at different wavelengths, e.g., 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 with different color particles, e.g., cyan, yellow, and magenta. By controlling the transparency or reflectivity of the different colors, a wide color spectrum can be created.

[0250] The surface of a substrate facing another substrate may be provided with two or more patterns, as in the case of, for example, embodiments, where outer substrates 41 and 43 may receive electrodes only on the inside, while an inner substrate, e.g., substrate 42, may have electrodes on both sides.

[0251] Both substrates 41 and 42 may be considered to be embodiments of an optical modulator. Similarly, both substrates 42 and 43 may be considered to be embodiments of an optical modulator.

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

[0253] Smart glazing can be used in other glazing applications as well, especially in buildings, offices, homes, greenhouses, and skylights, which are windows placed in the ceiling to allow sunlight to enter a room.

[0254] The optical modulator may have two optical states, for example, a transparent state and a non-transparent state or a reflective state and a non-reflective state. - switching to a second optical state, e.g. a non-transparent or non-reflective state, by creating an AC voltage on at least one of the first and second substrates and applying an AC current between at least the first and second electrodes on the first substrate and / or between the first and second electrodes on the second substrate; - switching to a first optical state, e.g., a transparent state or a reflective state, by creating an AC voltage between the first substrate and the second substrate and applying an AC current between a first electrode on the first substrate and a first electrode on the second substrate and / or between a second electrode on the first substrate and a second electrode on the second substrate. It 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 electrodes 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 portion of an interior surface area of at least one of the first and second substrates.

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

[0258] 8a-8b schematically show side views of an embodiment of a light modulator in use. Applying an electric field to electrodes on a substrate induces electric forces on particles. Using this effect, the particles can move around, thereby inducing different transparency or reflectivity states within the light modulator. A controller may control the electric field, e.g., 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 a substrate to better fine-tune the grayscaling and drive it to a non-transparent or non-reflective state. Multiple electrodes may also be used to support multiple segments on a substrate.

[0259] Figure 8a shows the light modulator with no electric field applied, in which no electric force is yet applied to the particles 30 suspended in the fluid 15.

[0260] In the configuration shown in Figure 8a, the conductive electrode pattern disposed on the upper substrate is fully 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, etc.

[0261] Alignment between the upper and lower electrode patterns contributes to a wider range of achievable levels of transparency or reflectivity. However, alignment is not required, as similar effects can be achieved without alignment. A range of transparency or reflectivity can also be achieved without alignment.

[0262] Note that in these examples, reference is made to a top substrate and a bottom substrate to refer to a substrate that is higher or lower on the page. The same substrates could also be referred to as, for example, a front substrate and a back substrate, because in glazing applications, the substrates would be aligned vertically rather than horizontally.

[0263] FIG. 8b shows a light modulator in which, for example, in instance P1, a potential +V1 is applied to each microwire electrode on the top substrate, while a negative voltage, e.g., −V1, is applied to each microwire electrode on the bottom substrate. Thus, in this case, the same positive potential is applied to all electrodes 13, and the same negative potential is applied to electrode 14. The potential difference causes negatively charged particles to flow near the electrode on the top substrate, where they substantially align with the top electrode. As a result, if both the top and bottom substrates are transparent, the transparency of the light modulator 10 will increase. Similarly, if, for example, the top substrate is transparent and the bottom substrate is reflective, and a solution containing positively charged particles flows near the electrode on the bottom substrate, where they substantially align with the bottom electrode, the reflectivity of the light modulator 10 will increase.

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

[0265] Interestingly, by switching between a positive potential on the electrode of the top substrate (and a negative potential on electrode 14), e.g., shown as electrode 13 in Figure 8b, and a positive potential on the electrode of the bottom substrate, e.g., shown as electrode 14 in Figure 8b, transparency or reflectivity can be maintained while reducing corrosion damage to the electrodes. This AC electric field can be achieved by applying AC potentials to the top and bottom electrodes.

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

[0267] FIG. 8c illustrates how a state of reduced transparency or reflectivity can be achieved. Alternating voltages are applied to the same substrate. For example, in an embodiment, as shown in FIG. 8c, a potential +V2 is applied to a first electrode, the next adjacent electrode has an opposite potential −V2, and so on. This can be achieved by applying a potential +V2 to electrode 13a and an opposite potential −V2 to electrode 13b. On an opposing substrate, a potential +V2 can be applied to electrode 14a, and an opposite potential −V2 can be applied to electrode 14b. For example, the electrodes can be arranged so that the electrodes on the substrates are aligned; an electrode on the upper substrate has a counter electrode on the lower substrate, and vice versa. For example, to reduce transparency or reflectivity, the counter electrodes can receive the same potential, while the neighboring electrodes receive opposite potentials. An embodiment is shown in FIG. 8c, where four electrodes are designated by reference numerals 13a, 13b, 14a, and 14b, with the rest of the electrodes following in an alternating order.

[0268] By using an AC drive cycle between the top and bottom substrates, diagonal and transverse electric fields are generated between the two substrates, which causes random diffusion of particles, thereby creating the closed state of the light modulator. As a result of this configuration, the particles move diagonally and transversely between the top and bottom substrates, and the diffusion of particles into the visible aperture of the light modulator contributes to the closed, opaque state of the light modulator.

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

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

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

[0272] Different electrode patterns may be used for the light modulator. Each electrode pattern may provide a range of grayscales, e.g., levels of transparency or reflectivity, that the light modulator can achieve. However, the specific range of grayscales for any particular electrode pattern may differ from another electrode pattern. In other words, different patterns may provide increased transparency or reflectivity or increased opacity, but the exact response to a drive signal depends on many factors, including the particular pattern used. The variation in the optical properties of the light modulator may have a fine resolution, e.g., less than 1 mm. Note that pixilation of the light modulator is not required to achieve different optical patterns, e.g., logos, that are visible in the light modulator.

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

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

[0275] For example, electrode materials can be copper, aluminum, gold, indium-tin oxide (ITO), etc. ITO is transparent, while Cu / Al is reflective; therefore, different electrode materials can be used to achieve different appearances regardless of the driving voltage. Similarly, different materials with different resistivities will produce different electric fields. For example, ITO will have a smaller electric field even when driven by the same voltage.

[0276] An embodiment of a method for modulating light includes applying an electric potential to a plurality of drive electrodes applied to two opposing substrates to cause modulation of light shining through the substrates, obtaining an electromagnetic field between the plurality of drive electrodes that results in electrophoretic movement of particles toward or from one of the plurality of drive electrodes, the two opposing substrates being as in the embodiment.

[0277] Many different ways of performing the method are possible, as will be apparent to one skilled in the art. For example, while the order of steps may be performed in the order shown, the order of steps may be varied, or some steps may be performed in parallel. Furthermore, other method steps may be inserted between 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 in part, in parallel. Furthermore, a given step may not be fully completed before the next step begins.

[0278] Driving the electrodes may use 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] Method embodiments may be implemented using software including 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, memory, optical disk, etc. The software may be transmitted as a signal along a wire or wirelessly, 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. Method embodiments may be implemented using a bitstream configured to configure programmable logic, e.g., a field programmable gate array (FPGA), to perform the method.

[0280] It will be appreciated that the subject matter of this disclosure also extends to computer programs, particularly computer programs on or within a carrier wave, adapted to carry out the subject matter of this disclosure. The program may be in the form of object code, such as source code, object code, code intermediate source, and partially compiled form, or any other form suitable for use in implementing method embodiments. An embodiment relating to a computer program product includes computer-executable instructions corresponding to each of the processing steps of at least one of the described methods. These instructions may be subdivided into subroutines and / or stored in one or more files, which may be statically or dynamically linked. Another embodiment relating to a computer program product 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 illustrates a computer-readable medium 1000 having a writable portion 1010 containing a computer program 1020, and a computer-readable medium 1001 also having a writable portion containing a computer program. The computer program 1020 includes instructions for causing a processor system to perform a light modulator method, according to an embodiment. For example, the processor system may be connected to a light 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 contemplated. Furthermore, while the computer-readable medium 1000 is illustrated here as an optical disk, it will be appreciated that the computer-readable medium 1000 may be any suitable computer-readable medium, such as a hard disk, solid-state memory, flash memory, or the like, and may be non-recordable or recordable. The computer program 1020 includes instructions for causing a processor system to perform the light 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 shown schematically in FIG. 9b. The circuit 1110 includes a processing unit 1120, e.g., a CPU, for executing computer program components to perform methods according to embodiments and / or implement modules or units thereof. The circuit 1110 includes a memory 1122 for storing programming code, data, etc. A portion of the memory 1122 may be read-only. The circuit 1110 may include a communication element 1126, e.g., an antenna, a connector, or both, and the like. The circuit 1110 may include a dedicated integrated circuit 1124 for performing some or all of the processing defined in the methods. The processor 1120, the memory 1122, the dedicated IC 1124, and the communication element 1126 may be connected to each other via an interconnect 1130, e.g., a bus. The processor system 1110 may be configured for contact and / or contactless communication using an antenna and / or connector, respectively.

[0283] For example, in an embodiment, the processor system 1140, e.g., a device, may include a processor circuit and a memory circuit, where the processor is 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, or the like. 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, e.g., a flash memory. The memory circuit may be a volatile memory, e.g., an SRAM memory. In the latter case, the device may include a non-volatile software interface, e.g., a hard drive, a network interface, or the like, configured to provide the software.

[0284] For example, a controller for a light modulator for controlling the voltages applied to the electrodes may comprise a processor circuit, but may also or alternatively comprise a state machine.

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

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

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

[0288] For example, a first property satisfied by building block 820 is that for at least one electrode in a plurality of interdigitated electrodes in building block 820, the maximum length between any two points on the electrode, measured along the electrode in building block 820, is at least twice the length of the diagonal of the building block. Indeed, in this example, this property is valid for multiple electrodes of building block 820.

[0289] For example, a second property satisfied by building block 820 is that building block 820 comprises electrodes that branch at nodes to form a tree. Building block 820 exhibits a highly branching tree, e.g., there is a first node at which an electrode branches into at least three lines, each connected to at least three second nodes that also branch into at least three lines. In practice, there may be three more second nodes connected to a third node at which the electrode similarly branches.

[0290] For example, a third property satisfied by the electrodes in a building block is that the angles at the nodes of the electrodes are well distributed over the range of 0 to 360. For example, the building block exhibits at least some angles in the range of 0-30, some angles in the range of 30-60, up to the range of 330-360. In practice, any range from x to x+30 is exhibited by the angles in FIG. 10a. In practice, this property is valid for multiple electrodes in building block 820.

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

[0292] For example, a fourth property satisfied by a 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 do not have to be combined as is done in building block 820. For example, one could have only characteristic 1, or only characteristic 2, or only characteristic 3, or only characteristic 4, or combinations, e.g., 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.

[0294] Building block 820 also satisfies the constraint that the distance between two neighboring lines is greater than a minimum and less than a maximum. Building block 820 is an example of a building block in which the electrodes reside in the same plane and do not intersect. Note that if intersecting electrodes are desired, this is not an obstacle. For example, two electrodes could intersect by having an insulator between the two electrodes at the intersection. The insulator could be the substrate itself; for example, one of the electrodes could be redirected through two vias to extend on the back of the substrate.

[0295] FIG. 10b.1 shows a schematic of a substrate 810 and a drive bus. A drive bus 812 and a drive bus 814 are shown. To create a substrate for an optical modulator, a building block 820 is repeated within the area bounded by the drive bus. The drive bus is arranged to drive the 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 opposing adjacent sides of the substrate. The electrodes 812 and 814 do not touch. In use, a varying voltage is applied to the electrodes 812 and 814 to create a voltage distribution that causes an optical effect between the substrate 810 and an opposing substrate (not shown in FIG. 10b.1).

[0296] In particular, the drive bus 812 or edge electrode extends along the left and top edges. At one point, a connection point, shown here at the top left, is provided for connecting the bus 812 to a controller. In particular, the drive bus 814 or edge electrode extends along the right and bottom edges. At one point, a connection point is provided for connecting the bus 814 to a controller. The bus 814 extends along the top edge outside the bus 812. An advantage of extending one electrode, such as the bus 814, along three edges is that both electrodes can be connected to form the same edge. That is, the entire optical modulator can be powered from a single edge of the substrate. The bus 814 here extends over a limited portion, for example, less than ¼ of the edge. The bus 814 could also extend further, approximately to the connection portion of the bus 812.

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

[0298] Fig. 10b.2 shows a schematic representation of a variation of the substrate 810 and drive buses. Shown are drive buses 812 and 814. As in Fig. 10b.1, building block 820 repeats within the area bounded by drive buses 812 and 814.

[0299] In addition to the drive busses along the edges of the substrate 810, further drive busses are shown extending within and across the interior of the substrate 810.

[0300] FIG. 10b.2 shows additional drive buses 815-819 extending across the substrate. Some of the additional drive buses, in this example buses 815 and 816, are connected to drive bus 814. Some of the additional drive buses, in this example buses 817 and 819, are connected to drive bus 812. Optional protrusions extend from the additional drive buses to extend along the edges of copies of the building blocks. Thus, every building block may have a drive bus extending along each of its edges, e.g., a first drive bus for two edges connected at a vertex of the building block, and a second drive bus for the other two edges connected at diagonally opposite vertices. The substrate of FIG. 10b.2 may also be combined with a mirror image.

[0301] The advantage of the arrangement shown in Figure 10b.2 is that power is distributed more evenly across the devices, and as a result, the transition is more uniform and completes faster.

[0302] Although the building blocks shown in Figures 10b.1 and 10b.2 have square building blocks, generally speaking, the building blocks may have any shape. In particular, any shape or shapes that tile a plane, e.g., repeatable shapes, may be used. In particular, the building blocks may have rectangular, e.g., non-square, shapes. For example, one side may be at least 1.5 times longer than the other side. The shape of the building blocks may be the same as the shape of the optical modulator, e.g., have the same relative dimensions.

[0303] The building blocks may be patterned using one or more building block stepper masks. An additional stepper may be used for the drive bus. A stepper may also be used where connections are made by overlapping metal deposition. For example, when the stepper is processing the metal for drive bus 812, there may be an overlap with where there was deposition of 820. Connections from the outside to electrodes, e.g., 812, may use conventional foil bolding or clips.

[0304] It should also be noted that while one type of building block may be repeated, multiple types of building blocks may be used. For example, the shape may be triangular. The shape of the building block may affect the shape of the overall device. This may be advantageous, for example, to adapt the form factor of an optical modulator. Furthermore, building blocks of different shapes may be combined within a single substrate. For example, a substrate may have a square or rectangular shape in the center and triangular shapes on the edges.

[0305] Using different shapes and / or dimensions is useful for substrates that do not have straight edges, as discussed further herein. Using different shapes and / or dimensions is also useful for curved substrates, e.g., non-flat substrates. While not strictly necessary, using different shapes for the building blocks allows the building blocks to better conform to the shape of the substrate. A curved substrate may be combined with another curved substrate to form a curved optical modulator. For example, in embodiments, the drive buses are arranged along the triangulation of the curved substrate, the drive buses follow the triangulation, and the building block shapes are arranged between the drive buses. For example, in embodiments, the building blocks surrounding the center of the substrate are square or rectangular, while the building blocks at the edges are triangular. The latter configuration can be achieved using two shapes or three or more shapes. It should be noted that while a curved substrate may be supported by a single-shaped building block, using multiple shapes may be advantageous. In general, building blocks of different shapes may be similarly 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 interdigitated drive electrodes applied to the substrate, each of the plurality of drive electrodes arranged in a pattern across the substrate, the plurality of interdigitated drive electrodes being arranged in an alternating pattern relative to one another 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 interdigitated electrodes extending in at least two directions across the building blocks, the interdigitated electrodes within the building blocks forming the drive electrodes, the substrate is curved, and the plurality of repeating building blocks include at least two different shapes.

[0306] Figure 10c schematically shows a detail of a corner of Figure 10d, discussed below. Figure 10c shows a corner of building block 820 and a portion of drive bus 812 and drive bus 814. Figures 10d-10d schematically show building block 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. Building block 820 repeats across the substrate in two directions by translation. The repetition can be a glide translation, e.g., a translation followed by a reflection.

[0307] 10c shows how electrodes formed by repeating building blocks may be connected to a drive bus, for example, electrode lines may extend from the drive bus to the electrodes within a building block.

[0308] Figure 10d shows a schematic detailing the repetition of building block 820 between buses 812 and 814. In Figure 10d, portions of four copies of the building block are shown. The edges between the building blocks are indicated with capital letters A, B, C, and D. Electrodes on one side of the building block are connected to electrodes on the opposite side of the electrode; note that in this case, the electrodes in the design match, so that aligning the building blocks is sufficient to create a continuous electrode.

[0309] In this example, Figure 10a is drawn so that the blocks overlap slightly when repeated across the substrate, as can be seen in Figure 10d. Having overlap can be avoided if desired, but this is advantageous. The overlap in this example is 3%. That is, 3% in the x-direction dimension of one building block overlaps 3% in the x-direction of the next block. The amount of overlap is preferably small, for example, between 1% and 5%. Larger or smaller overlaps are possible. It is also possible for there to be no overlap at all, in which case the building blocks would be aligned directly next to each other. The same is valid for the y-direction, with overlaps of, for example, 3%, between 1% and 5%, etc. being possible embodiments.

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

[0311] FIG. 11 schematically illustrates a cross section of an embodiment of a light modulator 700. Two substrates are shown in FIG. 11: substrate 772 and substrate 774. Interdigitated drive electrodes and drive buses are applied to their surfaces, for example, according to an embodiment. A spacer 750 is disposed between substrates 772 and 774 to maintain the substrates at a predetermined distance. The space between the two substrates is filled with a 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, etc.

[0312] FIG. 12a schematically illustrates an embodiment of a light modulator. In FIG. 12a, a corner of a substrate according to the embodiment is shown. A drive bus or edge connector is located along the top and right edge of the substrate. A drive electrode corresponding to a drive bus is connected to that drive bus at multiple points, e.g., a first point and a second point. For some portions of an electrode, two connections may be required to integrate the electrode, e.g., to ensure the entire electrode is connected. However, an electrode may be positioned to connect to the drive bus multiple times, even when it is not required to connect to the first electrode. For example, the first and second points may be connected along the drive bus but also through an electrode across the substrate. In that case, a portion of the drive bus between the first and second points may be removed. Removing this portion of the drive bus does not disconnect the drive bus from the power supply because the drive bus remains connected through the electrode. FIG. 12b illustrates an example in which a portion of the drive bus has been removed. FIG. 12c shows the same portion of the substrate, but highlights the electrodes connecting portions 902, 904, and 906.

[0313] Interrupting long electrode lines, especially straight lines, can be beneficial for reducing diffraction. If the edge connectors were only located at the edge of the device, as shown in the embodiment of Figures 10a-10d, for example, this would make only a small difference. However, for embodiments with drive buses that surround the building blocks, the impact is significant. There, straight lines around the building blocks would significantly increase diffraction and optical artifacts. Here, these straight lines are interrupted in multiple locations, thus reducing diffraction or optical artifacts. For example, drive buses such as those shown in Figures 6a-6d would benefit from removing portions of the drive bus.

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

[0315] 13 and 13b are highly convoluted, as 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 a building block and the diagonal of the building block (said ratio is greater than 2).

[0316] The drive electrodes in the substrate in Figure 13b are in the same plane and do not intersect. Note that this design fully connects the electrodes with no floating electrodes on the edges. Note that some electrodes on the edges of a building block are connected through electrodes in adjacent building blocks.

[0317] The building blocks are based on so-called Turing patterns. Turing patterns have been found to be advantageous because they generate fewer but longer branches. As a result, the design is less likely to form floating electrodes that may have to be treated separately. Turing patterns are also known as reaction-diffusion systems - in this particular example, the Gray-Scott equation was used.

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

[0319] FIG. 14a shows schematically an embodiment of a substrate in which the building blocks are rectangular, in this case square.

[0320] Figures 14b and 14c show schematically an embodiment of the substrate in which the building blocks are triangles, in this case right-angled triangles. Any other triangular shape is also possible.

[0321] An 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 Figures 14 and 14b. However, with triangular building blocks, a triangular substrate can be easily tiled, for example, at the edges, without the need for supporting partial building blocks or building blocks of different types.

[0322] FIG. 14d shows a schematic representation of an embodiment of the substrate in which the building blocks are hexagonal, in this case regular hexagons.

[0323] FIG. 14e shows a schematic representation of an embodiment of the substrate in which the building blocks are trapezoidal.

[0324] Figure 14f shows a schematic representation of an embodiment of a substrate in which the building blocks are polygons, in this case, for example, rectangular polygons with right angles. Note that the polygons need not be convex, as shown in Figure 14f. The polygons may also be polyominoes; for example, polygons constructed from integer squares. In the example shown, trominos are used. Other examples of polyominoes include tetrominoes and pentominoes. The polygons may also be isothetic polygons, for example, rectilinear polygons.

[0325] Figure 14g shows a schematic representation of an embodiment of a substrate in which the building blocks are square. Figure 14h shows a schematic representation of an embodiment of a substrate in which the building blocks are triangular. Note that substrates of various shapes can be supported by combining building blocks. Note also that with triangular building blocks, different shapes are possible for the substrate.

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

[0327] Supporting substrates of different shapes is advantageous for supporting different applications. For example, in cars, 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 contemplated embodiments:

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

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

[0332] Clause 3. A substrate as described in clause 1 or 2, wherein the electrode on the substrate comprises a plurality of nodes from which the electrode branches, the nodes being electrically connected through electrode lines, the plurality of nodes and connecting electrode lines forming a tree, the electrode comprising at least a first node (201) from which the electrode branches into at least three electrode lines, the first node (201) being directly connected to a second node (202) and to a third node (203) through electrode lines, and the electrode branches into at least three electrode lines at the second node and at the third node.

[0333] Article 4. - the angle between two directly connected electrode lines is randomly selected, and / or - the directly connected electrode lines in the building block form a plurality of angles, the angles covering an interval of 0 to 360 degrees, and in particular, for each particular interval of at least 30 consecutive angles, there is at least one angle within the plurality of angles that falls within the particular interval; and / or - Multiple 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 of clause 3, wherein the electrode line width is not constant along the electrode line.

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

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

[0336] Article 7. - the building blocks repeat across the substrate in at least two directions, and / or - multiple 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 - A substrate according to any one of clauses 1 to 6, wherein the substrate comprises non-repetitive electrode lines connected to the drive electrodes.

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

[0338] Article 9. - the building blocks are translated with and without mirroring and / or point reflection, and / or - A substrate according to any one of clauses 1 to 8, wherein a row or column of building blocks is mirrored along its length to form a next row or column of building blocks.

[0339] Clause 10. At least one drive bus is disposed on the substrate for each drive electrode to drive the drive electrode; - at least one drive bus is disposed on the edge of the substrate for each drive electrode to drive the drive electrode; and / or - the drive buses are only located on the edges of the board, and / or - A substrate according to any one of clauses 1 to 9, wherein drive buses are arranged between building blocks covering the substrate.

[0340] Clause 11. A substrate described in any one of clauses 1 to 10, wherein at least one drive bus is arranged on the substrate for each drive electrode to drive the drive electrode, and wherein at least one drive bus is arranged on an edge of the substrate and / or an edge of a building block, and wherein the drive bus has discontinuous portions, and the discontinuous portions are connected through drive electrodes driven by the drive bus.

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

[0342] Clause 13. The substrate of any one of clauses 1 to 12, wherein the drive electrodes have mirror symmetry.

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

[0344] Clause 15. An optical modulator comprising: - a first substrate and a second substrate, at least one of which is according to any one of clauses 1-14, the first and second substrates being arranged with their interiors facing each other, and a plurality of drive electrodes (111-114, 121-124) being applied to the interior of at least one of the first and second substrates; - an optical layer between the first substrate and the second substrate and the optical layer comprises: a fluid containing particles, the particles being electrically charged or chargeable; - an optical modulator comprising: a controller configured to apply an electric potential to a plurality of drive electrodes to obtain an electromagnetic field between the plurality of drive electrodes that results in electrophoretic movement of particles toward or from one of the plurality of drive electrodes, causing modulation of an optical property of the optical modulator.

[0345] Article 16. - An optical modulator as described in clause 15, wherein 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 pixelation noise metric of less than 6.05%, or 5%, or 4%.

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

[0347] Clause 18. A computer-implemented method for calculating a pixelation noise metric for an electrode pattern for a light modulator, comprising: - preparing a black and white design drawing to a specific size, in which 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 in the magnitude spectrum of the chirp z-transform (CZT) of the design image; - determining the higher peak value as the second maximum intensity in the magnitude spectrum chirp z-transform (CZT), excluding the main peak; - Calculating the pixelation noise metric as the ratio of the higher peak value to the main peak value; A computer-implemented method comprising:

[0348] Clause 19. The method of calculating a pixelation noise metric according to clause 18, wherein the design image is an 8-bit image, black is set to 0 and white is set to 255.

Claims

1. 1. A substrate for use in an optical modulator, comprising: - at least one drive electrode (111-114, 121-124) applied to a substrate, the drive electrode 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 being: - a substrate comprising one or more electrodes extending in at least two directions across a building block, the electrodes in a building block forming at least one drive electrode, and wherein for at least one electrode in a building block, the maximum length between any two points on said electrode, measured along said electrode in the building block, is at least twice the length of a diagonal of a building block unit.

2. 10. The substrate of claim 1, wherein the drive electrode pattern of the substrate has a calculated pixelation noise metric of less than 6.05%, or less than 5%, or less than 4%.

3. 3. The substrate of claim 1, wherein the electrodes in the building blocks comprise a plurality of nodes from which the electrodes branch, the nodes being electrically connected through electrode lines, the plurality of nodes and connecting electrode lines forming a tree, the electrodes comprising at least a first node (201) from which the electrodes branch into at least three electrode lines, the first node (201) being directly connected to a second node (202) and to a third node (203) through electrode lines, and the electrodes branch into at least three electrode lines at the second node and at the third node.

4. the angle between two directly connected electrode lines is randomly selected, and / or the directly connected electrode lines in the building blocks form a plurality of angles, the angles covering an interval of 0 to 360 degrees, and in particular, for each particular interval of at least 30 consecutive angles, there is at least one angle in the plurality of angles that falls within the particular interval; and / or - A number of nodes are randomly selected to cover the area of the building block, and / or the electrode lines are straight or curved, and / or A substrate according to claim 3, wherein the electrode line width is not constant along the electrode line.

5. the building blocks repeat across the substrate in at least two directions, and / or - multiple 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 A substrate according to any one of claims 1 to 4, wherein the substrate comprises non-repeating electrode lines connected to drive electrodes.

6. two electrodes in a building block that are not connected within the building block are connected in the substrate through a connection in a neighboring building block, and / or A substrate according to any one of claims 1 to 5, wherein the electrodes in a building block are connected to at least two sides of the building block.

7. - the building blocks are translated with and without mirroring and / or point reflection, and / or A substrate according to any one of claims 1 to 6, in which a row or column of building blocks is mirrored in its longitudinal direction to form a next row or column of building blocks.

8. at least one drive bus is disposed on the substrate for each drive electrode of the at least one drive electrode to drive the drive electrode; At least one drive bus is arranged on the edge of the substrate for each drive electrode to drive the drive electrode; and / or the drive buses are only located on the edges of the substrate, and / or A substrate according to any one of claims 1 to 7, in which drive buses are arranged between the building blocks covering the substrate.

9. 9. The substrate of claim 1, wherein at least one drive electrode is insulated from an edge of the substrate, and vias are connected from a surface of the substrate opposite the drive electrode to the insulated drive electrode for powering the insulated drive electrode and / or connecting the insulated drive electrode to another portion of the drive electrode on the substrate.

10. 10. The substrate of claim 1, wherein at least one drive bus is arranged on the substrate for each drive electrode to drive the drive electrode, the at least one drive bus being arranged on an edge of the substrate and / or an edge of a building block, the drive bus comprising discontinuous portions, the discontinuous portions being connected through drive electrodes driven by the drive bus.

11. The substrate of claim 1 , wherein at least one of the drive electrodes is a spanning tree of a tessellation.

12. The substrate of claim 1 , wherein the drive electrodes have mirror symmetry.

13. The substrate of claim 1 , wherein the substrate is non-rectangular.

14. the at least one drive electrode is a plurality of drive electrodes; a plurality of drive electrodes (111-114, 121-124) are interdigitated, each of the plurality of drive electrodes being arranged in a pattern across the substrate, the plurality of interdigitated drive electrodes being arranged in an alternating manner relative to one another on the substrate, the pattern of the plurality of drive electrodes across the substrate comprising a plurality of repeating building blocks, the building blocks being: - A substrate for use in an optical modulator according to any one of claims 1 to 13, comprising a plurality of interdigitated electrodes extending in at least two directions across the building block, the interdigitated electrodes in a building block forming drive electrodes, and for at least one electrode in the plurality of interdigitated electrodes in a building block, the maximum length between any two points on the electrode measured along the electrode in the building block is at least twice the length of a diagonal of a building block unit.

15. the plurality of drive electrodes comprises a first drive electrode and a second drive electrode; the shortest distance from any point in the substrate to the first drive electrode and to the second drive electrode is less than a threshold value; and / or the sum of the shortest distances from any point in the substrate to the first drive electrode and to the second drive electrode is less than a first threshold and / or exceeds a second threshold, and / or 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; and / or A substrate according to claim 14, wherein the horizontal and / or vertical size of the building blocks is at least 10 times the sum of the electrode line width and the electrode distance.

16. the drive electrodes are in the same plane and do not intersect, or A substrate according to claim 14 or 15, wherein the drive electrodes intersect within the substrate, a dielectric separating the intersecting drive electrodes at least at the points of intersection.

17. An optical modulator, a first substrate and a second substrate according to any one of claims 1 to 16, wherein the first and second substrates are arranged with their interiors facing each other and at least one drive electrode (111-114, 121-124) is applied to the interior of at least one of the first and second substrates, an optical layer between the first and second substrates and the optical layer comprises: an optical modulator comprising a controller configured to apply an electrical potential to the drive electrodes to cause modulation of an optical property of the optical modulator;

18. 17. The light modulator of claim 16, wherein the optical layer comprises particles, the particles being electrically charged or chargeable, and the controller is configured to apply a potential to the drive electrodes to obtain an electromagnetic field that results in electrophoretic movement of the particles towards or away from the drive electrodes, causing modulation of the optical properties of the light modulator.

19. 19. The light modulator of claim 17 or 18, wherein the first substrate and the second substrate are according to claim 14, and the controller is configured to apply a potential to the plurality of drive electrodes to obtain an electromagnetic field between the plurality of drive electrodes that results in electrophoretic movement of particles towards or from one of the plurality of drive electrodes, causing modulation of an optical property of the light modulator.

20. - A light modulator according to any one of claims 17 to 19, wherein the electrode pattern on the first substrate, the electrode pattern on the second substrate and / or the overlap of the electrode patterns of the first and second substrates has a calculated pixelation noise metric of less than 6.05%, or 5%, or 4%.

21. 1. A method of modulating light, comprising: - A method of modulating light comprising applying an electric potential to drive electrodes applied to two opposing substrates to obtain an electromagnetic field between the drive electrodes that results in electrophoretic movement of particles towards or from one of a plurality of drive electrodes, causing modulation of light shining through the substrates, wherein at least one or both of the two opposing substrates is a substrate according to any one of claims 1 to 16.

22. 1. A computer-implemented method for calculating a pixelation noise metric for an electrode pattern for a light modulator, comprising: - preparing a black and white design image to a specific dimension, where 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 in the magnitude spectrum of the chirp z-transform (CZT) of the design image; - determining the higher peak value as the second maximum intensity within the magnitude spectral chirp z-transform (CZT), excluding the main peak; - Calculating the pixelation noise metric as the ratio of the higher peak value to the main peak value A computer-implemented method comprising:

23. 23. The method of calculating a pixelation noise metric of claim 22, wherein the design image is an 8-bit image, with black set to 0 and white set to 255.

Images