Diffractive optical elements

Abstract

A method for producing a diffractive optical element (1) comprises the following steps: providing at least one substrate (3) having a surface (4), and generating a relief structure (2) in the surface (4) of the substrate (3) using a processing device (5). The processing device (5) comprises a probe (6) having a tip (7) having a radius (R) less than about 1 micrometer. The probe (6) is movable relative to the substrate (3). The relief structure (2) is generated by the action of the tip (7) on the surface (4) of the substrate (3) so that the distance (D) between the surface (8) of the relief structure (2) and the surface (4) of the substrate (3) varies substantially continuously along a third direction (z). The diffractive optical element (1) comprises a relief structure (2) having a surface (8), wherein, at least in a portion of the relief structure (2), the distance (D) between the surface (8) of the relief structure (2) and the surface (4) of the substrate (3) varies substantially continuously. A virtual image display device comprises at least a first diffractive optical element and a second diffractive optical element of such a diffractive optical element (1).

Description

Technical Field

[0001] The invention relates to a method for producing a diffractive optical element according to claim 1, a diffractive optical element produced by such a method according to claim 11, and a diffractive optical element according to claim 12. Furthermore, the invention relates to a virtual image display device according to claims 15 and 16 comprising such a diffractive optical element. Background Art

[0002] Diffractive optical elements are well known in the art and are commonly used to shape and classify electromagnetic radiation beams. As such, they find various applications such as optics and spectroscopy. The basic physical principle is diffraction, in which an electromagnetic radiation beam incident on a diffractive optical element at a specific incoming angle is diffracted from the diffractive optical element at a specific outgoing angle. Diffractive optical elements are based on periodic or non-periodic structures, in which the Fourier spectrum of the refractive index modulation along these structures controls how the incident electromagnetic radiation is diffracted. The relief structures generated in the surface of the diffractive optical element are mainly used for this purpose in technical applications. From US 4 895 790, the generation of multi-level diffractive optical elements is known, in which multiple binary masks are used when etching the multi-level structure into the optical element successively. However, the limitations of manufacturing such structures hinder the control of their Fourier spectrum, which in turn limits the functionality of the diffractive optical element. For example, the limited control of the Fourier spectrum of the diffractive optical element hinders the miniaturization of the diffractive optical system and also limits the quality of the diffraction images such as computer-generated holograms. In order to achieve multicolor inward coupling of light into an integrated holographic system, Huang, Zhiqin, Daniel L. Marks, and David R. Smith, "Out-of-plane computer-generated multicolor waveguide holography", Optica 6.2 (2019): 119-124 proposed inward coupling of three different laser colors at three highly specific angles. Such an inward coupling system is large and complex and is not practical for compact wearable devices, such as those desired in the field of virtual reality systems. Similar shortcomings can also be observed in the solution proposed in Mukawa, Hiroshi, et al., "A full-color eyewear display using planar waveguides with reflection volume holograms", Journal of the Society for Information Display 17.3 (2009): 185-193, where one diffractive optical element is used for inward coupling of each color of light. Summary of the invention

[0003] The object of the present invention is to overcome the disadvantages of the prior art. In particular, the object is to provide a method enabling simple and high-quality production of a diffractive optical element, which diffracts one or more electromagnetic radiation beams in a desired manner. More specifically, the object is to provide a method enabling the production of a diffractive optical element, which allows full control of its Fourier spectrum by including only the desired Fourier components and omitting all other unwanted Fourier components.

[0004] This object is achieved by a method according to claim 1. In particular, the method for producing a diffractive optical element comprises the following steps: i) providing at least one substrate having a surface extending in a first direction and in a second direction perpendicular to the first direction, and ii) generating a relief structure in the surface of the substrate using a processing device. The processing device comprises a probe having a tip. The tip has a radius of less than about 1 micrometer, preferably less than about 20 nanometers. The probe is movable relative to the substrate in a first direction, a second direction and a third direction perpendicular to the first and second directions, and wherein the relief structure is generated by the action of the tip on the surface of the substrate such that a distance between the surface of the relief structure and the surface of the substrate along the third direction varies substantially continuously along at least one of the first and second directions.

[0005] In the context of the present invention, the expression "continuous variation" should be understood in its mathematical sense. That is, the continuous variation of the distance between the surface of the relief structure and the surface of the substrate along at least one of the first direction and the second direction can be understood in the sense that the derivative is continuous, bounded and defined anywhere in the respective at least one of the first direction and the second direction. In other words, the relief structure has a shape that does not include any steps or edges or jumps. Or, figuratively speaking, the surface of the relief structure is smooth. The expression "substantially" should here indicate that the relief structure is continuous within the range allowed by the processing device, in particular its tip with a radius of less than about 1 micrometer, preferably less than about 20 nanometers (also see further below).

[0006] Therefore, the method according to the invention enables the production of a diffractive optical element with a continuous relief structure. This enables the Fourier spectrum of a single diffractive optical element to be controlled. In other words, the diffractive optical element generated by the method according to the invention contains all the information in the Fourier spectrum that is necessary for the interaction with one but especially with multiple colors of light. In other words again, the present method enables the production of a diffractive optical element with a grayscale relief structure. This prevents the need to couple different colors with different incoming angles or to have a diffractive optical element for each color - as is the case in systems of the prior art. Therefore, the present method allows simplification and miniaturization of diffractive optical technology, especially also in holographic applications requiring multicolor functionality. At the same time, higher quality holograms can be produced.

[0007] To this end, it should be noted that the relief structure can be entirely composed of a continuous shape as just described. However, it is also conceivable that the relief structure can include a continuous shape as just described, but can also include one or more parts with different shapes, for example with binary shapes. Thus, the processing device enables the relief structure to be generated according to the specific needs of the final use of the diffractive optical element.

[0008] The relief structure is preferably generated by the mechanical action and / or thermal action of the tip on the surface of the substrate. When generating the relief structure, the tip can be in direct contact with the surface of the substrate. That is, the tip of the probe can act immediately on the surface of the substrate and, for example, remove the part of the substrate on which the tip acts. The mechanical action can be to physically remove material from the surface of the substrate, that is, to selectively remove material from the surface of the substrate by a subtractive technique. For example, a thermal action can be applied by means of a heated tip, wherein the material from the surface of the substrate is selectively thermally decomposed and / or removed. The heating of the tip can be achieved by applying an electric current to the probe and thus the tip. Of course, these actions can be combined and the heated tip can be used to mechanically remove material from the substrate. In any case, the removal of material from the surface in the third direction is achieved by moving or pushing the heated probe and thus the tip into the surface of the substrate in the third direction. By changing the strength of the force applied to the surface by the probe in the z direction, the depth of the relief structure relative to the third direction is controlled. The processing device preferably corresponds to a thermal scanning probe lithography device known in the art. Therefore, it is particularly preferred to use a commercially available thermal scanning probe lithography device sold by SwissLitho AG. The use of such a processing device, in particular due to its spatial resolution, enables the generation of a relief structure that is continuous in the first direction and / or in the second direction on a larger length scale than a continuous relief structure obtained from a common etching process. Another advantage associated with such a device is that the probe can read out and analyze the generated relief structure when the relief structure is generated. That is, the tip can be used to scan the surface of the sample while the relief structure is written / created / patterned into the surface of the sample and the relief structure is also read or imaged at the same time. This generates a closed-loop feedback system that results in an accurate and precise profile of the surface relief structure.

[0009] The probe can be moved in a first direction and / or in a second direction with a step length of about 0.1 nm to 50 microns, in particular with a step length of about 0.1 nm to 100 nm, preferably with a step length of 5 nm to 50 nm, and particularly preferably with a step length of less than about 20 nm. Additionally or alternatively, the probe can be moved in a third direction with a step length of about 0.1 nm to 1 micron, preferably with a step length of 0.2 nm to 25 nm, and particularly preferably with a step length of less than about 2 nm.

[0010] By moving the probe and thus the tip in at least one of the first and second directions in the steps just mentioned, a relief structure having a plurality of protrusions and recesses extending in the first and / or second directions can be generated. In addition, by using a probe with a tip as initially described, a relief structure can be generated, wherein the minimum horizontal distance between two successive protrusions or recesses when viewed in the first and second directions, respectively, is less than about 20 nanometers. In particular, the minimum horizontal distance is about 10 nanometers. In addition, a relief structure having a minimum depth less than about 10 nanometers can also be generated. In particular, the minimum depth is about 0.2 nanometers. The depth extends in a third direction perpendicular to the first and second directions of the surface and thus the substrate, and when viewed in the first and second directions, the depth is formed between two successive protrusions or recesses.

[0011] The probe and therefore the tip can be moved in the first direction and / or in the second direction at a rate between about 1 Hz and 1000 kHz, preferably between about 1 kHz and 500 kHz. At the same time, it is conceivable that the tip acts on the surface of the substrate. In other words, it is conceivable that the probe is configured to pattern the relief structure at a rate between about 1 Hz and 1000 kHz, preferably between about 1 kHz and 500 kHz. It is also conceivable that the probe is configured to read the written pattern at the same time, i.e. read the relief structure at a given rate. Additionally or alternatively, the tip can be heated to a temperature in the range of about 100° C. to 1500° C., preferably a temperature in the range of about 700° C. to 1400° C. These parameters are set according to the size of the relief structure that should be generated and suitable for the material of the substrate.

[0012] The processing device may also include a controller, the controller being configured to control the probe based on controller data fed into the controller, wherein the controller data defines the relief structure along a horizontal plane spanned by the first direction and the second direction and is based on one or more functions. One or more functions preferably correspond to one or more continuous functions. The controller data is particularly preferably based on one or more sine functions. Other examples of conceivable functions for controlling the movement of the probe are Bessel functions or Gaussian functions. Therefore, it is conceivable to base the controller data on one or more continuous and smooth functions. In this way, the probe and therefore the tip perform continuous and possibly smooth movement. Then, when the tip acts on the surface of the substrate, the spatial profile defining the continuous and possibly smooth movement is traced into the surface of the substrate.

[0013] One or more sinusoidal functions can be represented by the following expressions:

[0014]

[0015] Among them, parameter A n is the amplitude,

[0016] Among them, the parameter k n is the spatial frequency,

[0017] Among them, the parameter α n is the angular direction along the horizontal plane,

[0018] Among them, the parameters is the phase, and

[0019] Among them, the parameter Δ n is the offset relative to the third direction.

[0020] Depending on the final application of the diffractive optical element, it is conceivable to base the controller data on the amplitude A n , spatial frequency k n , angular direction α n , Phase and offset Δ n An appropriate and predetermined value of at least one of .

[0021] In particular, the amplitude A n corresponds to the amplitude along the third direction. The amplitude of the relief structure is related to the intensity or efficiency of the diffraction of the incident electromagnetic radiation. For example, if the electromagnetic radiation should be diffracted with high intensity, the amplitude should be increased, and vice versa.

[0022] The spatial frequency is given by Given, where where Λ is the angle α along the horizontal plane n The spatial frequency of the relief structure is preferably chosen so that the in-plane wave vector of the electromagnetic radiation incident on the relief structure matches the in-plane wave vector of the output mode, the spatial frequency being given by the momentum matching equation:

[0023] in, as well as

[0024] is the in-plane wave vector of the incident electromagnetic radiation.

[0025] is the in-plane wave vector of the diffracted outgoing electromagnetic radiation.

[0026] is a unit vector along the direction of propagation of the incident electromagnetic radiation.

[0027] is the unit vector along the direction of propagation of the diffracted outgoing electromagnetic radiation.

[0028] is the unit vector in the plane along the direction of propagation of the diffracted outgoing electromagnetic radiation.

[0029] is the unit vector in the plane along the direction of propagation of the incident electromagnetic radiation.

[0030] is the wave vector of the relief structure, given by Given.

[0031] Λ is the wavelength of the relief structure defining the diffractive optical element.

[0032] is a unit vector along the direction of the relief structure, here along the surface of the substrate.

[0033] θ is the incident electromagnetic radiation (also referred to herein as θ in ) and the diffracted outgoing electromagnetic radiation (also referred to herein as θ out ) is an angle relative to a direction perpendicular to the surface of the substrate, here relative to a third direction.

[0034] n in is the refractive index of the medium through which the incident electromagnetic radiation propagates.

[0035] n out is the refractive index of the medium through which the diffracted outgoing electromagnetic radiation propagates.

[0036] λ0 is the vacuum wavelength of electromagnetic radiation.

[0037] As mentioned, the above parameters are preferably selected depending on the final application of the diffractive optical element. As such, the wavelength of the electromagnetic radiation that should be irradiated and diffracted by the diffractive optical element and the refractive index of the substrate are known. The angle of the incident electromagnetic radiation and the angle of the diffracted outgoing electromagnetic radiation are also set depending on the final application. For example, if the diffractive optical element should be used in a virtual image display device, the angle of the incident electromagnetic radiation is preferably set to normal incidence relative to the direction perpendicular to the surface of the substrate, i.e. 0°, and the angle of the diffracted outgoing electromagnetic radiation is preferably selected to be 90° relative to the direction perpendicular to the surface of the substrate, so that the diffracted outgoing electromagnetic radiation propagates parallel to the surface plane of the substrate.

[0038] Preferably choose the phase The relief structure is made to diffract the incoming beam of electromagnetic radiation in a symmetrical or asymmetrical manner. That is, the phase determines the symmetry of the relief structure and therefore determines the symmetry of the optical diffraction, i.e. the diffraction of the electromagnetic radiation at the relief structure. If the phase is selected so that the relief structure is symmetrical, the diffractive optical element diffracts equal amounts of incident electromagnetic radiation to positive and negative angles in a direction perpendicular to the surface of the substrate relative to the direction of the surface modulation (i.e., along the first direction or the second direction of the diffractive optical element). If the phase is selected so that the relief structure is asymmetrical, the diffractive optical element diffracts unequal amounts of incident electromagnetic radiation to the left and right sides of the diffractive optical element. The latter enables the so-called routing of the diffracted electromagnetic radiation to a specific angular direction. The (asymmetrical) relief structure should be understood here as being (a)symmetrical in the first direction or the second direction relative to a mirror plane passing through the surface of the relief structure in the third direction. That is, the phase can be selected so that the relief structure is symmetrical in the first direction (second direction) relative to a mirror plane extending along a plane spanned by the second direction (first direction) and the third direction.

[0039] For example, the surface profile of a relief structure, i.e., the surface of the relief structure in a horizontal plane spanned by a first direction and a second direction, can be defined as a two-component sinusoidal curve, given by the expression Given, where A1=2*A2, k2=2*k1, the offset Δ is chosen arbitrarily, and the relative phase parameter Determine the mirror symmetry of the function along the x-axis about a given point. If the relative phase is chosen so that The resulting two-component sine function is mirror-symmetric about the given point along the x-axis. If the relative phase is chosen so that The resulting two-component sine function is not mirror-symmetric along the x-axis. These symmetric and asymmetric surface relief profiles will diffract incident electromagnetic radiation into positive and negative angles of outgoing diffracted light with equal and unequal intensities, respectively. For applications where the same intensity of diffracted light is required for both positive and negative angles of outgoing diffracted radiation, the symmetric case will be desirable. For applications where it is desirable to "route" diffracted electromagnetic radiation into specific diffraction orders, such as in blazed gratings, the asymmetric case will be desirable.

[0040] The two or more sinusoidal functions f n (x,y) is preferably summed in a Fourier series:

[0041] F(x, y) = ∑ n f n (x, y)

[0042] For example, if the diffractive optical element is to be used to diffract electromagnetic radiation comprising red at 650 nm, green at 550 nm and blue at 475 nm, then in a first step the sine function f as outlined above is calculated for each of these three colors, ie n=3. n =(x,y). In a second step, the three sine functions are summed in a Fourier series as known in the art.

[0043] The controller data is preferably generated by the following steps:

[0044] (i) using one or more preferred sinusoidal functions f in a computing device n (x, y) to define the relief structure to be generated in the horizontal plane, thereby obtaining a model relief structure; and

[0045] (ii) discretizing the model relief structure of step (i) into pixels in a computing device, thereby obtaining discretized controller data, which are preferably stored in a digital file, particularly preferably in a bitmap file.

[0046] The computing device may correspond to a commercially available computing device known in the art, for example including software tools It should be noted that any other software tool capable of calculating and further processing one or more of the functions mentioned above may also be used. In this way, the parameters defined above are input into a computing device, for example into a software tool In this case, the computing device then computes the model relief structure. That is, preferably by using the amplitude A n The predetermined value and / or spatial frequency k n The predetermined value and / or angular direction α n The predetermined value and / or phase The predetermined value and / or offset Δ n The model relief structure is calculated using predetermined values ​​of . Using a computing device, the model relief structure is then preferably discretized into pixels and the pixelated data is then stored in a digital file such as a bitmap file. The digital file includes controller data fed into a controller that controls the movement of the probe.

[0047] The pixel preferably has a length of about 1 nanometer to 1 micrometer, preferably about 10 nanometers, in the first direction and / or in the second direction. In addition, it is preferred if the pixel is provided in the form of a square or rectangular pixel. Additionally or alternatively, it is preferred that the pixel is discretized into depth levels with a number of depth levels of at least 2^(m) along the third direction in the above-mentioned step (ii), wherein m is at least 3, preferably at least 5, and particularly preferably at least 8. That is, the controller data preferably includes a pixelated model relief structure that is discretized into depth levels with a number of depth levels of at least 8, preferably at least 32, and particularly preferably at least 256 along the third direction. The controller is preferably configured to assign the depth level to an actual depth, wherein the actual depth corresponds to the depth of the desired relief structure along the third direction. For example, if the desired relief structure has a depth of 50 nanometers, and if the controller data includes a model relief structure with 256 depth levels along the third direction, the controller can be configured to act on the substrate along the third direction with a step size of about 0.2 nanometers (i.e. 50 nanometers divided by 256). When generating a relief structure in at least one of the first direction and the second direction, the force applied to the tip preferably varies according to the depth level stored in the digital file. In the case where the controller data is based on one or more functions that are continuous and possibly also smooth, the digital file can be said to correspond to a grayscale digital file, wherein the force of the tip is applied according to the grayscale of the file. In the preferred case of a bitmap file, the bitmap can be converted into a relief structure in the substrate, wherein the depth at a specific position in the first direction, the second direction and the third direction corresponds to a specific grayscale of the bitmap.

[0048] The substrate preferably includes or comprises a thermosensitive material, preferably a polymer, particularly preferably poly(methyl methacrylate-to-methacrylic acid), poly-o-phthalaldehyde (PPA) or CSAR. CSAR corresponds to a copolymer based on methyl styrene-to-α-chloromethylacrylate, wherein a halogenated acid generator is added due to being commercially available. Therefore, the substrate may include one or more polymers that are sensitive to heat. In this case, the heatable tip of the probe may be arranged on the surface of the substrate, and the substrate may be locally decomposed and / or removed at the position where the substrate contacts the hot tip. However, it is also conceivable to locally remove the material of the substrate only by the mechanical action of the tip or by a combination of the heating action and the mechanical action of the tip.

[0049] The generation of the relief structure by means of the processing device can be carried out in a manner known in the art. For example, it is conceivable to generate a relief structure in the surface of a substrate, thereby obtaining a diffractive optical element. Thus, the diffractive optical element can be produced according to a maskless, direct writing technique. However, depending on the final application of the diffractive optical element, it is also conceivable to use the substrate comprising the relief structure as a resist pattern, which is traced into other materials by means of, for example, stripping, etching, electroplating, molding, etc.

[0050] Thus, in one aspect, it is conceivable to apply at least one of a dielectric film or a metal film or a transition metal film, such as a silver film, on the relief structure, thereby generating a relief structure in the dielectric film or the metal film or the transition metal film. In another step, a curable resin, such as a UV-curable epoxy resin, can be deposited on the dielectric film or the metal film or the transition metal film. Again in another step, a carrier is applied to the curable resin, the carrier preferably comprising a dielectric material, such as glass, metal, transition metal, semiconductor material such as silicon, a polymerizable polymer or a polymer. In other words, the relief structure generated in the surface of the substrate is traced into the dielectric film or the metal film or the transition metal film. The curable resin can then be cured. In a next step, a template stripping can be performed, so that the carrier, the cured resin, and the dielectric film or the metal film or the transition metal film, which is a negative of the relief structure, are removed from the substrate. The template strip thus generated corresponds to a diffractive optical element having a profile that is a negative of the surface relief structure defining the template.

[0051] On the other hand, it is conceivable that the method further comprises the step of providing another substrate, wherein the other substrate has a surface and extends along the first direction, the second direction and the third direction. The substrate can be arranged on the surface of the other substrate, and the relief structure of the substrate can be etched into the surface of the other substrate. In this way, the relief structure of the substrate is traced into the surface of the other substrate. Thus, a diffractive optical element consisting of another substrate having a surface with a relief structure is produced.

[0052] It should be noted here that at least one of a dielectric film or a metal film or a transition metal film, such as a silver film, may also be applied to a relief structure generated in the surface of another substrate, wherein template stripping is subsequently performed as outlined above.

[0053] The other substrate may include or comprise at least one of a polymerizable material, a polymer, a metal, a transition metal such as silver, a semiconductor material such as silicon, or a dielectric material such as glass.

[0054] The substrate of untreated state and / or another substrate can have at least about 1 millimeter, preferably about 1 millimeter to 300 millimeters of lateral expansion in the first direction and / or in the second direction.The untreated state refers to the state that does not generate relief structure in the surface of substrate and another substrate respectively.Additionally or alternatively, it is contemplated that the substrate of untreated state and / or another substrate have about 1 nanometer to 1 centimeter, preferably about 100 microns to 1 millimeter of expansion in the third direction.Expansion in the third direction corresponds to the thickness of untreated substrate and another substrate respectively.

[0055] The relief structure preferably extends on the surface of the substrate and / or on the surface of another substrate, having a lateral extension in the first direction and / or in the second direction of between about 100 nanometers and 50 micrometers, preferably about 1 micrometer. In other words, the relief structure preferably has a field size of a pattern area in the first direction and in the second direction, which ranges between about 100 nanometers and 50 micrometers, preferably about 1 micrometer. In order to generate large relief structures, it is conceivable to stitch together one or more of these patterned areas on the surface of the substrate. Alternatively, it is also conceivable to generate a large relief structure consisting of a single large patterned area.

[0056] That is, one or more relief structures may be generated in the surface of the substrate - and if applicable in the surface of the other substrate, wherein the one or more relief structures are preferably arranged next to each other or spaced apart from each other with respect to the first direction and / or the second direction. In this way, it is conceivable to generate two or more relief structures while using the same or different controller data. In other words, the relief structures may have the same or different shapes.

[0057] In another aspect of the invention, a diffractive optical element is produced by the method as described above.

[0058] In another aspect, a diffractive optical element is provided that includes a substrate having a surface. The substrate extends in a first direction, in a second direction perpendicular to the first direction, and in a third direction perpendicular to the first and second directions. The surface includes a relief structure having a surface. At least in a portion of the relief structure, a distance between the surface of the relief structure and the surface of the substrate along the third direction varies substantially continuously along at least one of the first and second directions. When viewed along at least one of the first and second directions, at least a portion of the relief structure includes a plurality of protrusions and recesses, wherein at least one of the following:

[0059] i. the minimum horizontal distance between at least one of a) two consecutive protrusions and b) two consecutive recesses along at least one of the first direction and the second direction is less than about 1 micrometer, preferably less than about 20 nanometers, particularly preferably, the minimum distance is about 10 nanometers, and

[0060] ii. The minimum depth extending in the third direction and formed along at least one of the first direction and the second direction between at least one of a) two consecutive protrusions and b) two consecutive recesses is less than about 100 nanometers, preferably less than about 10 nanometers, and particularly preferably, the minimum depth is about 0.2 nanometers.

[0061] That is, the diffractive optical element includes a surface having a relief structure. The relief structure defines a surface. At least a portion of the relief structure is configured so that the distance between the surface of the relief structure and the surface of the substrate changes in a substantially continuous manner along the first direction and / or the second direction. Here, the expressions "substantially" and "continuous" should also be understood as described above. That is, the expression "continuous" should be understood in its mathematical sense, and the expression "substantially" should indicate that the relief structure is continuous within the range allowed by the processing device for generating the relief structure, especially its spatial resolution. To this end, it should be noted that the relief structure does not need to include only a portion, but can be completely composed of a continuous shape as just described. However, it is also conceivable that the relief structure may include at least a portion having a continuous shape as just described, but may also include one or more portions having different shapes, such as binary shapes. In addition, at least this portion - possibly the entire relief structure - includes the minimum horizontal distance and the minimum depth (or vertical distance) as just described. However, it is also conceivable that the relief structure includes other portions where the minimum horizontal distance and / or the minimum depth are greater than the minimum horizontal distance and the minimum depth. For example, the minimum horizontal distance may be less than about 100 microns, and the minimum depth may be less than 10 microns. In any case, the relief structure may include at least two or more successive projections or recesses with a greater horizontal distance and / or depth. For example, when viewed along the third direction, the depth of the relief structure between two successive recesses or projections may be greater than about 10 nanometers, preferably greater than about 30 nanometers, particularly preferably greater than about 50 nanometers. When viewed along the first direction and / or the second direction, the horizontal distance between two successive projections or recesses may be greater than about 100 nanometers, preferably greater than about 10 microns.

[0062] At least a portion of the relief structure may comprise periodic or aperiodic shapes when viewed along a first portion extending in a first direction and / or when viewed along a second portion extending in a second direction. These shapes are preferably the result of controller data controlling the probe of the processing device and are preferably based on one or more continuous functions such as one or more sinusoidal functions as described above.

[0063] At least part of the relief structure is preferably configured so that at least one electromagnetic radiation beam having a given wavelength can be incident on the portion of the relief structure at at least one desired incoming angle and can be diffracted at at least one desired outgoing angle. That is, at least part of the relief structure preferably has such a shape that an electromagnetic radiation beam having a given wavelength can be incident on the portion of the relief structure at any desired incoming angle, and then the electromagnetic radiation beam will be diffracted at the portion to any desired one or more outgoing angles. This can also be achieved for more than one electromagnetic radiation beam, wherein for each beam, at least part of the relief structure contains a periodic or non-periodic component that will diffract the beam from the desired incoming angle to the desired outgoing angle. In other words, at least part of the relief structure is preferably configured so that the momentum matching equation explained above is satisfied. Alternatively, it is also conceivable that at least part of the relief structure is configured so that at least one electromagnetic radiation beam incident on the portion of the relief structure at at least one desired incoming angle is diffracted from the portion of the relief structure in such a way that the diffracted outgoing electromagnetic radiation interferes to form a specific light field. If one electromagnetic radiation beam is incident on a portion of a relief structure, the interference pattern so generated consists of two or more interference wavefronts generated upon diffraction of said one incoming electromagnetic beam. However, the generation of an interference pattern consisting of two or more interference wavefronts of the two or more incoming beams is equally possible for the case where two or more incoming beams of electromagnetic radiation are diffracted from a portion of a relief structure such that the diffracted outgoing electromagnetic radiation interferes to form a specific light field. In other words, a portion of a relief structure may be configured such that one or more electromagnetic radiation beams are diffracted at the relief structure in such a way that the electromagnetic radiation beams interfere to produce a specific light field. Such relief structures are particularly desirable, for example, in the field of computer-generated holograms.

[0064] At least a portion of the relief structure may be configured such that a first electromagnetic radiation beam having at least a first wavelength and incident on the portion of the relief structure at a first incoming angle is diffracted at a first outgoing angle, and a second electromagnetic radiation beam having a second wavelength different from the first wavelength and incident on the portion of the relief structure at a second incoming angle is diffracted at a second outgoing angle, wherein:

[0065] i. The first incoming angle is substantially equal to the second incoming angle, and the first outgoing angle is substantially equal to the second outgoing angle, or

[0066] ii. the first incoming angle is substantially equal to the second incoming angle, and the first outgoing angle is different from the second outgoing angle, or

[0067] iii. the first incoming angle is different from the second incoming angle, and the first outgoing angle is substantially equal to the second outgoing angle, or

[0068] iv. The first incoming angle is different from the second incoming angle, and the first outgoing angle is different from the second outgoing angle.

[0069] The incoming angle and the outgoing angle are defined relative to a direction normal to the surface of the substrate.

[0070] As previously outlined, the method according to the invention enables the generation of relief structures suitable for the final application of a diffractive optical element. To this end, the surface relief structure can be generated by controller data based on one or more sine functions, wherein the amplitude A n , spatial frequency k n , angular direction α n , Phase and offset Δ n In this way, a surface relief structure can be generated which meets one of the criteria i. to iv. listed above.

[0071] For example, if the diffractive optical element is to be used as a so-called RGB coupler, i.e. a multicolor red-green-blue coupler, as it is preferably used in an augmented reality device, the relief structure is preferably configured according to the criterion i mentioned above. That is, the relief structure is preferably configured so that three electromagnetic radiation beams of different wavelengths (here: λ1=650nm, λ2=550nm, λ3=475nm) are incident on the relief structure at a common specific incoming angle and are diffracted at the relief structure at a common specific outgoing angle. The common incoming angle is defined relative to the direction perpendicular to the surface of the substrate and is preferably 0°. The common outgoing angle is defined relative to the direction perpendicular to the surface of the substrate and is preferably 90°. Therefore, the beams are diffracted at the relief structure in the following manner: the beams propagate parallel to each other and parallel to the surface of the substrate and perpendicular to the incident direction. However, it is also possible to produce a relief structure that is configured so that one or more electromagnetic radiation beams are diffracted at the relief structure in the following manner: the electromagnetic radiation beams interfere to produce a specific light field. Such a relief structure would be desirable, for example, in the field of computer-generated holograms.

[0072] In another aspect, a virtual image display device is provided, comprising: a radiation source, preferably an image display element, a substrate, and at least a first diffractive optical element and a second diffractive optical element as described above. The radiation source is configured to emit at least one electromagnetic radiation beam, preferably at least one image frame. The first diffractive optical element is arranged on or in the substrate, so that at least one electromagnetic radiation beam incident on the first diffractive optical element is coupled into the substrate and propagates along the substrate. The second diffractive optical element is arranged on or in the substrate, so that at least one electromagnetic radiation beam propagated is coupled out of the substrate.

[0073] In another aspect, a virtual image display device is provided, the virtual image display device comprising: a radiation source, a substrate, and at least one diffractive optical element as described above. The radiation source is configured to emit at least one electromagnetic radiation beam. The diffractive optical element is arranged on or in the substrate so that at least one electromagnetic radiation beam incident on the diffractive optical element is diffracted in a manner that the diffracted outgoing electromagnetic radiation interferes to form a specific light field.

[0074] It is conceivable that the virtual image display device includes a diffractive optical element, which is configured and arranged so that at least one electromagnetic radiation beam emitted from a radiation source is incident on the diffractive optical element, and wherein the at least one electromagnetic radiation beam is then diffracted in the following manner: the diffracted outgoing electromagnetic radiation interferes to form a specific light field. However, it is also conceivable that the virtual image display device includes two or more diffractive optical elements as described above. In this case, one of the diffractive optical elements can be used to couple the electromagnetic radiation emitted from the radiation source into a substrate, in which the electromagnetic radiation thus coupled inwardly propagates along the substrate. Another diffractive optical element can be configured and arranged on the substrate so that the propagated electromagnetic radiation is diffracted and coupled out of the substrate in the following manner: the diffracted outgoing electromagnetic radiation interferes to form a specific light field as described above.

[0075] In addition, it is conceivable that the image display device in each case includes one or more optical systems, such as a first optical system, which is configured to receive at least one electromagnetic radiation beam, such as an image frame from an image display element, and relay at least one electromagnetic radiation beam to a first diffractive optical element. The virtual image display may include another component, such as another optical system, wherein the other optical system is arranged and configured to, for example, receive at least one electromagnetic radiation, such as an image frame coupled out of the substrate, and relay the at least one electromagnetic radiation beam to the outside. The substrate in each case preferably corresponds to a material with a high refractive index. Such a substrate is also referred to as an optical waveguide. Therefore, the image display element, the optical system, and the optical waveguide preferably correspond to components known in the art. In addition, the virtual image display can be configured to be worn by the user.

[0076] The fact of using a diffractive optical element according to the invention enables a compact virtual image display device to be provided and at the same time enables full control of the Fourier spectrum of the image generated by the image display element and diffracted by the diffractive optical element. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] The preferred embodiments of the invention are described below with reference to the accompanying drawings, which are for the purpose of illustrating the current preferred embodiments of the invention, rather than for the purpose of limiting the invention.

[0078] Figure 1a shows a schematic illustration of a method for producing a diffractive optical element according to the invention in a first state, wherein a processing device comprising a probe is about to act on the surface of a substrate to generate a relief structure;

[0079] Figure 1b In the second state, according to Figure 1b Schematic illustration of a method for producing a diffractive optical element, wherein a processing device including a probe acts on the surface of a substrate;

[0080] Figure 2a Different manufacturing approaches for producing diffractive optical elements according to the method of the invention are shown;

[0081] Figure 2b Shown by Figure 2a Schematic illustration of different diffractive optical elements obtained by the manufacturing route;

[0082] Figure 3 shows a schematic illustration of the physical relationship applied to determine the spatial frequency of a relief structure according to the method of the invention;

[0083] Figure 4 shows a schematic illustration of a possible diffraction scenario when electromagnetic radiation strikes a relief structure of a diffractive optical element according to another embodiment of the invention;

[0084] Figure 5 shows a schematic illustration of another possible diffraction scenario when electromagnetic radiation strikes a relief structure of a diffractive optical element according to another embodiment of the invention;

[0085] Figure 6 shows that when electromagnetic radiation strikes the Figure 5 The relief structure of the diffractive optical element is a schematic illustration of another possible diffraction scenario;

[0086] Figure 7 shows a schematic illustration of another possible diffraction scenario when electromagnetic radiation strikes a relief structure of a diffractive optical element according to another embodiment of the invention;

[0087] Figure 8a A bitmap showing a single sinusoidal model relief structure;

[0088] Figure 8b Shown along Figure 8a A cross section of the bitmap intercepted by the dotted line AA;

[0089] Figure 9a shows the topography of a diffractive optical element according to the invention comprising a relief structure in the shape of a single sinusoidal profile;

[0090] Figure 9b Shown along Figure 9a The cross section of the morphology is taken by the dotted line BB;

[0091] Fig.10a shows a scanning electron micrograph of a diffractive optical element according to the invention comprising a relief structure in the shape of a single sinusoidal profile;

[0092] Fig.10b Shown in accordance with Fig.10a Spectrally resolved reflectance measurements of diffractive optical elements at normal incidence;

[0093] Fig.11a A bitmap of a three-component sinusoidal model relief structure is shown;

[0094] Fig.11b Shown along Fig.11a A cross section of the bitmap intercepted by the dotted line CC;

[0095] Fig.12a shows the topography of a diffractive optical element including a relief structure in the shape of a three-component sinusoidal profile according to the invention;

[0096] Figure 12b Shown along Fig.12a The cross section of the morphology is taken by the dotted line DD;

[0097] Fig.13a shows a scanning electron micrograph of a diffractive optical element according to the invention comprising a relief structure in the shape of a three-component sinusoidal profile;

[0098] Fig.13b shows a spectrally resolved reflection measurement at normal incidence for a diffractive optical element according to FIGS. 11 and 12 ;

[0099] Fig.14a A bitmap showing a relief structure of a two-dimensional model;

[0100] Fig.14b Shown according to Fig.14a The morphological data of the two-dimensional model relief structure;

[0101] Fig.14c Shown includes from according to Fig.14a and Fig.14b Scanning electron micrograph of the diffractive optical element with a relief structure obtained from the bitmap and topographic data;

[0102] Fig.14d Shown according to Fig.14c k-space reflection measurement of diffractive optical elements;

[0103] Fig.15 shows a schematic illustration of a virtual image display device including a diffractive optical element according to the invention;

[0104] Fig.16 A schematic illustration of another virtual image display device comprising a diffractive optical element according to the invention is shown. DETAILED DESCRIPTION

[0105] exist Figures 1a to 2b In, different aspects are disclosed regarding a method according to the invention for producing a diffractive optical element 1 comprising a relief structure 2. Figures 3 to 7 The basic physical relationships associated with the generation of the relief structure 2 and the resulting diffraction scene are shown in FIG. Fig.14d , different examples of diffractive optical elements 1 according to the invention are shown and aspects regarding their production and characterization are discussed.

[0106] Therefore, according to the following Figure 1a and Figure 1b , the method for producing a diffractive optical element 1 according to the invention comprises the following steps: providing at least one substrate 3 having a surface 4, and producing a relief structure 2 in the surface 4 of the substrate 3 using a processing device 5. The substrate 3 extends in a first direction x, a second direction y perpendicular to the first direction x, and a third direction z perpendicular to the first direction x and the second direction y. The surface 4 of the substrate 3 extends in the first direction x and the second direction y, which span a horizontal plane xy. The processing device 5 comprises a probe 6 having a tip 7. The tip 7 has a radius R of approximately 10 nanometers. The probe 6, and therefore the tip 7, is movable relative to the substrate 3 in the first direction x, the second direction y and the third direction z. The relief structure 2 is generated by the action of the tip 7 on the surface 4 of the substrate 3, so that the distance D between the surface 8 of the relief structure 2 and the surface 4 of the substrate 3 along the third direction z varies substantially continuously along at least one of the first direction x and the second direction y, see for example Figures 4 to 7 , Figure 9a , Fig.10a , Fig.12a , Fig.13a and Fig.14c . As follows Figure 1b, for example, the surface 4 of the substrate 3 is understood to be the surface of the substrate 3 before the substrate 3 is treated by the treatment device 5. In other words, after the treatment of the substrate 3 by the treatment device 5, the surface 4 corresponds to the surface of the substrate outside the area comprising the relief structure 2. This in turn means that the surface 8 of the relief structure 2 corresponds to the surface of the substrate 3 comprising the relief structure 2. The probe 6 can be moved in the first direction x and in the second direction y with a step length of about 0.1 nanometers to 50 micrometers, for example with a step length of less than about 20 nanometers, and the probe 6 can be moved in the third direction z with a step length of about 0.1 nanometers to 1 micrometer, preferably with a step length of less than about 2 nanometers. Due to these small movement steps, a relief structure 2 comprising a plurality of recesses 9 and protrusions 10 is generated, wherein the minimum horizontal distance hd between two consecutive protrusions 10 and the recesses 9 along the first direction x and the second direction y is about 10 nanometers, and the minimum depth vd extending in the third direction z is about 0.2 nanometers. The tip 9 is also configured to scan the surface 8 of the relief structure 2 when it acts on the surface 4 of the substrate 3. This creates a closed-loop feedback system that results in an accurate and precise profile of the surface relief structure 2. The reading process consists of Figure 1b The wavy arrows in FIG.

[0107] The specific movement of the probe 6 is performed according to specific controller data which are fed to a controller 11 of a processing device 5 configured to control the probe 6. The controller data define the relief surface 2 along a horizontal plane xy and are based in this example on a sinusoidal function f n＝1 (x,y)(See Figures 8a to 10b ) or based on three sine functions f n＝3 (x,y)(See Figures 11a to 13b ),in, However, it should be noted that any number of sine functions is conceivable. In the case of two or more sine functions, the sine functions are summed in a Fourier series F(x, y)=∑ n f n (x, y). The parameters in this expression correspond to the amplitude A n , spatial frequency k n , angular direction α along the horizontal plane xy n , Phase and the offset Δ relative to the third direction z n .

[0108] According to the following Figure 2a , the one sine function or Fourier series is generated in the computing device 12, thereby obtaining the so-called model relief structure of the Fourier surface design. In the next step, the model relief structure is discretized into pixels, thereby obtaining discretized controller data stored in a digital file such as a bitmap file. Figure 2a Since the continuity provided by the sine function here results in a grayscale bitmap, this step is referred to as grayscale bitmap generation. Depending on the desired end application of the diffractive optical element 1 , a suitable manufacturing scheme is then selected for the further production of the diffractive optical element 1 .

[0109] Further as follows according to Figure 1, Figure 2a and Figure 2b , the different manufacturing schemes include direct writing, etching or template stripping as known in the art. That is, the substrate 3 can be a polymer such as PPA or PMMA / MA, wherein the relief structure 2 is generated into the surface 4 of the substrate 3 by the action of the probe 6 on the surface 4, and the diffractive optical element 1 is obtained thereby. This process is depicted in FIG. 1 . However, and as follows according to Figure 2b , it is also conceivable to apply such a polymer substrate 3 to the surface 15 of another substrate 14 by means of spin coating, for example, see step (a). In the next step (b), a relief structure 2 is generated in the surface 4 of the polymer applied to the other substrate 14 by means of a tip 7 acting on the surface 4. Thereby, another diffractive optical element 1 is generated. However, if the two-layer structure consisting of the polymer substrate 3 and the other substrate 14 is subjected to an etching process or a template stripping process, a different diffractive optical element 1 is obtained, see step (c). In the former case, a dielectric film or a metal film or a transition metal film such as a silver film 16 can be applied to the relief structure 2 generated in the polymer layer 3, thereby generating a relief structure 2 in the film 16, see step (d). In a further step, a curable resin such as a UV curable epoxy resin is deposited on the film 16. Again in a further step (e), a carrier 19 such as a glass plate is applied to the curable resin. The curable resin is then cured in a next step (f), the carrier 19, the cured resin and the film 16 including the relief structure 2 are removed from the substrate 3. The relief structure 2 thus produced, generated by template stripping, corresponds to the diffractive optical element 1. In the present example, the production of such a grayscale diffractive optical element 1 is carried out by means of a tip 7 heated to a temperature of about 750° C., a typical pixel size of about 10 nm, a total depth of the relief structure 2 in the third direction z of about 50 nm to 100 nm, and a dimension of the relief structure 2 in the horizontal plane xy of about 10 micrometers to 20 micrometers.

[0110] In the following, different diffractive optical elements 1 obtained by the method according to the invention are discussed in more detail. Common to all these diffractive optical elements 1 is that the controller data for controlling the probe 6 of the processing device 5 is based on one or more sinusoidal functions with predetermined values ​​of its parameters.

[0111] One of the basic physical principles utilized corresponds to the momentum matching principle, which enables the spatial frequency of the relief structure 2 of the diffractive optical element 1 to be selected so that the in-plane wave vector of the incident electromagnetic radiation matches the in-plane wave vector of the outgoing electromagnetic radiation. Said principle is described in more detail in the "Summary of the Invention" section of the present application and in Figure 3 It is schematically shown in Figure 3 middle, is the in-plane wave vector of the outgoing electromagnetic radiation, is the in-plane wave vector of the incident electromagnetic radiation, is a unit vector along the direction of propagation of the incident electromagnetic radiation, is the wave vector of the diffractive optical element 1, and θ in is the angle of the incident electromagnetic radiation relative to the normal direction (dashed line).

[0112] exist Figures 4 to 7 In , different conceivable diffraction scenarios are depicted. That is, in Figure 4 In the case of electromagnetic radiation EM with a given wavelength in At an angle θ in is incident on the relief structure 2 of the diffractive optical element 1 according to the invention. In this example, the electromagnetic radiation EM in The incident electromagnetic radiation EM may be incident from above the relief structure 2, for example from a top layer (not shown) applied on top of the surface 4 of the substrate 3 comprising the relief structure 2. It should be noted that the top layer is not necessary. Rather, it is also conceivable that there is no top layer and that the electromagnetic radiation is incident from a vacuum environment or an air environment. Furthermore, it should be noted that the electromagnetic radiation may be incident on the relief structure 2 from any direction, for example from within the substrate 3 comprising the relief structure 2 or from below. The incident electromagnetic radiation EM in As outgoing electromagnetic radiation EM out diffracted from the relief structure 2 and, depending on the design of the relief structure 2, the incident electromagnetic radiation EM in can be diffracted so that it returns to the top layer (θ diff,1 ) direction and enter the substrate 3 (θ diff,2 ), or diffracted through the substrate 3 to the other side (θ diff,3 ). Figure 5 An embodiment of a grayscale diffractive optical element 1 according to the invention is depicted, wherein a relief structure 2 is produced directly in a substrate 3 as a waveguide layer, so that incident electromagnetic radiation EM from a top layer (not shown) in diffracted into a waveguide mode EM that travels along the substrate 3 out . Figure 6 An embodiment of a grayscale diffractive optical element 1 is depicted, in which a relief structure 2 is produced directly in a substrate 3 as a waveguide layer, so that incident electromagnetic radiation EM indiffracted into the top layer (not shown) as EM out The same can be achieved for the modes diffracted into the bottom layer of the diffractive optical element 1. In particular, Figure 7 An embodiment of a diffractive optical element 1 according to the invention is depicted, which acts as an RGB coupler in a waveguide layer stack typically used in augmented reality devices. Here, the substrate 3 in the form of a top layer corresponds to a layer made of a polymer with a high refractive index, such as CSAR. However, other materials with a high refractive index are also conceivable. The top layer has a higher refractive index than another substrate 14 in the form of an intermediate layer, so that the top layer supports waveguide modes. Conceivable materials for the intermediate layer 14 are thermally grown silicon dioxide (SiO2) and the like. Red, green and blue EM in (further distinguished by the letters "R", "G" and "B") arrive at the diffractive optical element 1 from normal incidence and diffract into an angle such that it couples into the waveguide mode and acts as an EM out Furthermore, a further substrate 17 forming a bottom layer is arranged behind the intermediate layer 14 when looking from the top layer 3 towards the intermediate layer 14 in the third direction z. The bottom layer 17 may be made of silicon, but other materials are also conceivable.

[0113] As mentioned initially, depending on the final application of the diffractive optical element 1, the controller data may be based on the amplitude A n , spatial frequency k n , angular direction α n , Phase and offset Δ n - which is used to define the model relief structure 18 based on the sine function. Figure 8a A grayscale bitmap 13 depicts a single sinusoidal surface relief. The sinusoidal modulation is along a first direction x, and the model relief structure 18 is constant along a second direction y. The bitmap 13 is constructed from square pixels with a side length of 10 nm. The model relief structure 18 is divided into 256 depth levels (8-bit precision) along a third direction z, see Figure 8b .

[0114] Figure 9a Depicted is the topography of a single sinusoidal relief structure 2 generated in a polymer resist 3. The topography was measured in situ during the patterning process by a thermal scanning probe 6. The greyscale color map indicates the height of the measured points, where the zero value is normalized to a flat surface 4 outside the patterned area 2. Figure 9a The dashed lines in are cross-sections of the topography averaged over 1 micron (100 pixels). The black line is a fit to the desired relief structure 2, in this case a single sine curve, which was used to generate the bitmap 13 and the relief structure 2. The fitted sine function is given by the formula The fitting parameters return 24.8nm, 10.1 microns-1 , -3.14 radians, and -32.9 nm are used to define the parameters of the amplitude, spatial frequency, phase, and offset of the sine function, respectively.

[0115] Fig.10a Depicted is a scanning electron micrograph of a single sinusoidal relief structure 2 generated on a silver surface 16. The relief structure 2 was traced onto the silver surface 16 using template lift-off, wherein Figure 9a The polymer surface in 4 was used as a template. Fig.10b Corresponds to Fig.10a Spectrally resolved reflectance measurement at normal incidence of a single sinusoidal relief structure 2 on a silver surface 16 depicted in FIG. The drop in reflectivity at a photon energy of about 1.9 eV shows that electromagnetic radiation incident on the relief structure 2 is diffracted into modes that propagate along the silver surface 16 .

[0116] Fig.11a A grayscale bitmap 13 for a three-component sinusoidal model relief structure 18 is depicted. The sinusoidal modulation is along a first direction x, and the model relief structure 18 is constant along a second direction y. The bitmap 13 is constructed using square pixels with a side length of 10 nm. The model relief structure 18 is divided into 256 depth levels (8-bit precision) along a third direction z, see Fig.11b .

[0117] Fig.12a Depicted is the topography of a three-component sinusoidal relief structure 2 in a polymer resist 3. The topography was measured in situ during the patterning process by a thermal scanning probe 6. The greyscale color map indicates the height of the measured points, where the zero value is normalized to a flat surface 4 outside the patterned area 2. Figure 12b The cross section depicted in is averaged over 1 micron (100 pixels). The black line is a fit to the desired relief structure, in this case a three-component sine curve, which was used to generate the bitmap 13 and the model relief structure 18. The fitted sine function is given by the formula The fitting parameters return 10.5nm, 10.1 microns -1 The values ​​of -3.0 radians are used to define the parameters of the amplitude, spatial frequency, and phase of the first sine function, respectively. The fitting parameters return 8.8 nm, 12.1 microns -1 The values ​​of -1.3 radians are used to define the parameters of the amplitude, spatial frequency, and phase of the second sine function, respectively. The fitted parameters return 7.6 nm, 14.1 microns -1 The values ​​of 0.95 radians and 0.95 radians are used to define the parameters of the amplitude, spatial frequency and phase of the third sine function respectively. The fit parameters return a value of -34.9 nm for the offset parameter.

[0118] Fig.13aA scanning electron micrograph of a three-component sinusoidal relief structure 2 on a silver surface 16 is depicted. The relief structure 2 is traced onto the silver surface 16 using template lift-off, wherein the Fig.12a A polymer surface similar to the polymer surface depicted in 4 was used as a template. Fig.13b Spectrally resolved reflectance measurements corresponding to a three-component sinusoidal relief structure 2 on a silver surface 16 at normal incidence, with profiles from Figures 11 and 12. The drop in reflectivity at photon energies of about 1.9 eV, about 2.2 eV, and about 2.6 eV shows that light with these specific wavelengths at normal incidence on the relief structure 2 is diffracted into modes that propagate along the silver surface 16.

[0119] Fig.14a A bitmap 13 depicts a two-dimensional greyscale model relief structure 18 (quasicrystal with 8-fold rotational symmetry). Fig.14b The topographic data of the two-dimensional grayscale pattern is depicted. Fig.14c A scanning electron micrograph of the two-dimensional greyscale relief structure 2 is depicted. Fig.14d Corresponds to a k-space reflectometry of a two-dimensional greyscale relief structure 2 showing 8-fold rotational symmetry.

[0120] Fig.15 and Fig.16 Different embodiments of a virtual image display device 20 comprising a diffractive optical element 1 according to the invention are depicted. In particular, Fig.15 A virtual image display device 20 is depicted, comprising a radiation source in the form of an image display element 21, an optical system in the form of a lens 22, for example a collimating lens, a substrate 3 in the form of an optical waveguide, and three diffractive optical elements 1 according to the invention. The image display device 21 is configured to generate an image frame EM in , the image frame EM in By means of a lens 22, it is collimated onto a first diffractive optical element 1a arranged in the surface 4 of the optical waveguide 3. The first diffractive optical element 1a is configured so that the incident image frame EM in is coupled into the optical waveguide 3 and can propagate along the optical waveguide 3. Due to the surface profile of the relief structure 2 of the first diffractive optical element 1a, the incident image frame EM in The image frames are diffracted so that they propagate in opposite directions within the optical waveguide 3. One of the propagated image frames is then coupled out of the optical waveguide 3 at the second diffractive optical element 1b, and the other of the propagated image frames is coupled out of the optical waveguide 3 at the third diffractive optical element 1c. Fig.15 , the second diffractive optical element 1b and the third diffractive optical element 1c are configured so that the outcoupled beam EM out spread parallel to each other.

[0121] according to Fig.16The virtual image display device 20 comprises a first diffractive optical element 1a, which is configured so that incident electromagnetic radiation is coupled into a substrate 3 in the form of an optical waveguide. In this example, the relief structure 2 of the first diffractive optical element 1a is configured so that three beams of electromagnetic radiation with different wavelengths are coupled into the optical waveguide. Here, the three beams correspond to red EM in,R 、Green Light EM in,G and Blu-ray EM in_B The first diffractive optical element 1a is also configured so that the three beams propagate parallel to each other and parallel to the surface 4 of the optical waveguide 3. When the propagating beams are incident on the second diffractive optical element 1b, the beams are coupled out of the second diffractive optical element. In this example, the second diffractive optical element 1b is configured so that the outcoupled beam EM out The light beams interfere with each other, thereby generating an interference pattern to form a specific light field. The interference pattern can constitute a hologram, for example.

[0122] Here, the virtual image display device 20 according to both figures comprises a substrate 3 in the form of an optical waveguide made of a material with a high refractive index. The optical waveguide is arranged on another substrate 14 in the form of an intermediate layer, which in turn is arranged on a bottom layer 17, as described above with reference to Figure 7 as described.

[0123] The diffractive optical element 1 depicted in the accompanying drawings is produced by using poly(methyl methacrylate-co-methacrylic acid) (PMMA / MA, 33% methacrylic acid, AR-P 617.03, Allresist) as a thermosensitive polymer in which a grayscale relief structure 2 is generated, i.e., patterning is performed using thermal scanning probe lithography. As another substrate, a 2-inch silicon wafer was taken directly out of the factory packaging without any cleaning or additional preparation steps. A PMMA / MA film with a thickness of about 150 nm was spin-coated on a silicon substrate using a two-step spin coating process (step 1: 5 seconds spin time, 500 rpm spin speed, 500 rpm / s acceleration. Step 2: 40 seconds spin time, 2000 rpm spin speed, 2000 rpm / s acceleration). After spin coating, the substrate with the PMMA / MA layer was baked on a hot plate at 180° C. for 5 minutes.

[0124] The model relief structure - here a grayscale model relief structure - was designed in MATLAB. An analytical sine function was used to define the model relief structure. The model relief structure was then discretized into square pixels with a side length of 10 nm in the first direction x and the second direction y. The depth of the relief structure 2 along the third direction z was discretized into 256 depth levels to generate an 8-bit grayscale bitmap.

[0125] A grayscale relief structure 2 is made in the PMMA / MA layer using a commercial thermal scanning probe lithography tool 5 (NanoFrazor Explore, SwissLitho AG). The bitmap relief structure, i.e., discretized controller data, is uploaded to the tool, where 8-bit depth information is assigned to the physical pattern depth in the PMMA / MA layer. A silicon-based thermal scanning probe cantilever 6 (provided by SwissLitho AG) is loaded into the tool 5. The tool 5 is calibrated in the first direction x, the second direction y, and the third direction z by writing simple patterns in the PMMA / MA layer, measuring the topography of these patterns in situ, and adjusting the tip 7 temperature and writing force to minimize the error between the pattern design and the measured pattern depth. After calibration, the tool performs the desired patterning function.

[0126] After patterning, the PMMA / MA layer serves as a template for drawing a grayscale surface pattern or relief structure 2 onto the silver surface. The patterned polymer template is loaded into a thermal evaporator (Kurt J. Lesker Nano36) which is evacuated to a vacuum level of about 1×10-7 Torr. Evaporation was performed using silver particles (99.99%, Kurt J. Lesker) at a deposition rate of 1000 nm to cover the template with a high quality optically thick silver film (>500 nm). After evaporation, a UV curable epoxy was deposited on the silver film and a glass microscope slide was placed on top. The epoxy was cured under a UV lamp for 2 hours, after which the silver film was removed from the template, resulting in a grayscale surface pattern 2 on the smooth side of the silver film that was in contact with the template.

[0127] Optical measurements were performed using an inverted optical microscope (Nikon, Ti-U) with an air objective. The sample was illuminated with a broadband halogen lamp, and the reflected light was collected and imaged onto a complementary metal oxide semiconductor (CMOS) camera attached to a grating spectrometer. A beam splitter was used to separate the illumination and reflected light. A linear polarizer was placed in the collection path to filter out TE polarized light.

[0128] Reference Mark List

[0129] 1, 1a, 1b, 1c Diffractive optical elements

[0130] 2 Relief structure

[0131] 3. Substrate

[0132] 4. Surface of the substrate

[0133] 5. Processing device

[0134] 6 Probe

[0135] 7 Tip

[0136] 8 Surface with relief structure

[0137] 9 recess

[0138] 10 Bump

[0139] 11 Controller

[0140] 12 Computing Devices

[0141] 13 Bitmap

[0142] 14 Another substrate

[0143] 15 Surface of another substrate

[0144] 16 Membrane

[0145] 17 Another substrate

[0146] 18 Model relief structure

[0147] 19 Carrier

[0148] 20 Virtual image display device

[0149] 21 Image display element

[0150] 22 Optical System

[0151] x first direction

[0152] y Second direction

[0153] z The third direction

[0154] xy horizontal plane

[0155] D Distance

[0156] R Radius

[0157] hd horizontal distance

[0158] vd Depth

[0159] EM in Incident electromagnetic radiation

[0160] EM out Outgoing electromagnetic radiation

Claims

1. A method for producing a diffractive optical element (1), comprising the following steps: - providing at least one substrate (3), said at least one substrate (3) having a surface (4) extending in a first direction (x) and in a second direction (y) perpendicular to said first direction (x); as well as - generating a relief structure (2) in the surface (4) of the substrate (3) using a processing device (5); The processing device (5) comprises a probe (6) having a tip (7), wherein the tip (7) has a radius (R) of less than 1 micron, and wherein the probe (6) is movable relative to the substrate (3) in the first direction (x), the second direction (y) and a third direction (z) perpendicular to the first direction (x) and the second direction (y), and wherein the relief structure (2) is generated by the action of the tip (7) on the surface (4) of the substrate (3) so that the distance (D) between the surface (8) of the relief structure (2) and the surface (4) of the substrate (3) along the third direction (z) varies substantially continuously along at least one of the first direction (x) and the second direction (y), The processing device (5) further comprises a controller (11), wherein the controller (11) is configured to control the probe (6) based on controller data fed into the controller (11), wherein the controller data defines the relief structure (2) along a horizontal plane (xy) spanned by the first direction (x) and the second direction (y), Characterized in that the controller data is based on two or more sinusoidal functions f(x,y), and Wherein, the two or more sinusoidal functions are represented by the following expressions: Among them, parameter A n is the amplitude, Among them, the parameter k n is the spatial frequency, Among them, the parameter α n is the angular direction along the horizontal plane (xy), Among them, the parameters is the phase, and Among them, the parameter Δ n is the offset relative to the third direction (z), and wherein the probe (6) moves according to controller data fed to the controller (11) of the processing device (5), and The controller data is generated by the following steps: (i) using two or more sine functions f in the computing device (12) n (x, y) to define said relief structure (2) to be generated in said horizontal plane (xy), thereby obtaining a model relief structure (18); and (ii) discretizing the model relief structure (18) of step (i) into pixels in the computing device (12), thereby obtaining discretized controller data.

2. The method according to claim 1, wherein: The relief structure (2) is generated by mechanical and / or thermal action of the tip (7) on the surface (4) of the substrate (3), and / or Wherein, when generating the relief structure (2), the tip (7) directly contacts the surface (4) of the substrate (3), and / or Wherein, the processing device (5) is a thermal scanning probe lithography device.

3. The method according to claim 1 or 2, wherein: The probe (6) moves in the first direction (x) and / or in the second direction (y) with a step size of 0.1 nanometer to 50 micrometers, and / or wherein the probe (6) moves in the third direction (z) with a step length of 0.1 nanometer to 1 micrometer, and / or Wherein, the probe (6) moves in the first direction (x) and / or the second direction (y) at a rate between 1 Hz and 1000 kHz.

4. The method according to claim 1 or 2, wherein: The two or more sinusoidal functions f n (x,y) sums up in Fourier series: F(x,y)=∑ n f n (x,y)。 5. The method according to claim 1 or 2, wherein: applying at least one of a dielectric film or a metal film on the relief structure (2), thereby generating the relief structure (2) in the dielectric film or the metal film, wherein a curable resin is deposited on the dielectric film or the metal film, wherein a carrier (19) is applied to the curable resin, wherein the curable resin is cured, and The template stripping is performed so that the carrier (19), the cured resin, and the dielectric film or the metal film including the negative of the relief structure (2) are removed from the substrate (3).

6. The method according to claim 1 or 2, further comprising the step of providing another substrate (14), in, The further substrate (14) has a surface (15) extending in the first direction (x) and the second direction (y), wherein the substrate (3) is arranged on a surface (15) of the other substrate (14), and Therein, the relief structure (2) of the substrate (3) is etched into the surface (15) of the further substrate (14).

7. The method according to claim 6, wherein: The relief structure (2) of the substrate (3) and the relief structure (2) of the further substrate (14) are arranged adjacent to one another or spaced apart from one another with respect to the first direction (x) and / or the second direction (y).

8. The method according to claim 1, wherein: The tip (7) has a radius (R) of less than 20 nanometers.

9. The method according to claim 3, wherein: The probe (6) moves in the first direction (x) and / or in the second direction (y) with a step size of 0.1 nanometers to 100 nanometers.

10. The method according to claim 3, wherein: The probe (6) moves in the first direction (x) and / or in the second direction (y) with a step size of 5 nanometers to 50 nanometers.

11. The method according to claim 3, wherein: The probe (6) moves in the first direction (x) and / or in the second direction (y) with a step size of less than 20 nanometers.

12. The method according to claim 3, wherein: The probe (6) moves in the third direction (z) with a step size of 0.2 nanometers to 25 nanometers.

13. The method according to claim 3, wherein: The probe (6) moves in the third direction (z) with a step size of less than 2 nanometers.

14. The method according to claim 3, wherein: The probe (6) moves in the first direction (x) and / or the second direction (y) at a rate between 1 kHz and 500 kHz.

15. The method according to claim 1 or 2, wherein: The discretized controller data is stored in a digital file, or in a bitmap file.

16. The method according to claim 5, wherein: The metal film is a transition metal film.

17. The method according to claim 16, wherein: The transition metal film is a silver film (16), and / or Wherein, the curable resin is a UV-curable epoxy resin, and / or Wherein, the carrier (19) comprises a dielectric material, a metal, a semiconductor material, or a polymer.

18. The method according to claim 17, wherein: The dielectric material is glass, and / or the metal is a transition metal, and / or the semiconductor material is silicon.

19. A diffractive optical element (1) produced by the method according to claim 1.

20. The diffractive optical element (1) according to claim 19, wherein: When viewed along at least one of the first direction (x) and the second direction (y), at least a portion of the relief structure (2) comprises a plurality of protrusions (10) and recesses (9), wherein at least one of the following is true: i. the minimum horizontal distance (hd) between at least one of a) two consecutive protrusions (10) and b) two consecutive recesses (9) along at least one of the first direction (x) and the second direction (y) is less than 1 micrometer, and ii. the minimum depth (vd) extending in the third direction (z) and formed along at least one of the first direction (x) and the second direction (y) between at least one of a) two consecutive protrusions (10) and b) two consecutive recesses (9) is less than 100 nanometers, It is characterized in that the surface profile of the relief structure is defined as comprising two or more sinusoidal functions f represented by the expression n The sine curve of (x,y), and Wherein, at least one of the amplitude, the spatial frequency, the angular direction, the phase or the offset causes the diffractive optical element to be configured to diffract one or more specific incident beams of a given wavelength into one or more specific desired directions.

21. The diffractive optical element (1) according to claim 19 or 20, wherein: At least a portion of the relief structure (2) is configured to enable at least one electromagnetic radiation beam having a given wavelength to be transmitted at at least one desired incoming angle (θ in ) is incident on the portion of the relief structure (2) and is capable of transmitting at at least one desired outgoing angle (θ out ) under diffraction.

22. The diffractive optical element (1) according to claim 19 or 20, wherein: At least a portion of the relief structure (2) is configured to have at least a first wavelength and at a first incoming angle (θ in,1 ) is incident on said portion of said relief structure (2) at a first exit angle (θ out,1 ) and having a second wavelength different from the first wavelength (λ1) and at a second incoming angle (θ in,2 ) is incident on said portion of said relief structure (2) at a second electromagnetic radiation beam at a second outgoing angle (θ out,2 ) where: i. The first incoming angle (θ in,1 ) is equal to the second incoming angle (θ in,2 ), and the first outgoing angle (θ out,1 ) is equal to the second outgoing angle (θ out,2 ),or ii. The first incoming angle (θ in,1 ) is equal to the second incoming angle (θ in,2 ), and the first outgoing angle (θ out,1 ) is different from the second outgoing angle (θ out,2 ),or iii. The first incoming angle (θ in,1 ) is different from the second incoming angle (θ in,2 ), and the first outgoing angle (θ out,1 ) is equal to the second outgoing angle (θ out,2 ),or iv. The first incoming angle (θ in,1 ) is different from the second incoming angle (θ in,2 ), and the first outgoing angle (θ out,1 ) is different from the second outgoing angle (θ out,2 ).

23. The diffractive optical element (1) according to claim 21, wherein: The relief structure is configured to cause the at least one beam of electromagnetic radiation to diffract in such a way that diffracted outgoing electromagnetic radiation interferes to form a specific light field.

24. The diffractive optical element (1) according to claim 20, wherein: The minimum horizontal distance (hd) is less than 20 nanometers.

25. The diffractive optical element (1) according to claim 20, wherein: The minimum horizontal distance (hd) is 10 nanometers.

26. The diffractive optical element (1) according to claim 20, wherein: The minimum depth (vd) is less than 10 nanometers.

27. The diffractive optical element (1) according to claim 20, wherein: The minimum depth is 0.2 nanometers.

28. A virtual image display device (20), comprising: - radiation sources, - a substrate (3), and at least a first diffractive optical element (1a) and a second diffractive optical element (1b), each of which is a diffractive optical element (1) as claimed in any one of claims 19 to 20, wherein the radiation source is configured to emit at least one electromagnetic radiation beam; wherein the first diffractive optical element (1a) is arranged on or in the substrate (3) so that the at least one electromagnetic radiation beam incident on the first diffractive optical element (1a) is coupled into the substrate (3) and propagates along the substrate (3), and The second diffractive optical element (1b) is arranged on or in the substrate (3) so that at least one propagating electromagnetic radiation beam is coupled out of the substrate (3).

29. The virtual image display device (20) according to claim 28, wherein: The radiation source is an image display element (21), and / or Wherein, the radiation source is configured to emit at least one image frame.

30. A virtual image display device (20), comprising: - radiation sources, - a substrate (3), and - at least one diffractive optical element (1a, 1b) as claimed in any one of the preceding claims 19 to 20, wherein the radiation source is configured to emit at least one electromagnetic radiation beam; The diffractive optical element (1a, 1b) is arranged on or in the substrate (3) so that the at least one electromagnetic radiation beam incident on the diffractive optical element (1) is diffracted in such a way that the diffracted outgoing electromagnetic radiation interferes to form a specific light field.

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