Exposure parameter determination method and apparatus for volume holographic grating, and two-dimensional exit pupil expansion volume holographic optical waveguide

Abstract

Provided in the present application are an exposure parameter determination method and apparatus for a volume holographic grating, and a two-dimensional exit pupil expansion volume holographic optical waveguide. The method comprises: when the wavelengths of a first light beam and a second light beam are a first recording wavelength, rotating a vector of the first light beam, a vector of the second light beam, and a holographic photosensitive material multiple times, so as to obtain rotated vectors of the first light beam and the second light beam, and a rotated material position of the holographic photosensitive material; shifting the wavelengths of the first light beam and the second light beam to a second recording wavelength, and rotating at least once the rotated vectors of the first light beam and the second light beam, so as to obtain in-material vectors of the first light beam and the second light beam; on the basis of the in-material vectors of the first light beam and the second light beam, determining in-air vectors of the first light beam and the second light beam; and on the basis of the in-air vectors of the first light beam and the second light beam, determining the incident angles of the first light beam and the second light beam. The method can improve the manufacturing efficiency of a two-dimensional exit pupil expansion volume holographic optical waveguide including coupling-in, turning and coupling-out volume holographic gratings.

Description

Method and device for determining exposure parameters of volume holographic grating, and two-dimensional pupil expanding volume holographic optical waveguide

[0001] Cross-reference to Related Applications

[0002] The present application claims priority to the Chinese patent application No. 2024111018430, filed on August 12, 2024, and entitled "Method for determining exposure parameters of volume holographic grating and two-dimensional pupil expanding volume holographic optical waveguide", the content of which is incorporated herein by reference in its entirety. TECHNICAL FIELD

[0003] The present application relates to the technical field of optical waveguide, in particular, to a method and device for determining exposure parameters of volume holographic grating, and a two-dimensional pupil expanding volume holographic optical waveguide. BACKGROUND

[0004] The two-dimensional pupil expanding volume holographic optical waveguide is a kind of optical waveguide technology that forms volume holographic gratings inside holographic photosensitive material through double-beam interference, and uses the volume holographic gratings as the coupling-in, turning and coupling-out optical elements of the waveguide.

[0005] At present, when manufacturing the conventional two-dimensional pupil expanding volume holographic optical waveguide, the manufacturing of the coupling-in, turning and coupling-out volume holographic gratings needs to use coupling prisms, and the manufacturing process is complicated and the processing efficiency is low. The size of the optical waveguide is determined by the size of the prism in the exposure method based on prism coupling, and large-size optical waveguides need large-size coupling prisms and high-power lasers, resulting in high cost of equipment and optical devices.

[0006] The equivalent exposure technology of grating merging is used to manufacture the volume holographic optical waveguide, which can realize the prism-free manufacturing of the volume holographic optical waveguide, but this technology can only manufacture the coupling-in and coupling-out volume holographic gratings, and cannot manufacture the turning volume holographic gratings. Moreover, the two-dimensional pupil expansion can only be realized by combining two one-dimensional pupil expanding waveguides, and cannot realize the manufacturing of single-layer two-dimensional pupil expanding volume holographic optical waveguide containing coupling-in, turning and coupling-out volume holographic gratings. Among them, the two-dimensional pupil expanding waveguide combined by two one-dimensional pupil expanding waveguides cannot be applied to volume holographic augmented reality (AR) glasses.

[0007] Therefore, as the key of the automatic manufacturing of two-dimensional pupil expanding volume holographic waveguide, it is urgent to realize the prism-free manufacturing of the coupling-in, turning and coupling-out volume holographic gratings. SUMMARY

[0008] The present application aims at the deficiencies in the prior art, and provides a method and device for determining exposure parameters of volume holographic grating, and a two-dimensional pupil expanding volume holographic optical waveguide, to solve the problem of limitations in the current manufacturing of two-dimensional pupil expanding volume holographic optical waveguide in the prior art.

[0009] To achieve the above object, technical solutions adopted by embodiments of the present application are as follows.

[0010] In a first aspect, embodiments of the present application provide a method for determining exposure parameters of a volume holographic grating, the method comprising:

[0011] when the wavelength of the first light beam and the wavelength of the second light beam are a first recording wavelength, rotating the vector of the first light beam, the vector of the second light beam and the holographic photosensitive material multiple times to obtain a rotated vector of the first light beam, a rotated vector of the second light beam and a rotated material position of the holographic photosensitive material;

[0012] transforming the wavelength of the first light beam and the wavelength of the second light beam into a second recording wavelength, and rotating the rotated vector of the first light beam and the rotated vector of the second light beam at least once to obtain an in-material vector of the first light beam and an in-material vector of the second light beam;

[0013] determining an in-air vector of the first light beam and an in-air vector of the second light beam according to the in-material vector of the first light beam and the in-material vector of the second light beam;

[0014] determining an incident angle of the first light beam and an incident angle of the second light beam according to the in-air vector of the first light beam and the in-air vector of the second light beam, so as to perform interference exposure on the holographic photosensitive material located at the rotated material position according to the incident angle of the first light beam and the incident angle of the second light beam and obtain a volume holographic grating.

[0015] As an optional implementation manner, the rotating the vector of the first light beam, the vector of the second light beam and the holographic photosensitive material multiple times to obtain the rotated vector of the first light beam, the rotated vector of the second light beam and the rotated material position of the holographic photosensitive material comprises:

[0016] determining an X-axis rotation angle and a Y-axis rotation angle according to the vector of the first light beam and the vector of the second light beam;

[0017] rotating the vector of the first light beam, the vector of the second light beam and the holographic photosensitive material around an X-axis according to the X-axis rotation angle respectively to obtain a first intermediate rotated vector of the first light beam, a first intermediate rotated vector of the second light beam and a first intermediate rotated material position of the holographic photosensitive material;

[0018] rotating the first intermediate post-rotation vector of the first light beam, the first intermediate post-rotation vector of the second light beam and the holographic photosensitive material located at the first intermediate post-rotation material position around the Y axis by the Y axis rotation angle respectively to obtain a post-rotation vector of the first light beam, a post-rotation vector of the second light beam and a post-rotation material position of the holographic photosensitive material.

[0019] As an optional implementation, the X axis rotation angle and the Y axis rotation angle are determined according to the vector of the first light beam and the vector of the second light beam, including:

[0020] The grating vector is determined according to the difference between the vector of the first light beam and the vector of the second light beam.

[0021] The X axis rotation angle and the Y axis rotation angle are determined according to the grating vector.

[0022] As an optional implementation, the X axis rotation angle and the Y axis rotation angle are determined according to the grating vector, including:

[0023] The unit vector of the grating vector is determined.

[0024] The X axis rotation angle is determined according to the unit vector and the rotation matrix corresponding to the X axis.

[0025] The rotation unit vector of the unit vector after rotating around the X axis by the X axis rotation angle is determined.

[0026] The Y axis rotation angle is determined according to the rotation unit vector and the rotation matrix corresponding to the Y axis.

[0027] As an optional implementation, the post-rotation vector of the first light beam and the post-rotation vector of the second light beam are rotated at least once to obtain the material-in-vector of the first light beam and the material-in-vector of the second light beam, including:

[0028] The elimination rotation parameter is determined according to the post-rotation vector of the first light beam, the post-rotation vector of the second light beam and the rotation matrix corresponding to the Z axis, and the post-rotation vector of the first light beam and the post-rotation vector of the second light beam are positively rotated around the Z axis by the elimination rotation parameter to obtain the post-rotation vector of the first light beam and the post-rotation vector of the second light beam.

[0029] The vector of the first light beam after wavelength conversion and the vector of the second light beam after wavelength conversion are determined according to the post-rotation vector of the first light beam and the post-rotation vector of the second light beam.

[0030] rotating the vector of the first light beam after wavelength conversion and the vector of the second light beam after wavelength conversion around the Z axis according to the elimination rotation parameter in a reverse direction to obtain a rotated vector of the first light beam after wavelength conversion and a rotated vector of the second light beam after wavelength conversion;

[0031] rotating the rotated vector of the first light beam after wavelength conversion and the rotated vector of the second light beam after wavelength conversion around the Z axis according to a preset Z axis rotation angle to obtain the in-medium vector of the first light beam and the in-medium vector of the second light beam.

[0032] As an optional implementation, the determining the in-air vector of the first light beam and the in-air vector of the second light beam according to the in-medium vector of the first light beam and the in-medium vector of the second light beam comprises:

[0033] determining the in-air incident angle of the first light beam according to the in-medium vector of the first light beam, the rotated in-medium position of the holographic photosensitive material and the refractive index of the holographic photosensitive material;

[0034] determining the in-air vector of the first light beam according to the in-medium vector of the first light beam, the rotated in-medium position of the holographic photosensitive material, the refractive index of the holographic photosensitive material and the in-air incident angle of the first light beam;

[0035] determining the in-air incident angle of the second light beam according to the in-medium vector of the second light beam, the rotated in-medium position of the holographic photosensitive material and the refractive index of the holographic photosensitive material;

[0036] determining the in-air vector of the second light beam according to the in-medium vector of the second light beam, the rotated in-medium position of the holographic photosensitive material, the refractive index of the holographic photosensitive material and the in-air incident angle of the second light beam.

[0037] As an optional implementation, the determining the incident angle of the first light beam and the incident angle of the second light beam according to the in-air vector of the first light beam and the in-air vector of the second light beam comprises:

[0038] determining the polar angle of the first light beam according to the in-air vector of the first light beam and the Z axis component of the in-air vector of the first light beam;

[0039] determining the azimuth angle of the first light beam according to the X axis component of the in-air vector of the first light beam and the Y axis component of the in-air vector of the first light beam;

[0040] determining the polar angle of the second light beam according to the in-air vector of the second light beam and the Z axis component of the in-air vector of the second light beam;

[0041] determine the azimuth angle of the second light beam according to the X-axis component of the in-air vector of the second light beam and the Y-axis component of the in-air vector of the second light beam.

[0042] In a second aspect, the embodiments of the present application provide a device for determining exposure parameters of a volume holographic grating, the device comprising:

[0043] a rotating module configured to rotate the vector of the first light beam, the vector of the second light beam and the holographic photosensitive material multiple times to obtain a rotated vector of the first light beam, a rotated vector of the second light beam and a rotated material position of the holographic photosensitive material when the wavelength of the first light beam and the wavelength of the second light beam are first recording wavelengths;

[0044] The rotating module is further configured to transform the wavelength of the first light beam and the wavelength of the second light beam into second recording wavelengths, and rotate the rotated vector of the first light beam and the rotated vector of the second light beam at least once to obtain an in-material vector of the first light beam and an in-material vector of the second light beam.

[0045] a determining module configured to determine an in-air vector of the first light beam and an in-air vector of the second light beam according to the in-material vector of the first light beam and the in-material vector of the second light beam.

[0046] The determining module is further configured to determine an incident angle of the first light beam and an incident angle of the second light beam according to the in-air vector of the first light beam and the in-air vector of the second light beam, and perform interference exposure on the holographic photosensitive material located at the rotated material position according to the incident angle of the first light beam and the incident angle of the second light beam to obtain the volume holographic grating.

[0047] As an optional implementation manner, the rotating module is specifically configured to:

[0048] determine an X-axis rotation angle and a Y-axis rotation angle according to the vector of the first light beam and the vector of the second light beam;

[0049] rotate the vector of the first light beam, the vector of the second light beam and the holographic photosensitive material around the X axis according to the X-axis rotation angle respectively to obtain a first intermediate rotated vector of the first light beam, a first intermediate rotated vector of the second light beam and a first intermediate rotated material position of the holographic photosensitive material;

[0050] The first intermediate post-rotation vector of the first light beam, the first intermediate post-rotation vector of the second light beam, and the holographic photosensitive material located at the first intermediate post-rotation material position are rotated around the Y axis by the Y axis rotation angle respectively, to obtain a post-rotation vector of the first light beam, a post-rotation vector of the second light beam, and a post-rotation material position of the holographic photosensitive material.

[0051] As an optional implementation, the rotation module is specifically configured to:

[0052] The grating vector is determined according to the difference between the vector of the first light beam and the vector of the second light beam.

[0053] The X axis rotation angle and the Y axis rotation angle are determined according to the grating vector.

[0054] As an optional implementation, the rotation module is specifically configured to:

[0055] The unit vector of the grating vector is determined.

[0056] The X axis rotation angle is determined according to the unit vector and the rotation matrix corresponding to the X axis.

[0057] The rotation unit vector of the unit vector after being rotated around the X axis by the X axis rotation angle is determined.

[0058] The Y axis rotation angle is determined according to the rotation unit vector and the rotation matrix corresponding to the Y axis.

[0059] As an optional implementation, the rotation module is specifically configured to:

[0060] The elimination rotation parameter is determined according to the post-rotation vector of the first light beam, the post-rotation vector of the second light beam, and the rotation matrix corresponding to the Z axis, and the post-rotation vector of the first light beam and the post-rotation vector of the second light beam are positively rotated around the Z axis by the elimination rotation parameter, to obtain a positively post-rotation vector of the first light beam and a positively post-rotation vector of the second light beam.

[0061] The vector of the first light beam after wavelength conversion and the vector of the second light beam after wavelength conversion are determined according to the positively post-rotation vector of the first light beam and the positively post-rotation vector of the second light beam.

[0062] The vector of the first light beam after wavelength conversion and the vector of the second light beam after wavelength conversion are inversely rotated around the Z axis by the elimination rotation parameter, to obtain an inversely post-rotation vector of the first light beam after wavelength conversion and an inversely post-rotation vector of the second light beam after wavelength conversion.

[0063] The inverse rotation vectors of the first light beam after wavelength conversion and the second light beam after wavelength conversion are rotated around the Z axis according to a preset Z axis rotation angle, to obtain the material-in-vector of the first light beam and the material-in-vector of the second light beam.

[0064] As an optional implementation, the determination module is specifically configured to:

[0065] According to the material-in-vector of the first light beam, the material position of the holographic photosensitive material after rotation, and the refractive index of the holographic photosensitive material, the air-in-incident angle of the first light beam is determined.

[0066] According to the material-in-vector of the first light beam, the material position of the holographic photosensitive material after rotation, the refractive index of the holographic photosensitive material, and the air-in-incident angle of the first light beam, the air-in-vector of the first light beam is determined.

[0067] According to the material-in-vector of the second light beam, the material position of the holographic photosensitive material after rotation, and the refractive index of the holographic photosensitive material, the air-in-incident angle of the second light beam is determined.

[0068] According to the material-in-vector of the second light beam, the material position of the holographic photosensitive material after rotation, the refractive index of the holographic photosensitive material, and the air-in-incident angle of the second light beam, the air-in-vector of the second light beam is determined.

[0069] As an optional implementation, the determination module is specifically configured to:

[0070] According to the air-in-vector of the first light beam, the Z axis component of the air-in-vector of the first light beam, the polar angle of the first light beam is determined.

[0071] According to the X axis component of the air-in-vector of the first light beam and the Y axis component of the air-in-vector of the first light beam, the azimuth angle of the first light beam is determined.

[0072] According to the air-in-vector of the second light beam, the Z axis component of the air-in-vector of the second light beam, the polar angle of the second light beam is determined.

[0073] According to the X axis component of the air-in-vector of the second light beam and the Y axis component of the air-in-vector of the second light beam, the azimuth angle of the second light beam is determined.

[0074] In a third aspect, an embodiment of the present application provides a first computer device, comprising: a first processor, a first memory, and a first bus, the first memory storing first machine readable instructions executable by the first processor, when the first computer device is running, the first processor and the first memory communicate through the first bus, the first processor executes the first machine readable instructions to perform steps of the method for determining exposure parameters of volume holographic gratings as described in the first aspect.

[0075] In a fourth aspect, an embodiment of the present application provides a first computer readable storage medium, the first computer readable storage medium storing a first computer program, when the first computer program is run by the first processor, performing steps of the method for determining exposure parameters of volume holographic gratings as described in the first aspect.

[0076] In a fifth aspect, an embodiment of the present application provides a method for manufacturing volume holographic gratings, the method comprising:

[0077] obtaining the incidence angles of the first light beams and the incidence angles of the second light beams of the in-coupling volume holographic grating, the turning volume holographic grating, and the out-coupling volume holographic grating respectively determined by the method for determining exposure parameters of volume holographic gratings as described in the first aspect;

[0078] interference exposing the holographic photosensitive materials at the positions of the materials after rotation respectively according to the incidence angles of the first light beams and the incidence angles of the second light beams of the in-coupling volume holographic grating, the incidence angles of the first light beams and the incidence angles of the second light beams of the turning volume holographic grating, and the incidence angles of the first light beams and the incidence angles of the second light beams of the out-coupling volume holographic grating, to obtain the in-coupling volume holographic grating, the turning volume holographic grating, and the out-coupling volume holographic grating.

[0079] In a sixth aspect, an embodiment of the present application provides a device for manufacturing volume holographic gratings, the device comprising:

[0080] an obtaining module, configured to obtain the incidence angles of the first light beams and the incidence angles of the second light beams of the in-coupling volume holographic grating, the turning volume holographic grating, and the out-coupling volume holographic grating respectively determined by the method for determining exposure parameters of volume holographic gratings as described in the first aspect;

[0081] an interference module, configured to interference expose the holographic photosensitive materials at the positions of the materials after rotation respectively according to the incidence angles of the first light beams and the incidence angles of the second light beams of the in-coupling volume holographic grating, the incidence angles of the first light beams and the incidence angles of the second light beams of the turning volume holographic grating, and the incidence angles of the first light beams and the incidence angles of the second light beams of the out-coupling volume holographic grating, to obtain the in-coupling volume holographic grating, the turning volume holographic grating, and the out-coupling volume holographic grating.

[0082] In a seventh aspect, an embodiment of the present application provides a second computer device, comprising: a second processor, a second memory, and a second bus, the second memory storing second machine readable instructions executable by the second processor, when the second computer device is running, the second processor and the second memory communicate through the second bus, the second processor executes the second machine readable instructions to execute steps of the method for manufacturing a volume holographic grating according to the fifth aspect.

[0083] In an eighth aspect, an embodiment of the present application provides a second computer readable storage medium, the second computer readable storage medium storing a second computer program, when the second computer program is run by the second processor, the second computer program executes steps of the method for manufacturing a volume holographic grating according to the seventh aspect.

[0084] In a ninth aspect, an embodiment of the present application provides a two-dimensional pupil expanding volume holographic grating, the two-dimensional pupil expanding volume holographic grating comprising a coupling-in volume holographic grating, a turning volume holographic grating, and a coupling-out volume holographic grating, the coupling-in volume holographic grating, the turning volume holographic grating, and the coupling-out volume holographic grating are manufactured by the method for manufacturing a volume holographic grating according to the fifth aspect.

[0085] In a tenth aspect, an embodiment of the present application provides a two-dimensional pupil expanding volume holographic waveguide, the two-dimensional pupil expanding volume holographic waveguide comprising a waveguide base and the coupling-in volume holographic grating, the turning volume holographic grating, and the coupling-out volume holographic grating according to the ninth aspect, the coupling-in volume holographic grating, the turning volume holographic grating, and the coupling-out volume holographic grating are located at corresponding positions of the waveguide base.

[0086] The present application has the following beneficial effects:

[0087] The application provides a volume holographic grating exposure parameter determination method and device and a two-dimensional pupil expanding volume holographic optical waveguide. BRIEF DESCRIPTION OF DRAWINGS

[0088] In order to more clearly illustrate the technical solutions of the embodiments of the application, the following will briefly introduce the drawings needed to be used in the embodiments. It should be understood that the following drawings only show some of the embodiments of the application, and therefore should not be regarded as a limitation to the scope. For those skilled in the art, other related drawings can also be obtained without creative labor under the premise of the drawings.

[0089] Fig. 1 is a flowchart of the method for determining the exposure parameters of the volume holographic grating according to an embodiment of the application;

[0090] Fig. 2 is a flowchart of the method for determining the exposure parameters of the volume holographic grating according to an embodiment of the application, which shows the determination of the post-rotation vector of the first light beam, the post-rotation vector of the second light beam and the post-rotation material position of the holographic photosensitive material;

[0091] Fig. 3 is a flowchart of the method for determining the exposure parameters of the volume holographic grating according to an embodiment of the application, which shows the determination of the X-axis rotation angle and the Y-axis rotation angle;

[0092] Fig. 4 is another flowchart of the method for determining the exposure parameters of the volume holographic grating according to an embodiment of the application, which shows the determination of the X-axis rotation angle and the Y-axis rotation angle;

[0093] FIG. 5 is a flowchart of a method for determining the material-in-vector of the first light beam and the material-in-vector of the second light beam according to an embodiment of the present application;

[0094] FIG. 6 is a schematic diagram of the grating vector before and after wavelength conversion according to an embodiment of the present application;

[0095] FIG. 7 is a flowchart of a method for determining the air-in-vector of the first light beam and the air-in-vector of the second light beam according to an embodiment of the present application;

[0096] FIG. 8 is a flowchart of a method for determining the incident angle of the first light beam and the incident angle of the second light beam according to an embodiment of the present application;

[0097] FIG. 9 is a block diagram of a device for determining the exposure parameters of a volume holographic grating according to an embodiment of the present application;

[0098] FIG. 10 is a schematic diagram of a first computer device according to an embodiment of the present application;

[0099] FIG. 11 is a flowchart of a method for manufacturing a two-dimensional pupil expanding volume holographic grating according to an embodiment of the present application;

[0100] FIG. 12 is a block diagram of a device for manufacturing a two-dimensional pupil expanding volume holographic grating according to an embodiment of the present application;

[0101] FIG. 13 is a schematic diagram of a second computer device according to an embodiment of the present application;

[0102] FIG. 14 is a schematic diagram of an L-shaped two-dimensional pupil expanding volume holographic optical waveguide according to an embodiment of the present application;

[0103] FIG. 15 is a schematic diagram of the central field of view light ray transmission of a reflective two-dimensional pupil expanding volume holographic optical waveguide according to an embodiment of the present application;

[0104] FIG. 16 is a block diagram of a device for determining the exposure parameters of a volume holographic grating according to an embodiment of the present application. DETAILED DESCRIPTION

[0105] In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. It should be understood that the drawings in the present application only serve the purpose of description and illustration, and do not serve to limit the scope of protection of the present application. In addition, it should be understood that the schematic drawings are not drawn according to the actual proportions. The flowcharts used in the present application show the operations implemented according to some embodiments of the present application. It should be understood that the operations of the flowcharts can not be implemented in sequence, and the steps without logical context relationship can be reversed in sequence or implemented simultaneously. In addition, one or more other operations can be added to the flowcharts or one or more operations can be removed from the flowcharts under the guidance of the content of the present application.

[0106] In addition, the described embodiments are only some of the embodiments of the present application, not all the embodiments. The components of the embodiments of the present application described and shown in the drawings herein can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the claimed present application, but only represents selected embodiments of the present application. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0107] It should be noted that the term "comprise" will be used in the embodiments of the present application to indicate the presence of the features declared thereafter, but does not exclude the addition of other features.

[0108] Currently, it is difficult to realize the automated manufacturing of a single-layer two-dimensional pupil expanding volume holographic optical waveguide containing in-coupling, turning and out-coupling volume holographic gratings, resulting in limitations in the current application of two-dimensional pupil expanding volume holographic optical waveguide technology.

[0109] Based on the above-mentioned problems, this embodiment proposes a method, apparatus, and two-dimensional enlarged pupil volume holographic waveguide for determining exposure parameters of a volume holographic grating. When the wavelengths of the first beam and the second beam are the first recording wavelengths, the vectors of the first beam, the second beam, and the holographic photosensitive material are rotated around the X-axis by an X-axis rotation angle and then around the Y-axis by a Y-axis rotation angle to determine the rotated vectors of the first beam, the second beam, and the rotated material position of the holographic photosensitive material. The wavelengths of the first beam and the second beam are transformed into the second recording wavelength. Based on the X-axis components of the rotated vectors of the first and second beams, the rotated vectors of the first and second beams are rotated at least once to determine the material vectors of the first and second beams, thereby obtaining the air vectors of the first and second beams and determining the incident angles of the first and second beams. Using the polar angle and azimuth angle of the incident angle of the first beam and the polar angle and azimuth angle of the incident angle of the second beam as exposure parameters for the volume holographic grating, and by rotating the holographic photosensitive material twice, the exposure parameters of the volume holographic grating are determined based on the decoupling of wavelength transformation and the decoupling of spatial coordinates composed of polar angle and azimuth angle. This allows for more efficient fabrication of volume holographic gratings and can be applied to the automated manufacturing of two-dimensional pupil-expanding volume holographic waveguides, thereby reducing costs.

[0110] Figure 1 is a flowchart illustrating the method for determining the exposure parameters of a volume holographic grating according to an embodiment of this application. The execution subject of this method can be any computer device with computing power. As shown in Figure 1, the method includes:

[0111] S101. When the wavelengths of the first beam and the second beam are the first recording wavelengths, the vectors of the first beam, the second beam, and the holographic photosensitive material are rotated multiple times to obtain the rotated vectors of the first beam, the rotated vectors of the second beam, and the rotated material position of the holographic photosensitive material.

[0112] Optionally, the first beam R is the reference beam, and the second beam S is the object beam. The vector representation of the first beam is: K rx The vector of the first beam The component in the X-axis direction, K ry The vector of the first beam The component in the Y-axis direction, K rz The vector of the first beam The component in the Z-axis direction. Correspondingly, the vector representation of the second beam is... K sx The vector of the second beam The component in the X-axis direction, K sya vector of the second light beam a component in the Y-axis direction, K sz a vector of the second light beam a component in the Z-axis direction.

[0113] when the wavelength of the first light beam R and the wavelength of the second light beam S are both the first recording wavelength λ, the vector of the first light beam a vector of the second light beam and the holographic photosensitive material is rotated multiple times around different coordinate axes to obtain a rotated vector of the first light beam a rotated vector of the second light beam and a rotated material position of the holographic photosensitive material. Wherein, the rotated forward normal vector of the holographic photosensitive material is represented by and the reversed normal of the holographic photosensitive material the material position of the holographic photosensitive material is represented by, then the rotated material position of the holographic photosensitive material is represented by the rotated forward normal vector of the holographic photosensitive material and the rotated reversed normal vector of the holographic photosensitive material , the plane in which the holographic photosensitive material is located is a plane perpendicular to the normal vector.

[0114] It is worth noting that the above multiple rotations of the vector of the first light beam the vector of the second light beam and the holographic photosensitive material can be performed in a simulation environment in a simulation tool to obtain a rotated vector of the first light beam in the simulation environment a rotated vector of the second light beam a rotated forward normal vector of the holographic photosensitive material and a rotated reversed normal vector of the holographic photosensitive material or can be performed in an actual operation process to obtain a rotated vector of the first light beam in a real environment a rotated vector of the second light beam and the holographic photosensitive material to obtain a rotated vector of the first light beam in a real environment a rotated vector of the second light beam a rotated forward normal vector of the holographic photosensitive material and a rotated reversed normal vector of the holographic photosensitive material The present application does not make specific limitations thereto.

[0115] S102, the wavelength of the first light beam and the wavelength of the second light beam are converted to a second recording wavelength, and the rotated vector of the first light beam and the rotated vector of the second light beam are rotated at least once to obtain a material-in-vector of the first light beam and a material-in-vector of the second light beam.

[0116] Optionally, the vector of the first light beam the vector of the second light beam and the wavelength of the first light beam R and the wavelength of the second light beam S are transformed from a first recording wavelength λ to a second recording wavelength λ after multiple rotations of the holographic photosensitive material h , the wavelength is transformed to a second recording wavelength λ h the vector of the first light beam after rotation is the vector of the second light beam after rotation is After maintaining the position of the material after rotation of the holographic photosensitive material, the vector of the first light beam after rotation is and the vector of the second light beam after rotation is Rotating at least once around the same coordinate axis, the in-material vector of the first light beam R incident from the material is and the in-material vector of the second light beam S incident from the material is so that the in-material vector of the first light beam and the in-material vector of the second light beam are both located in a two-dimensional coordinate system kyokz where an equivalent plane is located, the in-material vector of the first light beam is and the in-material vector of the second light beam is the conversion relationship under different wavelengths and different Z-axis rotation angles γ.

[0117] wherein the in-material vector of the first light beam and the in-material vector of the second light beam the conversion relationship under different wavelengths and different Z-axis rotation angles γ is an equivalent exposure condition, which is established regardless of whether the first light beam R and the second light beam S satisfy the total reflection condition of the holographic photosensitive material and air, realizing decoupling of wavelength transformation.

[0118] S103, according to the in-material vector of the first light beam and the in-material vector of the second light beam, the in-air vector of the first light beam and the in-air vector of the second light beam are determined.

[0119] Optionally, according to the in-material vector of the first light beam R and the in-material vector of the second light beam S the in-air vector of the first light beam R incident from the air of a body holographic grating of different types and the in-air vector of the second light beam S incident from the air of a body holographic grating wherein the types of the body holographic grating include a transmission type body holographic grating and a reflection type body holographic grating, the first light beam R and the second light beam S of the transmission type body holographic grating are both directed to the positive direction of the Z-axis, the first light beam R of the reflection type body holographic grating is directed to the positive direction of the Z-axis, and the second light beam S is directed to the negative direction of the Z-axis.

[0120] S104, determining the incident angle of the first light beam and the incident angle of the second light beam according to the air vector of the first light beam and the air vector of the second light beam, so as to perform interference exposure on the holographic photosensitive material located at the material position after rotation according to the incident angle of the first light beam and the incident angle of the second light beam, and obtain a volume holographic grating.

[0121] Optionally, the air vector of the first light beam R incident from air The polar angle θ of the first light beam R incident from air to the holographic photosensitive material is determined r And the azimuth angle φ r , to obtain the incident angle of the first light beam R. Correspondingly, the air vector of the second light beam S incident from air The polar angle θ of the second light beam S incident from air to the holographic photosensitive material is determined s And the azimuth angle φ s , to obtain the incident angle of the second light beam S. The incident angle of the first light beam R and the incident angle of the second light beam S are taken as volume holographic grating exposure parameters, and the volume holographic grating is manufactured according to the volume holographic grating exposure parameters.

[0122] Specifically, the holographic photosensitive material located at the material position after rotation is illuminated according to the incident angle of the first light beam R and the incident angle of the second light beam S, the first light beam R and the second light beam S are incident from air to the holographic photosensitive material, and double-beam interference exposure is performed to obtain an equivalent exposure volume holographic grating. The two-dimensional pupil expanding volume holographic grating includes a coupling-in volume holographic grating, a coupling-out volume holographic grating and a turning volume holographic grating, and the three volume holographic gratings can be manufactured by exposure of the corresponding incident angle of the first light beam R and the incident angle of the second light beam S, respectively.

[0123] In the embodiment, before the wavelength of the first light beam and the wavelength of the second light beam are changed, the post-rotation vector of the first light beam, the post-rotation vector of the second light beam and the post-rotation material position of the holographic photosensitive material are determined through multiple rotations; after the wavelength of the first light beam and the wavelength of the second light beam are changed, the post-rotation material position of the holographic photosensitive material remains unchanged, the in-material vector of the first light beam and the in-material vector of the second light beam are determined through at least one rotation of the post-rotation vector of the first light beam and the post-rotation vector of the second light beam, the equivalent exposure conditions of the in-material vector of the first light beam and the in-material vector of the second light beam when the wavelength is changed are obtained, and the decoupling of the wavelength change is realized. Based on the equivalent exposure conditions of the in-material vector of the first light beam and the in-material vector of the second light beam, the in-air vector of the first light beam and the in-air vector of the second light beam are obtained, and then the incident angle of the first light beam and the incident angle of the second light beam are obtained, and the spatial decoupling is realized. The incident angle of the first light beam and the incident angle of the second light beam are taken as the volume holographic grating exposure parameters, and the first light beam and the second light beam are made to be incident on the holographic photosensitive material from the air according to the volume holographic grating exposure parameters, so that the holographic photosensitive material located at the post-rotation material position is subjected to double-beam interference exposure to manufacture the volume holographic grating. Through the wavelength change decoupling and the spatial decoupling, the required volume holographic grating can be exposed under equivalent conditions, so as to reduce the manufacturing difficulty and cost of the volume holographic grating.

[0124] Hereinafter, the process of rotating the vector of the first light beam, the vector of the second light beam and the holographic photosensitive material multiple times to obtain the post-rotation vector of the first light beam, the post-rotation vector of the second light beam and the post-rotation material position of the holographic photosensitive material will be described in detail.

[0125] FIG. 2 is a flowchart of obtaining the post-rotation vector of the first light beam, the post-rotation vector of the second light beam and the post-rotation material position of the holographic photosensitive material in the method for determining the volume holographic grating exposure parameters provided by the embodiment of the application, as shown in FIG. 2, the step of rotating the vector of the first light beam, the vector of the second light beam and the holographic photosensitive material multiple times to obtain the post-rotation vector of the first light beam, the post-rotation vector of the second light beam and the post-rotation material position of the holographic photosensitive material in the step S101 includes the following steps.

[0126] S201, determining the X-axis rotation angle and the Y-axis rotation angle according to the vector of the first light beam and the vector of the second light beam.

[0127] Optionally, when the wavelength of the first light beam R and the wavelength of the second light beam S are both the first recording wavelength λ, the vector of the first light beam and the vector of the second light beam are respectively calculated according to the vector of the first light beam and the vector of the second light beam and the X-axis rotation angle and the Y-axis rotation angle of the holographic photosensitive material.

[0128] S202, the vector of the first light beam, the vector of the second light beam and the holographic photosensitive material are rotated around the X-axis by the X-axis rotation angle respectively, to obtain the first intermediate post-rotation vector of the first light beam, the first intermediate post-rotation vector of the second light beam and the first intermediate post-rotation material position of the holographic photosensitive material.

[0129] Optionally, the vector of the first light beam is rotated around the X-axis by the X-axis rotation angle to obtain the first intermediate post-rotation vector of the first light beam The first intermediate post-rotation vector of the first light beam is determined based on the following formula

[0130] wherein, is the first intermediate post-rotation vector of the first light beam, T xα is the rotation matrix corresponding to the X-axis, is the vector of the first light beam, a is the X-axis rotation angle, K rxα , K ryα and K rzα are the components of the first intermediate post-rotation vector of the first light beam in the X-axis direction, the Y-axis direction and the Z-axis direction.

[0131] Correspondingly, the vector of the second light beam is rotated around the X-axis by the X-axis rotation angle to obtain the first intermediate post-rotation vector of the second light beam The first intermediate post-rotation vector of the second light beam is determined based on the following formula

[0132] wherein, is the first intermediate post-rotation vector of the second light beam, T xα is the rotation matrix corresponding to the X-axis, is the vector of the second light beam, a is the X-axis rotation angle, K sxα , K syα and K szα are the components of the first intermediate post-rotation vector of the second light beam in the X-axis direction, the Y-axis direction and the Z-axis direction.

[0133] Correspondingly, the holographic photosensitive material is rotated around the X-axis by the X-axis rotation angle, that is, the forward normal vector of the holographic photosensitive material and the reverse normal The first intermediate post-rotation normal vector of the holographic photosensitive material is obtained by rotating the holographic photosensitive material around the X axis by the X axis rotation angle, respectively The first intermediate post-rotation reverse normal vector of the holographic photosensitive material is obtained by rotating the holographic photosensitive material around the X axis by the X axis rotation angle, respectively The first intermediate post-rotation normal vector of the holographic photosensitive material is determined based on the following formula

[0134] Wherein, The first intermediate post-rotation normal vector of the holographic photosensitive material is determined based on the following formula xα The X axis corresponds to the rotation matrix, The normal vector of the holographic photosensitive material is determined based on the following formula +zxα , K +zyα and K +zzα The first intermediate post-rotation normal vector of the holographic photosensitive material is obtained by rotating the holographic photosensitive material around the X axis by the X axis rotation angle, respectively The components in the X axis direction, the Y axis direction and the Z axis direction.

[0135] The first intermediate post-rotation reverse normal vector of the holographic photosensitive material is determined based on the following formula

[0136] Wherein, The first intermediate post-rotation reverse normal vector of the holographic photosensitive material is determined based on the following formula xα The X axis corresponds to the rotation matrix, The reverse normal vector of the holographic photosensitive material is determined based on the following formula -zxα , K -zyα and K -zzα The first intermediate post-rotation reverse normal vector of the holographic photosensitive material is obtained by rotating the holographic photosensitive material around the X axis by the X axis rotation angle, respectively The components in the X axis direction, the Y axis direction and the Z axis direction. The first intermediate post-rotation normal vector of the holographic photosensitive material is obtained by rotating the holographic photosensitive material around the X axis by the X axis rotation angle, respectively The first intermediate post-rotation reverse normal vector of the holographic photosensitive material is obtained by rotating the holographic photosensitive material around the X axis by the X axis rotation angle, respectively The first intermediate post-rotation material position of the holographic photosensitive material is indicated.

[0137] S203, the first intermediate post-rotation vector of the first light beam, the first intermediate post-rotation vector of the second light beam and the holographic photosensitive material located at the first intermediate post-rotation material position are rotated around the Y axis by the Y axis rotation angle, respectively, to obtain the post-rotation vector of the first light beam, the post-rotation vector of the second light beam and the post-rotation material position of the holographic photosensitive material.

[0138] Optionally, the first intermediate post-rotation vector of the first light beam is obtained by rotating the first intermediate post-rotation vector of the first light beam around the Y axis by the Y axis rotation angle Rotating around the Y axis according to the Y axis rotation angle, a post-rotation vector of the first light beam is obtained The post-rotation vector of the first light beam is determined based on the following formula

[0139] wherein, is the post-rotation vector of the first light beam, is the first intermediate post-rotation vector of the first light beam, T yβ is the rotation matrix corresponding to the Y axis, is the vector of the first light beam, and α is the X axis rotation angle, and β is the Y axis rotation angle, K rxαβ , K ryαβ and K rzαβ are respectively the post-rotation vector of the first light beam in the X axis direction, the Y axis direction and the Z axis direction.

[0140] Correspondingly, the first intermediate post-rotation vector of the second light beam Rotating around the Y axis according to the Y axis rotation angle, a post-rotation vector of the second light beam is obtained The post-rotation vector of the second light beam is determined based on the following formula

[0141] wherein, is the post-rotation vector of the second light beam, is the first intermediate post-rotation vector of the second light beam, T yβ is the rotation matrix corresponding to the Y axis, is the vector of the second light beam, and α is the X axis rotation angle, and β is the Y axis rotation angle, K sxαβ , K syαβ and K szαβ are respectively the post-rotation vector of the second light beam in the X axis direction, the Y axis direction and the Z axis direction.

[0142] Correspondingly, the holographic photosensitive material located at the first intermediate post-rotation material position is rotated around the Y axis according to the Y axis rotation angle, that is, the first intermediate post-rotation positive normal vector of the holographic photosensitive material and the first intermediate post-rotation reverse normal vector of the holographic photosensitive material are respectively rotated around the Y axis according to the Y axis rotation angle, to obtain the post-rotation positive normal vector of the holographic photosensitive material and the post-rotation reverse normal vector of the holographic photosensitive material The post-rotation positive normal vector of the holographic photosensitive material is determined based on the following formula

[0143] wherein, is the rotated forward normal vector of the holographic photosensitive material, T yβ is the rotation matrix corresponding to the Y axis, is the first intermediate rotated forward normal vector of the holographic photosensitive material, is the forward normal vector of the holographic photosensitive material, a is the rotation angle of the X axis, b is the rotation angle of the Y axis, K +zxαβ , K +zyαβ and K +zzαβ are the rotated forward normal vectors of the holographic photosensitive material, respectively, the components in the X axis direction, the Y axis direction and the Z axis direction.

[0144] The rotated backward normal vector of the holographic photosensitive material is determined based on the following formula:

[0145] wherein, is the rotated backward normal vector of the holographic photosensitive material, T yβ is the rotation matrix corresponding to the Y axis, is the first intermediate rotated backward normal vector of the holographic photosensitive material, is the backward normal vector of the holographic photosensitive material, a is the rotation angle of the X axis, b is the rotation angle of the Y axis, K -zxαβ , K zyαβ and K zzαβ are the rotated backward normal vectors of the holographic photosensitive material, respectively, the components in the X axis direction, the Y axis direction and the Z axis direction. The rotated forward normal vector of the holographic photosensitive material and the rotated backward normal vector of the holographic photosensitive material represent the rotated material position of the holographic photosensitive material.

[0146] In this embodiment, when the wavelengths of the first and second beams are the first recording wavelengths, the vectors of the first and second beams, the X-axis rotation angle and Y-axis rotation angle of the holographic photosensitive material are determined based on the vectors of the first and second beams. The vectors of the first and second beams, as well as the holographic photosensitive material, are then rotated around the X-axis according to the X-axis rotation angle to obtain the first intermediate rotated vector of the first beam, the first intermediate rotated vector of the second beam, and the first intermediate rotated material position of the holographic photosensitive material. Then, the first intermediate rotated vectors of the first and second beams, and the holographic photosensitive material located at the first intermediate rotated material position, are rotated around the Y-axis according to the Y-axis rotation angle to obtain the rotated vectors of the first and second beams, and the rotated material position of the holographic photosensitive material. Determining the rotated vectors of the first and second beams before wavelength conversion, and the rotated material position of the holographic photosensitive material, facilitates wavelength decoupling after wavelength conversion.

[0147] The following is a detailed explanation of the process of determining the X-axis rotation angle and the Y-axis rotation angle based on the vectors of the first beam and the second beam.

[0148] Figure 3 is a flowchart illustrating the determination of the X-axis rotation angle and Y-axis rotation angle in the method for determining the exposure parameters of a volume holographic grating provided in this embodiment of the application. As shown in Figure 3, the step S201 above, which determines the X-axis rotation angle and Y-axis rotation angle based on the vector of the first beam and the vector of the second beam, includes:

[0149] S301. Determine the grating vector based on the difference between the vector of the first beam and the vector of the second beam.

[0150] Optionally, based on the vector of the first beam and the vector of the second beam Obtain the vector of the first beam Vector of the second beam The difference is The vector of the first beam Vector of the second beam The difference As grating vector

[0151] Specifically, according to the vector of the first beam Vector of the second beam The wavelengths of the first beam R, the second beam S, and the refractive index n of the holographic photosensitive material are used to determine the grating vector when both the wavelengths of the first beam R and the second beam S are the first recording wavelength λ, based on the following two formulas.

[0152] in, Let n be the grating vector, n be the refractive index of the holographic photosensitive material, λ be the first recording wavelength, and K be the grating vector. rx K ry and K rz The vectors of the first beam are respectively Components in the X, Y, and Z axes; K sx K sy and K sz The vectors of the second beam are respectively Components in the X, Y, and Z axes; θ r and φ r These are the polar angle and azimuth angle of the first beam R, respectively; θ s and φ s These are the polar angle and azimuth angle of the second beam S, respectively; Kx, K y and K z These are the grating vectors. Components in the X-axis, Y-axis and Z-axis directions.

[0153] S302. Determine the X-axis rotation angle and Y-axis rotation angle based on the grating vector.

[0154] Optionally, based on the grating vector Determine the intersection of the coordinate system origin and the grating vector. The axis containing vectors in the same direction is the axis of rotation, based on the relationship between the origin of the coordinate system and the grating vector. Using the axes containing vectors in the same direction and the rotation matrix in three-dimensional space, we determine the vector of the first beam when the wavelengths of the first beam R and the second beam S are both the first recording wavelength λ. Vector of the second beam The forward normal vector of holographic photosensitive material and the reverse normal of the holographic photosensitive material The X-axis rotation angle and the Y-axis rotation angle.

[0155] In this embodiment, the grating vector is determined when the wavelengths of the first and second beams are both the first recording wavelength, based on the difference between the vectors of the first and second beams. The axis containing the vector passing through the origin in the same direction as the grating vector is determined as the rotation axis. Then, based on the axis containing the vector in the same direction as the grating vector and the rotation matrix in three-dimensional space, the X-axis rotation angle and the Y-axis rotation angle are determined. This establishes the vectors of the first and second beams, and the X-axis and Y-axis rotation angles of the holographic photosensitive material when both wavelengths are the first recording wavelength.

[0156] The following is a detailed explanation of the process of determining the X-axis rotation angle and the Y-axis rotation angle based on the grating vector.

[0157] Figure 4 is another flowchart illustrating the determination of the X-axis rotation angle and Y-axis rotation angle in the method for determining the exposure parameters of a volume holographic grating provided in this application embodiment. As shown in Figure 4, the step S302 above, which involves determining the X-axis rotation angle and Y-axis rotation angle based on the grating vector, includes:

[0158] S401. Determine the unit vector of the grating vector.

[0159] Alternatively, by adjusting the grating vector Perform grating vector normalization processing to determine the distance between the grating vector and the origin of the coordinate system. The axis containing vectors in the same direction is the axis of rotation, and this axis is represented by a grating vector. unit vector The grating vector is determined based on the following formula. unit vector

[0160] in, For grating vectors, The magnitude of the grating vector. raster vector The unit vector, v x v y and v z These are the grating vectors. unit vector Components in the X-axis, Y-axis and Z-axis directions.

[0161] S402. Determine the X-axis rotation angle based on the unit vector and the rotation matrix corresponding to the X-axis.

[0162] Optionally, the rotation matrices in three-dimensional space include the rotation matrix corresponding to the X-axis, the rotation matrix corresponding to the Y-axis, and the rotation matrix corresponding to the Z-axis. The following formula represents the rotation matrix corresponding to the X-axis:

[0163] Assuming the grating vector unit vector Rotate α around the X-axis, according to the grating vector unit vector And the rotation matrix corresponding to the X-axis, the unit vector is obtained based on the following formula. The first unit vector of rotation after rotating about the X-axis by α The expression:

[0164] wherein, is a unit vector is a first rotation unit vector after rotating xα is a rotation matrix corresponding to the X-axis, is a grating vector is a unit vector of the grating vector xα , v yα and v zα are respectively a first rotation unit vector components in the X-axis direction, the Y-axis direction and the Z-axis direction.

[0165] Let the vector component v yα of the unit vector in the Y-axis direction be 0, and substitute it into the expression of the first rotation unit vector , according to the unit vector and the rotation matrix T xα corresponding to the X-axis, the X-axis rotation angle is determined based on the following formula:

[0166] wherein, a is the X-axis rotation angle, v y is a component of the unit vector of the grating vector in the Y-axis direction, and v z is a component of the unit vector of the grating vector in the Z-axis direction.

[0167] S403, determine a rotation unit vector of the unit vector after rotating around the X-axis according to the X-axis rotation angle.

[0168] Optionally, the unit vector is rotated around the X-axis according to the X-axis rotation angle a, the formula for determining the X-axis rotation angle is substituted into the expression of the first rotation unit vector , and the first rotation unit vector of the unit vector after rotating around the X-axis according to the X-axis rotation angle a is determined based on the following formula:

[0169] wherein, is a first rotation unit vector of the unit vector after rotating around the X-axis according to the X-axis rotation angle a, v xα is a component of the first rotation unit vector in the X-axis direction, and a component of the first rotation unit vector in the Y-axis direction is 0, and v zαThe first rotational unit vector The component in the Z-axis direction.

[0170] S404. Determine the Y-axis rotation angle based on the rotation unit vector and the rotation matrix corresponding to the Y-axis.

[0171] Alternatively, the following formula is the rotation matrix corresponding to the Y-axis:

[0172] Assuming the first rotation unit vector Rotate about the Y-axis by β, according to the first rotation unit vector And the rotation matrix corresponding to the Y-axis, the first rotation unit vector is obtained based on the following formula. The second unit vector after rotating about the Y-axis by β The expression:

[0173] in, The first rotational unit vector The second unit vector of rotation after rotating β around the Y-axis, T yβ This is the rotation matrix corresponding to the Y-axis. Let v be the first rotational unit vector. xαβ The second rotational unit vector The component in the X-axis direction, the second rotational unit vector. The component in the Y-axis direction is 0, v zαβ The second rotational unit vector The component in the Z-axis direction.

[0174] Let the second rotation unit vector The component v in the X-axis direction xαβ If the value is 0, substitute it into the second rotational unit vector mentioned above. In the expression, based on the second rotation unit vector And the rotation matrix T corresponding to the Y-axis yβ The Y-axis rotation angle is determined based on the following formula:

[0175] Where β is the rotation angle along the Y-axis, v xα The first rotational unit vector The component in the X-axis direction, v zα The first rotational unit vector The component in the Z-axis direction.

[0176] Determine the first rotational unit vector The second unit vector after rotating around the Y-axis by a rotation angle β. Specifically, the first rotation unit vector According to the Y-axis rotation angle β, the formula for determining the Y-axis rotation angle is substituted into the expression of the second rotation unit vector The first rotation unit vector is determined based on the following formula The second rotation unit vector after rotating the Y-axis rotation angle β around the Y-axis

[0177] wherein, The first rotation unit vector is The second rotation unit vector after rotating the Y-axis rotation angle β around the Y-axis, the second rotation unit vector The components in the X-axis and Y-axis directions are both 0, and v zαβ The second rotation unit vector is The component in the Z-axis direction.

[0178] By normalizing the grating vector The unit vector of the grating vector According to the X-axis rotation angle α, the grating vector is rotated around the X-axis, and then according to the Y-axis rotation angle β, the grating vector is rotated around the Y-axis, so that the second rotation unit vector There is no component in the X-axis and Y-axis directions, and there is only a component in the Z-axis direction, that is, the axis of the vector passing through the origin of the coordinate system and the grating vector is located on the Z-axis.

[0179] In this embodiment, by normalizing the grating vector, the unit vector of the grating vector is determined, and according to the unit vector and the rotation matrix corresponding to the X-axis, the X-axis rotation angle is determined. The unit vector is rotated around the X-axis according to the X-axis rotation angle, and the first rotation unit vector is determined; according to the first rotation unit vector and the rotation matrix corresponding to the Y-axis, the Y-axis rotation angle is determined. The first rotation unit vector is rotated around the Y-axis according to the Y-axis rotation angle, and the second rotation unit vector is determined. Through two rotations, the axis of the vector in the same direction as the grating vector is located on the Z-axis.

[0180] Hereinafter, the process of rotating the rotated vector of the first light beam and the rotated vector of the second light beam at least once to obtain the material-in-vector of the first light beam and the material-in-vector of the second light beam will be described in detail.

[0181] FIG. 5 is a flowchart of a process of obtaining the material-in-vector of the first light beam and the material-in-vector of the second light beam in the determination method of the exposure parameters of the volume holographic grating provided by the embodiments of the present application. As shown in FIG. 5, the step of rotating the rotated vector of the first light beam and the rotated vector of the second light beam at least once to obtain the material-in-vector of the first light beam and the material-in-vector of the second light beam in the step S102 includes:

[0182] S501, determine the elimination rotation parameter according to the post-rotation vector of the first light beam, the post-rotation vector of the second light beam and the rotation matrix corresponding to the Z axis, and perform forward rotation of the post-rotation vector of the first light beam and the post-rotation vector of the second light beam around the Z axis according to the elimination rotation parameter to obtain the forward post-rotation vector of the first light beam and the forward post-rotation vector of the second light beam.

[0183] Optionally, according to the post-rotation vector of the first light beam and the post-rotation vector of the second light beam in the X axis direction component K rxαβ and K sxαβ , determine whether the post-rotation vector of the first light beam and the post-rotation vector of the second light beam need to be forward rotated around the Z axis to eliminate the X axis direction component. Specifically, if the post-rotation vector of the first light beam in the X axis direction component K rxαβ and the post-rotation vector of the second light beam in the X axis direction component K sxαβ are both 0, it indicates that the post-rotation vector of the first light beam and the post-rotation vector of the second light beam do not have X axis components, and thus the post-rotation vector of the first light beam and the post-rotation vector of the second light beam do not need to be forward rotated around the Z axis, and the wavelength of the first light beam R and the wavelength of the second light beam S are directly converted into the second recording wavelength λ h , and the vector of the first light beam after wavelength conversion and the vector of the second light beam after wavelength conversion are rotated around the Z axis according to the preset Z axis rotation angle to obtain the intramaterial vector of the first light beam and the intramaterial vector of the second light beam

[0184] If the post-rotation vector of the first light beam and the post-rotation vector of the second light beam in the X axis direction component K rxαβ and the post-rotation vector of the second light beam in the X axis direction component K sxαβ are not both 0, it indicates that the post-rotation vector of the first light beam and the post-rotation vector of the second light beam have X axis components, and thus the post-rotation vector of the first light beam and the post-rotation vector of the second light beam The forward rotation vector of the first light beam is obtained by performing forward rotation around the Z axis according to the elimination rotation parameter and the forward rotation vector of the second light beam Wherein, the elimination rotation parameter can be the Z axis elimination rotation angle κ, used for eliminating the rotation vector of the first light beam by twice rotation and the rotation vector of the second light beam The component in the X axis direction.

[0185] The rotation vector of the first light beam is and the rotation vector of the second light beam is The forward rotation vector of the first light beam is determined according to the following formula by performing forward rotation around the Z axis by the Z axis elimination rotation angle κ and the forward rotation vector of the second light beam

[0186] Wherein, The forward rotation vector of the first light beam is T zκ The rotation matrix corresponding to the Z axis is The rotation vector of the first light beam R when the wavelength is the first recording wavelength λ is κ, and the Z axis elimination rotation angle is K rxαβ , K ryαβ and K rzαβ The rotation vector of the first light beam when the wavelength is the first recording wavelength λ is The component in the X axis direction, the Y axis direction and the Z axis direction. The forward rotation vector of the second light beam is The rotation vector of the second light beam S when the wavelength is the first recording wavelength λ is K sxαβ , K syαβ and K szαβ The rotation vector of the second light beam when the wavelength is the first recording wavelength λ is The component in the X axis direction, the Y axis direction and the Z axis direction.

[0187] The value of the Z axis elimination rotation angle κ is substituted into the formula for determining the forward rotation vector of the first light beam and the forward rotation vector of the second light beam , respectively, to obtain:

[0188] Wherein, and Both represent the forward rotation vector of the first light beam zκ The rotation matrix corresponding to the Z axis is is a post-rotation vector of the first beam R when the wavelength of the first beam R is the first recording wavelength λ, K is a Z-axis elimination rotation angle, and the positive post-rotation vector of the first beam is 0, K ryκ and K rzκ are the positive post-rotation vectors of the first beam are components in the Y-axis direction and the Z-axis direction. and both represent the positive post-rotation vector of the second beam, is a post-rotation vector of the second beam S when the wavelength of the second beam S is the first recording wavelength λ, and the positive post-rotation vector of the second beam is 0, K syκ and K szκ are the positive post-rotation vectors of the second beam are components in the Y-axis direction and the Z-axis direction.

[0189] S502, the wavelength of the first beam and the wavelength of the second beam are converted into a second recording wavelength, and the post-rotation vector of the first beam after wavelength conversion and the post-rotation vector of the second beam after wavelength conversion are determined according to the positive post-rotation vector of the first beam and the positive post-rotation vector of the second beam.

[0190] FIG. 6 is a schematic diagram of grating vectors before and after wavelength conversion provided by an embodiment of the present application, as shown in FIG. 6, the inner circle represents a vector circle corresponding to a wavelength of a first recording wavelength λ, when the wavelength of the first beam R and the wavelength of the second beam S are both the first recording wavelength λ, the vector of the first beam and the vector of the second beam are constructed as The outer circle represents a vector circle corresponding to a wavelength of a second recording wavelength λ h , when the wavelength of the first beam R and the wavelength of the second beam S are both the second recording wavelength λ h , the post-rotation vector of the first beam after wavelength conversion and the post-rotation vector of the second beam after wavelength conversion are also constructed as That is, the grating vectors formed by interference of two different wavelengths are the same.

[0191] wherein the size of the grating vector corresponding to the inner circle The size of the grating vector corresponding to the outer circle

[0192] The wavelength of the first beam R and the wavelength of the second beam S are both converted into the second recording wavelength λ hAt this time, the vector of the first beam after wavelength transformation is The vector after the second beam changes wavelength is Based on the vector after positive rotation of the first beam and the vector after the positive rotation of the second beam The vector after wavelength transformation of the first beam is determined based on the following formula. The angle ω between the equivalent plane and the Y-axis in the two-dimensional coordinate system kyokz, and the vector after the second beam wavelength transformation. Angle ω with the Y-axis:

[0193] in, K is the magnitude of the grating vector. ryκ and K rzκ The vectors after positive rotation of the first beam are respectively In the Y-axis and Z-axis directions, K syκ and K szκ The vectors after positive rotation of the second beam are respectively The components in the Y-axis and Z-axis directions, ω is the vector after the first beam has been transformed by wavelength. The angle with the Y-axis and the vector after the second beam's wavelength transformation The angle with the Y-axis, λ h λ is the second recording wavelength after wavelength transformation, and n is the refractive index of the holographic photosensitive material.

[0194] Based on the vector after wavelength transformation of the first beam The angle ω with the Y-axis, and the second recording wavelength λ h and the vector after the first beam has been converted to a different wavelength The component K in the Y-axis direction ryκ The wavelength transformation of the first beam R to the second recording wavelength λ is determined based on the following formula. h At that time, the vector of the first beam after wavelength transformation

[0195] in, λ is the vector of the first beam after wavelength transformation. h K is the second recording wavelength. ryκ The vector after wavelength transformation of the first beam In the Y-axis direction, sign(*) is used to determine the sign of *. If the vector of the first beam after wavelength transformation... The component K in the Y-axis direction ryκ If it is a positive number, then sign(*) = +; otherwise, sign(*) = -. The vector of the first beam after wavelength transformation in Figure 6. The component K in the Y-axis directionryκ If it is a positive number, sign(K) ryκ ) represents "+", and ω represents the vector of the first beam after wavelength transformation. The angle with the Y-axis.

[0196] Accordingly, based on the vector after the second beam has been transformed into a different wavelength The angle ω with the Y-axis, and the second recording wavelength λ h and the vector after the second beam wavelength is transformed The component K in the Y-axis direction syκ The wavelength transformation of the second beam S is determined to be the second recording wavelength λ based on the following formula. h At that time, the vector of the second beam after wavelength transformation

[0197] in, λ is the vector of the second beam after wavelength transformation. h K is the second recording wavelength. syκ The vector after wavelength transformation of the second beam The component in the Y-axis direction, sign ( * ) Used to determine the sign of *, if the vector of the second beam after wavelength transformation The component K in the Y-axis direction syκ If it is a positive number, then sign ( * ) =+, otherwise sigh ( * ) =-, the vector of the second beam after wavelength transformation in Figure 6 The component K in the Y-axis direction syκ If it is a positive number, sign ( K syκ) The symbol is "+", and ω is the vector of the second beam after wavelength transformation. The angle with the Y-axis.

[0198] It is worth noting that the second recording wavelength λ h The wavelength can be greater than or less than the first recording wavelength λ. The descriptions of the inner and outer edges of the vector circles for different wavelengths in Figure 6 are relative. The final expressions for the vectors after wavelength transformation of the first and second beams are consistent with the two formulas mentioned above. That is, the expressions for the vectors after wavelength transformation of the first and second beams are consistent with the expressions for the second recording wavelength λ. h It is independent of the magnitude relationship between the first recording wavelength λ and the wavelength.

[0199] S503, the vector after the wavelength transformation of the first light beam and the vector after the wavelength transformation of the second light beam are inversely rotated around the Z axis according to the elimination of the rotation parameter, to obtain the rotated vector after the wavelength transformation of the first light beam and the rotated vector after the wavelength transformation of the second light beam.

[0200] The vector after the wavelength transformation of the first light beam is and the vector after the wavelength transformation of the second light beam is Invertedly rotated around the Z axis according to the elimination of the rotation angle κ of the Z axis, and the wavelength of the first light beam R is determined as the second recording wavelength λ based on the following formula h The rotated vector after the wavelength transformation of the first light beam is And the wavelength of the second light beam S is the second recording wavelength λ h The rotated vector after the wavelength transformation of the second light beam is

[0201] Wherein, The rotated vector after the wavelength transformation of the first light beam is h The rotated vector after the wavelength transformation of the first light beam is κ, which is the elimination of the rotation angle of the Z axis, T z(-κ) The rotation matrix corresponding to the Z axis is The vector after the wavelength transformation of the first light beam is K′ rxαβ , K′ ryαβ And K′ rzαβ The rotated vector after the wavelength transformation of the first light beam is The components in the X axis direction, the Y axis direction and the Z axis direction. The rotated vector after the wavelength transformation of the second light beam is h The rotated vector after the wavelength transformation of the second light beam is The vector after the wavelength transformation of the second light beam is K′ sxαβ , K′ syαβ And K′ szαβ The rotated vector after the wavelength transformation of the second light beam is The components in the X axis direction, the Y axis direction and the Z axis direction.

[0202] S504, the rotated vector after the wavelength transformation of the first light beam and the rotated vector after the wavelength transformation of the second light beam are rotated around the Z axis according to the preset Z axis rotation angle, to obtain the material vector of the first light beam and the material vector of the second light beam.

[0203] Optionally, the rotated material position of the holographic photosensitive material is kept unchanged, the rotated vector after the wavelength transformation of the first light beam is Rotated around the Z axis according to the preset Z axis rotation angle, and the rotated vector after the wavelength transformation of the first light beam is The rotation matrix corresponding to the Z axis and the preset Z axis rotation angle obtain the material-in-vector of the first light beam

[0204] The material-in-vector of the first light beam is determined based on the following formula

[0205] Wherein, The material-in-vector of the first light beam is T zγ The rotation matrix corresponding to the Z axis is γ, and the preset Z axis rotation angle is The post-rotation vector after the wavelength transformation of the first light beam is T The conversion relationship when the wavelength of the first light beam R is transformed from the first recording wavelength λ to the second recording wavelength λ h .

[0206] Correspondingly, the post-rotation material position of the holographic photosensitive material is kept unchanged, and the post-rotation vector after the wavelength transformation of the second light beam is T Rotated around the Z axis according to the preset Z axis rotation angle, and the post-rotation vector after the wavelength transformation of the second light beam is T The material-in-vector of the second light beam is obtained by rotating the post-rotation vector after the wavelength transformation of the second light beam around the Z axis according to the preset Z axis rotation angle

[0207] The material-in-vector of the second light beam is determined based on the following formula

[0208] Wherein, The material-in-vector of the second light beam is T zγ The rotation matrix corresponding to the Z axis is γ, and the preset Z axis rotation angle is The post-rotation vector after the wavelength transformation of the second light beam is T The conversion relationship when the wavelength of the second light beam S is transformed from the first recording wavelength λ to the second recording wavelength λ h .

[0209] In this embodiment, the post-rotation vector of the first light beam and the post-rotation vector of the second light beam are respectively rotated forward around the Z axis to eliminate the rotation parameter, to obtain the post-rotation vector of the first light beam after forward rotation and the post-rotation vector of the second light beam after forward rotation. The wavelength of the first light beam and the wavelength of the second light beam are transformed into the second recording wavelength, and the vector of the first light beam after wavelength transformation and the vector of the second light beam after wavelength transformation are determined according to the post-rotation vector of the first light beam after forward rotation and the post-rotation vector of the second light beam after forward rotation. The vector of the first light beam after wavelength transformation and the vector of the second light beam after wavelength transformation are rotated reversely around the Z axis to eliminate the rotation parameter, to obtain the post-rotation vector of the first light beam after wavelength transformation and the post-rotation vector of the second light beam after wavelength transformation, and the post-rotation vector of the first light beam after wavelength transformation and the post-rotation vector of the second light beam after wavelength transformation are respectively rotated around the Z axis according to the preset rotation angle of the Z axis, to obtain the in-medium vector of the first light beam and the in-medium vector of the second light beam. The conversion relationship of the in-medium vector of the first light beam when the wavelength of the first light beam is transformed from the first recording wavelength to the second recording wavelength and the conversion relationship of the in-medium vector of the second light beam when the wavelength of the second light beam is transformed from the first recording wavelength to the second recording wavelength are determined, to realize the decoupling of wavelength transformation.

[0210] Next, the process of determining the in-air vector of the first light beam and the in-air vector of the second light beam according to the in-medium vector of the first light beam and the in-medium vector of the second light beam is described in detail.

[0211] FIG. 7 is a flowchart of determining the in-air vector of the first light beam and the in-air vector of the second light beam in the method for determining the exposure parameters of the volume holographic grating according to an embodiment of the present application, wherein the execution order of steps S701-S702 and steps S703-S704 in FIG. 7 can be interchanged. As shown in FIG. 7, the step of determining the in-air vector of the first light beam and the in-air vector of the second light beam according to the in-medium vector of the first light beam and the in-medium vector of the second light beam in the step S103 includes:

[0212] S701, determining the in-air incident angle of the first light beam according to the in-medium vector of the first light beam, the post-rotation material position of the holographic photosensitive material, and the refractive index of the holographic photosensitive material.

[0213] Optionally, when the type of the volume holographic grating is a transmission type volume holographic grating or a reflection type volume holographic grating, the first light beam R is directed to the positive direction of the Z axis, and the refraction angle ∠RN of the first light beam R is the included angle between the in-medium vector of the first light beam and the post-rotation normal vector of the holographic photosensitive material, i.e.

[0214] critical angle of total reflection ​​When the refraction angle ∠RN of the first light beam R is less than the critical angle θc of total reflection c , the first light beam R can be incident from the air and refracted into the inside of the holographic photosensitive material.

[0215] According to the refractive index n of the holographic photosensitive material and the refraction angle ∠RN of the first light beam R, the air incident angle ∠RN of the first light beam of the transmission volume holographic grating or the reflection volume holographic grating is determined based on the following formula a :

[0216] ∠RN a = sin -1 [nsin(∠RN)]

[0217] wherein ∠RN a is the air incident angle of the first light beam, n is the refractive index of the holographic photosensitive material, and ∠RN is the included angle between the material vector of the first light beam and the positive normal vector of the holographic photosensitive material after rotation, is the material vector of the first light beam, and is the positive normal vector of the holographic photosensitive material after rotation.

[0218] S702, according to the material vector of the first light beam, the material position of the holographic photosensitive material after rotation, the refractive index of the holographic photosensitive material, and the air incident angle of the first light beam, the air vector of the first light beam is determined.

[0219] Optionally, according to the material vector of the first light beam , the negative normal vector of the holographic photosensitive material after rotation , the refractive index n of the holographic photosensitive material, and the air incident angle ∠RN of the first light beam a , the air vector of the first light beam of the transmission volume holographic grating or the reflection volume holographic grating is determined based on the following formula

[0220] wherein is the air vector of the first light beam, n is the refractive index of the holographic photosensitive material, is the material vector of the first light beam, is the modulus of the material vector of the first light beam, is the negative normal vector of the holographic photosensitive material after rotation, and ∠RN a is the air incident angle of the first light beam. ​​​​

[0221] S703, determining the air incident angle of the second beam according to the material-in-vector of the second beam, the material position of the holographic photosensitive material after rotation, and the refractive index of the holographic photosensitive material.

[0222] Optionally, if the type of the volume holographic grating is a transmission type volume holographic grating, and the second beam S points to the positive direction of the Z axis, the refraction angle ∠SN of the second beam S is the included angle between the material-in-vector of the second beam and the positive normal vector of the holographic photosensitive material after rotation, that is,

[0223] total reflection critical angle When the refraction angle ∠SN of the second beam S is less than the total reflection critical angle θ c , the second beam S can be incident from the air 气 and refracted into the interior of the holographic photosensitive material.

[0224] According to the refractive index n of the holographic photosensitive material and the refraction angle ∠SN of the second beam S, the air incident angle ∠SN of the second beam of the transmission type volume holographic grating is determined based on the following formula: a :

[0225] ∠SN a = sin -1 [nsin(∠SN)]

[0226] Wherein, ∠SN a is the air incident angle of the second beam, n is the refractive index of the holographic photosensitive material, and ∠SN is the material-in-vector of the second beam and the positive normal vector of the holographic photosensitive material after rotation , the material-in-vector of the second beam is , and the positive normal vector of the holographic photosensitive material after rotation is .

[0227] If the type of the volume holographic grating is a reflection type volume holographic grating, and the second beam S points to the negative direction of the Z axis, the refraction angle ∠SN of the second beam S is the included angle between the material-in-vector of the second beam and the negative normal vector of the holographic photosensitive material after rotation, that is,

[0228] total reflection critical angle When the refraction angle ∠SN of the second beam S is less than the total reflection critical angle θ c , the second beam S can be incident from the air and refracted into the interior of the holographic photosensitive material. ​​​​

[0229] According to the refractive index n of the holographic photosensitive material and the refraction angle ∠SN of the second light beam S, the air incident angle ∠SN of the second light beam of the reflective volume holographic grating is determined based on the following formula a : ∠SN a = sin -1 [nsin(∠SN)]

[0230] wherein ∠SN a is the air incident angle of the second light beam, n is the refractive index of the holographic photosensitive material, and ∠SN is the included angle between the material vector of the second light beam and the reversed normal vector of the holographic photosensitive material after rotation is the material vector of the second light beam, is the reversed normal vector of the holographic photosensitive material after rotation.

[0231] S704, according to the material vector of the second light beam, the material position of the holographic photosensitive material after rotation, the refractive index of the holographic photosensitive material, and the air incident angle of the second light beam, the air vector of the second light beam is determined.

[0232] Optionally, for the transmissive volume holographic grating, according to the material vector of the second light beam the reversed normal vector of the holographic photosensitive material after rotation the refractive index n of the holographic photosensitive material and the air incident angle ∠SN of the second light beam, a the air vector of the second light beam of the transmissive volume holographic grating is determined based on the following formula

[0233] wherein is the air vector of the second light beam, n is the refractive index of the holographic photosensitive material, is the material vector of the second light beam, is the modulus of the material vector of the second light beam, is the reversed normal vector of the holographic photosensitive material after rotation, and ∠SN a is the air incident angle of the second light beam.

[0234] For the reflective volume holographic grating, according to the material vector of the second light beam the forward normal vector of the holographic photosensitive material after rotation the refractive index n of the holographic photosensitive material and the air incident angle ∠SN of the second light beam, a ​​​, the air-in-vector of the second beam of the reflection volume holographic grating is determined The air-in-vector of the second beam of the reflection volume holographic grating is determined based on the following formula

[0235] wherein, is the air-in-vector of the second beam, n is the refractive index of the holographic photosensitive material, is the material-in-vector of the second beam, is the modulus of the material-in-vector of the second beam, is the reverse normal vector of the holographic photosensitive material after rotation, ∠SN a is the air-in-incident angle of the second beam.

[0236] In this embodiment, the air-in-incident angle of the first beam is determined according to the material-in-vector of the first beam, the material position of the holographic photosensitive material after rotation, and the refractive index of the holographic photosensitive material, and the air-in-vector of the first beam is determined according to the material-in-vector of the first beam, the material position of the holographic photosensitive material after rotation, the refractive index of the holographic photosensitive material, and the air-in-incident angle of the first beam. The air-in-incident angle of the second beam is determined according to the material-in-vector of the second beam, the material position of the holographic photosensitive material after rotation, and the refractive index of the holographic photosensitive material, and the air-in-vector of the second beam is determined according to the material-in-vector of the second beam, the material position of the holographic photosensitive material after rotation, the refractive index of the holographic photosensitive material, and the air-in-incident angle of the second beam. The air-in-vector of the first beam and the air-in-vector of the second beam of different types of volume holographic gratings are determined.

[0237] The process of determining the incident angle of the first beam and the incident angle of the second beam according to the air-in-vector of the first beam and the air-in-vector of the second beam is described in detail below.

[0238] FIG. 8 is a flowchart of determining the incident angle of the first beam and the incident angle of the second beam in the method for determining the exposure parameters of the volume holographic grating provided by the embodiments of the present application, wherein the execution order of steps S801-S802 and steps S803-S804 in FIG. 8 can be interchanged. As shown in FIG. 8, the step of determining the incident angle of the first beam and the incident angle of the second beam according to the air-in-vector of the first beam and the air-in-vector of the second beam in the above step S104 comprises:

[0239] S801, determining the polar angle of the first beam according to the air-in-vector of the first beam and the Z-axis component of the air-in-vector of the first beam.

[0240] Optionally, the air-in-incident angle of the first beam is determined according to the air-in-vector of the first beam Determine the air vector of the first beam The component K in the Z-axis direction raz and the air vector of the first beam model According to the air vector of the first beam The component K in the Z-axis direction raz and the air vector of the first beam model The polar angle θ of the first beam is determined based on the following formula. r :

[0241] Where, θ r K is the polar angle of the first beam. raz The vector of the first beam in air. The air vector of the first beam The model.

[0242] S802. Determine the azimuth angle of the first beam based on the X-axis component of the air vector of the first beam and the Y-axis component of the air vector of the first beam.

[0243] Optionally, based on the air vector of the first beam Determine the air vector of the first beam Component K in the X-axis direction rax and the component K in the Y-axis direction ray According to the air vector of the first beam Component K in the X-axis direction rax and the component K in the Y-axis direction ray The azimuth angle φ of the first beam is determined based on the following formula. r :

[0244] Where, φ r K is the azimuth angle of the first beam. rax and K ray The air vectors of the first beam are respectively The components in the X-axis direction and the components in the Y-axis direction.

[0245] S803. Determine the polar angle of the second beam based on the air vector of the second beam and the Z-axis component of the air vector of the second beam.

[0246] Optionally, based on the air vector of the second beam Determine the air vector of the second beam The component K in the Z-axis direction saz and the air vector of the second beam model According to the air vector of the second beam The component K in the Z-axis direction saz and the air vector of the second beam model The polar angle θ of the second beam is determined based on the following formula. s :

[0247] Where, θ s K is the polar angle of the second beam. saz The vector in air for the second beam. The air vector of the second beam The model.

[0248] S804. Determine the azimuth angle of the second beam based on the X-axis component and the Y-axis component of the air vector of the second beam.

[0249] Optionally, based on the air vector of the second beam Determine the air vector of the second beam Component K in the X-axis direction sax and the component K in the Y-axis direction say According to the air vector of the second beam Component K in the X-axis direction sax and the component K in the Y-axis direction say The azimuth angle φ of the second beam is determined based on the following formula. s :

[0250] Where, φ s K is the azimuth angle of the second beam. sax and K say The air vectors of the second beam are respectively The components in the X-axis direction and the components in the Y-axis direction.

[0251] In this embodiment, the polar angle of the first beam is determined based on its air vector and its Z-axis component; the azimuth angle of the first beam is determined based on its X-axis and Y-axis components, and these angles are used as the incident angle of the first beam. Similarly, the polar angle of the second beam is determined based on its air vector and its Z-axis component; the azimuth angle of the second beam is determined based on its X-axis and Y-axis components, and these angles are used as the incident angle of the second beam. The incident angles of the first and second beams are then used as exposure parameters for the volume holographic grating, achieving spatial decoupling.

[0252] The process of determining the equivalent exposure parameters of the in-coupling volume holographic grating and the out-coupling volume holographic grating is described in detail below.

[0253] It is worth mentioning that in the two-dimensional pupil expanding volume holographic optical waveguide, the parameters of the in-coupling volume holographic grating and the out-coupling volume holographic grating are the same or mirror images, and the out-coupling volume holographic grating can be obtained by rotating the in-coupling volume holographic grating by 90°. In this case, the in-coupling volume holographic grating in the reflective two-dimensional pupil expanding volume holographic optical waveguide is taken as an example, and the process of determining the equivalent exposure parameters of the in-coupling volume holographic grating in the reflective two-dimensional pupil expanding volume holographic optical waveguide is described in detail.

[0254] It is assumed that the first light beam R has a certain incident angle θ y When θ y =0, it represents the case of vertical incidence of the first light beam R, the refractive index of the preset holographic photosensitive material is n=1.51, the first recording wavelength is λ=532 nm, the total reflection angle θ t =50°, the total reflection critical angle θ c =41.47°, i.e. (θ t =50°)>(θ c =41.47°). The vector of the first light beam R and the vector of the second light beam R are represented as:

[0255] The vector of the first light beam R and the vector of the second light beam R are represented as: The grating vector formed by the interference of the vector of the first light beam R and the vector of the second light beam R is represented as:

[0256] The unit vector of the grating vector is: The X-axis rotation angle α and the Y-axis rotation angle β are: β=0

[0257] Since the Y-axis rotation angle β is 0, there is no need to rotate around the Y-axis. At this time, the vector of the first light beam R, the vector of the second light beam R, and the holographic photosensitive material are rotated by 25° around the X-axis, and the rotated vectors of the first light beam R, the second light beam R, and the material position of the rotated holographic photosensitive material are represented as:

[0258]

[0259] ​​​​​​​​According to the three components of the post-rotation vector of the first light beam and the three components of the post-rotation vector of the second light beam, the post-rotation vector of the first light beam and the post-rotation vector of the second light beam are both located in the two-dimensional coordinate system kyokz in which the equivalent plane is located, and are located in the negative half of the Y-axis direction, that is, the post-rotation vector of the first light beam and the post-rotation vector of the second light beam both do not have a component in the X-axis direction, so it is not necessary to perform forward rotation of the post-rotation vector of the first light beam and the post-rotation vector of the second light beam around the Z-axis, that is, the Z-axis eliminates the rotation angle κ = 0, and the wavelength of the first light beam R and the wavelength of the second light beam S are transformed into the second recording wavelength λ h , the preset second recording wavelength λ h = 550 nm.

[0260] The calculated angle ω between the post-wavelength vector of the first light beam and the Y-axis in the two-dimensional coordinate system kyokz in which the equivalent plane is located and the angle ω between the post-wavelength vector of the second light beam and the Y-axis are ω = 69.55°, so in the case that the wavelength of the first light beam R and the wavelength of the second light beam S are both transformed into the second recording wavelength λ h , the post-wavelength vector of the first light beam is and the post-wavelength vector of the second light beam is , which is represented as:

[0261] The preset Z-axis rotation angle γ = 80°, the post-wavelength vector of the first light beam and the post-wavelength vector of the second light beam are rotated around the Z-axis according to the Z-axis rotation angle γ, so the intramaterial vector of the first light beam is represented as and the intramaterial vector of the second light beam is represented as

[0262] Therefore, the refraction angle ∠RN of the first light beam R and the refraction angle ∠SN of the second light beam S are represented as:

[0263] It can be seen that the refraction angle ∠RN of the first light beam R and the refraction angle ∠SN of the second light beam S are both less than the critical angle of total reflection θ c , so the first light beam R and the second light beam S can be incident from the air and refracted into the inside of the holographic photosensitive material.

[0264] Therefore, the air incidence angle ∠RN a of the first light beam and the air incidence angle ∠SN a of the second light beam are:

[0265] ∠RN a = 47.01°

[0266] ∠SN a =58.93°°

[0267] Air vector of the first beam of a reflective volume holographic grating and the air vector of the second beam Represented as:

[0268] Then the polar angle θ of the first beam r azimuth angle φ of the first beam r The polar angle θ of the second beam s And the azimuth angle φ of the second beam s for:

[0269] Table 1: Equivalent Exposure Parameters for Reflective Coupled Volume Holographic Gratings

[0270] Table 1 shows the equivalent exposure parameters of the reflective coupled-body holographic grating provided in the embodiments of this application. As shown in Table 1, the preset first recording wavelength λ is 532nm, and the preset second recording wavelength λ is... h The wavelength is 550nm, the refractive index n of the preset holographic photosensitive material is 1.51, and the preset total reflection angle θ is... t The Z-axis rotation angle is set to 50°, the preset Z-axis rotation angle γ is 80°, the calculated X-axis rotation angle α is 25°, and the Y-axis rotation angle β is 0°, thus determining the polar angle θ of the first beam. r The azimuth angle φ of the first beam is 33.32°. r The polar angle θ of the second beam is 18.95°. s The azimuth angle φ of the second beam is 142.85°. s It is -34.85°.

[0271] The following section uses a holographic grating with a bend in a reflective two-dimensional pupil expander holographic waveguide as an example to explain in detail the process of determining the equivalent exposure parameters of the holographic grating with a bend in a reflective two-dimensional pupil expander holographic waveguide.

[0272] The refractive index of the preset holographic photosensitive material is n = 1.51, the first recording wavelength is λ = 532 nm, and the total reflection angle is θ. t =50°, critical angle for total internal reflection θ c = 41.47°, that is, (θ) t =50°)>(θ c =41.47°). Vector of the first beam in the holographic grating. and the vector of the second beam Represented as:

[0273] the vector of the first light beam the vector of the second light beam the grating vector formed by the interference is expressed as:

[0274] the unit vector of the grating vector is:

[0275] the rotation angle a of the X axis and the rotation angle β of the Y axis are:

[0276] a = -30.79°

[0277] β = 27.11°

[0278] the vector of the first light beam the vector of the second light beam and the holographic photosensitive material is rotated -30.79° around the X axis and 27.11° around the Y axis, the vector of the first light beam after rotation, the vector of the second light beam after rotation and the position of the material of the holographic photosensitive material after rotation are expressed as:

[0279] It can be seen that the vector of the first light beam after rotation and the vector of the second light beam after rotation exist components in the X axis direction, the Y axis direction and the Z axis direction, and the vector of the first light beam after rotation and the vector of the second light beam after rotation need to be positively rotated around the Z axis to rotate the vector of the first light beam after rotation and the vector of the second light beam after rotation to the two-dimensional coordinate system k y ok z in the equivalent plane to eliminate the component of the vector of the first light beam after rotation and the vector of the second light beam after rotation in the X axis direction.

[0280] the positive rotation angle κ of the Z axis is -52.5953°, the positive vector of the first light beam after rotation and the positive vector of the second light beam after rotation is expressed as:

[0281] According to the three components of the positive vector of the first light beam after rotation and the three components of the positive vector of the second light beam after rotation, it can be seen that the positive vector of the first light beam after rotation and the positive vector of the second light beam after rotation are located in the two-dimensional coordinate system k y ok z in the equivalent plane, and are located in the negative half axis of the Y axis direction, that is, by rotation, the positive vector of the first light beam after rotation and the positive vector of the second light beam after rotation do not exist components in the X axis direction.

[0282] ​The wavelengths of the first beam R and the second beam S are converted into the second recording wavelength λ. h The second recording wavelength λ is preset. h =632nm.

[0283] The vector after the first beam wavelength is transformed is calculated. The two-dimensional coordinate system k containing the equivalent plane y OK z The included angle ω of the inner Y-axis and the vector after the second beam wavelength transformation The angle ω with the Y-axis is 86.96°, so the wavelengths of the first beam R and the second beam S are both transformed into the second recording wavelength λ. h In the case of the first beam after wavelength transformation, the vector is: And the vector after the second beam wavelength is Represented as:

[0284] Vector after wavelength transformation of the first beam Vector after wavelength conversion of the second beam The beams are rotated in reverse around the Z-axis according to the Z-axis rotation angle κ, and the wavelength of the first beam R is the second recording wavelength λ. h At that time, the rotated vector after the first beam changes wavelength And the wavelength of the second beam S is the second recording wavelength λ. h At that time, the rotated vector after the second beam changes wavelength Represented as:

[0285] With a preset Z-axis rotation angle γ = 10°, the vector after wavelength transformation of the first beam... and the vector after the second beam wavelength is transformed Rotating around the Z-axis by a rotation angle γ, the material vectors of the first beam and the second beam are expressed as follows:

[0286] Then the refraction angle ∠RN of the first beam R and the refraction angle ∠SN of the second beam S are:

[0287] ∠RN=39.68°

[0288] ∠SN=40.74°

[0289] It can be seen that the refraction angles ∠RN of the first beam R and ∠SN of the second beam S are both less than the critical angle θ for total internal reflection. c Both the first beam R and the second beam S can be incident from the air and refracted into the interior of the holographic photosensitive material.

[0290] the air incidence angle ∠RN of the first light beam a and the air incidence angle ∠SN of the second light beam a are:

[0291] ∠RN a = 74.63°

[0292] ∠SN a = 80.22°

[0293] the air vector of the first light beam of the reflective turning body holographic grating and the air vector of the second light beam are represented as:

[0294] the polar angle θ of the first light beam r , the azimuth angle φ of the first light beam r , the polar angle θ of the second light beam s and the azimuth angle φ of the second light beam s are:

[0295] Table 2: equivalent exposure parameter table of the reflective turning body holographic grating

[0296] Table 2 is the equivalent exposure parameter table of the reflective turning body holographic grating provided in the embodiment of the present application, as shown in Table 2, the preset first recording wavelength λ is 532 nm, the preset second recording wavelength λ h is 632 nm, the preset refractive index n of the holographic photosensitive material is 1.51, the preset full reflection angle θ t is 50°, the preset Z-axis rotation angle γ is 10°, the X-axis rotation angle α is-30.79° and the Y-axis rotation angle β is 27.11° obtained by calculation, the polar angle θ r of the first light beam is 34.72°, the azimuth angle φ r of the first light beam is 60.55°, the polar angle θ s of the second light beam is 143.99°, and the azimuth angle φ s of the second light beam is 45°.

[0297] Based on the same inventive concept, the embodiment of the present application also provides a volume holographic grating exposure parameter determination device corresponding to the volume holographic grating exposure parameter determination method, since the principle of the device in the embodiment of the present application solves the problem, which is similar to the above-mentioned volume holographic grating exposure parameter determination method of the embodiment of the present application, therefore the implementation of the device can be referred to the implementation of the method, and the repeated parts will not be described here.

[0298] Figure 9 is a module structure diagram of a device for determining exposure parameters of a volume holographic grating according to an embodiment of the present application. As shown in Figure 9, the device includes:

[0299] The rotating module is configured to rotate the vector of the first light beam, the vector of the second light beam, and the holographic photosensitive material a plurality of times when the wavelength of the first light beam and the wavelength of the second light beam are the first recording wavelength, to obtain a post-rotation vector of the first light beam, a post-rotation vector of the second light beam, and a post-rotation material position of the holographic photosensitive material.

[0300] The rotating module is further configured to transform the wavelength of the first light beam and the wavelength of the second light beam into the second recording wavelength, and rotate the post-rotation vector of the first light beam and the post-rotation vector of the second light beam at least once to obtain an in-material vector of the first light beam and an in-material vector of the second light beam.

[0301] The determining module is configured to determine an in-air vector of the first light beam and an in-air vector of the second light beam according to the in-material vector of the first light beam and the in-material vector of the second light beam.

[0302] The determining module is further configured to determine an incidence angle of the first light beam and an incidence angle of the second light beam according to the in-air vector of the first light beam and the in-air vector of the second light beam, so as to perform exposure interference on the holographic photosensitive material located at the post-rotation material position according to the incidence angle of the first light beam and the incidence angle of the second light beam and obtain a two-dimensional pupil expanding volume holographic grating.

[0303] As an optional implementation, the rotating module 901 is specifically configured to:

[0304] determine an X-axis rotation angle and a Y-axis rotation angle according to the vector of the first light beam and the vector of the second light beam.

[0305] rotate the vector of the first light beam, the vector of the second light beam, and the holographic photosensitive material around the X axis according to the X-axis rotation angle respectively to obtain a first post-rotation vector of the first light beam, a first post-rotation vector of the second light beam, and a first post-rotation material position of the holographic photosensitive material.

[0306] rotate the first post-rotation vector of the first light beam, the first post-rotation vector of the second light beam, and the holographic photosensitive material located at the first post-rotation material position around the Y axis according to the Y-axis rotation angle respectively to obtain the post-rotation vector of the first light beam, the post-rotation vector of the second light beam, and the post-rotation material position of the holographic photosensitive material.

[0307] As an optional implementation, the rotating module 901 is specifically configured to:

[0308] determine a grating vector according to a difference between the vector of the first light beam and the vector of the second light beam.

[0309] determine the X-axis rotation angle and the Y-axis rotation angle according to the grating vector.

[0310] As an optional implementation, the rotation module 901 is specifically configured to:

[0311] determine the unit vector of the grating vector.

[0312] determine the X-axis rotation angle according to the unit vector and the rotation matrix corresponding to the X-axis.

[0313] determine the rotation unit vector of the unit vector after rotating around the X-axis according to the X-axis rotation angle.

[0314] determine the Y-axis rotation angle according to the rotation unit vector and the rotation matrix corresponding to the Y-axis.

[0315] As an optional implementation, the rotation module 901 is specifically configured to:

[0316] determine the rotation elimination parameter according to the rotated vector of the first light beam, the rotated vector of the second light beam, and the rotation matrix corresponding to the Z-axis, and perform forward rotation around the Z-axis on the rotated vector of the first light beam and the rotated vector of the second light beam according to the rotation elimination parameter, to obtain a forward rotated vector of the first light beam and a forward rotated vector of the second light beam.

[0317] transform the wavelength of the first light beam and the wavelength of the second light beam into a second recording wavelength, and determine a vector of the first light beam after wavelength transformation and a vector of the second light beam after wavelength transformation according to the forward rotated vector of the first light beam and the forward rotated vector of the second light beam.

[0318] perform inverse rotation around the Z-axis on the vector of the first light beam after wavelength transformation and the vector of the second light beam after wavelength transformation according to the rotation elimination parameter, to obtain a rotated vector of the first light beam after wavelength transformation and a rotated vector of the second light beam after wavelength transformation.

[0319] rotate the rotated vector of the first light beam after wavelength transformation and the rotated vector of the second light beam after wavelength transformation around the Z-axis according to a preset Z-axis rotation angle, to obtain an intramaterial vector of the first light beam and an intramaterial vector of the second light beam.

[0320] As an optional implementation, the determination module 902 is specifically configured to:

[0321] determine the air incidence angle of the first light beam according to the intramaterial vector of the first light beam, the rotated material position of the holographic photosensitive material, and the refractive index of the holographic photosensitive material.

[0322] The air-in-vector of the first light beam is determined according to the material-in-vector of the first light beam, the material position of the holographic photosensitive material after rotation, the refractive index of the holographic photosensitive material, and the air-in-angle of incidence of the first light beam.

[0323] The air-in-angle of incidence of the second light beam is determined according to the material-in-vector of the second light beam, the material position of the holographic photosensitive material after rotation, and the refractive index of the holographic photosensitive material.

[0324] The air-in-vector of the second light beam is determined according to the material-in-vector of the second light beam, the material position of the holographic photosensitive material after rotation, the refractive index of the holographic photosensitive material, and the air-in-angle of incidence of the second light beam.

[0325] As an optional implementation, the determining module 902 is specifically configured to:

[0326] The polar angle of the first light beam is determined according to the air-in-vector of the first light beam and the Z-axis component of the air-in-vector of the first light beam.

[0327] The azimuth angle of the first light beam is determined according to the X-axis component of the air-in-vector of the first light beam and the Y-axis component of the air-in-vector of the first light beam.

[0328] The polar angle of the second light beam is determined according to the air-in-vector of the second light beam and the Z-axis component of the air-in-vector of the second light beam.

[0329] The azimuth angle of the second light beam is determined according to the X-axis component of the air-in-vector of the second light beam and the Y-axis component of the air-in-vector of the second light beam.

[0330] The embodiment also provides a first computer device, as shown in FIG. 10, which is a structural schematic diagram of the first computer device provided by the embodiment, and includes a first processor 101, a first memory 102, and a first bus 103. The first memory 102 stores first machine readable instructions (for example, execution instructions corresponding to the rotating module 901 and the determining module 902 in the device in FIG. 9) executable by the first processor 101. When the first computer device is running, the first processor 101 and the first memory 102 communicate through the first bus 103. When the first machine readable instructions are executed by the first processor 101, the steps of the method for determining volume holographic grating exposure parameters in the above embodiment are performed.

[0331] The embodiment also provides a first computer readable storage medium, which stores a first computer program. When the first computer program is run by a first processor, the steps of the method for determining volume holographic grating exposure parameters in the above embodiment are performed.

[0332] FIG. 11 is a flowchart of a method for manufacturing a volume holographic grating according to an embodiment of the present application. The method can be executed by any computer device having a computing capability. As shown in FIG. 11, the method comprises the following steps.

[0333] S1101, obtaining the incident angles of the first light beam and the second light beam of the in-coupling volume holographic grating, the incident angles of the first light beam and the second light beam of the turning volume holographic grating, and the incident angles of the first light beam and the second light beam of the out-coupling volume holographic grating, which are determined by the determination method of the volume holographic grating exposure parameters.

[0334] Optionally, the incident angles of the first light beam and the second light beam of the in-coupling volume holographic grating, the incident angles of the first light beam and the second light beam of the turning volume holographic grating, and the incident angles of the first light beam and the second light beam of the out-coupling volume holographic grating are obtained by the determination method of the volume holographic grating exposure parameters in the foregoing embodiments. The incident angles of the first light beam include the polar angle θ r and the azimuth angle φ r of the first light beam, and the incident angles of the second light beam include the polar angle θ s and the azimuth angle φ s of the second light beam.

[0335] S1102, performing interference exposure on the holographic photosensitive material at the material position after rotation according to the incident angles of the first light beam and the second light beam of the in-coupling volume holographic grating, the incident angles of the first light beam and the second light beam of the turning volume holographic grating, and the incident angles of the first light beam and the second light beam of the out-coupling volume holographic grating, respectively, to obtain the in-coupling volume holographic grating, the turning volume holographic grating, and the out-coupling volume holographic grating.

[0336] Optionally, the holographic photosensitive material at the material position after rotation is subjected to double-beam interference exposure according to the incident angles of the first light beam and the second light beam of the in-coupling volume holographic grating to obtain the in-coupling volume holographic grating. The holographic photosensitive material at the material position after rotation is subjected to double-beam interference exposure according to the incident angles of the first light beam and the second light beam of the turning volume holographic grating to obtain the turning volume holographic grating. The holographic photosensitive material at the material position after rotation is subjected to double-beam interference exposure according to the incident angles of the first light beam and the second light beam of the out-coupling volume holographic grating to obtain the out-coupling volume holographic grating. The material position after rotation of the holographic photosensitive material is a position obtained by rotating the holographic photosensitive material according to an X-axis rotation angle around the X-axis and then rotating the holographic photosensitive material according to a Y-axis rotation angle around the Y-axis.

[0337] In the embodiment, the incidence angles of the first light beams and the incidence angles of the second light beams of the in-coupling volume holographic grating, the turning volume holographic grating and the out-coupling volume holographic grating determined by the determination method of the volume holographic grating exposure parameters are obtained. The holographic photosensitive materials located at the positions of the materials after rotation are subjected to double-beam interference exposure according to the incidence angles of the first light beams and the incidence angles of the second light beams of the in-coupling volume holographic grating, the incidence angles of the first light beams and the incidence angles of the second light beams of the turning volume holographic grating and the incidence angles of the first light beams and the incidence angles of the second light beams of the out-coupling volume holographic grating, respectively, to obtain the in-coupling volume holographic grating, the out-coupling volume holographic grating and the turning volume holographic grating. The manufacturing of the two-dimensional pupil expanding volume holographic grating containing the in-coupling volume holographic grating, the turning volume holographic grating and the out-coupling volume holographic grating is realized, the efficiency and the reliability of the manufacturing of the volume holographic grating are improved, and the manufacturing cost is reduced.

[0338] Based on the same inventive concept, the application also provides a manufacturing device of a volume holographic grating corresponding to the manufacturing method of the volume holographic grating. Since the principle of the device in the embodiment of the application for solving the problem is similar to the manufacturing method of the volume holographic grating in the embodiment of the application, the implementation of the device can be referred to the implementation of the method, and the repeated parts will not be described herein.

[0339] FIG. 12 is a module structure diagram of the manufacturing device of the two-dimensional pupil expanding volume holographic grating provided by the embodiment of the application. As shown in FIG. 12, the device comprises:

[0340] The acquisition module 1201 is configured to acquire the incidence angles of the first light beams and the incidence angles of the second light beams of the in-coupling volume holographic grating, the turning volume holographic grating and the out-coupling volume holographic grating determined by the determination method of the volume holographic grating exposure parameters, respectively.

[0341] The interference module 1202 is configured to perform interference exposure on the holographic photosensitive materials located at the positions of the materials after rotation according to the incidence angles of the first light beams and the incidence angles of the second light beams of the in-coupling volume holographic grating, the incidence angles of the first light beams and the incidence angles of the second light beams of the turning volume holographic grating and the incidence angles of the first light beams and the incidence angles of the second light beams of the out-coupling volume holographic grating, respectively, to obtain the in-coupling volume holographic grating, the turning volume holographic grating and the out-coupling volume holographic grating.

[0342] The embodiment also provides a second computer device, as shown in FIG. 13, which is a structural schematic diagram of the second computer device provided by the embodiment, and includes a second processor 131, a second memory 132 and a second bus 133. The second memory 132 stores second machine readable instructions (for example, corresponding execution instructions of the device obtaining module 1201 and the interference module 1202 in FIG. 12) executable by the second processor 131. When the second computer device is running, the second processor 131 communicates with the second memory 132 through the second bus 133. When the second machine readable instructions are executed by the second processor 131, the steps of the method for manufacturing a volume holographic grating in the above embodiment are performed.

[0343] The embodiment of the present application also provides a second computer readable storage medium, and the second computer readable storage medium stores a second computer program. When the second computer program is run by a second processor, the steps of the method for manufacturing a volume holographic grating in the above embodiment are performed.

[0344] The embodiment of the present application also provides a two-dimensional pupil expanding volume holographic grating, and the two-dimensional pupil expanding volume holographic grating includes a coupling-in volume holographic grating, a turning volume holographic grating and a coupling-out volume holographic grating. The coupling-in volume holographic grating, the turning volume holographic grating and the coupling-out volume holographic grating are manufactured by the method for manufacturing a volume holographic grating described in the above embodiment.

[0345] The embodiment of the present application provides a two-dimensional pupil expanding volume holographic optical waveguide, and the two-dimensional pupil expanding volume holographic optical waveguide includes a waveguide base and the coupling-in volume holographic grating, the turning volume holographic grating and the coupling-out volume holographic grating described in the above embodiment. The coupling-in volume holographic grating, the turning volume holographic grating and the coupling-out volume holographic grating are located at corresponding positions of the waveguide base.

[0346] Optionally, FIG. 14 is a layout schematic diagram of an L-shaped two-dimensional pupil expanding volume holographic optical waveguide provided by the embodiment of the present application. As shown in FIG. 14, the L-shaped two-dimensional pupil expanding volume holographic optical waveguide includes a waveguide base 201, a coupling-in volume holographic grating 202, a turning volume holographic grating 203 and a coupling-out volume holographic grating 204. The grating parameters of the coupling-in volume holographic grating 202 are the same as the grating parameters of the coupling-out volume holographic grating 204. The coupling-in volume holographic grating 202 is rotated by 90 degrees to obtain the coupling-out volume holographic grating 204.

[0347] FIG. 15 is a central field of view light transmission schematic diagram of a reflective two-dimensional pupil expanding volume holographic optical waveguide provided by the embodiment of the present application. As shown in FIG. 15, the reflective two-dimensional pupil expanding volume holographic optical waveguide includes a waveguide base 301, a coupling-in volume holographic grating 302, a turning volume holographic grating 303 and a coupling-out volume holographic grating 304.

[0348] The first light beam is taken as the reference light R in For example, the reference light Rin The perpendicular incidence into the coupling-in volume holographic grating 302 generates diffracted light S in The reverse transmission, the diffracted light S in The included angle with the normal is θ t , θ t > θ c So that the diffracted light S in Reflects on the other surface of the waveguide substrate 301, and the reflected light R after one or more reflections (only one is exemplarily drawn in FIG. 14) t Incidence into the coupling-out volume holographic grating 304 generates diffracted light S t . The diffracted light S t Turns in the X direction, and after several times of total reflection in the waveguide substrate 301 (only one is exemplarily drawn in FIG. 14), the diffracted light S O . The parameters of the coupling-in volume holographic grating 303 and the coupling-out volume holographic grating 304 are the same.

[0349] The embodiment also provides a determination device of exposure parameters of a volume holographic grating, as shown in FIG. 16, the device comprises:

[0350] A first rotating module 111, configured to rotate a vector of a first light beam, a vector of a second light beam and a holographic photosensitive material for multiple times when a wavelength of the first light beam and a wavelength of the second light beam are first recording wavelengths, to obtain a rotated vector of the first light beam, a rotated vector of the second light beam and a rotated material position of the holographic photosensitive material;

[0351] A second rotating module 112, configured to transform the wavelength of the first light beam and the wavelength of the second light beam into second recording wavelengths, and rotate the rotated vector of the first light beam and the rotated vector of the second light beam for at least one time to obtain an in-material vector of the first light beam and an in-material vector of the second light beam;

[0352] A determination module 113, configured to determine an in-air vector of the first light beam and an in-air vector of the second light beam according to the in-material vector of the first light beam and the in-material vector of the second light beam, and determine an incidence angle of the first light beam and an incidence angle of the second light beam according to the in-air vector of the first light beam and the in-air vector of the second light beam, so as to perform interference exposure on the holographic photosensitive material located at the rotated material position according to the incidence angle of the first light beam and the incidence angle of the second light beam to obtain a volume holographic grating.

[0353] In the above embodiment, it is assumed that the refractive index of the holographic photosensitive material is the same as the refractive index of the waveguide substrate, so that the light from the waveguide substrate to the holographic photosensitive material or the light from the holographic photosensitive material to the waveguide substrate does not perform additional refraction calculation, when the refractive index of the holographic photosensitive material is different from the refractive index of the waveguide substrate, refraction will occur at the interface, which can be calculated once by the refraction theorem of three-dimensional space vector.

[0354] It is worth noting that in the above embodiment, the two-dimensional pupil expanding volume holographic optical waveguide distributes the in-coupling, turning and out-coupling volume holographic gratings, and the equivalent exposure conditions are given. The equivalent exposure method can also be used to manufacture single-layer full-color or three-layer full-color volume holographic optical waveguides. When one of the first light beam or the second light beam cannot satisfy the condition of being refracted into the material in the air, one or two coupling prisms can be used to couple the totally reflected light into the interior of the holographic photosensitive material for interference exposure. The exposure in this case also meets the requirements of equivalent exposure. The manufacture of two-dimensional pupil expanding volume holographic optical waveguide without prisms is one of the special solutions. The present application provides a general equivalent exposure design method for volume holographic optical elements. By solving the equivalent conditions of the two interfering lights, changing the angle or position of the incident light and the holographic photosensitive material, the manufacturing difficulty is reduced, the manufacturing efficiency and quality are improved, and the cost is reduced, which is conducive to the wide application of various volume holographic optical elements.

[0355] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working process of the system and device described above can refer to the corresponding process in the method embodiment, which will not be described herein. In the several embodiments provided in the present application, it should be understood that the disclosed system, device and method can be implemented by other ways. The above-described device embodiments are only schematic, for example, the division of the modules is only a logical function division, and the actual implementation can be another division manner, for example, a plurality of modules or components can be combined or integrated into another system, or some features can be ignored or not executed.

[0356] In addition, each of the functional units in the embodiments of the present application can be integrated in one processing unit, or each unit can exist alone physically, or two or more units can be integrated in one unit. When the functions are implemented in the form of software function units and sold or used as independent products, they can be stored in a computer readable storage medium. Based on such an understanding, the technical solutions of the present application essentially or partially consist of a software product and are realized in the form of a software program. The software product is stored in a storage medium, and includes a number of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the methods described in the embodiments of the present application. The foregoing storage medium includes various media that can store program codes, such as a U disk, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0357] The above merely provides the specific implementation of the present application, but the protection scope of the present application is not limited thereto, and any person skilled in the art can easily think of the changes or replacements within the technical scope disclosed by the present application, which shall be encompassed in the protection scope of the present application. Industrial applicability

[0358] Through the above-mentioned volume holographic grating exposure parameter determination method and device and two-dimensional pupil expanding volume holographic optical waveguide, before the wavelength of the first light beam and the wavelength of the second light beam change, the post-rotation vector of the first light beam, the post-rotation vector of the second light beam and the post-rotation material position of the holographic photosensitive material are determined through multiple rotations; after the wavelength of the first light beam and the wavelength of the second light beam change, the post-rotation material position of the holographic photosensitive material remains unchanged, and the in-material vector of the first light beam and the in-material vector of the second light beam are determined through at least one rotation of the post-rotation vector of the first light beam and the post-rotation vector of the second light beam, the equivalent exposure conditions of the in-material vector of the first light beam and the in-material vector of the second light beam when the wavelength changes are obtained, and wavelength decoupling is realized. Based on the equivalent exposure conditions of the in-material vector of the first light beam and the in-material vector of the second light beam, the in-air vector of the first light beam and the in-air vector of the second light beam are obtained, and then the incident angle of the first light beam and the incident angle of the second light beam are obtained, and spatial decoupling is realized. The incident angle of the first light beam and the incident angle of the second light beam are taken as the volume holographic grating exposure parameters, and according to the volume holographic grating exposure parameters, the first light beam and the second light beam are incident on the holographic photosensitive material from the air to perform double-beam interference exposure on the holographic photosensitive material at the post-rotation material position to manufacture the volume holographic grating. Through wavelength decoupling and spatial decoupling, the required volume holographic grating can be exposed under equivalent conditions, thereby reducing the manufacturing difficulty and cost of the volume holographic grating.

Claims

1. A method of determining exposure parameters for volume holographic gratings, characterized by, The method comprises: when the wavelength of the first light beam and the wavelength of the second light beam are first recording wavelengths, rotating the vector of the first light beam, the vector of the second light beam and the holographic photosensitive material multiple times to obtain the rotated vector of the first light beam, the rotated vector of the second light beam and the rotated material position of the holographic photosensitive material; transforming the wavelength of the first light beam and the wavelength of the second light beam into second recording wavelengths, and rotating the rotated vector of the first light beam and the rotated vector of the second light beam at least once to obtain the in-material vector of the first light beam and the in-material vector of the second light beam; determining the in-air vector of the first light beam and the in-air vector of the second light beam according to the in-material vector of the first light beam and the in-material vector of the second light beam; determining the incidence angle of the first light beam and the incidence angle of the second light beam according to the in-air vector of the first light beam and the in-air vector of the second light beam, so that the holographic photosensitive material at the rotated material position is subjected to interference exposure according to the incidence angle of the first light beam and the incidence angle of the second light beam to obtain a volume holographic grating.

2. The method of claim 1, wherein, The rotating the vector of the first light beam, the vector of the second light beam and the holographic photosensitive material multiple times to obtain the rotated vector of the first light beam, the rotated vector of the second light beam and the rotated material position of the holographic photosensitive material comprises: determining the X-axis rotation angle and the Y-axis rotation angle according to the vector of the first light beam and the vector of the second light beam; rotating the vector of the first light beam, the vector of the second light beam and the holographic photosensitive material around the X-axis according to the X-axis rotation angle respectively to obtain the first intermediate rotated vector of the first light beam, the first intermediate rotated vector of the second light beam and the first intermediate rotated material position of the holographic photosensitive material; rotating the first intermediate rotated vector of the first light beam, the first intermediate rotated vector of the second light beam and the holographic photosensitive material at the first intermediate rotated material position around the Y-axis according to the Y-axis rotation angle respectively to obtain the rotated vector of the first light beam, the rotated vector of the second light beam and the rotated material position of the holographic photosensitive material.

3. The method of claim 2, wherein, The determining the X-axis rotation angle and the Y-axis rotation angle according to the vector of the first light beam and the vector of the second light beam comprises: determining a grating vector according to the difference between the vector of the first light beam and the vector of the second light beam; determining the X-axis rotation angle and the Y-axis rotation angle according to the grating vector.

4. The method of claim 3, wherein, The determining the X-axis rotation angle and the Y-axis rotation angle according to the grating vector comprises: determining a unit vector of the grating vector; determining the X-axis rotation angle according to the unit vector and the rotation matrix corresponding to the X-axis; determining a rotated unit vector of the unit vector after rotating around the X-axis according to the X-axis rotation angle; determining the Y-axis rotation angle according to the rotated unit vector and the rotation matrix corresponding to the Y-axis.

5. The method of claim 1, wherein, The rotating the post-rotation vectors of the first light beam and the post-rotation vectors of the second light beam at least once to obtain the material-in vectors of the first light beam and the material-in vectors of the second light beam comprises: determining a rotation elimination parameter according to the post-rotation vectors of the first light beam, the post-rotation vectors of the second light beam and a rotation matrix corresponding to the Z axis, and performing forward rotation of the post-rotation vectors of the first light beam and the post-rotation vectors of the second light beam around the Z axis according to the rotation elimination parameter to obtain the post-forward-rotation vectors of the first light beam and the post-forward-rotation vectors of the second light beam; determining the post-wavelength-change vectors of the first light beam and the post-wavelength-change vectors of the second light beam according to the post-forward-rotation vectors of the first light beam and the post-forward-rotation vectors of the second light beam; performing inverse rotation of the post-wavelength-change vectors of the first light beam and the post-wavelength-change vectors of the second light beam around the Z axis according to the rotation elimination parameter to obtain the post-inverse-rotation vectors of the post-wavelength-change vectors of the first light beam and the post-inverse-rotation vectors of the post-wavelength-change vectors of the second light beam; rotating the post-inverse-rotation vectors of the post-wavelength-change vectors of the first light beam and the post-inverse-rotation vectors of the post-wavelength-change vectors of the second light beam around the Z axis according to a preset Z axis rotation angle to obtain the material-in vectors of the first light beam and the material-in vectors of the second light beam.

6. The method of claim 1, wherein, The determining the air-in vectors of the first light beam and the air-in vectors of the second light beam according to the material-in vectors of the first light beam and the material-in vectors of the second light beam comprises: determining an air-in incident angle of the first light beam according to the material-in vector of the first light beam, a post-rotation material position of the holographic photosensitive material and a refractive index of the holographic photosensitive material; determining the air-in vector of the first light beam according to the material-in vector of the first light beam, the post-rotation material position of the holographic photosensitive material, the refractive index of the holographic photosensitive material and the air-in incident angle of the first light beam; determining an air-in incident angle of the second light beam according to the material-in vector of the second light beam, the post-rotation material position of the holographic photosensitive material and the refractive index of the holographic photosensitive material; determining the air-in vector of the second light beam according to the material-in vector of the second light beam, the post-rotation material position of the holographic photosensitive material, the refractive index of the holographic photosensitive material and the air-in incident angle of the second light beam.

7. The method of claim 1, wherein, The determining the incident angles of the first light beam and the incident angles of the second light beam according to the air-in vectors of the first light beam and the air-in vectors of the second light beam comprises: determining a polar angle of the first light beam according to the air-in vector of the first light beam and a Z axis component of the air-in vector of the first light beam; determining an azimuth angle of the first light beam according to an X axis component of the air-in vector of the first light beam and a Y axis component of the air-in vector of the first light beam; determining a polar angle of the second light beam according to the air-in vector of the second light beam and a Z axis component of the air-in vector of the second light beam; and determining an azimuth angle of the second light beam according to an X axis component of the air-in vector of the second light beam and a Y axis component of the air-in vector of the second light beam. The azimuth angle of the second light beam is determined according to the X-axis component of the in-air vector of the second light beam and the Y-axis component of the in-air vector of the second light beam.

8. A method of manufacturing a volume holographic grating, characterized by, The method comprises: The first light beam and the second light beam of the in-coupling volume holographic grating, the turning volume holographic grating and the out-coupling volume holographic grating are obtained according to the first light beam and the second light beam of the in-coupling volume holographic grating, the first light beam and the second light beam of the turning volume holographic grating and the first light beam and the second light beam of the out-coupling volume holographic grating determined by the method for determining the exposure parameters of the volume holographic grating according to any one of claims 1-7. The first light beam and the second light beam of the in-coupling volume holographic grating, the first light beam and the second light beam of the turning volume holographic grating and the first light beam and the second light beam of the out-coupling volume holographic grating are obtained according to the first light beam and the second light beam of the in-coupling volume holographic grating, the first light beam and the second light beam of the turning volume holographic grating and the first light beam and the second light beam of the out-coupling volume holographic grating.

9. A two-dimensional pupil expanding volume holographic grating, characterized by, The two-dimensional pupil expanding volume holographic grating comprises the in-coupling volume holographic grating, the turning volume holographic grating and the out-coupling volume holographic grating, which are manufactured by the method for manufacturing the volume holographic grating according to claim 8.

10. A two-dimensional pupil expanding volume holographic optical waveguide, characterized by, The two-dimensional pupil expanding volume holographic grating comprises the waveguide substrate and the in-coupling volume holographic grating, the turning volume holographic grating and the out-coupling volume holographic grating according to claim 9, which are located at the corresponding positions of the waveguide substrate.

11. An apparatus for determining exposure parameters of a volume holographic grating, characterized by The device comprises: The first rotating module is configured to rotate the vector of the first light beam, the vector of the second light beam and the holographic photosensitive material multiple times to obtain the post-rotation vector of the first light beam, the post-rotation vector of the second light beam and the post-rotation material position of the holographic photosensitive material when the wavelength of the first light beam and the wavelength of the second light beam are the first recording wavelength. The second rotating module is configured to transform the wavelength of the first light beam and the wavelength of the second light beam into the second recording wavelength and rotate the post-rotation vector of the first light beam and the post-rotation vector of the second light beam at least once to obtain the in-material vector of the first light beam and the in-material vector of the second light beam. The determining module is configured to determine the in-air vector of the first light beam and the in-air vector of the second light beam according to the in-material vector of the first light beam and the in-material vector of the second light beam, and determine the incidence angle of the first light beam and the incidence angle of the second light beam according to the in-air vector of the first light beam and the in-air vector of the second light beam, so as to perform interference exposure on the holographic photosensitive material at the post-rotation material position according to the incidence angle of the first light beam and the incidence angle of the second light beam to obtain the volume holographic grating.

12. The apparatus of claim 11, wherein, The first rotating module is configured to: determine the X-axis rotation angle and the Y-axis rotation angle according to the vector of the first light beam and the vector of the second light beam; rotating the vector of the first light beam, the vector of the second light beam and the holographic photosensitive material according to the X-axis rotation angle around the X-axis respectively, to obtain a first intermediate post-rotation vector of the first light beam, a first intermediate post-rotation vector of the second light beam and a first intermediate post-rotation material position of the holographic photosensitive material; rotating the first intermediate post-rotation vector of the first light beam, the first intermediate post-rotation vector of the second light beam and the holographic photosensitive material located at the first intermediate post-rotation material position according to the Y-axis rotation angle around the Y-axis respectively, to obtain a post-rotation vector of the first light beam, a post-rotation vector of the second light beam and a post-rotation material position of the holographic photosensitive material.

13. The apparatus of claim 12, wherein, The first rotation module is specifically configured to: determine a grating vector according to the difference between the vector of the first light beam and the vector of the second light beam; determine the X-axis rotation angle and the Y-axis rotation angle according to the grating vector.

14. The apparatus of claim 13, wherein, The first rotation module is specifically configured to: determine a unit vector of the grating vector; determine the X-axis rotation angle according to the unit vector and a rotation matrix corresponding to the X-axis; determine a rotated unit vector of the unit vector after rotating around the X-axis according to the X-axis rotation angle; determine the Y-axis rotation angle according to the rotated unit vector and a rotation matrix corresponding to the Y-axis.

15. The apparatus of claim 11, wherein, The second rotation module is configured to: determine a rotation elimination parameter according to the post-rotation vector of the first light beam, the post-rotation vector of the second light beam and a rotation matrix corresponding to the Z-axis, and perform forward rotation of the post-rotation vector of the first light beam and the post-rotation vector of the second light beam around the Z-axis according to the rotation elimination parameter, to obtain a forward post-rotation vector of the first light beam and a forward post-rotation vector of the second light beam; determine a vector of the first light beam after wavelength conversion and a vector of the second light beam after wavelength conversion according to the forward post-rotation vector of the first light beam and the forward post-rotation vector of the second light beam; perform inverse rotation of the vector of the first light beam after wavelength conversion and the vector of the second light beam after wavelength conversion around the Z-axis according to the rotation elimination parameter, to obtain a post-rotation vector of the first light beam after wavelength conversion and a post-rotation vector of the second light beam after wavelength conversion; perform rotation of the post-rotation vector of the first light beam after wavelength conversion and the post-rotation vector of the second light beam after wavelength conversion around the Z-axis according to a preset Z-axis rotation angle, to obtain a material-in-vector of the first light beam and a material-in-vector of the second light beam.

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