Optimization control parameter calculation method for passive cascaded liquid crystal polarization grating

Abstract

The application discloses a calculation method for optimizing control parameters of a passive cascade liquid crystal polarization grating, and belongs to the technical field of liquid crystal polarization gratings. In order to solve the problem of low diffraction efficiency of the passive cascade polarization grating, the method comprises the following steps: calculating the layer control coefficient required by each layer of the cascade liquid crystal polarization grating at different deflection angles; calculating a sheet control coefficient of a liquid crystal adjustable half-wave plate; calculating a sheet applied voltage coefficient of each sheet of the liquid crystal adjustable half-wave plate from the emission end according to the sheet control coefficient and a polarization state of incident light, and establishing a sheet applied voltage coefficient set; and calculating a control voltage of each sheet of the liquid crystal adjustable half-wave plate according to the sheet control coefficient of each sheet of the liquid crystal adjustable half-wave plate and the angle of the incident light, so that the outgoing light of each layer is standard circularly polarized light, and a control voltage set of the cascade liquid crystal polarization grating is established. Under the premise of not changing the hardware structure, the sheet control coefficient, the sheet applied voltage coefficient and the sheet control voltage of each layer of the liquid crystal adjustable half-wave plate are optimized, and the problem of low diffraction efficiency of the passive cascade liquid crystal polarization grating is solved.

Description

Technical Field

[0001] This invention belongs to the field of liquid crystal polarization grating technology, specifically relating to a method for calculating optimized control parameters of passive cascaded liquid crystal polarization gratings. Background Technology

[0002] A liquid crystal polarization grating is a diffractive optical element, which includes two types: active liquid crystal polarization gratings and passive liquid crystal polarization gratings. Among them, the passive liquid crystal polarization grating is more technologically mature.

[0003] The diffraction efficiency of a laser-incident passive liquid crystal polarization grating depends on the polarization state and incident angle of the incident light. The diffraction efficiency is highest when the incident light is circularly polarized, and decreases as the incident angle increases.

[0004] After the incident light passes through the passive liquid crystal polarization grating, the light energy is mainly concentrated in the +1 and -1 orders. When the incident light is right-handed circularly polarized, the intensity of the outgoing light is mainly concentrated in the +1 order. When the incident light is left-handed circularly polarized, the energy of the outgoing light is mainly concentrated in the -1 order. When the incident light is linearly polarized or natural light, the energy of the outgoing light is evenly distributed between the +1 and -1 orders.

[0005] A liquid crystal tunable half-wave plate is constructed by depositing transparent electrodes on the inner sides of two parallel quartz glass plates, coating them with a transparent material, filling the space between the two parallel plates with liquid crystal molecules, and encapsulating them with a support. When the driving voltage exceeds the critical voltage of the liquid crystal tunable half-wave plate, the liquid crystal molecules begin to rotate away from the electrodes. The rotation angle depends on the driving voltage across the electrodes. By changing the driving voltage applied across the liquid crystal tunable half-wave plate through a liquid crystal controller, the phase delay can be altered. The control coefficient of the liquid crystal tunable half-wave plate indicates whether a driving voltage is applied; a control coefficient of 1 indicates that a driving voltage is applied, and a control coefficient of 0 indicates that no driving voltage is applied.

[0006] By adding an adjustable half-wave plate in front of a passive liquid crystal polarizing grating, a liquid crystal polarizing grating layer is formed by one adjustable half-wave plate and one passive liquid crystal polarizing grating. The adjustable half-wave plate controls the left-hand and right-hand rotation of the incident polarized light, while the passive liquid crystal polarizing grating achieves deflection of the outgoing beam at ±1 order angles (±θ). By connecting two identical passive liquid crystal polarizing gratings and two adjustable half-wave plates in series to form a "liquid crystal polarizing grating layer", deflection at three angles of 0°, -2θ, and +2θ can be achieved.

[0007] Multiple liquid crystal polarization grating layers are connected in series to form a cascaded liquid crystal polarization grating. Each liquid crystal polarization grating layer achieves a fixed angle of deflection. Multilayer liquid crystal polarization gratings can be combined to achieve a large angle range of deflection. Combination forms include binary, quasi-binary, and ternary, with the binary form being the most commonly used. The method for achieving large angle deflection using a binary combination is as follows: the first layer determines the angular resolution, and the diffraction angle of each subsequent layer is twice that of the previous layer. The achievable angles are integer multiples of the angular resolution. For example, if the angular resolution is 1.25°, the diffraction angles of subsequent layers are 2.5°, 5.0°, 10.0°, and 20.0°, respectively, resulting in achievable angles of 0°, ±1.25°, ±2.5°, ±3.75°, and so on. Theoretically, for an N-layer cascaded liquid crystal polarization grating, a total of 2... N+1 To achieve angle deflection control within a ±40° range at 1.25° intervals, a total of 5 layers of liquid crystal polarizing gratings are required (2 × 40° / 1.25° = 64, 2). N+1 =64, N=5), in order to achieve two-dimensional beam deflection, five identical liquid crystal polarization gratings are needed in the orthogonal directions. The total diffraction efficiency of the cascaded liquid crystal polarization gratings is the product of the diffraction efficiencies of a single liquid crystal polarization grating.

[0008] The control parameters for controlling the deflection of a passive cascaded polarization grating include layer control coefficients, sheet control coefficients, sheet voltage application coefficients, and sheet control voltage. Layer control coefficients, including 0, -1, and +1, primarily indicate that the deflection angle of a certain layer is 0°, positive, or negative. Sheet control coefficients, including -0.5 and +0.5, primarily indicate that the deflection angle of a certain adjustable half-wave liquid crystal sheet is positive or negative. Sheet control coefficients, including 0 and 1, primarily indicate whether a voltage is applied to a certain adjustable half-wave liquid crystal sheet. Sheet control voltage is the specific driving voltage for a certain adjustable half-wave liquid crystal sheet, and it is the final control parameter.

[0009] To achieve a specific deflection angle, the control coefficients of the tunable half-wave plate within different liquid crystal layers are often not unique, such as... Figure 1 As shown: To achieve a 0° deflection, the beam can be deflected by θ first (e.g., Figure 1 In the middle path one, θ is a positive number), then deflect -θ, or you can first deflect -θ (such as...). Figure 1In the first path (with a plate control coefficient of -0, 5, and θ being a positive number), the diffraction is then increased by +θ. When the incident angle of the first liquid crystal polarization grating in the liquid crystal polarization grating layer is (α, β) (α being a positive number), the incident angle of the second liquid crystal polarization grating can be either (α+θ, β) or (α-θ, β). The diffraction efficiency of the liquid crystal polarization grating varies under different incident angles, with higher diffraction efficiency at smaller incident angles. When the plate control coefficient of the tunable half-wave plate in front of the first liquid crystal polarization grating is -0, 5, the diffraction efficiency is even higher.

[0010] In the use of passive cascaded polarization gratings, the tunable half-wave plate of the liquid crystal typically only considers the case of perpendicular incidence (i.e., the incident angle is 0°), and the plate control voltage for each incident angle is a constant V0 (e.g., ...). Figure 2 In most cases, the incident light angle at the liquid crystal adjustable half-wave plate is not 0°, if a constant voltage V0 is still applied (e.g.) Figure 3 The light emitted after passing through the adjustable half-wave plate will change from ideally circularly polarized light to elliptically polarized light, thus causing a decrease in the efficiency of the liquid crystal polarization grating. By calculating the incident angle and the parameters of the adjustable half-wave plate, the plate control voltage V that makes the emitted light circularly polarized after passing through the adjustable half-wave plate can be obtained. opt If this voltage is applied to the tunable half-wave plate of the liquid crystal (e.g.) Figure 4 This will improve the diffraction efficiency of the liquid crystal polarization grating under tilted incidence.

[0011] The diffraction efficiency of a single passive liquid crystal polarization grating is close to 100% under 0° incident conditions. The diffraction efficiency decreases as the incident angle increases. After multiple cascaded gratings, the total diffraction efficiency drops by more than 50%. Currently, there is limited room for improving diffraction efficiency through hardware design, and no method has been found to improve the diffraction efficiency of passive liquid crystal polarization gratings by optimizing control voltage or other means. Summary of the Invention

[0012] To address the problem of low diffraction efficiency in passive cascaded polarization gratings, this invention proposes a method for calculating optimized control parameters of passive cascaded liquid crystal polarization gratings.

[0013] The present invention adopts the following technical solution to achieve the above-mentioned objectives:

[0014] A method for calculating optimized control parameters of a passive cascaded liquid crystal polarization grating, characterized by the following steps:

[0015] Step 1: Binarize the angle to be achieved and calculate the layer control coefficient required for each layer of the cascaded liquid crystal polarization grating at different deflection angles.

[0016] Step 2: Calculate the control coefficient of the liquid crystal tunable half-wave plate. When it contains a layer with a deflection angle of 0°, obtain the control coefficient that makes the incident angle smaller based on the deflection angle.

[0017] Step 3: Calculate the sheet-applied voltage coefficient of each tunable half-wave liquid crystal sheet starting from the emitting end based on the sheet control coefficient and the polarization state of the incident light, and establish a sheet-applied voltage coefficient set.

[0018] Step 4: Calculate the control voltage of each liquid crystal adjustable half-wave plate based on the power application coefficient of each liquid crystal adjustable half-wave plate and the incident light angle, so that the outgoing light of each layer is standard circularly polarized light, and establish a set of control voltages for cascaded liquid crystal polarization gratings.

[0019] The method for calculating the required deflection angle for each layer of the cascaded liquid crystal polarizing grating at different deflection angles, as described in step 1, is as follows:

[0020] Divide the desired 2D deflection angle by the deflection angular resolution to obtain the deflection factors M and N in the meridional and sagittal directions. Convert the decimal deflection factors M and N to binary deflection factors to obtain the weights of different bits in the meridional and sagittal directions: n1, n2, n3, n4, n5, n6, n7, n8, n9, n 10 ,n1,n2,n3,n4,n5,n6,n7,n8,n9,n 10 Relationship with M and N:

[0021] , n i =-1,0,1, the sign is the same as the deflection angle;

[0022] Establish layer control coefficient set n [i] .

[0023] Step 2 specifically involves determining two control coefficients n for each layer of a passively cascaded liquid crystal polarization grating. i1 n i2 ;n i1 n i2 satisfy:

[0024] n i1 +n i2 =n i (n) i1 n i2 =±0.5);

[0025] If n1=0, then: n 11 =0.5, n 12 =-0.5;

[0026] If n² = 0, then: n 21 =0.5, n 22 =-0.5;

[0027] For n i Layers with i=0 (i≥3):

[0028]

[0029] Each liquid crystal panel has an adjustable half-wave plate incident angle:

[0030]

[0031] Establish the incident angle set (α) for each adjustable half-wave plate of liquid crystal. [i1] α [i2] ,β [i1] ,β [i2] ).

[0032] The specific method for step 3 is as follows: If the incident light is right-hand circularly polarized light, and the liquid crystal polarization grating used is right-hand circularly polarized light deflected in the positive direction, the sheet voltage coefficients mi1 and mi2 of each tunable half-wave plate of the first layer are:

[0033] ;

[0034] If the incident light is left-handed circularly polarized, and the liquid crystal polarization grating used is right-handed circularly polarized with the polarization deflected in the positive direction, the sheet-applied voltage coefficient m of each tunable half-wave plate in the first layer is... i1 With m i2 for

[0035] ;

[0036] Establish the set of power application coefficients as (m [i1] m [i2] ).

[0037] Step 4 Specific Method: Based on the electrical coefficient of each adjustable half-wave plate of liquid crystal and the incident light angle (α) [i1] α [i2] ,β [i1] ,β [i2] ), from the formula:

[0038] ;

[0039] The molecular axis angle ψ corresponding to each adjustable half-wave plate can be calculated. ij When the applied voltage coefficient is equal to 0, no calculation is required; when the applied voltage coefficient is equal to 1, calculation is required. In the above formula: j represents the sequence number of the liquid crystal tunable half-wave plate of the layer, which is 1 or 2; d is the thickness of the liquid crystal layer; λ is the wavelength of the incident light; a, b and c represent the regression coefficients of the dispersion equation.

[0040] Then through the molecular axis angle ψ ij Relationship with liquid crystal driving voltage:

[0041]

[0042] In the formula: V ij and V C It is the optimized drive voltage and threshold voltage of the liquid crystal adjustable phase delayer, V o It is a voltage constant;

[0043] The optimal control voltage can be obtained by jointly calculating the two equations; a control voltage set V for a cascaded liquid crystal polarization grating can be established. [ij] .

[0044] The beneficial effects of this invention are as follows: By using this method, the sheet control coefficient that optimizes the diffraction efficiency can be calculated step by step based on the desired deflection angle and the hardware parameters of the passive cascaded polarization grating. The light path that optimizes the diffraction efficiency can be found, and then the sheet control voltage that optimizes the diffraction efficiency can be calculated. After applying the optimized sheet drive voltage to the passive cascaded polarization grating, the diffraction efficiency of the passive cascaded liquid crystal polarization grating can be improved without changing the hardware parameters. Attached Figure Description

[0045] Figure 1 This is a schematic diagram of different control paths for the same liquid crystal polarization grating layer.

[0046] Figure 2 This is a schematic diagram illustrating the high diffraction efficiency of a vertically incident tunable half-wave plate liquid crystal polarization grating.

[0047] Figure 3 This diagram illustrates the decrease in diffraction efficiency of a liquid crystal polarization grating when the voltage is not optimized and the liquid crystal is incident on an adjustable half-wave plate at a certain angle.

[0048] Figure 4 This diagram illustrates the optimal diffraction efficiency of a liquid crystal polarization grating, achieved by optimizing the voltage and accommodating the tunable half-wave plate incident at a specific angle.

[0049] Figure 5 This is the flowchart of the passive cascaded liquid crystal polarization grating optimization control parameter calculation method of the present invention. Detailed Implementation

[0050] The present invention will now be described in further detail with reference to the accompanying drawings.

[0051] A method for calculating optimized control parameters of passive cascaded liquid crystal polarization gratings, comprising the following steps:

[0052] Step 1: Binarize the angle to be achieved and calculate the layer control coefficient required for each layer of the cascaded liquid crystal polarization grating at different deflection angles.

[0053] The method for calculating the layer control coefficients required for each layer of a cascaded liquid crystal polarization grating at different deflection angles is as follows:

[0054] Divide the desired 2D deflection angle by the deflection angular resolution to obtain the deflection factors M and N in the meridional and sagittal directions. Convert the decimal deflection factors M and N to binary deflection factors to obtain the weights of different bits in the meridional and sagittal directions: n1, n2, n3, n4, n5, n6, n7, n8, n9, n 10 . n1, n2, n3, n4, n5, n6, n7, n8, n9, n 10 Relationship with M and N:

[0055] , n i =-1,0,1, the sign is the same as the deflection angle.

[0056] Establish layer control coefficient set n [i] .

[0057] Step 2: Calculate the control coefficient of the liquid crystal tunable half-wave plate. When it contains a layer with a deflection angle of 0°, obtain the control coefficient that makes the incident angle smaller based on the deflection angle.

[0058] Each layer of a passively cascaded liquid crystal polarization grating requires the determination of two control coefficients n. i1 n i2 n i1 n i2 satisfy:

[0059] n i1 +n i2 =n i (n) i1 n i2 =±0.5);

[0060] If n1=0, then: n 11 =0.5, n 12 =-0.5;

[0061] If n² = 0, then: n 21 =0.5, n 22 =-0.5.

[0062] For n i Layers with i=0 (i≥3):

[0063]

[0064] Each liquid crystal panel has an adjustable half-wave plate incident angle:

[0065]

[0066] Establish the incident angle set (α) for each adjustable half-wave plate of liquid crystal. [i1] α [i2],β [i1] ,β [i2] ).

[0067] Step 3: Calculate the sheet-applied voltage coefficient of each tunable half-wave liquid crystal sheet starting from the emitting end based on the sheet control coefficient and the polarization state of the incident light, and establish a sheet-applied voltage coefficient set.

[0068] If the incident light is right-hand circularly polarized, and the liquid crystal polarization grating used deflects the right-hand circularly polarized light in the positive direction, the sheet-applied voltage coefficient m of each tunable half-wave plate in the first layer is... i1 With m i2 for

[0069] ;

[0070] If the incident light is left-handed circularly polarized, and the liquid crystal polarization grating used is right-handed circularly polarized with the polarization deflected in the positive direction, the sheet voltage coefficients mi1 and mi2 of each tunable half-wave plate in the first layer are:

[0071] ;

[0072] Establish the set of power application coefficients as (m [i1] m [i2] ).

[0073] Step 4: Calculate the control voltage of each adjustable half-wave plate of liquid crystal based on the power application coefficient of each liquid crystal adjustable half-wave plate and the incident light angle, so that the outgoing light of each layer is standard circularly polarized light, and establish a set of control voltages for cascaded liquid crystal polarization gratings.

[0074] Based on the power application coefficient m of each adjustable half-wave plate of liquid crystal i1 With m i2 and the incident light angle (α) [i1] α [i2] ,β [i1] ,β [i2] ), from the formula:

[0075] ;

[0076] The molecular axis angle ψ corresponding to each adjustable half-wave plate can be calculated. ij When the applied voltage coefficient is equal to 0, no calculation is required; when the applied voltage coefficient is equal to 1, calculation is required. In the above formula: j represents the sequence number of the liquid crystal tunable half-wave plate of the layer, which is 1 or 2; d is the thickness of the liquid crystal layer; λ is the wavelength of the incident light; a, b and c represent the regression coefficients of the dispersion equation.

[0077] Then through the molecular axis angle ψ ij Relationship with liquid crystal driving voltage:

[0078]

[0079] In the formula: V ij and V C It is the optimized drive voltage and threshold voltage of the liquid crystal adjustable phase delayer, V o It is a voltage constant.

[0080] The optimal control voltage can be obtained by jointly calculating the two equations. A control voltage set V for a cascaded liquid crystal polarization grating is then established. [ij] .

Claims

1. A method for calculating optimized control parameters of a passive cascaded liquid crystal polarization grating, characterized in that... The method includes the following steps: Step 1: Binarize the angle to be achieved and calculate the layer control coefficient required for each layer of the cascaded liquid crystal polarization grating at different deflection angles. Step 2: Calculate the control coefficient of the liquid crystal tunable half-wave plate. When it contains a layer with a deflection angle of 0°, obtain the control coefficient that makes the incident angle smaller based on the deflection angle. Step 3: Calculate the sheet-applied voltage coefficient of each tunable half-wave liquid crystal sheet starting from the emitting end based on the sheet control coefficient and the polarization state of the incident light, and establish a sheet-applied voltage coefficient set. Step 4: Calculate the control voltage of each adjustable half-wave plate of liquid crystal based on the power application coefficient of each liquid crystal adjustable half-wave plate and the incident light angle, so that the outgoing light of each layer is standard circularly polarized light, and establish a set of control voltages for cascaded liquid crystal polarization gratings. The method for calculating the required deflection angle for each layer of the cascaded liquid crystal polarizing grating at different deflection angles, as described in step 1, is as follows: Divide the desired 2D deflection angle by the deflection angular resolution to obtain the deflection factors M and N in the meridional and sagittal directions. Convert the decimal deflection factors M and N to binary deflection factors to obtain the weights of different bits in the meridional and sagittal directions: n1, n2, n3, n4, n5, n6, n7, n8, n9, n 10 ;n1, n2, n3, n4, n5, n6, n7, n8, n9, n 10 Relationship with M and N: , n i =-1,0,1, the sign is the same as the deflection angle; Establish layer control coefficient set n [i] ; Step 2 specifically involves determining two control coefficients n for each layer of a passively cascaded liquid crystal polarization grating. i1 n i2 ;n i1 n i2 satisfy: n i1 +n i2 =n i (n i1 ,n i2 =±0.5); If n1=0, then: n 11 =0.5, n 12 =-0.5; If n² = 0, then: n 21 =0.5, n 22 =-0.5; For n i Layers with i = 0 (i ≥ 3): ； Each liquid crystal panel has an adjustable half-wave plate incident angle: ； Establish the incident angle set (α) for each adjustable half-wave plate of liquid crystal. [i1] α [i2] ,β [i1] ,β [i2] ); The specific method for step 3 is as follows: If the incident light is right-hand circularly polarized light, and the liquid crystal polarization grating used is right-hand circularly polarized light deflected in the positive direction, the sheet voltage coefficients mi1 and mi2 of each tunable half-wave plate of the first layer are: ； If the incident light is left-handed circularly polarized, and the liquid crystal polarization grating used is right-handed circularly polarized with the polarization deflected in the positive direction, the sheet-applied voltage coefficient m of each tunable half-wave plate in the first layer is... i1 With m i2 for: ； Establish the power application coefficient set as (m [i1] m [i2] ); Step 4 Specific Method: Based on the electric coefficient of each adjustable half-wave plate of liquid crystal and the incident light angle (α) [i1] α [i2] ,β [i1] ,β [i2] ), from the formula: ； Calculate the molecular axis angle ψ for each adjustable half-wave plate. ij When the applied voltage coefficient is equal to 0, no calculation is required; when the applied voltage coefficient is equal to 1, calculation is required. In the above formula: j represents the sequence number of the liquid crystal tunable half-wave plate of the layer, which is 1 or 2; d is the thickness of the liquid crystal layer; λ is the wavelength of the incident light; a, b and c represent the regression coefficients of the dispersion equation. Then through the molecular axis angle ψ ij Relationship with liquid crystal driving voltage: ； In the formula: V ij and V C It is the optimized drive voltage and threshold voltage of the liquid crystal adjustable phase delay device, V o It is a voltage constant; The optimal control voltage can be obtained by jointly calculating the two equations; a control voltage set V for a cascaded liquid crystal polarization grating can be established. [ij] .

Images