High-precision light column display method and system based on liquid crystal variable refractive index

Abstract

The present invention discloses a high-precision light column display method and system based on liquid crystal variable refractive index. The method includes: generating a multi-dimensional driving signal with spatial gradient characteristics according to the preset spatial distribution parameters of the target light column, and dynamically changing the molecular arrangement state of the liquid crystal electro-optic refractive index adjustment layer through the coupling regulation of the voltage amplitude and frequency of the multi-dimensional driving signal, so as to establish a refractive index gradient field that matches the requirements of the axial phase distribution of the light column. Through the discrete collaborative mapping mechanism of the waveguide mode-phase field and the dual-loop dynamic anti-interference architecture, the present invention realizes the real-time generation of high-resolution light columns and stable transmission in complex environments without mechanical scanning components, and has both high precision and strong robustness.

Description

Technical Field

[0001] This application relates to the technical field of high-precision light column display, and particularly to a high-precision light column display method and system based on liquid crystal variable refractive index. Background Art

[0002] The light column display technology plays a key role in fields such as three-dimensional holography, optical manipulation, and augmented reality. Its performance core depends on the precise control of the beam phase distribution and the transmission stability. However, the existing technology is subject to the dual limitations of physical mechanisms and system design, and faces the following challenges:

[0003] 1. The traditional liquid crystal light column regulation scheme designs the driving signal based on the continuous refractive index model. However, due to the periodic structure constraint of the actual optical waveguide (such as photonic crystal waveguide), it only supports the transmission of discretized Bloch modes. This physical characteristic leads to the mismatch between continuous phase modulation and the waveguide eigenmode, causing the leakage of light field energy to non-target modes during transmission, seriously damaging the spatial continuity of the light column.

[0004] 2. The strong coupling characteristic between the polarization state and the transmission mode in the optical waveguide under dynamic perturbation. The environmental temperature change, mechanical vibration and other perturbations will cause polarization dispersion through the birefringence effect, and then distort the phase distribution. The existing methods usually adopt static compensation or single-dimensional regulation (such as only correcting the voltage amplitude), and cannot cope with the non-linear coupling effect between polarization and phase in the dynamic scenario, ultimately resulting in irreversible distortion at the edge of the light column.

[0005] In the current technology, although the phase modulator based on mechanical scanning can partially improve the resolution, its response speed and system complexity are difficult to meet the requirements of real-time interaction; while the traditional electro-controlled liquid crystal scheme has the advantage of fast response, but due to the single driving dimension (only voltage amplitude regulation) and open-loop control architecture, it cannot take into account both the mode matching accuracy and the dynamic anti-interference ability. Summary of the Invention

[0006] In order to solve the above problems, an embodiment of the present invention provides a high-precision light column display method based on liquid crystal variable refractive index. The method includes:

[0007] According to the preset spatial distribution parameters of the target light column, generate a multi-dimensional driving signal with spatial gradient characteristics. Through the coupled regulation of the voltage amplitude and frequency of the multi-dimensional driving signal, dynamically change the molecular arrangement state of the liquid crystal electro-optic refractive index adjustment layer, and establish a refractive index gradient field that matches the requirements of the axial phase distribution of the light column;

[0008] Couple the incident light beam into the total reflection transmission channel of the optical waveguide structure, perform spatial phase modulation on the transmitted light beam based on the refractive index gradient field, and generate a discretized base light field that adapts to the geometric constraint conditions of the optical waveguide structure through the geometric boundary constraint effect of the optical waveguide structure;

[0009] Apply polarization state synchronous control to the discretized base optical field, dynamically correct the polarization dispersion angle deviation of each diffraction order using the birefringence compensation algorithm, and generate an N-order controllable diffraction optical field with a fixed phase relationship through multi-stage diffraction synthesis;

[0010] Introduce the N-order controllable diffraction optical field into the free space propagation domain, achieve the spatial superposition of each order diffraction field through Fresnel diffraction integral, reconstruct a continuous high-precision light column shape, and use the wavefront distortion amount detected by the light column edge detection feedback to inversely correct the voltage regulation parameters of the drive signal to form a dynamic closed-loop calibration mechanism.

[0011] Furthermore, the multi-dimensional drive signal generation method includes:

[0012] Establish a transfer function matrix between the drive voltage and phase modulation according to the Bloch mode eigen-equation of the optical waveguide structure;

[0013] Perform an inverse operation on the transfer function matrix through a feedforward neural network to generate a pre-distorted drive signal including inter-mode coupling compensation;

[0014] Load the pre-distorted drive signal onto the traveling wave electrode of the electro-optic modulator to form a refractive index gradient field with a spatio-temporal distribution.

[0015] Furthermore, the optical waveguide structure is a photonic crystal waveguide, and the optical waveguide structure includes:

[0016] A hexagonal close-packed air hole array arranged periodically along the propagation direction, and the duty cycle of the air holes matches the group velocity distribution of the Bloch mode;

[0017] A graded refractive index cladding covering the waveguide sidewall, whose refractive index distribution along the radial direction is a hyperbolic secant function, used to constrain the paraxial propagation characteristics of the refractive index gradient field.

[0018] Furthermore, the polarization state synchronous control method includes:

[0019] Integrate a polarization beam splitter at the input end of the photonic crystal waveguide to decompose the incident light into TE mode and TM mode orthogonal polarization components;

[0020] Apply the odd and even channel voltages in the pre-distorted drive signal to the TE mode and TM mode respectively;

[0021] Through the time-domain interleaved scanning method, make the birefringence delay of the orthogonal polarization components form a complementary distribution in space.

[0022] Furthermore, the wavefront distortion amount detection method includes:

[0023] Collect the diffraction spots of the orthogonally polarized components by using the output end of the polarization beam splitter;

[0024] Input the diffraction spots into the error backpropagation module of the feedforward neural network to calculate the deviation between the actual phase distribution and the target Bloch mode;

[0025] Generate wavefront correction parameters in the form of Zernike polynomial coefficients based on the deviation.

[0026] Furthermore, the dynamic closed-loop calibration mechanism includes:

[0027] Input the Zernike polynomial coefficients into the input layer of the feedforward neural network to form a first feedback loop;

[0028] Dynamically weight and correct the eigenvalues of the transfer function matrix through a Kalman filter to form a second feedback loop;

[0029] The outputs of the first feedback loop and the second feedback loop are convolved and fused in the Fourier spectrum domain of the waveguide mode.

[0030] Furthermore, the discretized substrate optical field synthesis method includes:

[0031] Construct the discretization constraint conditions of the Bloch wave vector according to the reciprocal lattice vector space distribution of the photonic crystal waveguide;

[0032] Project the continuous phase distribution of the refractive index gradient field onto the basis vectors of the reciprocal lattice vector space;

[0033] Screen the discretized phase components that satisfy the group velocity matching condition of the Bloch mode through the Gibbs sampling algorithm.

[0034] Furthermore, the generation of N - order controllable diffraction light field includes:

[0035] Set a 4f optical filtering system at the output end of the photonic crystal waveguide;

[0036] Insert a spiral phase plate corresponding to the target topological charge number in the Fourier plane of the 4f optical filtering system;

[0037] Suppress the diffraction efficiency of non - target order Bloch modes through the mode field matching effect of the graded refractive index cladding.

[0038] A high - precision light column display system based on liquid crystal variable refractive index, the system includes:

[0039] Refractive gradient regulation model, which generates a multi-dimensional driving signal with spatial gradient characteristics according to the preset spatial distribution parameters of the target light column, and dynamically changes the molecular arrangement state of the liquid crystal electro-optic refractive index adjustment layer through the coupling regulation of the voltage amplitude and frequency of the multi-dimensional driving signal, and establishes a refractive index gradient field matching the phase distribution requirement of the light column axis;

[0040] Waveguide substrate generation model, which couples the incident light beam into the total reflection transmission channel of the optical waveguide structure, performs spatial phase modulation on the transmitted light beam based on the refractive index gradient field, and generates a discretized substrate light field adapted to the geometric constraint conditions of the optical waveguide through the geometric boundary constraint effect of the optical waveguide structure;

[0041] Polarization diffraction synthesis model, which applies synchronous polarization state regulation to the discretized substrate light field, dynamically corrects the polarization dispersion angle deviation of each diffraction order by using the birefringence compensation algorithm, and generates an N-order controllable diffraction light field with a fixed phase relationship through multi-stage diffraction synthesis;

[0042] Closed-loop dynamic reconstruction model, which introduces the N-order controllable diffraction light field into the free space propagation domain, realizes the spatial superposition of each order diffraction field through the Fresnel diffraction integral, reconstructs a continuous and high-precision light column shape, and uses the wavefront aberration amount detected and fed back at the light column edge to reversely correct the voltage regulation parameters of the driving signal to form a dynamic closed-loop calibration mechanism.

[0043] Technical effects and advantages of the high-precision light column display method and system based on liquid crystal variable refractive index provided by the present invention:

[0044] Through the discretized cooperative mapping mechanism of the waveguide mode-phase field and the double-loop dynamic anti-interference architecture, the present invention realizes the real-time generation of high-resolution light columns and stable transmission in complex environments without mechanical scanning components, and has both high precision and strong robustness. The present invention integrates the reciprocal lattice vector constraint characteristics of the photonic crystal waveguide into the generation of the driving signal, and maps the continuous refractive index gradient field into a phase distribution compatible with the waveguide eigenmode through the discretized substrate light field synthesis algorithm, fundamentally eliminating the problem of light field breakage caused by mode mismatch, and significantly improving the spatial consistency of the light column shape; constructing a double-loop cooperation enables the light column to maintain a sub-wavelength-level edge sharpness under complex interference; combining the joint regulation of the 4f optical system and the spiral phase plate, screening the optimal discrete phase components through the Gibbs sampling algorithm, greatly improving the light field energy ratio of the target diffraction order, effectively suppressing the stray light interference, and realizing the efficient directional transmission of the light column energy; constructing a non-linear driving model based on the feedforward neural network, dynamically analyzing the complex mapping relationship between the waveguide mode and the driving signal, and adapting to different medium environments (such as air, liquid, flexible substrate) without hardware reconstruction. Description of the Drawings

[0045] Figure 1 It is the flow chart of the high-precision light column display method based on liquid crystal variable refractive index in Embodiment 1;

[0046] Figure 2 It is the schematic connection diagram of the high-precision light column display system based on liquid crystal variable refractive index in Embodiment 2. Specific Embodiment

[0047] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0048] Embodiment 1: Please refer to Figure 1 As shown, the embodiment of the present invention provides a high-precision light column display method based on liquid crystal variable refractive index. The method includes:

[0049] According to the preset spatial distribution parameters of the target light column, a multi-dimensional driving signal with spatial gradient characteristics is generated. Through the coupling regulation of the voltage amplitude and frequency of the multi-dimensional driving signal, the molecular arrangement state of the liquid crystal electro-optic refractive index adjustment layer is dynamically changed, and a refractive index gradient field matching the phase distribution requirement of the light column axis is established.

[0050] The incident light beam is coupled into the total reflection transmission channel of the optical waveguide structure. Based on the refractive index gradient field, spatial phase modulation is performed on the transmitted light beam. Through the geometric boundary constraint effect of the optical waveguide structure, a discretized base light field adapted to the geometric constraint conditions of the optical waveguide is generated.

[0051] Polarization state synchronous regulation is applied to the discretized base light field. The polarization dispersion angle deviation of each diffraction order is dynamically corrected using the birefringence compensation algorithm. An N-order controllable diffraction light field with a fixed phase relationship is generated through multi-stage diffraction synthesis.

[0052] The N-order controllable diffraction light field is introduced into the free space propagation domain. Through the Fresnel diffraction integral, the spatial superposition of each order diffraction field is realized, and a continuous high-precision light column form is reconstructed. Using the wavefront distortion amount detected and fed back at the light column edge, the voltage regulation parameters of the driving signal are reversely corrected to form a dynamic closed-loop calibration mechanism.

[0053] The multi-dimensional driving signal generation method includes:

[0054] According to the Bloch mode eigen-equation of the optical waveguide structure, a transfer function matrix of driving voltage and phase modulation is established.

[0055] The Bloch mode eigen - equation is used to describe the propagation characteristics of electromagnetic waves in a periodic optical waveguide. Its eigen - solutions correspond to the form of guided modes supported by the optical waveguide. By substituting the dielectric constant distribution parameters of the liquid - crystal electro - optic refractive index - tuning layer into the equation, a transfer - function matrix of drive voltage and phase modulation is constructed. The transfer - function matrix quantitatively characterizes the mapping relationship between the voltage amplitude and frequency combination applied to the traveling - wave electrodes and the alignment state of liquid - crystal molecules. Its dimension is determined by the number of independently controllable electrode units in the optical waveguide.

[0056] The inverse operation of the transfer - function matrix is performed by a feed - forward neural network to generate a pre - distortion drive signal that includes compensation for inter - mode coupling.

[0057] To perform the inverse operation of the transfer - function matrix, a feed - forward neural network is used for non - linear approximation. The input layer of the neural network is the theoretical voltage vector calculated according to the target phase distribution. The hidden layer includes multiple layers of non - linear activation nodes to simulate the inter - mode coupling effect, and the output layer generates the drive - signal parameters including pre - distortion compensation.

[0058] Exemplarily:

[0059] When the target phase gradient requires a phase difference of π / 4 between adjacent electrode units in the optical waveguide, the neural network will predict the amount of reverse - coupling compensation to be superimposed according to historical training data and generate a pre - distortion voltage sequence that can cancel mode crosstalk. During the training process, by comparing the error between the actual phase - modulation result and the theoretical value for back - propagation, the network weight parameters are continuously optimized, and finally the pre - distortion accuracy of the drive signal reaches the sub - wavelength level.

[0060] The pre - distortion drive signal is loaded onto the traveling - wave electrodes of the electro - optic modulator to form a refractive - index gradient field with spatio - temporal distribution.

[0061] When loading the pre - distortion drive signal output by the neural network onto the traveling - wave electrodes of the optical - waveguide structure, the spatio - temporal synchronization of electromagnetic - wave propagation needs to be considered. The traveling - wave electrodes adopt a distributed - capacitance coupling design, and the propagation speed of its electrical signal matches the group velocity of the light beam in the optical waveguide.

[0062] Exemplarily:

[0063] When the drive frequency is set to 10 kHz, the voltage amplitude of the traveling - wave electrodes can be dynamically adjusted in the range of 0 V to 5 V. By controlling the voltage - gradient direction and amplitude - change rate of adjacent electrode units, a refractive - index gradient field with a specific spatial frequency can be formed within the liquid - crystal layer. The spatial - distribution characteristics of the refractive - index gradient field are strictly matched with the axial - phase requirements of the light beam, thus ensuring the discretization accuracy of the base light field during the subsequent light - field modulation process. During this process, the parasitic - capacitance effect between electrodes has been pre - compensated by the pre - distortion algorithm, avoiding the refractive - index - distribution distortion caused by signal delay.

[0064] The above-mentioned multi-dimensional driving signal generation method effectively solves the problem of non-linear phase modulation caused by mode coupling in traditional open-loop driving by introducing a neural network-driven predistortion mechanism. The refractive index gradient field generated by the multi-dimensional driving signal generation method can reach the physical limit of the waveguide periodic structure in terms of lateral resolution, and the broadening range of the gradient transition region is controlled within 20% of the size of a single electrode unit, laying a foundation for the precise synthesis of the subsequent discretized substrate optical field.

[0065] The optical waveguide structure is a photonic crystal waveguide, including:

[0066] A hexagonal close-packed air hole array arranged periodically along the propagation direction, and the duty cycle of the air holes matches the group velocity distribution of the Bloch mode.

[0067] The construction process of the photonic crystal waveguide needs to meet the dual requirements of Bloch mode and group velocity regulation. The ratio of the air hole period to the lattice constant (i.e., the duty cycle) is optimized through photonic bandgap engineering. In the design, the selection of the air hole duty cycle needs to match the eigenfield distribution of the Bloch mode at the target working wavelength.

[0068] Exemplarily:

[0069] When operating in the visible light band, by adjusting the duty cycle so that the cut-off frequency of the photonic bandgap overlaps with the range of the group velocity of the guided mode required for light column display, it can ensure that the light beam propagates with quasi-linear group velocity dispersion characteristics inside the waveguide.

[0070] This design enables the wave vector spatial distribution of the light beam to quickly respond to the refractive index change and maintain the wavefront continuity during the phase modulation process when the driving signal induces the liquid crystal refractive index gradient field.

[0071] A graded refractive index cladding covering the waveguide sidewall, whose refractive index distributes according to the hyperbolic secant function along the radial direction, is used to constrain the paraxial propagation characteristics of the refractive index gradient field.

[0072] The graded refractive index cladding set at the waveguide sidewall adopts a refractive index regulation strategy with a hyperbolic secant function distribution. The material of the graded refractive index cladding is composed of a polymer doped with nanoparticles with a concentration gradient distribution, and its refractive index decreases along the radial direction from the waveguide core layer interface according to the law of , where is the refractive index reference value of the core layer, is the attenuation coefficient; this distribution characteristic can equivalently form a lens-like focusing effect, so that during the establishment of the refractive index gradient field, the paraxial-transmitted optical field components are suppressed by the exponentially decaying loss.

[0073] Exemplarily:

[0074] When the refractive index gradient field established within the liquid crystal layer causes the light beam to undergo lateral deflection, the energy of the paraxial component will be confined within the effective mode field diameter of the waveguide by the gradually varying refractive index potential barrier in the cladding, preventing the distortion of the substrate optical field caused by the leakage of high-order modes.

[0075] In a specific implementation, the duty cycle of the air hole array and the cladding attenuation coefficient need to be co-optimized through joint simulation; by solving the eigen-solutions of the Maxwell equations using the finite element method, it can be observed that when the air hole duty cycle is within a specific range, the Bloch modes supported by the waveguide reach an equilibrium state between the lateral confinement ability and the group velocity modulation sensitivity; at this time, the depth of the potential well formed by the cladding refractive index gradient exactly compensates for the mode coupling perturbation caused by the liquid crystal refractive index gradient field, enabling the phase distribution of the transmitted light beam to always be synchronized with the axial phase requirements of the target light column; this synergistic effect ensures that even during the high-order diffraction synthesis process, the spatial frequency components of the discretized substrate optical field still strictly satisfy the geometric constraint conditions of the optical waveguide structure, avoiding the reduction of diffraction efficiency caused by mode mismatch.

[0076] Through the design of the above optical waveguide structure, the photonic crystal waveguide realizes the shaping and screening of the spatial spectrum of the substrate optical field. When the incident light beam is coupled into the waveguide, its high-order spatial frequency components are filtered out by the bandgap effect of the air hole array, while the fundamental mode component maintains stable transmission characteristics under the constraint of the gradually varying cladding. This spectrum shaping effect and the pre-distortion driving signal form a spatial-spectrum complementary mechanism, jointly ensuring the linearity and dynamic range of the phase modulation of the transmitted light beam by the refractive index gradient field, providing a high-fidelity physical carrier for subsequent multi-stage diffraction synthesis.

[0077] The polarization state synchronous control method includes:

[0078] Integrate a polarization beam splitter at the input end of the photonic crystal waveguide to decompose the incident light into orthogonal polarization components of the TE mode and the TM mode.

[0079] Integrate a cascaded polarization beam splitter at the waveguide input end. This device consists of a birefringent crystal prism and a phase compensation layer, which can decompose the incident light into two orthogonal polarization components, the TE mode (transverse electric mode) and the TM mode (transverse magnetic mode); during the decomposition process, utilize the sensitivity of the hexagonal close-packed air hole array in the photonic crystal waveguide to the polarization state, and by adjusting the prism cutting angle, align the electric field vector of the TE mode with the main axis of the air hole array, while the magnetic field component of the TM mode forms a strong coupling with the gradually varying refractive index cladding of the waveguide sidewall, enabling the two polarization components to occupy different equivalent refractive index channels in the waveguide, laying a physical foundation for subsequent independent control.

[0080] Apply the odd and even channel voltages in the pre-distortion driving signal to the TE mode and the TM mode respectively.

[0081] Since the group velocity dispersion of the TE mode is significantly affected by the air hole duty ratio, and the mode field distribution of the TM mode is more sensitive to the cladding refractive index gradient, the pre-distortion signals generated by the neural network need to decouple the characteristics for different polarization states.

[0082] Exemplarily:

[0083] When dealing with the TE mode, the driving voltage applied to the odd-numbered electrode columns needs to mainly compensate for the mode coupling distortion caused by the air hole array; while for the TM mode, the voltage of the even-numbered columns focuses on suppressing the paraxial phase drift brought by the graded cladding; this polarization separation strategy for odd and even channels enables the pre-distortion algorithm to perform directional correction for the optical field distortion mechanisms of different polarization states.

[0084] Through the time-domain interleaved scanning method, the birefringence delays of the orthogonal polarization components form a complementary distribution in space.

[0085] Each refresh period is divided into multiple time windows. In the odd-numbered windows, the odd-numbered electrode columns corresponding to the TE mode are preferentially driven, while in the even-numbered windows, the even-numbered electrode columns of the TM mode are activated.

[0086] Exemplarily:

[0087] During a scanning period with a duration of τ, in the first 0.5τ period, the refractive index gradient required for the TE mode is established in the liquid crystal layer through the odd-numbered column voltage, and in the latter 0.5τ period, the voltage is switched to the even-numbered column voltage to regulate the phase distribution of the TM mode. Since the response time of the liquid crystal material is much smaller than τ, the birefringence delay effects of the two polarization components will form an alternating complementary phase grating in space, and the polarization state fusion is realized in the observation plane through the persistence of vision effect.

[0088] When the TE mode generates a π / 2 phase delay under the odd-numbered column drive, the TM mode obtains a -π / 2 delay through even-numbered column compensation. After the two are superimposed in space, a complete π phase difference closed loop is formed. This complementary mechanism not only cancels the polarization-dependent loss inherent in the waveguide structure, but also suppresses the polarization crosstalk noise below the background noise level through the time-averaging effect.

[0089] Through the above-mentioned synchronous regulation of the polarization state, the regulation dimension of the pre-distortion driving signal is effectively extended to the polarization domain, and at the same time, it can form an organic cooperation with the waveguide structure characteristics. The hexagonal symmetry of the air hole array provides a geometric constraint for the separation of the TE mode and the TM mode, while the mode field screening effect of the graded cladding ensures the mode purity of each polarization component during the regulation process; this multi-physical field coupling design enables the high-precision light column display system to break through the crosstalk bottleneck of traditional polarization multiplexing technology and provide a high-contrast physical light field substrate for dynamic holographic imaging.

[0090] The detection methods of the wavefront distortion amount include:

[0091] The diffracted spots of the orthogonal polarization components are collected at the output end of the polarization beam splitter.

[0092] Exemplarily:

[0093] When the mode field diameter of the TE mode at the output end face of the waveguide is 10 μm, the magnification of the objective lens is set to 40 times, so that a single pixel can resolve a wavefront phase gradient change of 0.25 μm. The collected diffracted spots are transmitted through a polarization-maintaining optical fiber to a high-speed image sensor to form an interference fringe pattern containing spatial phase information.

[0094] The diffracted spots are input into the error backpropagation module of the feedforward neural network to calculate the deviation between the actual phase distribution and the target Bloch mode.

[0095] First, the complex amplitude distribution of the spot is extracted by Fourier transform, decomposed into an amplitude term and a phase term. After the phase term is processed by the phase unwrapping algorithm, it is compared pixel by pixel with the ideal phase distribution of the target Bloch mode.

[0096] Exemplarily:

[0097] When the target mode requires a spiral phase distribution to be formed at the output end face of the waveguide, the neural network will perform a convolution operation on the actually measured phase gradient and the theoretical helicity to generate an error matrix containing the spatial frequency characteristics of the aberration. This error matrix updates the network weights through the backpropagation path, so that the subsequent generated pre-distortion driving signal automatically compensates for the cumulative phase error.

[0098] Wavefront correction parameters in the form of Zernike polynomial coefficients are generated based on the deviation.

[0099] The mapping process from the error matrix to the Zernike polynomial coefficients uses the mode orthogonal decomposition method. The mode orthogonal decomposition method includes:

[0100] The phase deviation is projected onto the basis function space of 36-term Zernike polynomials, and the coefficient weights of each order are obtained by least squares fitting.

[0101] Exemplarily:

[0102] When the coefficient of the defocus term (Z4) in the measured wavefront is 0.15λ, it indicates the existence of axial non-uniformity in the refractive index gradient field of the liquid crystal layer, and the voltage gradient slope of the driving signal needs to be adjusted; if the coefficients of the astigmatism terms (Z5 / Z6) exceed the threshold, it reflects the misalignment of the polarization beam splitter, and a mechanical fine-tuning mechanism needs to be triggered for compensation.

[0103] The effectiveness of the detection method for wavefront aberration variables stems from the physical correspondence between Zernike polynomials and the aberrations of optical systems. When the refractive index gradient field of the liquid crystal layer undergoes thermally induced deformation due to environmental temperature fluctuations, the resulting wavefront aberration mainly manifests as low-order aberrations (such as coma and trefoil aberration). By monitoring the change trend of the Zernike coefficient vector in real time, the system mismatch direction can be predicted in advance and a compensation amount can be injected. For example, when it is detected that the coefficient of Z7 (vertical coma) continues to increase, the neural network will automatically superimpose a reverse tilt phase on the odd-column drive signal to cancel the phase nonlinearity caused by the thermal expansion of the material through the pre-distortion algorithm.

[0104] Through the above detection method for wavefront aberration variables, the training data set of the neural network can also be dynamically expanded. The Zernike coefficients and the corresponding drive signal adjustment amounts generated during each wavefront correction process are recorded as new training samples, enabling the network to gradually master the non-linear mapping relationship between environmental disturbances and system responses. This self-learning ability enables the light column display system to still provide guarantee for the stable synthesis of multi-level diffraction light fields in the face of disturbances such as mechanical vibration and temperature drift, and at the same time form a synergistic effect with polarization spatio-temporal control, that is, the Zernike coefficients not only correct the overall wavefront aberration, but also optimize the polarization state consistency of TE / TM modes respectively through the odd-even term separation mechanism, and finally achieve the output of a light field with controllable full Stokes parameters.

[0105] The dynamic closed-loop calibration mechanism includes:

[0106] Input the Zernike polynomial coefficients into the input layer of the feedforward neural network to form the first feedback loop.

[0107] Dynamically weighted correction is performed on the eigenvalues of the transfer function matrix through a Kalman filter to form the second feedback loop.

[0108] In a photonic crystal waveguide, the eigenvectors of the transfer function matrix correspond to the field distribution patterns of Bloch modes, while the eigenvalues characterize the mode attenuation rate and the phase accumulation speed; and the Kalman filter can, through the recursive prediction-correction algorithm, estimate the eigenvalue drift amount caused by environmental disturbances in real time; for example, when the temperature rises and causes the refractive index of the waveguide core layer to decrease, the filter will predict the real part change rate of the TE mode eigenvalue based on historical observation data and apply a negative feedback weight to suppress its deviation from the set value.

[0109] The outputs of the first feedback loop and the second feedback loop are convolved and fused in the Fourier spectrum domain of the waveguide mode.

[0110] Perform a two-dimensional Fourier transform on the drive signal correction amount output by the first feedback loop to obtain its spectral amplitude-phase distribution; at the same time, map the eigenvalue correction parameter of the second feedback loop to the frequency-domain transfer coefficient of the transfer function; the first feedback loop and the second feedback loop perform a complex convolution operation in the spatial frequency domain to achieve the collaborative optimization of low-frequency phase error correction and high-frequency noise suppression.

[0111] The core advantage of the dynamic closed-loop calibration mechanism lies in the time-constant complementarity of the dual loops. The first feedback loop, based on the fast inference ability of the neural network (microsecond-level response), mainly compensates for the deterministic distortion caused by the nonlinearity of the drive signal; the second feedback loop, relying on the state prediction characteristics of the Kalman filter (millisecond-level update), focuses on suppressing the random errors brought about by the drift of environmental parameters. The two achieve dynamic balance through the weight allocation of the Fourier-domain convolution kernel, giving the first loop a higher weight in the startup phase for rapid convergence, and increasing the contribution of the second loop during steady-state operation to maintain long-term stability.

[0112] The discrete substrate optical field synthesis method includes:

[0113] According to the reciprocal lattice vector spatial distribution of the photonic crystal waveguide, construct the discretization constraint conditions of the Bloch wave vector; the construction method includes:

[0114] First, based on the periodic structure of the hexagonal lattice air hole array, construct a three-dimensional coordinate system in the reciprocal lattice vector space, and then determine the allowed Bloch wave vector discretization in the reciprocal lattice vector space by calculating the Fourier transform of the waveguide lattice basis vectors. For example, when the waveguide lattice constant is 5 μm, the reciprocal lattice vector basis vector spacing is 2π / (3 μm), forming discrete wave vector nodes with a hexagonal distribution.

[0115] Project the continuous phase distribution of the refractive index gradient field onto the basis vectors of the reciprocal lattice vector space. The projection method uses the mode orthogonal decomposition technique. The method includes treating the continuous phase surface generated by the liquid crystal layer as a metasurface, and performing a dot product operation on the phase gradient of each pixel point with the reciprocal lattice vector basis vectors to obtain the weight coefficients of the corresponding discrete wave vector components. For example, when the phase gradient direction in a certain region forms a 30° angle with the reciprocal lattice vector basis vector G1, this gradient will be decomposed into the projection components of G1 and its adjacent basis vectors G2 and G3, forming a discrete wave vector combination.

[0116] Screen the discretized phase components that satisfy the Bloch mode group velocity matching condition through the Gibbs sampling algorithm; when the group velocity angle between two wave vector components k1 and k2 exceeds the waveguide mode coupling threshold, their joint probability weight decays exponentially. During the sampling process, the Markov chain Monte Carlo method is used to traverse the possible component combinations and gradually converge to the lowest energy state.

[0117] The physical essence of the discrete basis optical field synthesis method lies in reconstructing the continuous optical field by utilizing the discrete transmission characteristics of the waveguide. The reciprocal lattice vector projection transforms the traditional continuous phase modulation into an eigenmode excitation problem, fundamentally avoiding the energy loss outside the waveguide cut-off frequency. The statistical optimization mechanism introduced by Gibbs sampling effectively solves the problem of group velocity mismatch caused by multimode coupling.

[0118] Meanwhile, the eigenvalues of the transfer function corrected by the Kalman filter provide real-time parameter updates for the energy function of Gibbs sampling; the feedback of the Zernike coefficients of the discrete basis optical field, in turn, optimizes the weight distribution of the reciprocal lattice vector projection, enabling the adaptive adjustment of the spatial distribution density of the discrete components; the finally formed discrete basis optical field provides an optimization space with clear physical constraints for the neural network to generate high-fidelity predistortion signals.

[0119] In the Nth-order controllable diffractive optical field, N is a preset value, and the generation of the Nth-order controllable diffractive optical field includes:

[0120] A 4f optical filtering system is arranged at the output end of the photonic crystal waveguide.

[0121] A spiral phase plate corresponding to the target topological charge number is inserted into the Fourier plane of the 4f optical filtering system.

[0122] Through the mode field matching effect of the graded refractive index cladding, the diffraction efficiency of non-target order Bloch modes is suppressed.

[0123] When the discrete basis optical field and the 4f spectral filtering act jointly, the former constrains the physical realizability of the spatial frequency components through the reciprocal lattice vector projection, and the latter uses the spiral phase modulation to screen the eigenmodes that conform to the target angular momentum state. The graded refractive index cladding, as a spatial filter, further suppresses the stray modes excited by waveguide defects or environmental perturbations, laying a physical foundation for the light column display system to achieve sub-wavelength precision dynamic holographic projection.

[0124] Embodiment 2: As Figure 2 shown, based on the same inventive concept as the high-precision light column display method based on liquid crystal variable refractive index in the foregoing embodiment, this application provides a high-precision light column display system based on liquid crystal variable refractive index. The system in the embodiment of this application and the method embodiment are based on the same inventive concept. Among them, the system includes:

[0125] A refractive gradient regulation model, which generates a multi-dimensional driving signal with spatial gradient characteristics according to the preset spatial distribution parameters of the target light column. Through the coupled regulation of the voltage amplitude and frequency of the multi-dimensional driving signal, the molecular arrangement state of the liquid crystal electro-optic refractive index adjustment layer is dynamically changed, and a refractive index gradient field matching the phase distribution requirement of the light column axis is established.

[0126] The waveguide substrate generation model couples the incident light beam into the total reflection transmission channel of the optical waveguide structure, performs spatial phase modulation on the transmitted light beam based on the refractive index gradient field, and generates a discretized substrate light field adapted to the geometric constraint conditions of the optical waveguide through the geometric boundary constraint effect of the optical waveguide structure.

[0127] The polarization diffraction synthesis model applies synchronous polarization state regulation to the discretized substrate light field, dynamically corrects the polarization dispersion angle deviation of each diffraction order by using the birefringence compensation algorithm, and generates an N-order controllable diffraction light field with a fixed phase relationship through multi-stage diffraction synthesis.

[0128] The closed-loop dynamic reconstruction model introduces the N-order controllable diffraction light field into the free space propagation domain, realizes the spatial superposition of each order diffraction field through the Fresnel diffraction integral, reconstructs a continuous and high-precision light column shape, and uses the wavefront distortion amount detected and fed back by the light column edge to inversely correct the voltage regulation parameters of the drive signal to form a dynamic closed-loop calibration mechanism.

[0129] Obviously, those skilled in the art can make various modifications and variations to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention is also intended to include these modifications and variations.

[0130] The above are only the preferred specific embodiments of the embodiments of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present application, according to the technical solution and its concept of the present application, makes equivalent substitutions or changes, and should be covered by the protection scope of the present application.

Claims

1. A high-precision light column display method based on a liquid crystal variable refractive index, characterized in that The method includes: Generating a multi-dimensional driving signal with spatial gradient characteristics according to the preset spatial distribution parameters of the target light column, and dynamically changing the molecular arrangement state of the liquid crystal electro-optic refractive index adjustment layer through the coupling regulation of the voltage amplitude and frequency of the multi-dimensional driving signal, so as to establish a refractive index gradient field matching the axial phase distribution requirement of the light column; Coupling the incident light beam into the total reflection transmission channel of the optical waveguide structure, performing spatial phase modulation on the transmitted light beam based on the refractive index gradient field, and generating a discretized base light field adapted to the geometric constraint conditions of the optical waveguide through the geometric boundary constraint effect of the optical waveguide structure; Applying polarization state synchronous regulation to the discretized base light field, dynamically correcting the polarization dispersion angle deviation of each diffraction order by using the birefringence compensation algorithm, and generating an N-order controllable diffraction light field with a fixed phase relationship through multi-stage diffraction synthesis; Introducing the N-order controllable diffraction light field into the free space propagation domain, realizing the spatial superposition of each order diffraction field through the Fresnel diffraction integral, reconstructing a continuous and high-precision light column shape, and using the wavefront distortion amount detected by the light column edge detection to reversely correct the voltage regulation parameters of the driving signal to form a dynamic closed-loop calibration mechanism.

2. The high-precision light column display method based on liquid crystal variable refractive index according to claim 1, characterized in that: The multi-dimensional driving signal generation method includes: Establishing a transfer function matrix of driving voltage and phase modulation according to the Bloch mode eigen-equation of the optical waveguide structure; Performing an inverse operation on the transfer function matrix through a feedforward neural network to generate a pre-distorted driving signal including inter-mode coupling compensation; Loading the pre-distorted driving signal onto the traveling wave electrode of the electro-optic modulator to form a refractive index gradient field with spatio-temporal distribution.

3. The high-precision light column display method based on liquid crystal variable refractive index according to claim 2, wherein The optical waveguide structure is a photonic crystal waveguide, and the optical waveguide structure includes: A hexagonal close-packed air hole array arranged periodically along the propagation direction, and the duty cycle of the air holes matches the group velocity distribution of the Bloch mode; A graded refractive index cladding covering the waveguide sidewall, and its refractive index is distributed in a hyperbolic secant function along the radial direction, which is used to constrain the paraxial propagation characteristics of the refractive index gradient field.

4. The high-precision light column display method based on liquid crystal variable refractive index according to claim 3, characterized in that: The polarization state synchronous regulation method includes: Integrating a polarization beam splitter at the input end of the photonic crystal waveguide to decompose the incident light into TE-mode and TM-mode orthogonal polarization components; Applying the odd and even channel voltages in the pre-distorted driving signal to the TE mode and TM mode respectively; Through the time-domain interleaved scanning method, making the birefringence delay amounts of the orthogonal polarization components form a complementary distribution in space.

5. The high-precision light column display method based on liquid crystal variable refractive index according to claim 4, characterized in that, The wavefront distortion amount detection method includes: Collecting the diffraction spots of the orthogonal polarization components by using the output end of the polarization beam splitter; Inputting the diffraction spots into the error backpropagation module of the feedforward neural network to calculate the deviation amount between the actual phase distribution and the target Bloch mode; Generating wavefront correction parameters in the form of Zernike polynomial coefficients based on the deviation amount.

6. The high-precision light column display method based on liquid crystal variable refractive index according to claim 5, characterized in that, The dynamic closed-loop calibration mechanism includes: Inputting the Zernike polynomial coefficients into the input layer of the feedforward neural network to form a first feedback loop; Dynamically weighting and correcting the eigenvalues of the transfer function matrix through a Kalman filter to form a second feedback loop; The outputs of the first feedback loop and the second feedback loop are convolved and fused in the Fourier spectral domain of the waveguide mode.

7. The high-precision light column display method based on liquid crystal variable refractive index according to claim 4, characterized in that The discrete base optical field synthesis method includes: Constructing a discretization constraint condition of the Bloch wave vector according to the reciprocal lattice vector space distribution of the photonic crystal waveguide; Projecting the continuous phase distribution of the refractive index gradient field onto the basis vectors of the reciprocal lattice vector space; Screening discrete phase components that satisfy the group velocity matching condition of the Bloch mode through the Gibbs sampling algorithm.

8. The high-precision light column display method based on liquid crystal variable refractive index according to claim 7, wherein, The generation of the Nth-order controllable diffracted optical field includes: Setting a 4f optical filtering system at the output end of the photonic crystal waveguide; Inserting a spiral phase plate corresponding to the target topological charge number in the Fourier plane of the 4f optical filtering system; Suppressing the diffraction efficiency of non-target-order Bloch modes through the mode field matching effect of the graded refractive index cladding.

9. A high-precision light column display system based on a liquid crystal variable refractive index, characterized in that, The system includes: A refractive gradient regulation model, which generates a multi-dimensional drive signal with spatial gradient characteristics according to the preset spatial distribution parameters of the target light column. Through the coupling regulation of the voltage amplitude and frequency of the multi-dimensional drive signal, the molecular arrangement state of the liquid crystal electro-optic refractive index adjustment layer is dynamically changed, and a refractive index gradient field matching the axial phase distribution requirement of the light column is established; A waveguide substrate generation model, which couples the incident light beam into the total reflection transmission channel of the optical waveguide structure, performs spatial phase modulation on the transmitted light beam based on the refractive index gradient field, and generates a discretized base optical field adapted to the geometric constraint conditions of the optical waveguide structure through the geometric boundary constraint effect of the optical waveguide structure; A polarization diffraction synthesis model, which applies synchronous polarization state regulation to the discretized base optical field, dynamically corrects the polarization dispersion angle deviation of each diffraction order by using a birefringence compensation algorithm, and generates an Nth-order controllable diffracted optical field with a fixed phase relationship through multi-stage diffraction synthesis; A closed-loop dynamic reconstruction model, which introduces the Nth-order controllable diffracted optical field into the free space propagation domain, realizes the spatial superposition of each order of diffracted fields through Fresnel diffraction integration, reconstructs a continuous and high-precision light column shape, and uses the wavefront distortion amount detected and fed back at the light column edge to reversely correct the voltage regulation parameters of the drive signal to form a dynamic closed-loop calibration mechanism.

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