CN-122018190-A - Airy pulse time domain evolution track regulation and control method based on liquid crystal orientation design

CN122018190ACN 122018190 ACN122018190 ACN 122018190ACN-122018190-A

Abstract

The invention provides an Airy pulse time domain evolution track regulation and control method based on liquid crystal orientation design, and relates to the technical field of ultrafast optics. The method comprises the steps of firstly constructing a theoretical model for transmitting Airy pulses in a liquid crystal medium, establishing a nonlinear mapping relation between a liquid crystal molecular orientation angle, group velocity dispersion and third-order dispersion, establishing a polynomial function relation between a dispersion parameter and a liquid crystal molecular orientation angle trigonometric function item by utilizing numerical fitting based on the mapping relation, designing a space distribution rule of the liquid crystal molecules along a propagation direction according to a target time domain track, determining dispersion distribution in the liquid crystal medium by establishing linear correlation between the trigonometric function item and the propagation distance, and finally aligning the liquid crystal molecules according to the space distribution rule. According to the invention, by designing the space orientation gradient of the liquid crystal, a dynamic dispersion environment is constructed on a transmission path, and the precise linear regulation and control of the self-acceleration, self-deceleration and track bending degree of Airy pulses are realized.

Inventors

GAO MEINI
DAI HAITAO
FENG SHOUZHONG
WANG QIANG
LI YAFENG
SHI XIN

Assignees

安徽理工大学

Dates

Publication Date: 20260512
Application Date: 20260304

Claims (10)

1. The Airy pulse time domain evolution track regulation method based on liquid crystal orientation design is characterized by comprising the following steps of: s1, constructing a theoretical model of transmission of Airy pulses in a liquid crystal medium, and establishing a nonlinear mapping relation between a liquid crystal molecular orientation angle and group velocity dispersion and third-order dispersion of the liquid crystal medium; step S2, based on the nonlinear mapping relation, establishing a polynomial function relation between the group velocity dispersion and the third-order dispersion and a trigonometric function term of the liquid crystal molecular orientation angle respectively by adopting a numerical fitting method; s3, designing a space distribution rule of a liquid crystal molecular orientation angle along the propagation direction of the light wave according to a target time domain evolution track of the Airy pulse, and determining dispersion distribution of a liquid crystal medium along the propagation direction by establishing linear correlation between the trigonometric function item and the propagation distance; And S4, aligning and arranging liquid crystal molecules in the liquid crystal box according to the space distribution rule, so that the incident Airy pulse is subjected to dynamic dispersion modulation when passing through the liquid crystal medium, and the time domain evolution track of the Airy pulse is changed.
2. The method for regulating and controlling the time domain evolution track of the Airy pulse based on the liquid crystal orientation design according to claim 1, wherein in the step S1, the transmission of the Airy pulse in a liquid crystal medium follows a dispersion-dominated wave equation: ; Wherein, the For the electric field envelope to be present, In order for the propagation distance to be sufficient, In order to be able to take time, In units of imaginary numbers, In order to achieve group velocity dispersion, Is third-order dispersion; the liquid crystal molecular orientation angle Corresponding effective refractive index The method meets the following conditions: ; Wherein, the Is the ordinary refractive index of the liquid crystal, Is the extraordinary refractive index.
3. The method for regulating and controlling the time domain evolution track of Airy pulses based on liquid crystal orientation design according to claim 2, wherein the group velocity dispersion is characterized in that And third-order dispersion Determined by the following formula: ; Wherein, the For angular frequency, wave number From the formula It is determined that the number of the cells, Is the speed of light.
4. The method for regulating and controlling the time domain evolution trajectory of the airy pulse based on the liquid crystal alignment design according to claim 1, wherein in the step S2, the polynomial function relation includes a fitting expression for a first initial state and a second initial state: For a first initial state: ; ; for the second initial state: ; ; Wherein, the Is the orientation angle of liquid crystal molecules; The fit coefficients for the group velocity dispersions are respectively, Fitting coefficients for third-order dispersion, respectively.
5. The method for adjusting and controlling the time domain evolution trajectory of the airy pulse based on the liquid crystal alignment design according to claim 4, wherein in the step S3, the linear correlation is established for the first initial state, specifically: ; Wherein, the In order for the propagation distance to be sufficient, The first initial state corresponds to the orientation angle of liquid crystal molecules Along with it The axis is graded from 0 degrees to 90 degrees.
6. The method for adjusting and controlling the time domain evolution trajectory of the airy pulse based on the liquid crystal alignment design according to claim 4, wherein in the step S3, the linear correlation is established for the second initial state, specifically: ; Wherein, the In order for the propagation distance to be sufficient, The second initial state corresponds to the orientation angle of the liquid crystal molecules Along with it The axis is graded from 90 degrees to 0 degrees.
7. The method for regulating and controlling the time domain evolution track of Airy pulse based on liquid crystal orientation design according to claim 5 or 6, wherein the propagation distance in the linear correlation is characterized in that Distance from dimensionless distance The relation of (2) is: ; Wherein, the For normalizing propagation distance, it is defined as , For the initial pulse width of the pulse-width modulation, Is the group velocity dispersion value of the input terminal.
8. The method for adjusting and controlling the time domain evolution track of Airy pulse based on liquid crystal alignment design according to claim 7, wherein in said step S4, the frequency domain electric field of the adjusted and controlled Airy pulse Expressed as: ; Wherein, the For the frequency domain distribution of the initial electric field, As a function of the frequency domain variation, And Is a phase modulation parameter.
9. The method for regulating and controlling the time domain evolution track of Airy pulses based on liquid crystal orientation design according to claim 8, wherein the phase modulation parameter is as follows And Defined by the formula: ; ; Wherein, the And And the fitting coefficients are respectively.
10. The method for regulating and controlling the time domain evolution track of the Airy pulse based on the liquid crystal alignment design according to claim 1, wherein in the step S4, the method for aligning the liquid crystal molecules comprises any one of a friction alignment method, a digital micromirror device photo-alignment method and a laser direct writing alignment method.

Description

Airy pulse time domain evolution track regulation and control method based on liquid crystal orientation design Technical Field The invention relates to the technical field of ultrafast optics and light field regulation, in particular to an Airy pulse time domain evolution track regulation method based on liquid crystal orientation design. Background Airy pulse is taken as a finite energy light wave packet with diffraction-free, self-healing and self-accelerating characteristics, and has important application potential in the front fields of photon bullet generation, particle manipulation, plasma channel construction and the like. In practical optical system applications, in order to meet specific signal synchronization, delay control or energy transport requirements, precise tailoring and customization of the time domain evolution behavior of the airy pulse are often required. The parabolic time domain trajectory of the Airy pulse is mainly determined by the initial spectral phase distribution and the dispersion characteristics of the transmission medium, and in a conventional isotropic medium, the dispersion coefficient of the material is usually constant, so that once the Airy pulse is generated, the evolution trajectory is locked, and the Airy pulse is difficult to adapt to a complex and changeable transmission environment. The existing optical pulse dispersion regulation and control technology mainly depends on passive devices such as grating pairs and prisms, and once the devices are prepared, the dispersion structures of the devices are physically fixed, and generally only uniform or periodic dispersion distribution can be provided, so that a continuously-changing dispersion gradient environment is difficult to construct on an optical wave propagation path. Although the dynamic behavior of the pulses can be altered by nonlinear effects in the fiber, this generally requires that the incident light have extremely high peak power to excite the nonlinear response of the medium, and the high power mode of operation not only increases the energy consumption of the system, but also is susceptible to side effects such as spectral broadening, waveform splitting, or signal noise, affecting signal integrity. The liquid crystal material has physical basis for constructing a non-uniform refractive index field due to large optical double refractive index and high controllability, and is an ideal candidate medium for realizing miniaturized dispersion management. However, there is a very complex nonlinear dependence between the orientation angle of the liquid crystal molecules and the group velocity dispersion and third-order dispersion perceived by the light waves, which makes the exact reverse design of linearization trajectories directly using liquid crystals facing great theoretical difficulties. At present, a systematic method capable of converting the complex nonlinear physical quantity into a simple geometric design parameter so as to realize on-demand customization of the finite energy Airy pulse time domain behavior is not available. Disclosure of Invention The invention aims to provide an Airy pulse time domain evolution track regulation method based on liquid crystal orientation design, which aims to solve the problems pointed out in the background technology. The invention provides an Airy pulse time domain evolution track regulation method based on liquid crystal orientation design, which comprises the following steps: s1, constructing a theoretical model of transmission of Airy pulses in a liquid crystal medium, and establishing a nonlinear mapping relation between a liquid crystal molecular orientation angle and group velocity dispersion and third-order dispersion of the liquid crystal medium; step S2, based on the nonlinear mapping relation, establishing a polynomial function relation between the group velocity dispersion and the third-order dispersion and a trigonometric function term of the liquid crystal molecular orientation angle respectively by adopting a numerical fitting method; s3, designing a space distribution rule of a liquid crystal molecular orientation angle along the propagation direction of the light wave according to a target time domain evolution track of the Airy pulse, and determining dispersion distribution of a liquid crystal medium along the propagation direction by establishing linear correlation between the trigonometric function item and the propagation distance; And S4, aligning and arranging liquid crystal molecules in the liquid crystal box according to the space distribution rule, so that the incident Airy pulse is subjected to dynamic dispersion modulation when passing through the liquid crystal medium, and the time domain evolution track of the Airy pulse is changed. Optionally, in the step S1, the transmission of the eiri pulse in the liquid crystal medium follows a dispersion-dominated wave equation: ; Wherein, the For the electric field envelope to be present,In o