CN-121978834-A - Super-structured grating design method and super-structured grating

CN121978834ACN 121978834 ACN121978834 ACN 121978834ACN-121978834-A

Abstract

The invention provides a super-structured grating design method and a super-structured grating, the method comprises the steps of determining the transverse period length of the super-structured grating along a first direction according to an incidence characteristic parameter of an incident wave and a preset propagation diffraction order set, determining an auxiliary phase parameter according to a preset power distribution proportion of each propagation diffraction order in the propagation diffraction order set, determining the thickness of a substrate by taking a real part of the equivalent load impedance density as a constraint based on the auxiliary phase parameter and an analytical expression of a preset equivalent load impedance density, determining the equivalent load impedance density of a super-atom based on the incidence characteristic parameter, the preset strip width, the thickness of the substrate, the transverse period length and the auxiliary phase parameter and combining the analytical expression, determining the longitudinal period length of the super-atom along a second direction based on the incidence characteristic parameter, and determining the arm length of the super-atom according to the longitudinal period length, the incidence characteristic parameter, the strip width, the effective dielectric constant of the super-structured grating and the equivalent load impedance density.

Inventors

TAN ZHEN
DING XINHAO
YU MEI

Assignees

南通大学

Dates

Publication Date: 20260505
Application Date: 20260119

Claims (10)

1. A method of designing a super-structured grating comprising a plurality of super-atoms periodically arranged on a substrate along a first direction, comprising: Determining the transverse period length of the super-structured grating along the first direction according to the incidence characteristic parameters of the incident wave and a preset propagation diffraction order set; determining auxiliary phase parameters according to preset power distribution ratios of all propagation diffraction orders in the propagation diffraction order set; Based on the auxiliary phase parameter and a pre-constructed analytical expression of equivalent load impedance density, determining the thickness of the substrate by taking the real part of the equivalent load impedance density as a constraint; determining the equivalent load impedance density of the super atoms based on the incidence characteristic parameter, the preset strip width of the super atoms, the thickness of the substrate, the transverse period length and the auxiliary phase parameter and combining the analytical expression; And determining the longitudinal period length of the super atom along the second direction based on the incidence characteristic parameter, and determining the arm length of the super atom according to the longitudinal period length, the incidence characteristic parameter, the strip width, the effective dielectric constant of the super-structure grating and the equivalent load impedance density.
2. The method for designing an ultra-structured grating according to claim 1, wherein determining a transverse period length of the ultra-structured grating along the first direction according to the incident characteristic parameter of the incident wave and the preset set of propagation diffraction orders comprises: Determining the selectable range of the transverse period length according to the propagation diffraction order set and the incidence characteristic parameter so that the propagation diffraction order can be propagated under the incidence condition corresponding to the incidence characteristic parameter; And in the optional range, determining a specific value of the transverse period length according to a target emergent direction corresponding to at least one propagation diffraction order in the propagation diffraction order set.
3. The method of claim 1, wherein determining the auxiliary phase parameter according to a power distribution ratio preset for each propagation diffraction order in the set of propagation diffraction orders comprises: normalizing the power of each propagation diffraction order in the propagation diffraction order set according to a preset power distribution proportion to obtain target power of each propagation diffraction order; Based on far field interaction of the super-structured grating, establishing a mapping relation between diffraction field amplitude values of all propagation diffraction orders and incidence characteristic parameters and equivalent polarization currents in the super-structured grating; And expressing the equivalent polarization current as a complex form containing the auxiliary phase parameter, and substituting the diffraction field amplitude into the far-field mapping relation to solve the auxiliary phase parameter, so that the diffraction field amplitude of each propagation diffraction order meets the power distribution proportion.
4. The method according to claim 1, wherein determining the thickness of the substrate with the real part of the equivalent load impedance density as a constraint by the analytic expression based on the auxiliary phase parameter and the pre-constructed equivalent load impedance density includes: based on the incidence characteristic parameter, the transverse period length and the propagation diffraction order set, determining a longitudinal wave number corresponding to each propagation diffraction order, and establishing an expression of a reflection coefficient and a transmission coefficient of each propagation diffraction order on the substrate relative to the thickness of the substrate according to the longitudinal wave number; substituting the reflection coefficient and the transmission coefficient into an analytical expression of the equivalent load impedance density, and solving the thickness of the substrate by taking the real part of the analytical expression as a constraint condition.
5. The method of super-structure grating design as recited in claim 4, further comprising: Under normal incidence condition, constraining the thickness of the substrate to obtain a target thickness for suppressing non-target propagation diffraction orders in the propagation diffraction order set, wherein the non-target propagation diffraction orders are propagation diffraction orders with zero or less than a preset threshold corresponding to the power distribution ratio in the preset power distribution ratio, and the method comprises the following steps: Establishing a mode suppression condition for making the diffraction field amplitude of the non-target propagation diffraction order smaller than a preset amplitude or making the power of the non-target propagation diffraction order smaller than a preset power based on the analytical expression of the pre-constructed equivalent load impedance density, so as to take the mode suppression condition as a constraint on the thickness of the substrate; and constructing an over-constraint equation set about the thickness of the substrate by taking the mode suppression condition and the condition that the real part of the equivalent load impedance density is zero as constraints on the thickness of the substrate, and solving the over-constraint equation set by adopting a least square method to determine the target thickness of the substrate.
6. The method of claim 1, wherein the pre-construction of the analytical expression for equivalent load impedance density comprises: Establishing a corresponding relation between the equivalent load impedance density, a total electric field and an equivalent polarization current based on the periodicity of the super-structured grating and boundary conditions; and carrying out convergence processing on divergent items caused by array summation in the corresponding relation to obtain an analytical expression of the calculated equivalent load impedance density.
7. The method of claim 1, wherein determining a longitudinal period length of the super atom in the second direction based on the incident characteristic parameter comprises: determining the wavelength of the incident wave in the background medium based on the incident characteristic parameter; The longitudinal period length is set to a sub-wavelength less than the wavelength in the background medium to uniformly distribute the equivalent load impedance density of the super-atoms in the second direction.
8. A super-structured grating, comprising: a plurality of superatoms periodically arranged along a first direction; wherein the super-structured grating has a transverse period length along the first direction; each of the superatoms includes a conductive strip, and an extension formed by the conductive strip; The transverse period length, the thickness of the substrate, the strip width of the conductive strip and the arm length of the extension part meet the passive lossless condition that the real part of the equivalent load impedance density of the super atom is zero under the preset incidence characteristic parameter and the preset propagation diffraction order set.
9. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements the method of super-structured raster design of any one of claims 1 to 7 when the program is executed by the processor.
10. A non-transitory computer readable storage medium having stored thereon a computer program, wherein the computer program when executed by a processor implements the method of super-structured raster design of any of claims 1 to 7.

Description

Super-structured grating design method and super-structured grating Technical Field The invention relates to the technical field of gratings, in particular to a super-structured grating design method and a super-structured grating. Background The precise regulation and control of electromagnetic waves is an important foundation of modern photonics and radio frequency technology, and the application range of the precise regulation and control of electromagnetic waves comprises the fields of imaging, sensing, wireless communication, radar and the like. The super surface (Metasurface) is usually a two-dimensional array formed by sub-wavelength super atoms, wave front regulation and control are realized through engineering design of electromagnetic response of the unit, and alternatively, the super-structured grating adopts different design ideas, and selective control of a diffraction channel (diffraction order) is realized through a periodic structure, so that the functions of abnormal reflection, abnormal refraction, beam splitting and the like are realized. The design of existing supersurfaces is mostly based on the "locally responsive surface" assumption that the reflection/transmission response of each location (or each superatom) is mainly determined by the local incident field and the phase gradient is formed by imparting different surface impedances to modulate the exiting wavefront. However, under large angle beam deflection or multi-functional operation scenarios, the super surface is prone to efficiency limitation, and there are inherent challenges when multiple diffraction orders need to be controlled simultaneously, one of the reasons is that the local assumption is difficult to satisfy global electromagnetic boundary conditions, and strong anomalous reflection often requires cooperative support of complex modes such as non-local coupling and evanescent waves/near fields. In contrast, a super-structured grating designs a desired current distribution from a global perspective to enhance the shaping ability of far-field patterns by sparsely arranging super-atoms in a period and utilizing selective interference to suppress unwanted diffraction orders. Conventional wisdom generally considers that "a single superatom per cycle suppresses one diffraction order" and so more modes tend to require an increase in the number of superatoms in the unit cell, which inevitably increases design complexity and exacerbates manufacturing requirements. Therefore, given the incident condition and the target power distribution requirement, it is still difficult to consider the requirement of efficiently introducing energy into the target propagation diffraction order and suppressing the non-target propagation diffraction order in the single super atomic structure in the prior art, and there is a need for a super-structure grating design scheme capable of realizing multi-channel diffraction regulation while maintaining the structural simplification. Disclosure of Invention The invention provides a super-structured grating design method and a super-structured grating, which are used for solving the defect that in the prior art, under given incidence conditions and target power distribution requirements, high-efficiency introduction and suppression of a super-structured grating with useless diffraction orders are difficult to achieve under a single super-atomic structure. The invention provides a super-structure grating design method, which comprises a plurality of super-atoms periodically arranged on a substrate along a first direction, wherein the super-structure grating comprises a transverse period length of the super-structure grating along the first direction according to an incidence characteristic parameter of an incident wave and a preset propagation diffraction order set, an auxiliary phase parameter is determined according to a preset power distribution proportion of each propagation diffraction order in the propagation diffraction order set, the thickness of the substrate is determined by taking a real part of the equivalent load impedance density as a constraint on the basis of the auxiliary phase parameter and an analytical expression of a preset equivalent load impedance density, the thickness of the substrate is determined by taking a real part of the equivalent load impedance density as a zero, and the equivalent load impedance density of the super-structure grating is determined by combining the analytical expression on the basis of the incidence characteristic parameter, the preset strip width of the substrate, the transverse period length and the auxiliary phase parameter. The method for designing the super-structured grating comprises the steps of determining the transverse period length of the super-structured grating along the first direction according to the incidence characteristic parameters of incident waves and a preset propagation diffraction order set, determining the optional range of the tr