Disclosure of Invention
The embodiment of the invention provides an optical rectification element based on a super-surface grating and a design method thereof, which are used for realizing that two beams of plane waves with the same polarization and wavelength are incident on the element from different angles, so that the two beams of plane waves can be coupled into one beam of plane wave to be emitted, and simultaneously, better optical rectification is realized.
On one hand, a method for designing a light rectifying element based on a super-surface grating is provided, which is characterized by comprising the following steps: selecting a target working wave band, a target incidence angle and a target emergence angle to determine initial structure parameters of the super-surface grating; carrying out binary coding on the initial structure parameters to obtain corresponding initial binary parameters; optimizing the initial binary parameters based on a multi-objective optimization algorithm to obtain initial optimized structure parameters; and performing boundary optimization on the preliminary optimized structure parameters according to the manufacturing process requirements to obtain optimal structure parameters.
In some embodiments, optimizing the initial binary parameters based on a multi-objective optimization algorithm to obtain preliminary optimized structural parameters comprises:
carrying out optical modeling by taking the initial binary parameter as a current binary parameter and calculating a light rectification evaluation value corresponding to the current binary parameter according to an evaluation function;
judging whether the currently calculated light rectification evaluation value meets the optimization termination condition, if not, optimizing the current binary parameter to calculate a new light rectification evaluation value;
and if the currently calculated light rectification evaluation value meets the optimization termination condition, taking the light rectification evaluation value meeting the optimization termination condition as a preliminary optimization evaluation value, and restoring and calculating a preliminary optimization structure parameter by using a binary parameter corresponding to the preliminary optimization evaluation value.
In some embodiments, performing optical modeling with an initial binary parameter as a current binary parameter and calculating a light rectification evaluation value corresponding to the current binary parameter according to an evaluation function, includes:
establishing an optical model according to the current binary parameters and calculating the angular spectrum and the reflectivity of the plane wave of the target working waveband under the target incident angle based on the optical model;
and substituting the angular spectrum and the reflectivity into an evaluation function to calculate a light rectification evaluation value corresponding to the initial binary parameter.
In some embodiments, the determining whether the currently calculated light rectification evaluation value satisfies the optimization termination condition includes:
sorting and selecting the currently calculated light rectification evaluation value based on a non-dominated sorting algorithm;
and judging whether the current sorting and selecting result meets the requirement that the front edge N of pareto is unchanged and N is an integer greater than 0, if so, judging that the optimization termination condition is met, and otherwise, judging that the optimization termination condition is not met.
In some embodiments, the optimizing the current binary parameter to calculate a new light rectification evaluation value includes:
optimizing the current binary parameter by adopting a multi-objective optimization algorithm to obtain a new binary parameter;
establishing an optical model based on the new binary parameters and calculating the angular spectrum and the reflectivity of the plane wave of the target working waveband under the target incident angle based on the optical model;
and substituting the angular spectrum and the reflectivity into an evaluation function to calculate a light rectification evaluation value corresponding to the new binary parameter.
In some embodiments, the preliminary optimization of the structural parameters is performed by boundary optimization according to the requirement of the manufacturing process to obtain the optimal structural parameters, which includes the following steps:
performing discrete coding on the preliminary optimization structure parameters to obtain parameters to be optimized, and determining an optional parameter range according to process requirements and the parameters to be optimized;
traversing all parameters in the optional parameter range and finding out the optimal optional parameters;
and restoring and calculating the corresponding super-surface grating structure parameter by using the optimal optional parameter, and taking the super-surface grating structure parameter as an optimal structure parameter.
In some embodiments, traversing all parameters within the range of selectable parameters and finding the optimal selectable parameter comprises the steps of:
if the parameters in the current optional parameter range are not empty, selecting one parameter in the optional parameter range to calculate the corresponding light rectification evaluation value;
judging whether the currently calculated light rectification evaluation value is superior to the current evaluation value reference, if so, replacing the current evaluation value reference with the currently calculated light rectification evaluation value, and continuously selecting a parameter in the optional parameter range to calculate the corresponding light rectification evaluation value;
if the currently calculated light rectification evaluation value is not superior to the current evaluation value reference, continuously selecting one parameter to calculate the corresponding light rectification evaluation value after eliminating the currently selected parameter in the current optional parameter range;
and taking the last remaining parameter in the current optional parameter range as the optimal optional parameter.
In some embodiments, the selecting a parameter within the selectable parameter range to calculate its corresponding light rectification evaluation value includes:
establishing an optical model according to the selected parameters and calculating the angular spectrum and the reflectivity of the plane wave of the target working waveband under the target incident angle based on the optical model;
and substituting the angular spectrum and the reflectivity into an evaluation function to calculate a light rectification evaluation value corresponding to the initial binary parameter.
Another aspect provides a light rectifying element based on a super-surface grating, characterized in that,
the optical rectifying element is a three-layer structure consisting of a metal substrate layer, a dielectric layer and a metal grating layer;
the three-layer structure meets the optimal structure parameters;
the optimal structure parameters comprise a minimum interval, a minimum size, a transverse minimum resolution size and a longitudinal minimum resolution size.
In some embodiments, the metal base layer is a silver layer;
the dielectric layer is a silicon dioxide film layer;
the metal grating layer is made of gold.
The embodiment of the invention can realize the light rectification function of coupling two beams of plane waves into one beam when plane waves with two angles enter and only one angle exits, and simultaneously inhibit other non-target orders. Because the coded parameters can be optimized, the incident angle can be not limited, and a certain angle for plane wave incident at any two angles of a specific wave band to be reflected or transmitted is designed, so that the light rectification function has certain universality, and the designed light rectification element has wider working bandwidth and better manufacturability.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be obtained by a person skilled in the art without any inventive step based on the embodiments of the present invention, are within the scope of the present invention.
As shown in fig. 1, an embodiment of the present invention provides a method for designing an optical rectification element based on a super-surface grating, which includes the steps of:
s100, selecting a target working wave band, a target incidence angle and a target emergence angle to determine initial structure parameters of the super-surface grating;
s200, carrying out binary coding on the initial structure parameters to obtain corresponding initial binary parameters;
s300, optimizing the initial binary parameters based on a multi-objective optimization algorithm to obtain initial optimized structure parameters;
and S400, performing boundary optimization on the preliminary optimized structure parameters according to the manufacturing process requirements to obtain the optimal structure parameters.
It should be noted that the multi-objective optimization algorithm includes, but is not limited to, an NSGA2 algorithm, an NSGA3 algorithm or a multi-objective evolutionary algorithm, a multi-objective particle swarm algorithm, a multi-objective simulated annealing algorithm, a multi-objective ant colony algorithm, a multi-objective immune algorithm, a multi-objective distributed search algorithm, and the like, and combinations or variations of related algorithms.
It is understood that the incident angle and the exit angle may be set arbitrarily within the range of the physical law constraint in step S100, and the preliminary design of the light rectifying element may be performed in a manner that plane waves of two angles are incident and plane waves of only one angle are emitted through step S100. Step S200 is to use a binary coding method to facilitate control of consideration factors of the minimum size, the minimum interval, and the minimum longitudinal resolution size, and the optimization of the structural parameters is already achieved by performing binary coding on the initial structural parameters obtained by the preliminary design and optimizing the parameters after the binary coding by using a multi-objective optimization algorithm. The performance of the light rectifying element is further improved by optimizing based on the encoded parameters, and meanwhile, the consideration factor of the transverse minimum resolution size can be further controlled, so that the optimization scheme can be adjusted according to the requirements of the manufacturing process to obtain a better size.
Through the scheme of the embodiment, the light rectification function that two planar waves are coupled into one beam and only one planar wave is emitted from two angles can be realized, and other non-target orders are inhibited. Because the coded parameters can be optimized, the incident angle can be not limited, and a certain angle for plane wave incident at any two angles of a specific wave band to be reflected or transmitted is designed, so that the light rectification function has certain universality, and the designed light rectification element has wider working bandwidth and better manufacturability.
As shown in fig. 3, in some embodiments, step S300 further includes the steps of:
s310, carrying out optical modeling by taking the initial binary parameter as a current binary parameter and calculating a light rectification evaluation value corresponding to the current binary parameter according to an evaluation function;
s320, judging whether the currently calculated light rectification evaluation value meets the optimization termination condition, if not, optimizing the current binary parameter to calculate a new light rectification evaluation value;
and S330, if the currently calculated light rectification evaluation value meets the optimization termination condition, taking the light rectification evaluation value meeting the optimization termination condition as a preliminary optimization evaluation value, and restoring and calculating a preliminary optimization structure parameter by using a binary parameter corresponding to the preliminary optimization evaluation value.
It should be noted that, because the optimization process is an iterative process, in the real-time process of the actual scheme, the step S320 often needs to be repeated for multiple times to make the light rectification evaluation value after iterative optimization meet the optimization termination condition, so as to reach the local optimal value.
In the embodiment, the coded binary parameter is calculated as the corresponding light rectification evaluation value through optical modeling, so that the structural parameter is optimized through optimization of the light rectification evaluation value.
In some embodiments, step S310 further comprises the steps of:
s311, establishing an optical model according to the current binary parameter and calculating the angular spectrum and the reflectivity of the plane wave of the target working waveband under the target incident angle based on the optical model;
and S312, substituting the angular spectrum and the reflectivity into an evaluation function to calculate a light rectification evaluation value corresponding to the initial binary parameter.
The present embodiment provides a method for obtaining a light rectification evaluation value corresponding to a binary parameter by modeling the parameter. Wherein, the optical model can select common electromagnetic simulation software such as FDTD, CST, comsol, and model which can be established based on improved finite element method, time domain finite difference method and other algorithms; the evaluation function is set to obtain good rectification effect, and the core evaluation indexes are target secondary reflectivity (or reflectivity) and target level contrast (or target level reflectivity ratio), wherein the higher the target secondary reflectivity (or reflectivity ratio), the better the target level contrast, and the contrast is the intensity of the target level divided by the strongest intensity of other levels (the ratio can be the sum of the other levels). Evaluation functions based on such target settings are all available.
In some embodiments, the determining in step S320 whether the currently calculated light rectification evaluation value satisfies the optimization termination condition further includes:
s321, sorting and selecting the currently calculated light rectification evaluation value based on a non-dominated sorting algorithm;
and S322, judging whether the current sequencing and selecting result meets the requirement that the front edge N of pareto is unchanged and N is an integer greater than 0, if so, judging that the optimization termination condition is met, otherwise, judging that the optimization termination condition is not met.
It should be noted that the optimization termination condition may be determined by the concepts of the longest computation time, the smallest inter-generation progress, and the largest inter-generation progress, the pareto leading edge of the current generation is computed for each generation, the inter-generation progress of one leading edge is computed according to the values of the pareto leading edges of two generations, and N may be set to 15, that is, the optimization termination condition to be satisfied is that the pareto leading edge is not changed for 15 generations. In addition, a target value may be set and may be terminated when the current result exceeds or reaches an optimal value.
In some embodiments, optimizing the current binary parameter in step S320 to calculate a new light rectification evaluation value further includes the steps of:
s323, optimizing the current binary parameter by adopting a multi-objective optimization algorithm to obtain a new binary parameter;
s324, establishing an optical model based on the new binary parameter and calculating the angular spectrum and the reflectivity of the plane wave of the target working waveband under the target incident angle based on the optical model;
and S325, substituting the angular spectrum and the reflectivity into an evaluation function to calculate a light rectification evaluation value corresponding to the new binary parameter.
It should be noted that the multi-objective optimization algorithm includes a multi-objective evolutionary algorithm, a multi-objective particle swarm algorithm, a multi-objective simulated annealing algorithm, a multi-objective ant colony algorithm, a multi-objective immune algorithm, a multi-objective distributed search algorithm, and the like.
In some embodiments, step S400 further comprises the steps of:
s410: performing discrete coding on the preliminary optimization structure parameters to obtain parameters to be optimized, and determining an optional parameter range according to process requirements and the parameters to be optimized;
s420: traversing all parameters in the optional parameter range and finding out the optimal optional parameters;
s430: and restoring and calculating the corresponding super-surface grating structure parameter by using the optimal optional parameter, and taking the super-surface grating structure parameter as an optimal structure parameter.
The embodiment provides a method for further performing boundary optimization on the basis of preliminary optimization of the structural parameters to obtain the optimal structural parameters. Firstly, discretizing the preliminarily optimized framework parameters in a discrete coding mode to obtain a variable parameter range, and then adjusting the variable parameter range according to the process requirement so as to enable the parameters for subsequent boundary optimization to meet the process parameter conditions.
As shown in fig. 4, in some embodiments, step S420 further includes the steps of:
s421: selecting a parameter in the selectable parameter range to calculate a corresponding light rectification evaluation value;
s422: judging whether the currently calculated light rectification evaluation value is superior to the current evaluation value reference, if so, replacing the current evaluation value reference with the currently calculated light rectification evaluation value, and continuously selecting a parameter in the optional parameter range to calculate the corresponding light rectification evaluation value;
s423: if not, after the currently selected parameter is removed from the range of the currently selectable parameter, one parameter is continuously selected to calculate the corresponding light rectification evaluation value;
s424: if only one parameter remains in the current optional parameter range, taking the remaining parameter as the optimal optional parameter.
It should be noted that, an evaluation value criterion may be set as a preliminary optimization evaluation value, and in step S422, when the currently calculated light rectification evaluation value is determined for the first time, the currently calculated light rectification evaluation value is compared with the preliminary optimization evaluation value, and if the currently calculated light rectification evaluation value is better than the preliminary optimization evaluation value, the previously calculated light rectification evaluation value is used as the current evaluation value criterion instead of the preliminary optimization evaluation value for comparison after the light rectification evaluation value is calculated next time.
It can be understood that by repeating the processes of S421 to S423, the parameter corresponding to the evaluation value that is not better than the current evaluation value reference can be continuously eliminated from the selectable parameter range, and finally the parameter corresponding to the optimal evaluation value in the selectable parameter range remains.
The present embodiment provides a method of traversing all parameters and finding the optimal optional parameters.
In some embodiments, step S430 further comprises the steps of:
s431: establishing an optical model according to the selected parameters and calculating the angular spectrum and the reflectivity of the plane wave of the target working waveband under the target incident angle based on the optical model;
s432: and substituting the angular spectrum and the reflectivity into an evaluation function to calculate a light rectification evaluation value corresponding to the initial binary parameter.
In a specific embodiment, firstly, the working wave band is selected to be within the range of 550nm-670nm, two incident angles are about +/-30 degrees respectively, and the emergence angle is 0 degree; establishing a grating equation system:
d(sinθi1-sinθr)=n1λ
d(sinθi2-sinθr)=n2λ;
in the equation set, d is the period of the super-surface grating; thetai1A first angle of incidence set at 30 degrees; thetai2Set at-30 degrees for the second angle of incidence; thetarSetting the emergence angle as 0 degree; λ is wavelength, set at 600 nm; n is1And n2The value of (d) is +/-2, and d is 2.4 um.
As shown in fig. 2, a metal substrate is selected as a silver substrate, a dielectric thin film is selected as a silicon dioxide thin film, a metal grating is a grating made of gold material, h1 is the height of a gold layer, h2 is the height of a silicon dioxide layer, and h3 is the height of a silver layer. The size of 50nm is selected as the minimum manufacturing interval and structure minimum size, so that gold binary codes in one grating period can be 48 gold (coded as 1) and gold (coded as 0) with the width of 50nm, h1 is coded as 001, and h2 is coded as 011; selecting the size of 10nm as the longitudinal minimum resolution size, wherein the height of gold is in the range of 20-50nm and is respectively coded as 00, 01, 10 and 11; the dielectric heights range from 60 to 130nm and are coded as 000,001. cndot. cndot.111, and a total of 53 binary codes can be obtained by the aforementioned 48-bit gold and gold-free combined coding, 2-bit coding of a 2-bit gold height h1 and 3-bit coding of a dielectric height h2, wherein each binary code corresponds to a structure size of the super-surface grating.
After the coding is finished, a multi-target genetic algorithm is selected for global optimization, 200 binary random numbers with 53 bits are generated as initial binary codes, an FDTD simulation model is established according to the input codes, and p-polarized plane waves are simulated at two target incidence angles (theta)i1And thetai2) The reflected light field is further scattered and sampled to obtain 61 wavelengths, a far field (angular spectrum) with 201 discrete angles between-90 and 90 degrees and the reflectivity at the corresponding wavelength. The evaluation function used for global optimization is:
wherein r represents a reflectance, far represents a far field (angular spectrum) of FDTD simulation at a corresponding angle, and evaluation values at two target incident angles are calculated from the evaluation function, and the reflectance of a diffraction order near 0 degree in the far field (angular spectrum) is higher, and the intensity multiple of the diffraction order near 0 degree to other diffraction orders is higher. And sequencing, selecting, crossing and mutating the calculated evaluation values according to a maximum optimization NSGA2 algorithm to obtain a next-generation binary code, and stopping optimizing and outputting the current corresponding evaluation values and all binary codes until the obtained pareto front edge is unchanged for several generations (15 generations can be used). And taking the result that the evaluation values corresponding to the two incident angles are respectively high and the sum of the evaluation values corresponding to the two incident angles is the highest, and taking the structural parameter corresponding to the result as a preliminary optimization structural parameter to form the preliminarily optimized light rectifying element. As shown in fig. 7, the light rectifying element after the preliminary optimization is modeled to obtain a simulated far-field spectrum display at 30 degrees incidence, and the light rectifying element is in an axisymmetric structure. In the simulation, the results of the-30 degree incident angle are almost axisymmetric with the results of the 30 degree incident angle.
As shown in fig. 5, after obtaining a preliminary structure size of the optical rectifying element according to the current corresponding evaluation value and all binary codes, discretizing and coding each parameter of the structure size, where h1 is the height of the gold layer, h2 is the height of the silicon dioxide layer, w1, w3, w5, w7, w9, w11 are codes of the grating nano-strip interval, and w2, w4, w6, w8, w10, w12 are codes of the grating nano-strip width. The manufacturing process precision is 5nm, the interval and the minimum width of the nano-strips are 50nm, the thickness ranges of gold and silicon dioxide are respectively 20-50nm and 70-130nm, the current structural parameter values after discretization coding are constrained by boundary conditions, and an optional parameter range is formed for subsequent optimization selection.
Selecting a discretized coded parameter in a selectable parameter range, calculating evaluation values at two incidence angles through FDTD simulation parameters in a far field (angular spectrum) under the incidence of +/-30 degrees according to the evaluation function, considering that the current evaluation value is more optimal if the two evaluation values are increased relative to the previously calculated evaluation value or the sum and difference of the two evaluation values are decreased, accepting the selected parameter, and taking the current evaluation value as a comparison object of the subsequently calculated evaluation value. And if the evaluation value corresponding to the selected parameter is not better, eliminating the selected parameter until no parameter is selectable in the selectable parameter range. If the evaluation value is more optimal, a new parameter is continuously selected in the selectable parameter range, the corresponding evaluation value is obtained by the same method and compared with the evaluation value which is taken as the comparison object in the previous time, and the optimal evaluation value and the corresponding parameter are found in the selectable parameter range to obtain the final light rectifying element. The light rectifying element finally obtained is shown in fig. 6, and is seen to be a symmetrical structure, which is axially symmetrical in the far field at incidence of ± 30 degrees. The far field incident at 30 degrees is shown in fig. 8, so the light rectifying element has the light rectifying function of coupling the p-wave incident at about ± 30 degrees (the specific angle is determined by the grating equation) of two beams in the 550nm-670nm wave band to 0 degree for emission.
On the other hand, the embodiment of the invention also provides the optical rectification element based on the super-surface grating, which is obtained by the design method, wherein the optical rectification element is a three-layer structure consisting of a metal substrate layer, a dielectric layer and a metal grating layer; the three-layer structure meets the optimal structure parameters; the optimal structure parameters include minimum spacing, minimum size, transverse minimum resolution size, longitudinal minimum resolution size.
Preferably, the metal substrate layer is a silver layer; the dielectric layer is a silicon dioxide film layer; the material of the metal grating layer is gold.
The foregoing are merely exemplary embodiments of the present invention, which enable those skilled in the art to understand or practice the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.