CN111240011A - Method for designing super-oscillation annular belt pieces of metal film with different annular widths - Google Patents
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Abstract
A design method of a metal film super-oscillation ring band piece with unequal ring widths comprises the steps of establishing an optimization target according to the distribution characteristics of a required diffraction light field under the condition of laser vertical illumination with a fixed wavelength, setting parameters of the metal film super-oscillation ring band piece by utilizing the optimization target and micro-nano processing conditions, calculating each polarization electric field component and light field intensity distribution after the super-oscillation ring band piece by utilizing a vector angle spectrum theory and a fast Hankel conversion algorithm, establishing a fitness function model by combining a diffraction light field optimization target, calculating the fitness of each ring band piece, optimizing and adjusting each ring width of the ring band piece by adopting a particle position searching method and combining variation operation in a genetic algorithm, and finally solving the metal film super-oscillation ring band piece which is closest to or meets the requirement of the optimization target through iterative operation. The invention is based on the ring belt structure with different ring widths, and adopts an optimization method of particle position search, thereby being capable of optimizing the metal film super-oscillation ring belt piece with less ring belts and better performance.
Description
Technical Field
The invention belongs to the technical field of micro-nano optics and nano photonics, and particularly relates to a design method of a super-oscillation annular band sheet of a metal film with different annular widths.
Background
The smallest detail that any conventional optical system or optical instrument can resolve an object, as affected by the diffraction limit, is d0λ/(2NA), where λ is the illumination wavelength and NA is the numerical aperture of the optical system. The super-oscillation (super-oscillation) phenomenon means that a band-limited function exists, the oscillation frequency in a local area is far larger than the maximum frequency component contained in the local area, and light spots with the size smaller than the diffraction limit can be formed in a local space by utilizing Optical super-oscillation (Optical super-oscillation) to realize super-resolution focusing which breaks through the diffraction limit. In recent years, a method for realizing super-resolution focusing by using a super-oscillation ring band sheet has attracted extensive attention in the field of micro-nano optics, and has become an important research subject in the field.
The design of the conventional metal film super-oscillation ring belt sheet is mostly based on the assumption of equal ring width, namely the width of each light blocking ring and each light transmitting ring must be integral multiple of the minimum set ring width. As in 2012, the university of south ampton, uk focused coherent light beams with simple binary amplitude type multi-zone metal film microstructure diffraction elements, with the loop width satisfying an integer multiple setting of the minimum loop width (see document e.t.f.rogers, j.lindberg, t.roy, et al.a super-aperture lens optical microscope for subwavelength imaging. nature Materials). In 2013, Harbin industry university has designed a series of binary amplitude super-oscillation ring zone sheets based on the assumption of equal ring width, and super-resolution focusing is realized (see the literature LiuT, Tan J, Liu J, et al. vector design of super-optics lens. OpticsExpress,2013,21(13): 15090). In 2019, a centimeter-scale metal film super-oscillation annular band sheet is optimally designed by northwest industrial university, but still based on the precondition of equal annular width (see documents Li W, Yu Y, Yuan W. Flexiblefocusing paper optimization of center-meter-scale plate super-oscillators in nano-scale, 2019,11(1): 311-) 320).
The existing metal film super-oscillation ring band optimization algorithm is mainly divided into two types, namely a binary-based particle swarm algorithm and a binary-based genetic algorithm. In 2013, the Singapore national university designs a super-oscillation ring zone plate based on a binary particle swarm algorithm, and realizes longitudinal light field focusing based on radial polarized light (see the documents Ye H, Qiu C W, Huang K, et al. creation of a longitudinal polarized subwavelength H hot spot with an ultra-thin planar lens: vector Rayleigh-Sommerfeld method. laser Physics letters,2013,10(6): 065004). In 2015, the university of Western-Ann transportation designed multiple binary amplitude type super-oscillating lenses based on binary genetic algorithm (see Liu T, Shen T, Yang S, et al. subwavelengthfocusing by binary multi-annular plates: design lens and experience. journal of Optics,2015,17(3): 035610). In addition, research institutions such as national institute of photoelectric technology, Chongqing university, northwest industrial university, Nanjing university and the like also carry out deep research on the optimization algorithm of the super-oscillation ring band plate based on binary particle swarm or genetic algorithm and make certain progress.
For example, chinese patent CN201610599066.6 discloses a far-field super-diffraction three-dimensional hollow focal spot planar focusing device, CN201810220342.2 discloses a far-field super-diffraction three-dimensional hollow focal spot planar focusing device, both of which adopt equal ring width design, that is, each ring width is an integral multiple of the minimum set ring width.
The metal film super-oscillation ring band piece with the same ring width has the advantages of easy coding, simple structure and flexible modulation. The disadvantages are that: firstly, under the premise of equal ring width, the ring width of each ring belt piece must be integral multiple of the minimum ring width, and the final optimization degree of the ring belt pieces is limited to a certain extent. Meanwhile, in order to obtain a focusing light spot with a smaller size, the equal-ring-width metal film super-oscillation ring belt sheet often comprises a plurality of ring belt structures, and certain challenges are brought to micro-nano processing.
Chinese patent CN201910005119.0 discloses a design method of a metal film super-oscillation ring belt piece, which adopts non-equal ring width design, but selects a traditional genetic algorithm on an optimization algorithm.
Therefore, the existing superoscillation ring band optimization algorithm, namely a binary-based particle swarm algorithm and a binary-based genetic algorithm, has the advantages that the optimization target is concentrated into the equal-ring-width metal film superoscillation ring band or the equal-ring-width medium superoscillation ring band, the optimization target is the code of the transmittance of each ring band, and certain limitation exists.
Disclosure of Invention
In order to overcome the defects of the traditional metal film super-oscillation ring belt piece in model structure and optimization algorithm, the invention aims to provide a design method of a metal film super-oscillation ring belt piece with unequal ring widths, which improves the optimization degree of the ring belt structure through setting of unequal ring widths, improves the optimization efficiency and the degree of freedom through a particle position search algorithm, and can efficiently optimize the super-oscillation ring belt piece with fewer ring belts and better performance.
In order to achieve the purpose, the invention adopts the technical scheme that:
a design method of a super-oscillation annular band piece of a metal film with different annular widths comprises the following steps:
step one, under the condition of fixed wavelength laser vertical illumination, setting the distribution characteristics of a required metal film super-oscillation ring band plate focusing light field, and establishing an optimization target according to the distribution characteristics of the required diffraction light field.
Specifically, for single focus optimization, the metal film superoscillatory ring plate optimization objectives include: focusing spot focal length, transverse full width at half maximum, axial focal depth, focal plane transverse dark field side lobe intensity value and axial light field distribution side lobe intensity value; for the optical needle optimization, the optimization target of the metal film super-oscillation ring band sheet comprises the following steps: focusing the focal length of the optical needle, the transverse full width at half maximum, the axial focal depth or the optical needle length, the focal plane transverse dark field side lobe intensity value and the axial optical field distribution side lobe intensity value.
Step two, setting the structural parameters of the metal film super-oscillation ring band sheet according to the optimization target and the existing micro-nano processing conditions: diameter D, center shielding radius RbFocusing focal length f, number N of ring belts and minimum ring width delta R, and setting working parameters of the metal film super-oscillation ring belt sheet: illumination laser wavelength lambda, laser polarization state and working medium refractive index nw。
The specific setting requirements may be: the diameter D of the ring belt is more than or equal to 10 lambda; focal length f>Lambda; the number N of the ring belts is more than or equal to 2; the minimum ring width delta R is more than or equal to 100 nm; center shielding radius RbR is less than or equal to 0.8R, and R is the radius of the ring belt sheet; the wavelength lambda of the illumination laser is more than or equal to 10 nm; the laser polarization state is linear polarization, circular polarization or radial polarization; the working medium is selected from air, oil or water.
And step three, according to the set parameters in the step two, randomly initializing a plurality of metal film super-oscillation ring belt pieces with different ring widths, wherein the centers of the metal film super-oscillation ring belt pieces are shielded, regarding each ring belt piece as an independent individual, and enabling all the individuals to form an initial population.
The specific method can be as follows: firstly, determining the central shielding radius R of the annular belt piecebAt the center shielding radius RbTo the zone segment radius R (R)bR) randomly generating N-1 division points XiThe ultra-oscillation ring band piece is composed of N ring bands determined by a central circle and dividing points, the transmittance is coded through binary numbers, 0 represents that the ring band is not transparent, 1 represents that the ring band is transparent, the transmittance of the central circle is set to be 0, the transmittance of the ring band is 0 from inside to outside, 1 alternates until the outermost ring band, and the region outside the structure of the ring band piece is provided with a metal film for shielding, and the transmittance is 0.
And step four, calculating the components of each polarized electric field and the intensity distribution of the optical field behind each ring band in the population by using a vector angle spectrum theory and a fast Hankel transformation algorithm based on the metal film super-oscillation ring band structure in the initial population in the step three.
The specific calculation process can be as follows: according to the incident light intensity distribution and the transmittance distribution of the metal film super-oscillation annular band plate, the angular spectrum distribution of the diffraction light field is obtained after the annular band plate is obtained through one-time Hankel transformation, and the polarization electric field components and the light field intensity distribution are obtained after the annular band plate is obtained through one-time Hankel transformation.
And step five, establishing a fitness function model by combining the diffraction light field optimization target in the step one according to the intensity distribution of the diffraction light field of each metal film super-oscillation ring band sheet in the step four, and calculating the fitness of each ring band sheet.
The specific calculation method is as follows: according to the calculation results in the fourth step, the deviation F of the actual value and the target value of the focal length, the transverse full width at half maximum and the axial focal depth is respectively calculated1、F2、F3And the maximum value F of the transverse dark field side lobe and the axial dark field side lobe of the focal plane3、F4By setting a weighting coefficient w1、w2、w3、w4、w5Combining five optimization targets into a total fitness calculation function
F is the fitness of the super-oscillation ring band piece, wherein w1～5∈[0,1]And is and
and step six, according to the fitness of each metal film super-oscillation ring band piece, optimizing and adjusting the width of each ring of the ring band piece by adopting a particle position searching method and combining variation operation in a genetic algorithm, and finally solving the metal film super-oscillation ring band piece which is closest to or meets the requirement of an optimization target through iterative operation.
The specific process of optimization is as follows:
701) randomly generating an inclusion PsCalculating the fitness value F of each individual in the population according to the fitness function model established in the fifth stepi，i＝1,2,…,PsRecording the individual with the best fitness in the initial population as a historical optimal individual;
702) according to the speciesArranging the fitness value of each individual in the group, regarding the segmentation point of the individual as a particle capable of freely moving, and setting the moving distance delta X of all the particles in the individual relative to the initial positioniI 1,2, …, N-1, the maximum distance Δ X of movementmaxIs set to be delta R/C1The minimum moving distance DeltaX corresponds to the individual with the worst fitness in the populationminIs set to be delta R/C2Corresponding to the individuals with the best fitness in the population, C1，C2Determined according to the actual parameters of the annular band piece and meets the requirement C2≥C1The moving distance of the particles of other individuals is in an interval (delta R/C) according to the fitness value of the individual (delta R/C)2,ΔR/C1) The inner parts are uniformly distributed;
703) according to the mutation probability PmRandomly generating a random number r for each individual, if r is less than or equal to PmThen, the individual is subjected to variation operation to move the individual particles by the interval (Δ R/C)2,ΔR/C1) A random number in (2);
704) for each individual in the population, the individual particle movement distance Δ X is determined according to steps 702) and 703)iLet all particles in the individual be at + - Δ XiThe new particle sequence is sequenced after the movement is finished, the distance between adjacent particles is controlled to be larger than the minimum ring width delta R, so that a new population is generated, the fitness of all individuals in the new population is calculated, the original population is replaced by the new population, meanwhile, the historical optimal individual is updated, then, the step 702 is returned), a new iteration is performed, and the steps are repeated until the set iteration number N is reachedg；
705) Number of iterations completed NgAnd then obtaining an individual with the optimal fitness in the whole optimization process, namely the metal film super-oscillation ring band piece with the focusing effect closest to the design effect, and finishing the optimization.
The invention is based on a metal film concentric ring structure with unequal width, a circular metal film shield is arranged at the center of the structure and in the region outside the structure, and the purpose of setting the center shield is to filter out incident light with lower spatial frequency, so that smaller focusing light spots are obtained at a focal plane. The method comprises the steps of generating required transmittance distribution for a specific annular band by setting a metal film or not, calculating three-dimensional space diffraction optical field distribution of laser at any distance after the laser passes through a super-oscillation annular band by using vector angle spectroscopy theory and a fast Hankel conversion algorithm under the condition of vertical illumination of a laser beam with given wavelength, adjusting and optimizing the annular band width of the annular band by using a particle position search algorithm according to individual fitness, and simultaneously jumping out a local optimal solution by fusing a variation idea in the algorithm to obtain the metal film super-oscillation annular band meeting a design target.
Compared with the traditional equal-ring-width ring belt piece design method, the invention adopts the unequal-ring-width ring belt piece design method to improve the final optimization degree of the ring belt piece, and can optimize the metal film super-oscillation ring belt piece meeting the design requirement under the condition of less ring belt structures.
Compared with the existing superoscillation zone plate optimization algorithm, the method adopts the particle position search algorithm when optimizing the zone plate structure, and finally optimizes the zone plate with the light-transmitting zone plates with different widths. The superoscillation ring band sheet optimization algorithm used in the invention is a particle position search algorithm fused with the genetic algorithm variation idea, realizes the adjustment of the ring band width by searching the ring band dividing point position, and has the capability of efficiently optimizing the metal film superoscillation ring band sheet with excellent focusing performance.
Therefore, the method overcomes the defects of the traditional metal film super-oscillation ring belt piece in model structure and optimization algorithm, and can efficiently optimize the metal film super-oscillation ring belt piece with fewer rings and better performance. The designed metal film super-oscillation annular sheet can be used in the fields of far-field high-resolution microscopic imaging, nano lithography, femtosecond laser processing, particle manipulation and the like.
Drawings
FIG. 1 is a schematic diagram of the operation of the metal film super-oscillating ring band sheet of the present invention.
FIG. 2 is a flow chart of an algorithm used for optimizing the super-oscillation zone plate structure of the metal film in the invention.
FIG. 3 is a schematic diagram of a two-dimensional structure of a metal film super-oscillating ring strip sheet according to the present invention.
FIG. 4 is a graph showing the transmittance of the super-oscillating band in the radial direction according to the embodiment of the present invention.
Fig. 5 is a comparison graph of theoretical calculation results of light intensity distribution of the super-oscillation ring band piece along the optical axis direction and FDTD electromagnetic simulation results in the embodiment of the present invention.
FIG. 6 is a diagram illustrating the theoretical calculation result of the intensity distribution of the optical field in the Y-Z plane of the super-oscillating ring strip according to the embodiment of the present invention.
FIG. 7 is a diagram of FDTD electromagnetic simulation results of the optical field intensity distribution of the super-oscillating ring strip in the Y-Z plane in the embodiment of the present invention.
Detailed Description
The following detailed description of the embodiments of the present invention is made with reference to the accompanying drawings and a single focus optimization example.
As shown in figure 1, laser vertical illumination with the wavelength of 632.7nm (one actually measured laser wavelength) is selected, single-focus focusing is realized at a certain distance from the position behind the girdle, the intensity distribution of a diffraction light field is calculated by utilizing a vector angle spectrum theory, and the structure of the girdle is optimized by adopting a particle position search algorithm, so that the metal film super-oscillation girdle sheet meeting the design requirement is finally obtained.
(1) Calculation of intensity of diffraction light field in vector angle spectrum theory
When the illumination beam is linearly polarized light which vibrates along the X direction and is vertical to the incident light of the zone plate, the metal film super-oscillates any point behind the zone plate
The diffraction optical field distribution is calculated as follows:
in the formula, Ex(r,z)，Ey(r,z)，
Respectively representing spatial points
In the x, y, z directionThe electric field strength. A. the0(l) An angular spectrum representing the electric field at the rear surface of the diffraction screen, expressed as:
in the formula (I), the compound is shown in the specification,
l denotes the spatial radial angular frequency. J. the design is a square0And J1Respectively representing the zeroth and first order bessel functions of the first kind. t (r) represents a transmittance function of the metal film super-oscillation loop sheet, and t (r) is 0, and t (r) is 1, and t (r) represents light transmission at the position. g (r) represents an amplitude distribution function of incident light, and if the incident light beam is a uniform plane wave, g (r) is 1.
Total light intensity at point
When the illuminating light beam is left-handed circularly polarized light which is vertical to the annular band plate, the ultra-oscillation is carried out at any point behind the annular band plate
The diffraction optical field distribution is calculated as follows:
at this time, the process of the present invention,
total light intensity at point
(2) Multi-optimization target fitness function model
For a single-focus focusing model, the optimized targets comprise a focal length, a transverse full width at half maximum, a transverse maximum side lobe and an axial maximum side lobe of a focal plane, and the finally established multi-target fitness function mathematical model is as follows:
wherein f represents an actual value of the focal length of the focus, and f' represents a design value of the focal length of the focus; (0, z)1)，(z2,zend) The interval represents a dark field area of the light spot along the optical axis direction; fzActual value, F ', representing axial depth of focus'zA design value representing an axial depth of focus; (r)1,r2) The interval represents a dark field area of the light spot along the radial direction in the focal plane; FWHMxyIs the actual value of the transverse full width at half maximum of the diffracted light field, FWHM'xyIs the design value of the transverse full width at half maximum of the diffracted light field.
On the basis of the multi-target fitness function mathematical model, a fitness calculation formula is as follows:
in the formula, wiThe weighted values of the optimization targets can be distributed according to the actual optimization requirements to meet the requirements
And w1～5∈[0,1]。
(3) Solving an optimization problem using a particle location search algorithm
The superoscillation ring band optimization algorithm adopted by the invention is different from the traditional binary particle swarm algorithm and the binary genetic algorithm, is a particle position search algorithm which integrates the variation idea of the genetic algorithm, and has the following basic idea as shown in figure 2: the method comprises the steps of firstly providing the designed ring number of a ring belt piece, coding the transmittance of the ring belt through binary numbers, randomly generating a series of division points to initialize a plurality of ring belt structures with different ring widths, wherein the division points can be regarded as randomly moving particles, then calculating the fitness of each ring belt structure by using an established fitness function calculation model, determining the random moving distance of the particles through the fitness, realizing the global search of the particle position, increasing the uncertainty of the particle movement through variation, and avoiding the optimization from falling into the local optimum. Compared with the traditional optimization algorithm, the method has stronger searching capability and more definite optimization direction, simultaneously overcomes the defect of numerous rings of the traditional super-oscillation ring belt, and can efficiently optimize the super-oscillation ring belt with fewer rings and better performance by utilizing the algorithm.
(4) Design results and examples
In this example, linear polarized light with a wavelength of 632.7nm and a vibration direction along the X direction in fig. 1 is selected as the incident light, and the working medium is selected to be air. The structural parameters and focusing performance of the metal film super-oscillation ring band piece obtained by optimization solution are shown in table 1, and the ring structure and transmittance of the super-oscillation ring band piece are shown in table 2. The two-dimensional structure of the super-oscillation ring belt piece is shown in fig. 3, and the transmittance of the super-oscillation ring belt piece in the radial direction is shown in fig. 4.
TABLE 1 structural parameters and focusing properties of the superoscillatory ring band pieces
TABLE 2 ultra-oscillating band structure and transmittance
| |
1 | 2 | 3 | 4 | 5 | 6 | 7 |
| |
1 | 0 | 1 | 0 | 1 | 0 | 1 |
| Δri(μm) | 0.893 | 0.455 | 1.863 | 1.752 | 0.377 | 1.727 | 1.887 |
| |
8 | 9 | 10 | 11 | 12 | 13 | 14 |
| |
0 | 1 | 0 | 1 | 0 | 1 | 0 |
| Δri(μm) | 1.467 | 0.604 | 0.228 | 0.342 | 0.970 | 1.059 | 1.376 |
Table 1 shows that the diameter D of the ring band piece is 60 μm, the number of rings is 14, and DbRepresents the diameter of the central shielding circle, and is designed to be 30 μm, and the minimum ring width Δ R is designed to be 0.2 μm. In Table 2, NiRepresents the ith annulus of the annulus segment, tiRepresents the transmittance, Δ r, of the ith zoneiRepresenting the loop width of the i-th loop. The results show that: the designed annulus patch has an actual minimum annulus width of 0.228 μm, which is greater than the designed minimum annulus width by 0.2 μm. Full width at half maximum FWHM of focal plane focusing light spot along Y directionyAt 0.401 λ, much less than the diffraction limit of 0.5 λ, super-resolution focusing is achieved. Due to the longitudinal electric field EzFull width at half maximum FWHM of focal plane focused spot in the X-directionx0.97 λ, but experiments have shown that in high numerical aperture microscopy imaging systems, due to the effect of the imaging system polarization filtering, the longitudinal electric field intensity is severely attenuated in far field regions such as the focal plane, with the electric field intensity dominated by the transverse electric field intensity component (see literature Yuan G, Rogers E T F, Roy T, et alzOn the premise of the design, the designed annular band piece also realizes super-resolution focusing along the direction of the focal plane X. Meanwhile, the number of the rings of the super-oscillation ring band piece designed in the example is only 14, and micro-nano processing is easy.
In the present embodiment, a Finite Difference Time Domain (FDTD) method is used to perform simulation analysis on the zone focusing, and the parameters of the simulation model are as follows: the substrate is made of quartz glass and has the thickness of 5 mu m; the metal film is made of aluminum and has the thickness of 100 nm; vibrating in X direction with full field scattering field (TFSF) light source and wavelength of 632.7 nm; the working medium is selected to be air, and the refractive index is 1; the FDTD three-dimensional simulation area is x, y: [ -30,30], z: [ -2,20] (units are μm); the grid size of the divisions was 20nm × 20nm × 20 nm.
Fig. 5 shows a comparison result between a theoretical calculation result of the intensity distribution of the super-oscillation ring band piece in the optical axis direction and an FDTD electromagnetic simulation result in this example, and fig. 6 and 7 are schematic diagrams of the theoretical calculation result of the intensity distribution of the optical field of the super-oscillation ring band piece in the Y-Z plane and the FDTD electromagnetic simulation result in this example, respectively. The theoretical calculation result of the super-oscillation ring band piece is well consistent with the simulation result, and the feasibility of the method is fully explained.
While the invention has been described in connection with specific embodiments thereof, it will be understood that these should not be construed as limiting the scope of the invention, which is defined in the following claims, and any variations which fall within the scope of the claims are intended to be embraced thereby.
Claims (7)
1. A design method of a super-oscillation annular band piece of a metal film with different annular widths is characterized by comprising the following steps:
firstly, under the condition of fixed wavelength laser vertical illumination, setting the distribution characteristics of a required metal film super-oscillation ring band plate focusing light field, and establishing an optimization target according to the distribution characteristics of a required diffraction light field;
step two, setting the structural parameters of the metal film super-oscillation ring band sheet according to the optimization target and the existing micro-nano processing conditions: diameter D, center shielding radius RbFocusing focal length f, number N of ring belts and minimum ring width delta R, and setting working parameters of the metal film super-oscillation ring belt sheet: illumination laser wavelength lambda, laser polarization state and working medium refractive index nw；
Step three, according to the set parameters in the step two, randomly initializing a plurality of metal film super-oscillation ring belt pieces with different ring widths, wherein the centers of the metal film super-oscillation ring belt pieces are shielded, regarding each ring belt piece as an independent individual, and enabling all the individuals to form an initial population;
step four, based on the metal film super-oscillation ring zone plate structure in the initial population in the step three, calculating each polarization electric field component and light field intensity distribution behind each ring zone plate in the population by using a vector angle spectrum theory and a fast Hankel transformation algorithm;
step five, establishing a fitness function model by combining the diffraction light field optimization target in the step one according to the intensity distribution of the diffraction light field of each metal film super-oscillation ring band sheet in the step four, and calculating the fitness of each ring band sheet;
and step six, according to the fitness of each metal film super-oscillation ring band piece, optimizing and adjusting the width of each ring of the ring band piece by adopting a particle position searching method and combining variation operation in a genetic algorithm, and finally solving the metal film super-oscillation ring band piece which is closest to or meets the requirement of an optimization target through iterative operation.
2. The method for designing a metal film super-oscillating ring patch with unequal ring widths according to claim 1, wherein in the step one, for single-focus optimization, the metal film super-oscillating ring patch optimization target comprises: focusing spot focal length, transverse full width at half maximum, axial focal depth, focal plane transverse dark field side lobe intensity value and axial light field distribution side lobe intensity value; for the optical needle optimization, the optimization target of the metal film super-oscillation ring band sheet comprises the following steps: focusing the focal length of the optical needle, the transverse full width at half maximum, the axial focal depth or the optical needle length, the focal plane transverse dark field side lobe intensity value and the axial optical field distribution side lobe intensity value.
3. The method for designing the ultra-oscillating annular band of the metal film with different annular widths according to claim 1, wherein in the second step, the specific setting requirements of the parameters of the ultra-oscillating annular band of the metal film are as follows: the diameter D of the ring belt is more than or equal to 10 lambda; focal length f>Lambda; the number N of the ring belts is more than or equal to 2; the minimum ring width delta R is more than or equal to 100 nm; center shielding radius RbR is less than or equal to 0.8R, and R is the radius of the ring belt sheet; the wavelength lambda of the illumination laser is more than or equal to 10 nm; the laser polarization state is linear polarization, circular polarization or radial polarization(ii) a The working medium is selected from air, oil or water.
4. The method for designing the ultra-oscillating ring strip of the unequal-ring-width metal film according to claim 1, wherein in the third step, the method for randomly initializing the ultra-oscillating ring strip of the unequal-ring-width metal film comprises the following steps: firstly, determining the central shielding radius R of the annular belt piecebAt the center shielding radius RbTo the zone segment radius R (R)bR) randomly generating N-1 division points XiThe ultra-oscillation ring band piece is composed of N ring bands determined by a central circle and dividing points, the transmittance is coded through binary numbers, 0 represents that the ring band is not transparent, 1 represents that the ring band is transparent, the transmittance of the central circle is set to be 0, the transmittance of the ring band is 0 from inside to outside, 1 alternates until the outermost ring band, and the region outside the structure of the ring band piece is provided with a metal film for shielding, and the transmittance is 0.
5. The method for designing the metal film super-oscillating annular band with unequal annular widths according to claim 1, wherein in the fourth step, the calculation process of each polarized electric field component and the optical field intensity distribution after the metal film super-oscillating annular band is as follows: according to the incident light intensity distribution and the transmittance distribution of the metal film super-oscillation annular band plate, the angular spectrum distribution of the diffraction light field is obtained after the annular band plate is obtained through one-time Hankel transformation, and the polarization electric field components and the light field intensity distribution are obtained after the annular band plate is obtained through one-time Hankel transformation.
6. The method for designing the ultra-oscillating annular band sheet of the metal film with the unequal ring width according to claim 1, wherein in the fifth step, the calculation method of the fitness is as follows: according to the calculation results in the fourth step, the deviation F of the actual value and the target value of the focal length, the transverse full width at half maximum and the axial focal depth is respectively calculated1、F2、F3And the maximum value F of the transverse dark field side lobe and the axial dark field side lobe of the focal plane4、F5By setting a weighting coefficient w1、w2、w3、w4、w5Combining five optimization targets into a total fitness calculation function
F is the fitness of the super-oscillation ring band piece, wherein w1～5∈[0,1]And is and
7. the method for designing the ultra-oscillating annular band of the metal film with different annular widths according to claim 1, wherein in the sixth step, the specific process of optimization is as follows:
701) randomly generating an inclusion PsCalculating the fitness value F of each individual in the population according to the fitness function model established in the fifth stepi，i＝1,2,…,PsRecording the individual with the best fitness in the initial population as a historical optimal individual;
702) arranging the individuals according to the fitness value of each individual in the population, regarding the segmentation point of the individual as a particle capable of freely moving, and setting the moving distance delta X of all the particles in the individual relative to the initial position of the particleiI 1,2, …, N-1, the maximum distance Δ X of movementmaxIs set to be delta R/C1The minimum moving distance DeltaX corresponds to the individual with the worst fitness in the populationminIs set to be delta R/C2Corresponding to the individuals with the best fitness in the population, C1，C2Determined according to the actual parameters of the annular band piece and meets the requirement C2≥C1The moving distance of the particles of other individuals is in an interval (delta R/C) according to the fitness value of the individual (delta R/C)2,ΔR/C1) The inner parts are uniformly distributed;
703) according to the mutation probability PmRandomly generating a random number r for each individual, if r is less than or equal to PmThen, the individual is subjected to variation operation to move the individual particles by the interval (Δ R/C)2,ΔR/C1) A random number in (2);
704) for each individual in the population, the individual particle movement distance Δ X is determined according to steps 702) and 703)iLet all particles in the individual be at + - Δ XiThe new particle sequence is sequenced after the movement is finished, the distance between adjacent particles is controlled to be larger than the minimum ring width delta R, so that a new population is generated, the fitness of all individuals in the new population is calculated, the original population is replaced by the new population, meanwhile, the historical optimal individual is updated, then, the step 702 is returned), a new iteration is performed, and the steps are repeated until the set iteration number N is reachedg；
705) Number of iterations completed NgAnd then obtaining an individual with the optimal fitness in the whole optimization process, namely the metal film super-oscillation ring band piece with the focusing effect closest to the design effect, and finishing the optimization.
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