Near-field enhanced needle tip reverse design method in radial polarization vector light beam tight focusing light field

Abstract

The invention discloses a near-field enhanced needle tip reverse design method in a radial polarization vector light beam tight focusing light field, and the method comprises the steps: optimizing the three-dimensional configuration of a circular symmetric conical needle tip through the rotation symmetry of a central shaft, and converting the three-dimensional configuration into the reverse design of a circular symmetric rotation two-dimensional boundary line shape; the reverse design of the circular symmetric rotation two-dimensional boundary line is converted into optimization of a limited number of Bernstein polynomial subitem coefficients by using the deformation quantity of the Bernstein polynomial table type two-dimensional boundary streamline relative to the original straight line; a machine learning optimization algorithm with robustness is introduced to realize reverse design; the target function is set as a local field intensity average enhancement factor of the arc rotation surface corresponding to the curvature radius of the tip of the needle tip; in order to suppress inversion of the rotation boundary in the optimization process, the maximum deformation quantity is used for constraining a circular symmetric rotation two-dimensional boundary streamline, and the nonlinear grid is used for smoothly constraining the deformation of a boundary line adjacent domain. According to the invention, high-efficiency and customizable optimization design of the streamline near-field enhanced needle tip in a specific vector light field is realized.

Description

Technical Field

[0001] The present invention relates to the field of surface plasma local field enhancement technology and intelligent optoelectronic design in optical weak signal detection, and more specifically, to a near-field enhancement needle tip reverse design method in a tightly focused light field of a radially polarized vector beam. Background Art

[0002] Due to its surface plasma properties, the noble metal nanotip has a high charge density at the tip, which can form a local field enhancement. It can not only be used to detect weak signals, but also break through the optical diffraction limit to achieve deep nanofocusing. Tip-enhanced Raman scattering can achieve enhanced Raman spectroscopy imaging of single-molecule structures, and the near-field enhanced tip is the core component of tip-enhanced Raman scattering scanning imaging. The radially polarized vector beam tightly focuses the light field. Since its axial component is conducive to the formation of a larger local field enhancement at the tip of the tip, it is often used as the excitation light field of the near-field enhanced tip. Under a specific vector light field, the tip configuration is very sensitive to the local field enhancement. Designing the tip configuration in a specific vector light field is a more effective means to improve the near-field enhancement performance of the tip. There is a highly nonlinear relationship between the interaction between light and micro-nano structures, the geometric parameters of micro-nano structures and the near-field enhancement performance indicators. The machine learning optimization algorithm can efficiently optimize the near-field enhancement performance target by iteratively finding the optimal solution for parameter configuration under constraints.

[0003] There are many configurations of near-field enhancement tips. Among them, the conical near-field enhancement tip has the simplest structure and is more common in the commercial market. However, even in the tightly focused light field of a radially polarized vector beam, the local field enhancement generated by the conical tip is limited, resulting in a weak detectable near-field signal, which reduces the success rate of the tip-enhanced scanning imaging system to test the sample signal. The pyramid-shaped near-field enhancement tip replaces the conical surface with an angular surface. Using template stripping manufacturing technology, high-quality, uniform, and ultra-sharp (tip curvature radius of 10nm) pyramid-shaped tips can be mass-produced. In the tightly focused light field of a radially polarized vector beam, the pyramid-shaped tip can achieve a scanning imaging resolution of 18nm. However, the ultra-sharp pyramid-shaped tip only considers improving the sharpness of the tip tip, and does not consider the optimization of the effective area outside the tip curvature radius. The grating-type near-field enhancement tip introduces a grating structure in the effective area above the tip tip to couple more light to the tip tip to enhance the near-field enhancement of the tip tip. However, the grating-type needle tip requires the processing of grooves of specific width and depth in the effective area above the tip of the needle tip, which greatly increases the difficulty of processing and reduces the feasibility of actual production.

[0004] Due to the limitation of the preparation process, it is difficult to prepare an ultra-sharp needle tip, and the design of improving the sharpness of the needle tip is limited. On the contrary, optimizing the shape of the effective area above the tip of the needle tip is a more feasible design solution. Moreover, the actual processing of the tip of the nano needle tip is mostly streamlined with smooth surfaces and flowing lines. Therefore, in order to achieve a streamlined near-field enhanced needle tip with high efficiency and customizable optimization design, the present invention proposes a reverse design method for the near-field enhanced needle tip in a tightly focused light field of a radially polarized vector beam. Summary of the invention

[0005] The purpose of the present invention is to realize the design of a streamlined near-field enhancement needle tip with high efficiency and customization, and propose a reverse design method of a near-field enhancement needle tip in a tightly focused light field of a radially polarized vector beam.

[0006] To solve the above problems, the technical solution of the present invention is as follows:

[0007] A reverse design method for a near-field enhancement needle tip in a tightly focused light field of a radially polarized vector beam is characterized in that, for a conical near-field enhancement needle tip located at the center of the tightly focused light field of a radially polarized vector beam, the rotational symmetry of the central axis of the tightly focused light field of the radially polarized vector beam and the conical near-field enhancement needle tip is utilized to optimize the three-dimensional shape of the circularly symmetric conical needle tip and convert it into a reverse design of a circularly symmetric rotational two-dimensional boundary line shape.

[0008] Based on the vector diffraction theory, the tightly focused light field of a radially polarized vector beam is expressed as follows:

[0009]

[0010]

[0011]

[0012]

[0013]

[0014]

[0015] In the above formula, J n is the first-order Bessel function of n, k0 is the wave vector, β0 is the pupil radius r p With the waist radius r b ratio, f is the focal length of the objective lens, NA is the numerical aperture of the objective lens, and n0 is the refractive index of the surrounding environment.

[0016] The finite element method (FEM) is used to calculate the electromagnetic field at the needle tip in the tightly focused light field of the radially polarized vector beam.

[0017] Specifically, taking the perfect matching layer (PML) as the boundary condition, the Helmholtz equation for the electric field vector E is calculated:

[0018]

[0019] In the above formula, ε r =(n r -ik r ) 2 , n r and k r are the real and imaginary parts of the complex refractive index of the material used, respectively.

[0020] The circularly symmetrical needle tip is mainly composed of precious metals such as gold and silver, and the near-field enhanced response wavelength of its surface plasma is mainly in the visible light band.

[0021] Furthermore, in the reverse design of the circularly symmetrically rotated two-dimensional boundary line shape, in the optimization setting, Bernstein polynomials are used to express the deformation of the two-dimensional boundary streamline relative to the original straight line, and the reverse design of the circularly symmetrically rotated two-dimensional boundary line is converted into optimizing a finite number of Bernstein polynomial sub-item coefficients.

[0022] Specifically, the n-th order Bernstein polynomial is as follows:

[0023]

[0024] In the above formula, b i are the Bernstein polynomial coefficients.

[0025] The initial line segment z0=l(r0) passing through the given two endpoints P1(r1,z1) and P2(r2,z2) can be expressed as follows after parameterization by t:

[0026]

[0027] The Bernstein polynomial is introduced to describe the relative displacement of the optimization boundary line:

[0028]

[0029] Through two points P1(r1,z1) and P2(r2,z2), the optimized boundary curve can be expressed as:

[0030]

[0031] Furthermore, the reverse design of the circularly symmetric rotated two-dimensional boundary line shape is achieved by introducing a robust machine learning optimization algorithm, and a gradient descent algorithm that can optimize highly nonlinear problems is selected.

[0032] Specifically, the form of the optimization problem of the optimization algorithm is as follows:

[0033]

[0034] in, and are the upper and lower bounds of the variable x. During the optimization process, a scalar objective function f is assumed: and constraint c: (M≤N) second-order continuous and differentiable.

[0035] Furthermore, the objective function of the reverse design of the circularly symmetric rotation of the two-dimensional boundary line shape is set as the average enhancement factor of the local field strength of the circular arc rotation surface corresponding to the radius of curvature of the needle tip.

[0036] Specifically, the formula for calculating the average enhancement factor (AEF) of the local field strength of the arc rotation surface corresponding to the radius of curvature of the needle tip is as follows:

[0037]

[0038] In the above formula, E b is the background electric field without the needle tip, and S is the arc rotation surface corresponding to the radius of curvature of the tip of the needle tip.

[0039] Furthermore, during the optimization process of the reverse design of the circularly symmetrically rotated two-dimensional boundary line shape, in order to suppress the reversal of the rotation boundary deformation, the two-dimensional boundary line is circularly symmetrically rotated with the maximum deformation amount as a constraint.

[0040] Specifically, the maximum deformation constraint is used to rotate the two-dimensional boundary line, and the maximum deformation constraint of the rotation boundary line is set to D max :

[0041]

[0042] Furthermore, nonlinear mesh smoothing constraints are applied to the deformation of the adjacent domains of the boundary line.

[0043] In order to verify the performance of the optimized near-field enhancement tip, the local field enhancement factor (EF) is calculated:

[0044]

[0045] In the above formula, E b is the background electric field without the needle tip.

[0046] In terms of design method, this scheme utilizes the tightly focused light field of the radially polarized vector beam and the central axis symmetry of the conical enhanced tip to optimize the three-dimensional configuration of the circularly symmetric conical tip and transform it into the reverse design of the circularly symmetric rotated two-dimensional boundary line shape, which greatly reduces the amount of electromagnetic field calculation of the three-dimensional configuration during the iterative optimization process and improves the optimization efficiency of the near-field enhanced tip.

[0047] Secondly, in terms of design method, this scheme uses Bernstein polynomials to express the deformation of two-dimensional boundary streamlines relative to the original straight line, and transforms the reverse design of circularly symmetrically rotated two-dimensional boundary lines into a finite number of coefficients for optimizing Bernstein polynomial sub-terms, thereby achieving the customizability of the streamlined near-field needle tip and reducing the number of parameters for iterative optimization, further improving the optimization efficiency.

[0048] Thirdly, in terms of design method, this scheme selects a gradient descent algorithm that can optimize highly nonlinear problems, takes the average enhancement factor of the local field strength of the arc rotation surface corresponding to the curvature radius of the tip as the objective function, and constrains the circular symmetric rotation of the two-dimensional boundary streamlines with the maximum deformation variable to suppress the inversion of the rotation boundary during the optimization process, and constrains the deformation of the adjacent domain of the boundary line with nonlinear grid smoothing. Finally, a highly efficient and customizable optimization design of a streamlined near-field enhancement tip in a specific vector light field is achieved.

[0049] Fourthly, the performance of the near-field enhanced needle tip designed and optimized in this scheme does not rely on improving the sharpness of the tip, but mainly focuses on optimizing the configuration of the effective area above the tip. The streamlined near-field enhanced needle tip has a smooth surface and flowing lines, making it more feasible for actual processing. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 Schematic diagram of the conical near-field enhancement needle tip located at the center of the tightly focused light field of the radially polarized vector beam.

[0051] Figure 2 A schematic diagram of the reverse design for implementing the conversion into a circularly symmetric rotated two-dimensional boundary line shape.

[0052] Figure 3 To implement the tightly focused light field of the radially polarized vector beam and its directional component distribution.

[0053] Figure 4 To implement the 9th order Bernstein polynomial sub-term curve of the 1st to 9th order Bernstein polynomial.

[0054] Figure 5 This is a curve showing the variation of the objective function ANE with the number of iterations during the reverse design process of the circularly symmetric rotation two-dimensional boundary line shape.

[0055] Figure 6To implement the reverse design process, the coefficients of the 1st to 9th order Bernstein polynomial sub-terms change with the number of iterations.

[0056] Figure 7 To implement the relative displacement of the boundary curves optimized for the 0th, 1st, 3rd, 5th, 7th, and 40th iterations and their corresponding optimized boundary curves.

[0057] Figure 8 To implement the local field enhancement of the streamlined near-field enhancement needle tip optimized for the 0th, 1st, 3rd, 5th, 7th, and 40th iterations.

[0058] Fig. 9 To implement the local field enhancement of the streamlined near-field enhancement needle tip of the 23rd iterative optimization with the optimized length H being 0.375λ0. DETAILED DESCRIPTION

[0059] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the drawings in the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0060] Combined with Figure 1 The present invention implements a method for reverse design of a near-field enhancement needle tip in a tightly focused light field of a radially polarized vector beam, which is to reversely optimize the tip configuration based on a conical near-field enhancement needle tip located at the center of the tightly focused light field of a radially polarized vector beam.

[0061] Furthermore, combined with Figure 2 , the radially polarized vector beam is used to tightly focus the light field and the conical near-field is used to enhance the rotational symmetry of the central axis of the needle tip, and the three-dimensional configuration of the conical needle tip is optimized and converted into a reverse design of the circularly symmetric rotation two-dimensional boundary line P1P2 shape.

[0062] Exemplarily, the conical needle tip is made of gold material, and its cone angle θ c The tip curvature radius is 30°. c The tip arc center is located at point O, the optimized length H from the center point O is 0.5λ0, and the excitation light wavelength λ0 is 633nm.

[0063] Based on the vector diffraction theory, the tightly focused light field of a radially polarized vector beam is expressed as follows:

[0064]

[0065]

[0066]

[0067]

[0068]

[0069]

[0070] In the above formula, J n is the first-order Bessel function of n, and k0 is the wave vector 2π / λ0. For example, the pupil radius r p With the waist radius r b The ratio β0 is 1, the focal length f of the objective lens is 4 mm, the numerical aperture NA of the objective lens is 0.75, and the refractive index n0 of the surrounding air environment is 1.

[0071] Specifically, attached Figure 3 The radial polarization vector beam is implemented to tightly focus the light field and its directional component distribution. Figure 3 , the polarization state of the visible light field is rotationally symmetric about the central axis, and the radial component |E| of the light field r | distributed outside the spot, axial component |E z |Focus on the central axis of the light spot.

[0072] Combined with Figure 2 The finite element method (FEM) is used to calculate the electromagnetic field at the tip of the needle in the tightly focused light field of the radially polarized vector beam implemented above through finite mesh generation.

[0073] Combined with Figure 2 Specifically, the Helmholtz equation for the electric field vector E is calculated using the perfect matching layer (PML) as the boundary condition:

[0074]

[0075] Specifically, in the above formula, ε r =(n r -ik r ) 2 . For example, in combination with the attached Figure 2 , n r and k r are the real and imaginary parts of the complex refractive index of the gold (Au) tip, respectively.

[0076] Combined with Figure 2In the reverse design of the circularly symmetrically rotated two-dimensional boundary line shape, in the optimization setting, the deformation of the two-dimensional boundary line relative to the original straight line P1P2 is expressed by a Bernstein polynomial. Exemplarily, the reverse design of the circularly symmetrically rotated two-dimensional boundary line is converted into the optimization of the coefficients of the 1st to 9th order Bernstein polynomial sub-items of the 9th order Bernstein polynomial.

[0077] Specifically, the 9th order Bernstein polynomial is as follows:

[0078]

[0079] In the above formula, n is 9, b i is a system of Bernstein polynomials of order 1 to 9.

[0080] Attached Figure 4 It is the 1st to 9th order normalized coefficient Bernstein polynomial sub-term of the 9th order Bernstein polynomial. Its lines are smooth and flowing, and the peaks are staggered to ensure the customization of the streamlined near-field needle tip.

[0081] Furthermore, the 1st to 9th order Bernstein polynomial system is optimized, which reduces the number of parameters for iterative optimization and improves the optimization efficiency.

[0082] Combined with Figure 2 Specifically, through the two end points P1(r1,z1) and P2(r2,z2) of the rotation boundary line, the initial line segment z0=l(r0) can be expressed as follows after parameterization by t:

[0083]

[0084] The Bernstein polynomial is introduced to describe the relative displacement of the optimization boundary line:

[0085]

[0086] Through two points P1(r1,z1) and P2(r2,z2), the optimized boundary curve can be expressed as:

[0087]

[0088] Furthermore, the reverse design of the circularly symmetric rotated two-dimensional boundary line shape is achieved by introducing a robust machine learning optimization algorithm, and a gradient descent algorithm that can optimize highly nonlinear problems is selected.

[0089] For example, an interior point optimization algorithm (IPOPT) is introduced, and the form of the optimization problem is as follows:

[0090]

[0091] in, and are the upper and lower bounds of the variable x. During the optimization process, a scalar objective function f is assumed: and constraint c: (M≤N) second-order continuous and differentiable.

[0092] Furthermore, the objective function of the reverse design of the circularly symmetric rotation of the two-dimensional boundary line shape is set as the average enhancement factor of the local field strength of the circular arc rotation surface corresponding to the radius of curvature of the needle tip.

[0093] Exemplarily, the radius of curvature r of the tip of the needle tip is calculated as follows: c The formula of the average enhancement factor (AEF) of the local field strength of the corresponding arc rotation surface is as follows:

[0094]

[0095] For example, in combination with Figure 3 , in the above formula, E b The above implementation of the radial polarization vector beam without the existence of a needle tip tightly focuses the light field. Figure 2 , S is the radius of curvature of the tip of the needle tip in the above implementation c It is the arc rotation surface corresponding to 25nm.

[0096] Furthermore, during the optimization process of the reverse design of the circularly symmetrically rotated two-dimensional boundary line shape, in order to suppress the reversal of the rotation boundary deformation, the two-dimensional boundary line is circularly symmetrically rotated with the maximum deformation amount as a constraint.

[0097] Specifically, the maximum deformation constraint is used to rotate the two-dimensional boundary line, and the maximum deformation constraint of the rotation boundary line is set to D max :

[0098]

[0099] For example, D max It is 25nm.

[0100] Furthermore, the deformation of the boundary line adjacent domain adopts nonlinear mesh smoothing constraints.

[0101] Preferably, a Yeoh nonlinear mesh smoothing constraint is employed to allow a maximum boundary displacement before mesh elements are inverted.

[0102] Attached Figure 5 To implement the above, the objective function ANE changes with the number of iterations in the reverse design process of the circularly symmetrically rotated two-dimensional boundary line shape. Figure 5, AEF increases with the number of iterations and finally converges to 68, indicating that the present invention achieves efficient reverse design of the near-field enhancement tip.

[0103] Attached Figure 6 To implement the above, the coefficients of the 1st to 9th order Bernstein polynomials change with the number of iterations during the reverse design process. Figure 6 , the coefficients of the 1st to 9th order Bernstein polynomial sub-terms change with the increase of the number of iterations and then converge, which shows the feasibility of transforming into optimizing the coefficients of a finite number of Bernstein polynomial sub-terms.

[0104] Figure 7 To implement the above, the relative displacement of the boundary curve optimized at the 0th, 1st, 3rd, 5th, 7th, and 40th iterations in the reverse design process and its corresponding optimized boundary curve. Figure 7 The relative displacement of the boundary curve optimized by the 0th, 1st, 3rd, 5th, 7th, and 40th iterations can be constructed by optimizing the coefficients of a finite number of Bernstein polynomial sub-terms, and then obtaining the corresponding optimized boundary curve.

[0105] In order to verify the performance of the optimized near-field enhancement tip, the local field enhancement factor (EF) is calculated:

[0106]

[0107] Specifically, in the above formula, in the above formula, E b is the background electric field without the needle tip. Figure 3 , E b To implement the radially polarized vector beam tightly focusing the light field.

[0108] Figure 8 To implement the above, the local field strength of the streamlined near-field enhancement needle tip optimized at the 0th, 1st, 3rd, 5th, 7th, and 40th iterations is enhanced. Figure 8 The local field strength enhancement of the streamlined near-field enhancement needle tip optimized for the 0th, 1st, 3rd, 5th, 7th, and 40th iterations increases with the number of iterations. The maximum field strength enhancement factor before optimization is 20.7, and the maximum field strength enhancement factor after 40 optimizations reaches 252, which is mainly concentrated at the end of the needle tip. This shows that the reverse design method of the present invention can improve the field strength enhancement performance of the streamlined near-field enhancement needle tip after configuration optimization by 12.2 times.

[0109] It should be noted that the above-mentioned embodiments are merely exemplary and do not constitute a limitation on the protection scope of the present application. The above-mentioned embodiments can be modified or replaced by equivalents. For example, when implementing the focusing light field, different focusing lens parameters and different excitation light wavelengths can be selected; when implementing the needle tip cone angle θ cIt can be selected in the range of 10 to 100°, and the tip curvature radius r c The range of 0 to 0.25λ0 can be selected, and the material can be replaced by gold, silver, and a combination of gold and silver. When implementing the optimization algorithm, MMA, SNOPT, and IPOPT can be selected. The optimization length H can be selected in the range of 0.20 to 1.0λ0. The maximum value constrains the boundary deformation, D max The range of 0 to 0.5λ0 can be selected; the deformation of the adjacent domain of the constraint boundary line can be selected by Winslow, hyperelasticity, and Yeoh nonlinear grid smoothing. The technical solution of the present invention can be implemented by partial or complete modification and selection according to actual needs.

[0110] For example, Fig. 9 In order to change the optimized length H described in the above embodiment to 0.375λ0, the local field enhancement of the streamlined near-field enhancement needle tip optimized in the 23rd iteration. Fig. 9 , indicating that by modifying the optimized length H, the maximum field strength enhancement factor of the optimized needle tip reaches 365, and its enhancement performance can be further improved.

[0111] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the purpose and scope of the technical solution of the present invention, which should be included in the scope of the claims of the present invention.

Claims

1. A method for reverse design of near-field enhanced needle tip in a tightly focused light field of a radially polarized vector beam, characterized in that: For the conical near-field enhancement tip located at the center of the tightly focused light field of a radially polarized vector beam, the three-dimensional configuration of the circularly symmetric conical tip is optimized by utilizing the rotational symmetry of the tightly focused light field of the radially polarized vector beam and the central axis of the conical near-field enhancement tip, and is converted into a reverse design of a circularly symmetric rotational two-dimensional boundary line shape.

2. According to claim 1, a method for reverse design of near-field enhanced needle tip in a tightly focused light field of a radially polarized vector beam, characterized in that: The circularly symmetrical needle tip is mainly composed of precious metals such as gold and silver, and the near-field enhanced response wavelength of its surface plasma is mainly in the visible light band.

3. According to claim 1, a method for reverse design of near-field enhanced needle tip in a tightly focused light field of a radially polarized vector beam, characterized in that: In the reverse design of the circularly symmetrically rotated two-dimensional boundary line shape, in the optimization setting, Bernstein polynomials are used to express the deformation of the two-dimensional boundary streamline relative to the original straight line, and the reverse design of the circularly symmetrically rotated two-dimensional boundary line is converted into optimizing a finite number of Bernstein polynomial sub-item coefficients.

4. According to claim 1, a method for reverse design of near-field enhanced needle tip in a tightly focused light field of a radially polarized vector beam, characterized in that: The reverse design of the circularly symmetric rotated two-dimensional boundary line shape is achieved by introducing a robust machine learning optimization algorithm, and a gradient descent algorithm that can optimize highly nonlinear problems is selected.

5. According to claim 1, a method for reverse design of near-field enhanced needle tip in a tightly focused light field of a radially polarized vector beam, characterized in that: The objective function of the reverse design of the circularly symmetrically rotated two-dimensional boundary line shape is set as the average enhancement factor of the local field strength of the circular arc rotation surface corresponding to the curvature radius of the needle tip.

6. According to claim 1, a method for reverse design of near-field enhanced needle tip in a tightly focused light field of a radially polarized vector beam, characterized in that: The reverse design of the circularly symmetrically rotated two-dimensional boundary line shape, in the optimization process, in order to suppress the inversion of the rotation boundary deformation, the circularly symmetrically rotated two-dimensional boundary streamline is constrained by the maximum deformation; the deformation of the adjacent domain of the boundary line is constrained by nonlinear mesh smoothing.

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