A method for reverse design of near-field enhanced needle tip in tight focusing of radially polarized vector beam

Abstract

The application discloses a kind of radial polarization vector light beam tight gathering light field in near-field enhancement needle tip reverse design method, utilize central axis rotation symmetry, the three-dimensional configuration of circularly symmetric conical needle tip is optimized, is converted into the reverse design of circularly symmetric rotation two-dimensional boundary line shape;With Bernstein polynomial expression two-dimensional boundary streamline relative to the deformation variable of original straight line, the reverse design of circularly symmetric rotation two-dimensional boundary line is converted into optimization finite Bernstein polynomial subterm coefficient;Robust machine learning optimization algorithm is introduced to realize reverse design;Objective function is set as needle tip tip curvature radius corresponding circular arc rotation surface local field intensity average enhancement factor;To suppress the deformation of rotating boundary to appear reverse in optimization process, with maximum deformation variable constraint circularly symmetric rotation two-dimensional boundary streamline, with nonlinear grid smoothing constraint the deformation of adjacent area of boundary line.The application realizes the efficient, customizable optimization design of streamline type near-field enhancement needle tip in specific vector light field.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of surface plasmon local field enhancement technology and intelligent optoelectronic design in optical weak signal detection, and more particularly to a near-field enhancement needle tip reverse design method in a radially polarized vector beam tight focusing light field. BACKGROUND

[0002] The noble metal nanometer needle tip can form local field enhancement due to its surface plasmon property, and the high oscillation charge density at the tip end can not only be used for detecting weak signals, but also can break through the optical diffraction limit to achieve deep nanometer focusing. The needle tip enhanced Raman scattering can realize the enhanced Raman spectrum imaging of single molecule structure, and the near-field enhancement needle tip is the core component of the needle tip enhanced Raman scattering scanning imaging. The radially polarized vector beam tight focusing light field is often used as the excitation light field of the near-field enhancement needle tip because the axial component of the radially polarized vector beam tight focusing light field is conducive to the formation of a larger local field enhancement at the tip end of the needle tip. The needle tip configuration is very sensitive to the local field enhancement under a specific vector light field. Designing the needle tip configuration in a specific vector light field is a more effective means to improve the near-field enhancement performance of the needle tip. There is a highly nonlinear relationship between the interaction of light and micro-nano structures and the geometric parameters of the micro-nano structure and the near-field enhancement performance index. The machine learning optimization algorithm can iteratively find the optimal solution of the parameter configuration under the constraint condition, and can efficiently optimize the near-field enhancement performance target.

[0003] There are many configurations of the near-field enhancement needle tip. Among them, the conical near-field enhancement needle tip has the simplest structure and is commonly seen in the commercial market. However, even in the radially polarized vector beam tight focusing light field, the local field enhancement generated by the conical needle tip is limited, resulting in weak near-field signals that can be detected, and reducing the success rate of the needle tip enhanced scanning imaging system in testing sample signals. The pyramid-shaped near-field enhancement needle tip replaces the conical surface with an angular surface. The template stripping manufacturing technology can be used to mass-produce high-quality, uniform, and super-sharp (tip end curvature radius of 10 nm) pyramid-shaped needle tips. In the radially polarized vector beam tight focusing light field, the pyramid-shaped needle tip can achieve a scanning imaging resolution of 18 nm. However, the super-sharp pyramid-shaped needle tip only considers improving the sharpness of the tip end, and does not consider the optimization of the effective area other than the tip end curvature radius. The grating-shaped near-field enhancement needle tip introduces a grating structure above the tip end of the needle tip to couple more light to the tip end of the needle tip to improve the near-field enhancement of the tip end of the needle tip. However, the grating-shaped needle tip requires machining grooves with a specific width and depth above the effective area of the tip end of the needle tip, which greatly increases the processing difficulty and reduces the feasibility of actual production.

[0004] Due to the limitation of the preparation process, the super-sharp needle tip is difficult to prepare, and the design of improving the sharpness of the needle tip is limited. On the contrary, the design scheme of optimizing the shape of the effective area above the needle tip is more feasible. Moreover, the actual processing of the nanometer needle tip is mostly streamlined with smooth surface and smooth lines. Therefore, in order to realize the efficient and customizable optimization design of the streamlined near-field enhancement needle tip, the present application provides a reverse design method of near-field enhancement needle tip in a tightly focused light field of radial polarization vector beam. SUMMARY

[0005] The present application aims to efficiently and customizably realize the design of the streamlined near-field enhancement needle tip, and provides a reverse design method of near-field enhancement needle tip in a tightly focused light field of radial polarization vector beam.

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

[0007] A reverse design method of near-field enhancement needle tip in a tightly focused light field of radial polarization vector beam, characterized in that for a conical near-field enhancement needle tip located at the center of the tightly focused light field of radial polarization vector beam, the three-dimensional shape of the circularly symmetric conical needle tip is optimized and converted into the reverse design of the two-dimensional boundary line shape of circularly symmetric rotation by utilizing the rotational symmetry of the tightly focused light field of radial polarization vector beam and the central axis of the conical near-field enhancement needle tip.

[0008] Wherein, based on the vector diffraction theory, the tightly focused light field of radial polarization vector beam is represented as follows:

[0009]

[0010]

[0011]

[0012]

[0013]

[0014]

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

[0016] The electromagnetic field at the needle tip in the above tightly focused light field of radial polarization vector beam is calculated by using the finite element method (FEM).

[0017] Specifically, the Helmholtz equation about the electric field vector E is calculated with the Perfect matching layer (PML) as the boundary condition:

[0018]

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

[0020] The circularly symmetric needle tip is mainly composed of noble metals such as gold and silver, and the surface plasmon near-field enhancement response wavelength is mainly in the visible light band.

[0021] Further, the inverse design of the circularly symmetric rotating two-dimensional boundary line shape is converted into the optimization of a limited number of Bernstein polynomial sub-term coefficients by using the deformation amount of the two-dimensional boundary streamline relative to the original straight line in the Bernstein polynomial expression.

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

[0023]

[0024] In the above formula, b i is the Bernstein polynomial coefficient.

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

[0026]

[0027] The relative displacement of the optimized boundary line is described by introducing the Bernstein polynomial:

[0028]

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

[0030]

[0031] Further, the inverse design of the circularly symmetric rotating two-dimensional boundary line shape is realized by introducing a robust machine learning optimization algorithm, and the gradient descent algorithm which can optimize highly nonlinear problems is selected.

[0032] Specifically, the optimization algorithm optimizes the problem in the form as follows:

[0033]

[0034] wherein, and are the upper and lower bounds of the variable x, the optimization process assumes that the scalar objective function and the constraint is second-order continuously derivable.

[0035] Further, the reverse design of the circularly symmetric rotating two-dimensional boundary line shape sets the target function as the average enhancement factor of the local field strength of the circular arc rotating surface corresponding to the tip curvature radius.

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

[0037]

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

[0039] Further, in the reverse design of the circularly symmetric rotating two-dimensional boundary line shape, in the optimization process, to suppress the occurrence of reverse rotation of the rotating boundary deformation, the circularly symmetric rotating two-dimensional boundary line is constrained by the maximum deformation variable.

[0040] Specifically, the maximum deformation variable of the rotating two-dimensional boundary line is set as D max :

[0041]

[0042] Further, a nonlinear grid smoothing constraint is adopted for the deformation of the adjacent region of the boundary line.

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

[0044]

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

[0046] The present scheme uses the tight focusing field of the radial polarization vector beam and the central axis symmetry of the conical enhanced needle to optimize the three-dimensional configuration of the circularly symmetric conical needle and convert it into the reverse design of the circularly symmetric rotating two-dimensional boundary line shape, greatly reducing the electromagnetic field calculation amount of the three-dimensional configuration in the iterative optimization process and improving the optimization efficiency of the near-field enhanced needle.

[0047] In the second aspect, the present scheme uses the deformation amount of the two-dimensional boundary streamline relative to the original straight line in the form of Bernstein polynomial to convert the reverse design of the circularly symmetric rotating two-dimensional boundary line into the optimization of the coefficients of the Bernstein polynomial subitems, realizes the customization of the streamline near-field needle, and further improves the optimization efficiency by reducing the parameter amount of the iterative optimization.

[0048] In the third aspect, the present scheme uses the gradient descent algorithm which can optimize highly nonlinear problems as the design method, uses the average enhancement factor of the local field intensity of the circular arc rotating surface corresponding to the curvature radius of the needle tip as the objective function, uses the maximum deformation constraint to constrain the circularly symmetric rotating two-dimensional boundary streamline, and uses the nonlinear grid smoothing to constrain the deformation of the adjacent area of the boundary line. Finally, the efficient and customizable optimization design of the streamline near-field enhanced needle in a specific vector light field is realized.

[0049] In the fourth aspect, the present scheme designs and optimizes the near-field enhanced needle, and the performance of the needle does not depend on the improvement of the sharpness of the needle tip. Instead, the configuration of the effective area above the needle tip is optimized, and the streamline near-field enhanced needle has a smooth surface and smooth lines, so it has better feasibility in actual processing. BRIEF DESCRIPTION OF DRAWINGS

[0050] Figure 1 It is a schematic diagram of the conical near-field enhanced needle located at the center of the tight focusing field of the radial polarization vector beam.

[0051] Figure 2 It is a schematic diagram of the reverse design of the circularly symmetric rotating two-dimensional boundary line shape.

[0052] Figure 3 It is the tight focusing field of the radial polarization vector beam and the distribution of its directional components.

[0053] Figure 4 It is the 1st-9th order Bernstein polynomial subitem curve of the 9th order Bernstein polynomial.

[0054] Figure 5 It is a curve showing the change of the objective function ANE with the number of iterations in the reverse design process of the circularly symmetric rotating two-dimensional boundary line shape.

[0055] Figure 6The variation of the 1st-9th order Bernstein polynomial sub-item coefficient with the iteration number in the implementation of the reverse design process.

[0056] Figure 7 The relative displacement amount of the boundary curve of the 0th, 1st, 3rd, 5th, 7th, and 40th iteration optimization and the corresponding optimized boundary curve.

[0057] Figure 8 The local field enhancement of the streamlined near-field enhancement needle tip of the 0th, 1st, 3rd, 5th, 7th, and 40th iteration optimization.

[0058] Figure 9 The local field enhancement of the streamlined near-field enhancement needle tip of the 23rd iteration optimization with an optimized length H of 0.375λ0. DETAILED DESCRIPTION

[0059] To make the objects, technical solutions, and advantages of the present application clearer, the technical solutions in the present application will be described below in conjunction with the drawings in the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative labor fall within the protection scope of the present application.

[0060] In conjunction with the drawings, Figure 1 The present application implements the reverse design method of the near-field enhancement needle tip in the radial polarization vector beam tight focusing light field. The method is based on the conical near-field enhancement needle tip located at the center of the radial polarization vector beam tight focusing light field, and performs reverse optimization on the needle tip configuration.

[0061] Further, in conjunction with the drawings, Figure 2 The three-dimensional configuration of the conical needle tip is optimized and converted into the reverse design of the circularly symmetric two-dimensional boundary line P1P2 shape by utilizing the rotational symmetry of the radial polarization vector beam tight focusing light field and the central axis of the conical near-field enhancement needle tip.

[0062] Exemplarily, the conical needle tip is composed of gold material, the conical angle θ c is 30°, the tip curvature radius r c is 25 nm, the tip circular arc center is located at point O, the optimized length H from the center O is 0.5λ0, and the excitation light wavelength λ0 is 633 nm.

[0063] Based on the vector diffraction theory, the radial polarization vector beam tight focusing light field is represented as follows:

[0064]

[0065]

[0066]

[0067]

[0068]

[0069]

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

[0071] Specifically, the attached Figure 3 is implemented to tightly focus the radial polarization vector light beam and the distribution of its directional components. In combination with the attached Figure 3 , it can be seen that the polarization state of the visible light field is rotationally symmetric about the central axis, and the radial component |E r of the light field |E| is distributed outside the light spot, and the axial component |E z is concentrated on the central axis of the light spot.

[0072] In combination with the attached Figure 2 , the electromagnetic field at the needle tip in the above-mentioned implementation of the radial polarization vector light beam tightly focused light field is calculated by finite element method (FEM) through finite grid subdivision.

[0073] In combination with the attached Figure 2 , specifically, the Helmholtz equation about the electric field vector E is calculated with a perfect matching layer (PML) as the boundary condition:

[0074]

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

[0076] In combination with the attached Figure 2, the inverse design of the circularly symmetric rotating two-dimensional boundary line shape, in the optimization setting, the deformation variable of the two-dimensional boundary line with respect to the original straight line P1P2 is expressed by the Bernstein polynomial. Exemplarily, the inverse design of the circularly symmetric rotating two-dimensional boundary line is converted into the optimization of the 1st to 9th order Bernstein polynomial subterm coefficient of the 1st to 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 the 1st to 9th order Bernstein polynomial coefficient.

[0080] The Figure 4 is the 1st to 9th order normalized coefficient of the 9th order Bernstein polynomial Bernstein polynomial subterm, which has smooth and smooth lines, and staggered peak positions to ensure the customizability of the streamline near-field needle tip.

[0081] Further, the optimization of the 1st to 9th order Bernstein polynomial coefficient reduces the amount of parameters in the iterative optimization, and improves the optimization efficiency.

[0082] In combination with the Figure 2 Specifically, the initial line segment z0=l(r0) can be expressed as:

[0083]

[0084] The relative displacement of the optimized boundary line is described by introducing the Bernstein polynomial:

[0085]

[0086] The optimized boundary curve can be expressed as:

[0087]

[0088] Further, the inverse design of the circularly symmetric rotating two-dimensional boundary line shape is realized by introducing a robust machine learning optimization algorithm, and the gradient descent algorithm which can optimize highly nonlinear problems is selected.

[0089] Exemplarily, the Interior Point OPTimizer (IPOPT) is introduced, and the optimization problem is as follows:

[0090]

[0091] wherein, and are the upper and lower bounds of the variable x, the optimization process assumes that the scalar objective function and the constraints are twice continuously differentiable.

[0092] Further, the inverse design of the circularly symmetric rotating two-dimensional boundary line shape, the objective function is set to the average enhancement factor of the local field intensity of the circular arc rotating surface corresponding to the tip end curvature radius.

[0093] Exemplarily, the tip end curvature radius r c of the above-mentioned implementation is 25 nm, and the formula of the average enhancement factor (AEF) of the local field intensity of the circular arc rotating surface is as follows:

[0094]

[0095] Exemplarily, in combination with the attached Figure 3 , in the above formula, E b is the tight focusing light field of the radial polarization vector light beam without the tip. Figure 2 , S is the circular arc rotating surface corresponding to the tip end curvature radius r c of the above-mentioned implementation is 25 nm.

[0096] Further, in the inverse design of the circularly symmetric rotating two-dimensional boundary line shape, in order to suppress the reverse rotation of the deformed rotating boundary, the maximum deformation variable is used as a constraint for the circularly symmetric rotating two-dimensional boundary line.

[0097] Specifically, the maximum deformation variable is used as a constraint for the rotating two-dimensional boundary line, and the maximum deformation variable of the rotating boundary line is set to D max :

[0098]

[0099] Exemplarily, D max is 25 nm.

[0100] Further, the deformation of the adjacent area of the boundary line adopts a nonlinear grid smoothing constraint.

[0101] Preferably, the Yeoh nonlinear grid smoothing constraint is adopted to allow the maximum boundary displacement before the grid element is reversed.

[0102] The attached Figure 5 is the curve of the change of the objective function ANE with the number of iterations in the implementation of the inverse design process of the circularly symmetric rotating two-dimensional boundary line shape. In combination with the attached Figure 5, and finally converges to 68, which indicates that the near-field enhanced needle tip is efficiently designed by the reverse design method.

[0103] Figure 2 shows the change of the Bernstein polynomial coefficients of the first 9 orders in the reverse design process. Figure 6 Figure 3 shows the change of the Bernstein polynomial coefficients of the first 9 orders in the reverse design process. Figure 6 Figure 4 shows the change of the Bernstein polynomial coefficients of the first 9 orders in the reverse design process.

[0104] Figure 7 Figure 5 shows the relative displacement of the boundary curves of the 0th, 1st, 3rd, 5th, 7th and 40th iterations in the reverse design process. Figure 7 Figure 6 shows the relative displacement of the boundary curves of the 0th, 1st, 3rd, 5th, 7th and 40th iterations in the reverse design process.

[0105] To verify the performance of the optimized near-field enhanced needle tip, the local field intensity enhancement factor (EF) is calculated:

[0106]

[0107] Specifically, in the above formula, E b is the background electric field without the needle tip. Figure 7 shows the background electric field without the needle tip. Figure 3 is the background electric field without the needle tip. Figure 7 shows the background electric field without the needle tip. b To implement the tight focusing of the radially polarized vector beam, the light field is focused.

[0108] Figure 8 Figure 8 shows the local field intensity enhancement of the streamline near-field enhanced needle tip of the 0th, 1st, 3rd, 5th, 7th and 40th iterations in the reverse design process. Figure 8 Figure 9 shows the local field intensity enhancement of the streamline near-field enhanced needle tip of the 0th, 1st, 3rd, 5th, 7th and 40th iterations in the reverse design process.

[0109] It should be noted that the above-described embodiments are merely exemplary and do not constitute a limitation on the scope of protection of the present application. The above-described embodiments can be modified or replaced by equivalents, for example, to implement the focusing light field, different focusing objective parameters and different excitation light wavelengths can be selected; to implement the needle tip cone angle θ cThe curvature radius r of the tip can be selected in the range of 10-100° c The material can be selected from gold, silver, and combinations of gold and silver. The optimization algorithm can be selected from MMA, SNOPT, and IPOPT. The optimized length H can be selected in the range of 0.20-1.0λ0. The maximum constraint boundary deformation D can be selected in the range of 0-0.25λ0. max The material can be selected from gold, silver, and combinations of gold and silver. The optimization algorithm can be selected from MMA, SNOPT, and IPOPT. The optimized length H can be selected in the range of 0.20-1.0λ0. The maximum constraint boundary deformation D can be selected in the range of 0-0.25λ0.

[0110] Exemplarily, Figure 9 To change the optimized length H to 0.375λ0, the local field enhancement of the streamlined near-field enhanced tip in the 23th iteration is shown in FIG. 23. The local field enhancement of the streamlined near-field enhanced tip in the 23th iteration is shown in FIG. 24. Figure 9 It is shown that the maximum field enhancement factor of the tip is optimized to 365 by changing the optimized length H, and the performance of the tip can be further improved.

[0111] Finally, it should be noted that the above examples are only used to illustrate the technical solutions of the present application, and are not intended to limit the same. Although the present application has been described in detail with reference to the foregoing examples, those skilled in the art should understand that the technical solutions of the present application can be modified or replaced by equivalents without departing from the spirit and scope of the present application, and all such modifications or replacements should be included in the scope of the claims of the present application.

Claims

1. A method for near-field enhancement tip reversal design in a tightly focused optical field of a radially polarized vector beam, characterized in that, For a conical near-field enhancement tip located at the center of a tightly focused radially polarized vector beam, the three-dimensional configuration optimization of the circularly symmetric conical tip is transformed into a reverse design of the circularly symmetric rotating two-dimensional boundary line shape by utilizing the rotational symmetry between the tightly focused radially polarized vector beam and the central axis of the conical near-field enhancement tip. Specifically, based on vector diffraction theory, a tightly focused radially polarized vector beam is represented; using the finite element method, the electromagnetic field at the tip in the tightly focused radially polarized vector beam is calculated through finite mesh partitioning; the Helmholtz equation for the electric field vector E is calculated using a perfectly matched layer as the boundary condition; and the deformation of the two-dimensional boundary streamline relative to the original straight line is expressed using Bernstein polynomials, transforming the reverse design of the circularly symmetric rotating two-dimensional boundary line into optimizing a finite number of Bernstein polynomial sub-term coefficients.

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

3. The near-field enhancement tip reversal design method for a radially polarized vector beam in a tightly focused optical field according to claim 1, characterized in that, The reverse design of the circularly symmetric rotating two-dimensional boundary line shape is achieved by introducing a robust machine learning optimization algorithm, selecting a gradient descent algorithm that can optimize highly nonlinear problems.

4. The near-field enhancement tip reversal design method for a radially polarized vector beam in a tightly focused optical field according to claim 1, characterized in that, The reverse design of the circularly symmetric rotating two-dimensional boundary line shape has an objective function set as the local field strength average enhancement factor of the circular arc rotating surface corresponding to the radius of curvature of the needle tip.

5. The near-field enhancement tip reversal design method for a radially polarized vector beam in a tightly focused optical field according to claim 1, characterized in that, In the reverse design of the circularly symmetric rotating two-dimensional boundary line shape, during the optimization process, in order to suppress the reversal of the deformation of the rotating boundary, the circularly symmetric rotating 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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