Method for realizing direction-adjustable one-way lateral scattering based on generalized cylindrical vector beam

Abstract

The application relates to a direction-adjustable unidirectional lateral scattering implementation method based on a generalized cylindrical vector beam, belonging to the technical fields of nanophotonics, structural light regulation and optical detection. A radial polarization light passes through a first half-wave plate and a second half-wave plate to generate a generalized cylindrical vector beam, and then passes through a microscopic objective to generate a tight focusing light field. Two nanospheres are arranged on the focal plane along the x-axis at intervals, and the two nanospheres constitute a nanoantenna structure and are located at the center position of the focal point. The radii, relative positions and gaps between the two nanospheres are set, and a suitable working wavelength is matched, so that the nanoantenna structure generates unidirectional lateral far-field scattering dominated by electric dipole response and magnetic dipole response under the excitation of the tight focusing generalized cylindrical vector beam. The polarization angle of the generalized cylindrical vector beam is changed, so that the direction of the unidirectional lateral far-field scattering changes with the polarization angle, and the method has wideband applicability in the 810nm-850nm waveband.

Description

Technical Field

[0001] This invention belongs to the fields of nanophotonics, structured light manipulation and optical detection technology, and relates to a method for achieving directional adjustable unidirectional transverse scattering based on a generalized cylindrical vector beam. Background Technology

[0002] Nanoantennas, capable of modulating local electromagnetic fields and far-field radiation directions on subwavelength scales, are crucial structural units for nanophotonic devices, optical sensing, and far-field scattering signal manipulation. High-refractive-index dielectric nanostructures exhibit low absorption loss in the visible and near-infrared bands and can simultaneously support both electrical and magnetic responses, providing the means to adjust the scattering direction through multipole interference. In typical dielectric nanoparticles, when the amplitudes and phases of the electric and magnetic dipole moments satisfy a specific relationship, their radiation fields can undergo constructive interference in one direction and destructive interference in the opposite direction, thereby enhancing scattering in a specific direction and suppressing backscattering, forming directional scattering. When the direction of the multipole interference enhancement of the radiation field lies in a transverse plane perpendicular to the direction of incident light propagation, directional transverse scattering can be achieved. Furthermore, metallic nanostructures exhibit strong local plasmon responses, while dielectric nanostructures possess electromagnetic resonance responses with low absorption losses. Combining these two to form a heterogeneous double nanosphere structure can simultaneously introduce metallic plasmon resonances and dielectric Mie resonances, thereby altering the contribution ratio of the electric dipole and magnetic dipole responses. Directional scattering schemes based on this mechanism can be applied to scenarios such as optical path coupling, angle readout, displacement detection, and structured optical field response analysis.

[0003] For unidirectional transverse scattering, tightly focused light fields exhibit richer electromagnetic field components compared to plane wave excitation. Tightly focused radially polarized light and angularly polarized light can excite electric dipole, magnetic dipole, or higher-order multipole responses in nanostructures in different directions, and form a scattering main lobe perpendicular to the incident light propagation direction through the coherent superposition of these responses. Compared to ordinary linearly polarized light, cylindrical vector beams have spatially varying polarization distributions within their cross-sections; by introducing a variable polarization angle into radially polarized light, a generalized cylindrical vector beam can be formed, causing the transverse and longitudinal electromagnetic field components of the tightly focused light field to change with the polarization angle. Therefore, the spatial polarization distribution of the structured light field can serve as an important degree of freedom for adjusting the far-field scattering direction of nanostructures.

[0004] In existing methods, the relative contribution of the multipolar response in the nanostructure can be altered by constructing incident light fields with different polarization distributions or by adjusting the amplitude, phase, and polarization state of the incident light field, thereby achieving active control of the directional scattering direction. However, some methods still require adjusting the position of the nanostructure relative to the focal point, redesigning the structural geometry, or matching the amplitude and phase between multiple optical paths to achieve directional control. This makes it difficult to flexibly control unidirectional transverse scattering when the nanostructure is fixed. For heterogeneous double nanosphere structures, the small size and narrow gaps in their geometry mean that positional deviations caused by mechanical movement can disrupt the correspondence between the scattering direction and structural parameters. Quantitative characterization of directional scattering relies on stable far-field acquisition and orientation angle extraction, which are prerequisites for optical control, encoding, and detection applications. Summary of the Invention

[0005] This invention addresses the problems of existing technologies by providing a method for achieving unidirectional transverse scattering based on a generalized cylindrical vector beam with adjustable direction. It utilizes a generalized cylindrical vector beam with variable polarization angle to tightly focus and excite a gold-silicon heterostructure double nanosphere with a fixed structure, thereby achieving unidirectional transverse far-field scattering with adjustable direction without depending on the relative position of the nanostructure and the focal point. Furthermore, it establishes a characterizable scattering response relationship based on the far-field scattering direction angle, enabling the function of directly reading the polarization state of the beam from the far field.

[0006] A method for achieving directionally adjustable unidirectional transverse scattering based on a generalized cylindrical vector beam includes the following steps:

[0007] Step 1) A radially polarized beam of light passes through the first half-wave plate and the second half-wave plate to generate a generalized cylindrical vector beam. After passing through the microscope objective, it generates a tightly focused light field. Two nanospheres are placed at intervals along the x-axis on the focal plane to form a nanoantenna structure, and the nanoantenna structure is located at the center of the focal point.

[0008] Step 2) Set the radius, relative position, and gap between the two nanospheres, and match a suitable operating wavelength so that the nanoantenna structure generates unidirectional transverse far-field scattering dominated by electric dipole response and magnetic dipole response under the excitation of a tightly focused generalized column vector beam.

[0009] Step 3) Under the condition that the structural parameters of the nanoantenna design remain unchanged, change the polarization angle of the generalized cylindrical vector beam to change the relative contribution of the electric dipole response and magnetic dipole response excited inside the nanoantenna structure, thereby changing the unidirectional transverse far-field scattering direction with the polarization angle.

[0010] Step 4) Calculate and collect the lateral far-field scattering intensity distribution under different polarization angles, and determine the lateral far-field scattering direction angle based on the distribution.

[0011] Step 5) After aligning the geometric center of the nanoantenna structure with the optical field center of the tightly focused generalized cylindrical vector beam, the nanoantenna structure will be excited to produce directionally adjustable unidirectional transverse scattering.

[0012] The advantages of this invention are:

[0013] 1) The active adjustment of the unidirectional transverse far-field scattering direction can be achieved simply by changing the polarization angle of the generalized cylindrical vector beam, without the need to adjust the geometric parameters or spatial position of the nano-antenna structure, thus avoiding errors introduced by mechanical displacement.

[0014] 2) Lateral scattering principal axis angle θ and polarization angle The relationship between them satisfies θ≈2 The linear relationship between the scattering direction and the polarization angle can be controlled proportionally, providing a direct readout calibration relationship for optical angle sensing.

[0015] 3) ED in electric dipole and magnetic dipole responses x ED y ED z and MD x MD y MD z The relative contributions of each component vary with the polarization angle, revealing the multipolar response mechanism of the polarization angle in regulating the far-field scattering direction;

[0016] 4) In the near-infrared band from 810nm to 850nm, the modulation effect in this direction is effective and it has broadband working capability. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0018] Figure 1 This is a schematic diagram of the optical path mechanism of the present invention. Figure 1 The components include: radially polarized light 1, first half-wave plate 2, second half-wave plate 3, generalized cylindrical vector beam 4, microscope objective 5, and gold-silicon heterostructure double nanospheres 6.

[0019] Figure 2(a) shows the results of this invention at different polarization angles at a wavelength of 834 nm. The two-dimensional far-field scattering distribution diagram below (normalized far-field scattering intensity distribution in the xy plane).

[0020] Figure 2(b) shows the results of this invention at different polarization angles at a wavelength of 834 nm. The two-dimensional far-field scattering distribution diagram below (normalized far-field scattering intensity distribution in the xz plane).

[0021] Figure 2(c) shows the results of this invention at different polarization angles at a wavelength of 834 nm. The three-dimensional far-field radiation map (three-dimensional far-field scattering distribution) is shown below.

[0022] Figure 3 The transverse scattering principal axis angle θ and the polarization angle of the generalized cylindrical vector beam at a wavelength of 834 nm are given in this embodiment of the invention. Linear fitting plot between them.

[0023] Figure 4(a) shows the polarization angle of the present invention. ( Multipole moment expansion at 0°.

[0024] Figure 4(b) shows the polarization angle of the present invention. ( Multipole moment expansion at 45°.

[0025] Figure 4(c) shows the polarization angle of the present invention. ( Multipole moment expansion at 90°.

[0026] Figure 5(a) shows the polarization angle of the present invention. ( Normalized scattering power plots of electric and magnetic dipole moment components at 0°.

[0027] Figure 5(b) shows the polarization angle of the present invention. ( Normalized scattering power plots of electric and magnetic dipole moment components at 45°.

[0028] Figure 5(c) shows the invention at different polarization angles. ( Normalized scattering power plots of electric and magnetic dipole moment components at 90°.

[0029] Figure 6(a) shows the invention at different operating wavelengths and different polarization angles. Far-field scattering distribution in the xy plane at λ=810nm.

[0030] Figure 6(b) shows the results of this invention at different operating wavelengths and polarization angles. Far-field scattering distribution in the xy plane at λ=834nm.

[0031] Figure 6(c) shows the invention at different operating wavelengths and different polarization angles. Far-field scattering distribution in the xy plane at λ=850nm. Detailed Implementation

[0032] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0033] A method for achieving directionally adjustable unidirectional transverse scattering based on a generalized cylindrical vector beam includes the following steps:

[0034] 1) Excitation of gold-silicon heterostructured nanospheres using a tightly focused generalized columnar vector beam, such as... Figure 1 As shown, a radially polarized light beam 1 propagating along the z-axis passes sequentially through the first half-wave plate 2 and the second half-wave plate 3 to form a generalized cylindrical vector beam 4. The relative angle of the fast axes of the two half-wave plates is adjusted... And utilize the polarization angle and Satisfying linear relationship This allows for continuous adjustment of the polarization state of the generalized cylindrical vector beam. Subsequently, the generalized cylindrical vector beam is focused by microscope objective 5 to generate a tightly focused light field. The numerical aperture NA of the objective is 0.9. Gold-silicon heterostructure double nanospheres are placed along the x-axis on the focal plane, with the gold nanospheres placed on the positive x-axis and the silicon nanospheres placed on the negative x-axis. The gap between them is set to d, and the nanostructure is integrated as a whole, with its geometric center aligned with the center of the tightly focused light field.

[0035] 2) Adjust the radii of the two nanospheres in the above antenna structure, the spacing between them, and the relative position of the nanostructure and the tightly focused light field, and match a suitable wavelength so that the nanoantenna structure generates unidirectional transverse far-field scattering dominated by electric dipole response and magnetic dipole response under the excitation of the tightly focused generalized cylindrical vector beam.

[0036] The first step is to calculate the polarization angle using the Richard-Wolf vector diffraction integral. Electromagnetic field distribution of a generalized cylindrical vector beam after tight focusing for different values. The spatial polarization distribution of the generalized cylindrical vector beam is determined by the polarization angle. The decision is made; after the beam is tightly focused by the microscope objective, the longitudinal electric field component, the transverse electric field component, and the transverse magnetic field component in the focal region all change with... The value of varies. The above calculation results of the tightly focused field distribution under different polarization angles provide the incident light field conditions for the subsequent structural parameter design and electromagnetic response calculation of gold-silicon heterostructure double nanospheres.

[0037] The second step involves setting the radius of the gold sphere in the nanoantenna structure to 80 nm and the radius of the silicon sphere to 120 nm, with the spacing d between them set to 10 nm. Under these structural parameters, a tightly focused generalized cylindrical vector beam is used as the excitation field, and the near-field electromagnetic field and far-field scattering intensity distribution of the gold-silicon heterostructure nanospheres are calculated using the finite element method. Subsequently, while keeping the radii of the gold sphere, the silicon sphere, the spacing d, and the relative focal position of the nanostructure constant, the polarization angle of the generalized cylindrical vector beam is changed. The transverse far-field scattering distribution corresponding to different polarization angles was obtained.

[0038] The third step, after obtaining the far-field scattering distribution under different polarization angles, involves performing a polar coordinate transformation on the far-field scattering intensity in the xy plane, and extracting the direction of the scattering main lobe center and the direction of the scattering principal axis to obtain the corresponding transverse scattering principal axis angle θ. Further, the different polarization angles... The corresponding θ is organized into angle data and then linearly fitted. Through the above processing, different polarization angles can be analyzed. The corresponding scattering direction angle is extracted from the two-dimensional far-field scattering map below, and the scattering direction change presented in image form is converted into comparable angle data to verify the regulation relationship of unidirectional lateral scattering direction with polarization angle.

[0039] The fourth step involves performing a multipole moment expansion on the near-field electromagnetic field distribution. The contributions of the electric dipole moment ED, magnetic dipole moment MD, electric quadrupole moment EQ, and magnetic quadrupole moment MQ to far-field scattering are calculated, yielding the relationship between the total scattered power (Total) and wavelength. Based on this, the dominant electric and magnetic dipole moment components are further decomposed to obtain the ED component. x ED y ED z and MD x MD y MD z Each has its own normalized scattering power. The above decomposition process can accurately determine which multipole response the main scattering contribution originates from and reveal the polarization angle. The modulation law of each multipole moment component on the transverse far-field scattering direction when the time is changed.

[0040] The fifth step involves selecting 834 nm as the optimal working wavelength to analyze the gold-silicon heterostructure nanospheres at different polarization angles. The variation of the lower transverse far-field scattering direction was investigated. Subsequently, the broadband characteristics of this structure were examined: the operating wavelength was extended to the 810nm to 850nm range, and the variation of each wavelength within this range was analyzed. The far-field scattering distribution in the xy plane under conditions of 0°, 45° and 90° were solved respectively to verify that the structure has broadband adaptability in the unidirectional transverse scattering direction modulation effect in the near-infrared band.

[0041] 3) At the operating wavelength of 834nm, the polarization angle When the angles are 0°, 30°, 45°, 60°, and 90°, the direction of the far-field scattering main lobe in the xy-plane varies with... The change is shown in Figure 2(a); the change of the far-field scattering distribution in the xz plane with the polarization angle is shown in Figure 2(b). Figure 2(c) further illustrates the change with the corresponding polarization angle. The three-dimensional far-field radiation is obtained. The above results show that the method does not require adjustment of the structural parameters of the nanoantenna itself or its spatial position relative to the tightly focused light field, but can achieve controllable adjustment of the unidirectional transverse far-field scattering direction simply by changing the spatial polarization structure of the incident generalized cylindrical vector beam.

[0042] 4) Different polarization angles at the 834nm working wavelength After rearranging the corresponding transverse scattering principal axis angle θ, we can obtain θ and The linear fitting relationship. Figure 3 The reference curve θ=2 is also given in the text. .Depend on Figure 3 It can be seen that the extracted angular data fits the reference relationship well, indicating that the transverse scattering principal axis angle θ can be used as a characterizing the polarization angle of the generalized cylindrical vector beam. The corresponding far-field scattering direction angle.

[0043] 5) Figures 4(a), 4(b), 4(c), 5(a), 5(b), and 5(c) present the multipole moment expansion results, used to explain the main contribution sources of the transverse far-field scattering direction modulation. Figures 4(a), 4(b), and 4(c) respectively show... The curves of ED, MD, EQ, MQ, and Total as a function of wavelength were obtained at 0°, 45°, and 90°. Within the investigated wavelength range, the electric dipole response and magnetic dipole response constitute the main contributions to scattering, while the contribution of the higher-order quadrupole moment response is relatively small. Figures 5(a), 5(b), and 5(c) further present the details of the variation of each component of ED and MD at different polarization angles. Below, ED x ED y ED z and MD x MD y MD z The relative contributions of each component change with wavelength, and this component-level change is consistent with the change in the direction of the main lobe of the transverse far-field scattering revealed in Figure 2.

[0044] 6) Figures 6(a), 6(b), and 6(c) show the polarization angles at three working wavelengths of 810 nm, 834 nm, and 850 nm, respectively. The transverse far-field scattering distribution in the xy-plane at 0°, 45°, and 90° was analyzed. The results show that the directionally adjustable unidirectional transverse far-field scattering effect achieved by this method is not limited to a single wavelength point; it can be achieved within the range of 810 nm to 850 nm by adjusting the polarization angle of the generalized cylindrical vector beam. By changing the lateral scattering direction, the broadband response capability of the structure was verified.

[0045] The above description is merely an embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for achieving unidirectional transverse scattering based on a generalized cylindrical vector beam, characterized in that, Includes the following steps: Step 1) A radially polarized beam of light passes through the first and second half-wave plates to generate a generalized cylindrical vector beam. After passing through a microscope objective, it generates a tightly focused light field. Two nanospheres are placed at intervals along the x-axis on the focal plane to form a nanoantenna structure, which is positioned at the center of the focal point. Step 2) Set the radii, relative positions, and gap between the two nanospheres, and match a suitable operating wavelength so that the nanoantenna structure generates unidirectional transverse far-field scattering dominated by electric dipole and magnetic dipole responses under the excitation of a tightly focused generalized cylindrical vector beam. Step 3) Under the condition that the structural parameters of the nanoantenna design remain unchanged, change the polarization angle of the generalized cylindrical vector beam to change the relative contributions of the electric dipole response and magnetic dipole response excited inside the nanoantenna structure, thereby changing the unidirectional transverse far-field scattering direction with the polarization angle. Step 4) Calculate and collect the lateral far-field scattering intensity distribution under different polarization angles, and determine the lateral far-field scattering direction angle based on this distribution. Step 5) After aligning the geometric center of the nanoantenna structure with the optical field center of the tightly focused generalized cylindrical vector beam, the nanoantenna structure will be excited to produce directionally adjustable unidirectional transverse scattering.

2. The method for achieving directional adjustable unidirectional transverse scattering based on a generalized cylindrical vector beam according to claim 1, characterized in that: The nanoantenna structure consists of two nanospheres: a gold nanosphere and a silicon nanosphere. The gold nanosphere has a radius of 80 nm, and the silicon nanosphere has a radius of 120 nm. The gap between the two nanospheres is 10 nm.

3. The method for achieving directional adjustable unidirectional transverse scattering based on a generalized cylindrical vector beam according to claim 2, characterized in that... The materials of the two nanospheres are unrestricted and can be selected from any combination of metals, dielectric materials, or semiconductor materials.

4. The method for achieving directionally adjustable unidirectional transverse scattering based on a generalized cylindrical vector beam according to claim 1, characterized in that... The generation method of generalized cylindrical vector beams is unrestricted, but it requires that the polarization angle be variable, and the change of polarization angle causes changes in the polarization distribution and electromagnetic field component distribution of the tightly focused light field.

5. The method for achieving directional adjustable unidirectional transverse scattering based on a generalized cylindrical vector beam according to claim 1, characterized in that: When the operating wavelength is any value within the range of 810nm to 850nm, any change in the polarization angle will cause a corresponding deflection in the unidirectional transverse far-field scattering direction.

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