CN115165759A - Optical spin Hall displacement measurement method for three-dimensional nanoparticles - Google Patents
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Abstract
The invention discloses a method for measuring the optical spin Hall displacement of three-dimensional nano particles, which comprises the following steps: s1, irradiating ellipsoidal nanoparticles by circularly polarized light and generating a spin Hall effect; s2, adjusting the wavelength of the circularly polarized light to meet the condition alpha under the wavelength 1 ＝β 1 To maximize the optical spin hall shift; wherein alpha is 1 And beta 1 Is the first term in the scattering coefficient of the ellipsoidal nanoparticles, alpha 1 Representing the contribution of an electric dipole to the fringe field, β 1 Represents the contribution of the magnetic dipole to the fringe field; s3, under the condition of alpha 1 ＝β 1 Next, the optical spin hall shift of the ellipsoidal nanoparticle was measured. The invention utilizes the ellipsoidal nano particles to satisfy alpha when circularly polarized light is irradiated 1 ＝β 1 Under the condition, the optical spin Hall displacement is maximized, and the optical spin Hall displacement is enhanced by adjusting the wavelength of light, so that the optical spin Hall displacement measurement of the ellipsoidal nanoparticles is realized.
Description
Technical Field
The invention relates to the technical field of optical spin Hall displacement measurement, in particular to an optical spin Hall displacement measurement method of three-dimensional nanoparticles.
Background
Spin-orbit interaction (the interconversion between spin angular momentum and orbital angular momentum) is associated with the focusing, scattering or imaging of light and is an embodiment of the conservation of angular momentum of photons. A plurality ofInteresting phenomena are closely related to spin-orbit interactions. Among them, the spin hall effect of light is the most attractive one. In the spin hall effect of light, the light will experience a plane of scattering (in the two-dimensional case, e.g., the case of refraction and reflection of a light beam on a plane, the scattering plane refers to the plane defined by the incident ray, the normal, the refracted and reflected ray, and in the three-dimensional case, the scattering plane refers to the unit vector of the polar angle direction and the radial direction in a spherical coordinate system
Plane formed) i.e. optical spin hall displacement. The optical spin hall shift is typically small compared to the wavelength of light. However, with the development of modern optical technology, such shifts may affect the accurate determination of the position of scattered light. Meanwhile, in an optical imaging system with elliptically polarized light, it is found that the optical spin hall shift is comparable to the wavelength. Optical spin hall shifts present both challenges and opportunities. On the one hand, the optical spin hall displacement may affect the resolution of the super resolution microscope. On the other hand, the optical spin hall displacement can find various applications in a spin-dependent system with light, such as designing a beam splitter, or detecting a local physical field (e.g., an electric field, a magnetic field, etc.), measuring the conductivity and chemical reaction rate of a substance.
In general, the optical spin hall effect itself is weak, and it is observed in experiments that a quantum weak measurement technique is required. Referring to fig. 1, the experimental process of the weak measurement of the optical spin hall displacement quantum is shown. Wherein (a) is a helium neon laser source outputting linear polarized light beam with 633nm wavelength. A half-wave plate (HWP) is used to modulate the beam intensity. The two polarizers (P1 and P2) are pre-selected and post-selected, respectively, for the state of the probe light. The Variable Angle Prism (VAP) refracts the light beam that undergoes the optical spin hall shift. The focal lengths of the lenses L1 and L2 are 25 and 125mm, respectively; [ extracted from: science,2008,319,787.] (b) is a diagram of the three processes of Preselection (Preselection), weak coupling (Weak coupling) and post-selection (Postselection) in the course of a Weak measurement. [ extracted from: reports on Progress in Physics,2017,80 (6): 066401.
Weak measurement of light is generally divided into three steps, pre-selection, weak coupling and post-selection. A first step of passing an incident beam through a polarizer P1 to a preselected state; secondly, incident light hits an air-glass interface to generate weak coupling effect; and finally, post-selecting the scattered light by using a second polarizer P2 to obtain a characteristic value of the scattered field. This enables the displacement of the post-selected beam to be increased significantly by several orders of magnitude, since the transmission directions of the two polarizers are opposite. By the weak measurement method, the optical spin Hall displacement can reach the measurable precision. In the experiment, the measured displacement resolution reaches
Left and right.
In summary, the current measurement method mainly focuses on spin hall displacement measurement on a two-dimensional scattering plane, the measurement of the spin hall displacement of the three-dimensional nanoparticle only has a theoretical calculation result, and the experimental measurement is difficult because the spin hall displacement is weak.
Disclosure of Invention
The invention aims to provide a method for measuring the optical spin Hall displacement of three-dimensional nanoparticles, which can be used for enhancing the optical spin Hall displacement by adjusting the wavelength of light and further realizing the optical spin Hall displacement measurement.
In order to solve the above problems, the present invention provides a method for measuring a three-dimensional nanoparticle optical spin hall displacement, comprising the steps of:
s1, irradiating ellipsoidal nanoparticles by circularly polarized light and generating a spin Hall effect;
s2, adjusting the wavelength of the circularly polarized light to meet the condition alpha under the wavelength 1 ＝β 1 To maximize the optical spin hall displacement; wherein alpha is 1 And beta 1 Is the first term in the scattering coefficient of the ellipsoidal nanoparticles, alpha 1 Representing the contribution of an electric dipole to the fringe field, β 1 Represents the contribution of the magnetic dipole to the fringe field;
s3, inCondition alpha 1 ＝β 1 Next, the optical spin hall displacement of the ellipsoidal nanoparticles was measured.
As a further improvement of the invention, the electric field E of the scattered field for left-handed circularly polarized light sca And a magnetic field H sca Expressed as:
wherein i represents an imaginary unit; k represents a wave number; ω represents angular frequency; μ represents a magnetic permeability; a is a n And beta n Scattering coefficient for the ellipsoidal nanoparticles;
the superscript (3) represents a third class of ellipsoid vector wave function, subscripts e and o represent parity relations about an azimuth phi and correspond to cos (m phi) and sin (m phi) respectively, and m and n represent summation indexes.
As a further improvement of the present invention, the optical spin hall displacement of the ellipsoidal nanoparticles is expressed as:
wherein, delta SH Representing the optical spin hall displacement of the ellipsoidal nanoparticles; r represents the distance from the observation point to the origin;
representative spherical coordinate system
Unit vector of
S φ And S r The azimuthal and radial components of the fringe field poynting vector.
As a further improvement of the present invention, substituting formula (1) and formula (2) into formula (3) yields:
wherein i (θ) is the normalized far-field scattering intensity of the ellipsoidal nanoparticles:
wherein σ n ＝[S 1n (cosθ)/sinθ]Hexix- n ＝d[S 1n (cosθ)]/dθ。
As a further improvement of the invention, the method also comprises the following steps:
and S4, calculating the geometric parameters of the detected ellipsoidal nanoparticles according to the measured optical spin Hall displacement of the ellipsoidal nanoparticles.
As a further improvement of the present invention, step S4 includes:
s41, calculating the conditions alpha of the ellipsoidal nanoparticles with different geometric parameters 1 ＝β 1 The optical spinning Hall displacement is obtained, and the mapping relation between the geometric parameters of the ellipsoidal nanoparticles and the optical spinning Hall displacement is obtained;
and S42, obtaining the geometric parameters of the detected ellipsoidal nanoparticles according to the mapping relation and the measured optical spin Hall displacement of the detected ellipsoidal nanoparticles.
As a further improvement of the invention, the ellipsoidal nanoparticles are oblate ellipsoids, spherical spheroids or prolate ellipsoids.
As a further improvement of the present invention, the circularly polarized light is left-handed circularly polarized light or right-handed circularly polarized light.
The invention also provides an electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements the steps of any one of the methods described above when executing the program.
The invention also provides a computer-readable storage medium, on which a computer program is stored, which program, when being executed by a processor, is adapted to carry out the steps of any of the methods described above.
The invention has the beneficial effects that:
the invention utilizes the ellipsoidal nano particles to satisfy alpha when circularly polarized light is irradiated 1 ＝β 1 Under the condition, the optical spin Hall displacement is maximized, and the optical spin Hall displacement measurement of the ellipsoidal nanoparticles is further realized.
The foregoing description is only an overview of the technical solutions of the present invention, and in order to make the technical means of the present invention more clearly understood, the present invention may be implemented in accordance with the content of the description, and in order to make the above and other objects, features, and advantages of the present invention more clearly understood, the following preferred embodiments are described in detail with reference to the accompanying drawings.
Drawings
FIG. 1 is a schematic diagram of an experimental process of weak measurement of a conventional optical spin Hall displacement quantum;
FIG. 2 is a schematic diagram of the spin Hall effect of near field and far field light for ellipsoidal nanoparticles;
FIG. 3 is a graph illustrating the modulation of optical spin Hall shift and light scattering intensity by the morphology of silicon nanoparticles with dual symmetry in accordance with the present invention;
fig. 4 is a diagram of the detection plane and the far field displacement detected by the detector in the present invention.
Detailed Description
The present invention is further described below in conjunction with the drawings and the embodiments so that those skilled in the art can better understand the present invention and can carry out the present invention, but the embodiments are not to be construed as limiting the present invention.
Example one
The embodiment discloses a method for measuring optical spin Hall displacement of three-dimensional nanoparticles, which comprises the following steps:
s1, irradiating ellipsoidal nanoparticles by using circularly polarized light and generating a spin Hall effect;
s2, adjusting the wavelength of the circularly polarized light to meet the condition alpha under the wavelength 1 ＝β 1 Rotating Hall displacement by the maximized light; wherein alpha is 1 And beta 1 Is the first term in the scattering coefficient of the ellipsoidal nanoparticles, alpha 1 Representing the contribution of an electric dipole to the fringe field, β 1 Represents the contribution of the magnetic dipole to the fringe field;
s3 under the condition of alpha 1 ＝β 1 Next, the optical spin hall displacement of the ellipsoidal nanoparticles was measured.
The theoretical basis of the invention is as follows:
as shown in fig. 2, it is a schematic diagram of spin hall effect of near-field and far-field light of the ellipsoidal nanoparticles. The curve trace of the poynting vector line in the vicinity of the nanoparticles results in a lateral displacement Δ in the far field SH . Far-field detectors show the scattered intensity distribution of circularly polarized incident light of opposite helicity, i.e. left-handed circularly polarized (LCP) light or right-handed circularly polarized (RCP) light. When the helicities of the incident light are opposite, the displacement of the center of the field intensity measured on the detection plane changes direction. k represents a wavevector representing the direction of incident light (circular polarized light), incident along the z-axis in a cartesian coordinate system (x, y, z). The detector (detector) receives scattered light in the far field for imaging, and the two inset images in fig. 2 are images received by the detector. Such that the observer perceives the particle at the origin as having a displacement delta from the origin SH And represents the optical spin hall displacement.
The key point of the invention is that the form of the spherical/ellipsoidal nano particles depends on the scattering characteristic, and the invention uses the generalized Lorentz-Mie theory to solve the scattering field. Without loss of generality, we consider left-handed circularly polarized (LCP) light to irradiate nanoparticles in three morphologies, namely spherical, oblate ellipsoid, and prolate ellipsoid. The aspect ratios AR of the three shapes (prolate ellipsoid AR = a/b, oblate ellipsoid AR = b/a, where a and b are the lengths of the major and minor half axes of the ellipsoid), are AR respectively sphere =1 (subscript sphere stands forSpherical), AR oblate < 1 (subscript oblate indicates oblate ellipsoid), AR prolate > 1 (subscript prolate denotes prolate ellipsoid).
The scattered field is a key physical quantity to solve for the spin hall displacement of light and the far field scattering intensity. The fringe field can be developed from an ellipsoid vector wave function. For left-handed circularly polarized light, the electric field E of the fringe field sca And a magnetic field H sca Expressed as:
wherein i represents an imaginary unit; k represents a wave number; ω represents angular frequency; μ represents a magnetic permeability; a is n And beta n Is the scattering coefficient of the ellipsoidal nanoparticles;
the superscript (3) represents a third class of ellipsoid vector wave function, subscripts e and o represent parity relations about an azimuth phi and correspond to cos (m phi) and sin (m phi) respectively, and m and n represent summation indexes.
For normal incidence (incident light parallel to the z-axis) or very small angles of incidence, take m =1. Note that although the scattered field of the ellipsoidal nanoparticles is calculated in an ellipsoidal coordinate system, for convenience, the components of the scattered field can be easily converted into corresponding spherical coordinate components. In far field approximation, the scattered field can be represented in the asymptotic form of an ellipsoid vector wave function in a spherical coordinate system. Substituting the asymptotic expression to obtain the asymptotic form of the scattering field in the spherical coordinate system, namely
(subscripts r, θ, φ denote fringe field electric fields E sca And magnetic field H sca In-sphere coordinate system
Middle rim
The components of the three unit vector directions).
When the nanoparticles scatter, a lateral shift with respect to the particle position, i.e. a spin hall shift of the light, occurs in the far field. The spin hall displacement of light is caused by the spin-orbit interaction of light caused by the refractive index gradient at the particle interface. Is defined as:
wherein, delta SH Representing the optical spin hall displacement of the ellipsoidal nanoparticles; r represents the distance from the observation point to the origin;
representative spherical coordinate system
Unit vector of (1)
S φ And S r Azimuthal component of the vector for fringe field poynting (in spherical coordinate system)
Middle rim
Component in unit vector direction) and radial component (in spherical coordinate system)
Middle rim
The component in the direction of the unit vector).
Substituting the formula (1) and the formula (2) into the formula (3) to obtain the spin Hall displacement of the far field as follows:
wherein i (θ) is the normalized far-field scattering intensity of the ellipsoidal nanoparticles and is:
wherein σ n ＝[S 1n (cosθ)/sinθ]Hexix- n ＝d[S 1n (cosθ)]And/d θ is a function defined in an ellipsoid coordinate system as a function of the scattering angle. The aspect ratio AR approaches 1, considering only the dipole term, equation (3) can be simplified as:
its form is similar to that of the spherical particles (AR = 1).
Let us study the relationship between the spin hall displacement of light and the corresponding far-field scattering intensity. Equation (3) clearly shows that the spin hall displacement magnitude is inversely proportional to the scattering intensity, which is similarly problematic in most two-dimensional cases. For high-dimensional dielectric nanoparticles, the main method to enhance the spin hall shift is to use dual nanospheres with equal electric and magnetic dipole modes. The dual nanospheres meet the first Kerker condition (alpha) 1 ＝β 1 ) And therefore the backscattering is almost zero. However, enhanced spin hall shifts typically occur when the large scattering angle approaches backscatter. Under the first Kerker condition, the light scattering of spherical nanoparticles is generally weak, and under this condition, both electric and magnetic dipole modes are far from resonance. The above-described optical properties of nanospheres are the primary reason why a given material cannot achieve both high spin hall-shift and large scattering intensity.
FIG. 3 isThe optical spin hall displacement and the light scattering intensity are tuned by the morphology of the silicon nanoparticles with dual symmetry. Wherein, (a) is a comparison of the light spin hall displacement and scattering intensity of flat ellipsoid (AR = 0.5) and sphere (AR = 1.0) nanoparticles at the same wavelength (scattering angle θ) is the same as the polar angle θ in the spherical coordinate system). (b) Scattering coefficients (scattering coefficients) in different morphologies are related to the size parameter (size parameter q). (c) Schematic diagram of optimal size and shape for dual symmetric silicon nanoparticles; wherein the inset shows that at resonance, oblate spheroid (AR)<1) More suitable for making the electric dipole mode alpha 1 And magnetic dipole mode beta 1 Overlap at resonance. (q represents a size parameter of the particles, defined as q = ka, k is the wave number, k =2 π/; a is the length of the semimajor axis of the ellipsoid; λ represents the wavelength of the incident light).
Specifically, as seen from fig. 3 (a), by using the nanoparticles of the optimal morphology, the scattering intensity is increased by one order of magnitude. The scattering intensity of an oblate ellipsoid is more than ten times stronger than that of a sphere in all scattering directions. Meanwhile, the oblate ellipsoid keeps the enhancement of the spin Hall displacement, even slightly larger than the situation of a ball. The wavelength-scale spin hall displacement is caused by interference of electric and magnetic dipole modes of the same phase and magnitude.
However, the wavelength-scale spin hall shift, the dual condition (α) of nanospheres (AR = 1) only at non-resonance (q = 0.77) 1 ＝β 1 ) This can be achieved as shown in (b) of fig. 3. By adjusting the morphology of the nanoparticles, we can find an optimal geometry to maximize resonance scattering. As shown in fig. 3 (b), the scattering coefficient amplitude (marked with a circle) at the overlap increases with decreasing AR of the particle, and the scattering intensity is proportional to the square of the scattering coefficient. Thus, the scattering intensity of an optimal oblate ellipsoid may be ten times greater than that of a spherical particle, given a refractive index. The relationship between the optimum geometry and the particle size parameter q is given in fig. 3 (c). For a given size of nanoparticle, both oblate ellipsoids (AR < 1) and prolate ellipsoids (AR > 1) can have optimal aspect ratios to enhance the spin Hall shift. However, as the nanoparticles move from a short ellipseThe spheres are changed to prolate ellipsoids having a smaller scattering coefficient at the overlap than the corresponding spheres (see the inset diagram in (c) of fig. 3). Therefore, an oblate ellipsoid can be selected instead of a prolate ellipsoid, thereby realizing the enhancement of the spin hall displacement and the scattering intensity at the same time. In summary, manipulating the morphology of the particles provides an additional degree of freedom to manipulate both the value and phase of the scattering coefficient, i.e. to cause the electric and magnetic dipole modes to overlap at resonance, rather than at the tail away from resonance.
The invention also provides an experimental scheme for detecting the far field offset of the scattered light. The detector being perpendicular to the radial vector
(in a spherical coordinate system)
Middle rim
Unit vector direction) and is along
Direction (in spherical coordinate system)
Middle rim
Unit vector direction) is rotated about the nanoparticle center. It is worth noting that, first, the intensity distribution of the scattered light is not a single poynting vector line, but rather is made up of a bundle of field lines in the detection plane, defined as
(S (r, θ) represents a poynting vector;
pointing from the origin to a detection point (r) on the detection plane 0 ，θ 0 ) Unit vector of (d). The detected displacement is represented by intensity distributionPeak value of (d) and detection point (r) on the detection plane 0 ，θ 0 ) The intercept therebetween, as shown in fig. 4 (a). It should be noted that the detected displacement and the calculated spin hall displacement are not exactly the same, but they have a consistent directional trend and the same scattering angle. A rough result can be seen by comparing the detected shift in fig. 3b (σ = -1, indicating that the incident light is left circularly polarized light) with the corresponding spin hall shift in fig. 3 a.
Fig. 4 is a detection plane and the far field displacement detected by the detector. Fig. 4 (a) is a schematic diagram of a detection plane perpendicular to the radial vector. Displacement mu p The transverse distance between the scattering intensity peak value and the observation point is measured by a rectangular coordinate system in the detection plane. (k denotes wave vector, representing incident light direction; half-wave plate (Half-wave plate) for switching between left-handed and right-handed incident light;
representing two orthogonal unit vectors in the probe plane, substantially in relation to a spherical coordinate system
In
The unit vectors are equivalent;
pointing from the centre of the particle to a detection point (r) on the detection plane 0 ，θ 0 ) A unit vector of (a);
a unit vector pointing from the center of the particle to any point on the detection plane; (μ, ν) dimensionless coordinates of points on the detection plane). In fig. 4, (b) is μ when the polarization of incident light is switched between left-hand σ = -1 and right-hand σ =1 p (coordinates corresponding to the maximum value of the scattered light intensity distribution). Measuring the displacement mu on the detection plane p (σ = -1) and the direction and amplitude trends of spin hall displacement calculated in (a) of fig. 3The same is true. In FIG. 4 (c) is a comparison of normalized scattering intensity I (μ) on the detection surface for oblate ellipsoid and spherical nanoparticles. The incident wavelength was set to 1064nm. Helicity σ = ± 1 represents right-or left-handed polarized light incidence. Other parameters are the same as those in fig. 3 (a).
Secondly, determining the exact initial position or scattering angle of the detector and the nanoparticles remains a challenge; therefore, it is difficult to directly measure the intercept. One can measure the difference 2 mu between the lateral distance variations of different incident polarizations p To address this difficulty. The helicity of the incident light can be changed by a half-wave plate. Incident light of opposite helicity will only change the sign of the detected displacement and the spin hall displacement. Therefore, when we change the helicity of incident light, the change in the traversing distance is as shown in fig. 4 (b). Furthermore, our calculations demonstrate that this method is robust to particle position, i.e. the detector is not centered on the particle, or the particle is moving (e.g. away from the origin). Although the magnitude of the traversing and the scattering intensity may vary, the difference between the displacements measured on the scattering plane at opposite helicity incidence is 2 μ p Remain unchanged.
The invention utilizes the ellipsoidal nano particles to satisfy alpha when circularly polarized light is irradiated 1 ＝β 1 Under the condition, the optical spin Hall displacement is the maximum value, and further the optical spin Hall displacement measurement of the ellipsoidal nanoparticles is realized.
From the above theory, we found that the ellipsoidal nanoparticles with different geometric parameters are in the condition alpha 1 ＝β 1 The lower part corresponds to the maximum optical spin Hall displacement, so that the mapping relation between the geometric parameters of the ellipsoidal nanoparticles and the optical spin Hall displacement can be obtained. Furthermore, the geometric parameters of the detected ellipsoidal nanoparticles can be obtained by actually measuring the optical spin Hall displacement of the obtained ellipsoidal nanoparticles and combining the mapping relation.
Therefore, optionally, the optical spin hall displacement measurement method of the three-dimensional nanoparticle of the present invention further comprises the steps of:
and S4, calculating the geometric parameters of the detected ellipsoidal nanoparticles according to the measured optical spin Hall displacement of the ellipsoidal nanoparticles. Specifically, step S4 includes:
s41, calculating the conditions alpha of the ellipsoidal nanoparticles with different geometric parameters 1 ＝β 1 The optical spin Hall displacement is carried out, and the mapping relation between the geometric parameters of the ellipsoidal nanoparticles and the optical spin Hall displacement is obtained;
and S42, obtaining the geometric parameters of the detected ellipsoidal nanoparticles according to the mapping relation and the measured optical spin Hall displacement of the detected ellipsoidal nanoparticles.
Example two
The embodiment discloses an electronic device, which comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein the processor executes the program to realize the steps of the optical spin hall displacement measurement method for the three-dimensional nanoparticles in the first embodiment.
EXAMPLE III
The present embodiment discloses a computer-readable storage medium, on which a computer program is stored, which when executed by a processor implements the steps of the method for measuring optical spin hall displacement of three-dimensional nanoparticles described in the first embodiment.
The above embodiments are merely preferred embodiments for fully illustrating the present invention, and the scope of the present invention is not limited thereto. The equivalent substitution or change made by the technical personnel in the technical field on the basis of the invention is all within the protection scope of the invention. The protection scope of the invention is subject to the claims.
Claims (10)
1. A method for measuring the optical spin Hall displacement of three-dimensional nanoparticles is characterized by comprising the following steps:
s1, irradiating ellipsoidal nanoparticles by circularly polarized light and generating a spin Hall effect;
s2, adjusting the wavelength of the circularly polarized light to meet the condition alpha under the wavelength 1 ＝β 1 To maximize the optical spin hall shift; wherein alpha is 1 And beta 1 Is the second in the scattering coefficient of the ellipsoidal nanoparticlesAn term, α 1 Representing the contribution of an electric dipole to the fringe field, β 1 Represents the contribution of the magnetic dipole to the fringe field;
s3 under the condition of alpha 1 ＝β 1 Next, the optical spin hall shift of the ellipsoidal nanoparticle was measured.
2. The method of claim 1, wherein the electric field E of the fringe field for left-handed circularly polarized light is sca And magnetic field H sca Expressed as:
wherein i represents an imaginary unit; k represents a wave number; ω represents angular frequency; μ represents a magnetic permeability; a is n And beta n Is the scattering coefficient of the ellipsoidal nanoparticles;
for an ellipsoid vector wave function, the superscript (3) represents a third type of ellipsoid vector wave function, the subscripts e and o represent parity relations with respect to the azimuth angle phi, which correspond to cos (m phi) and sin (m phi), respectively, and m and n represent summation indexes.
3. The method of claim 2, wherein the optical spin hall displacement of the ellipsoidal nanoparticle is expressed as:
wherein, delta SH Representing the optical spin of the ellipsoidal nanoparticlesHall displacement; r represents the distance from the observation point to the origin;
representative spherical coordinate system
Unit vector of (1)
S φ And S r The azimuthal component and the radial component of the fringe field poynting vector.
4. The optical spin hall displacement measurement method of three-dimensional nanoparticles as claimed in claim 3, wherein the formula (1) and the formula (2) are substituted into the formula (3) to obtain:
wherein i (θ) is the normalized far-field scattering intensity of the ellipsoidal nanoparticles and is:
wherein σ n ＝[S 1n (cosθ)/sinθ]Hexix- n ＝d[S 1n (cosθ)]/dθ。
5. The method for measuring the optical spin hall displacement of three-dimensional nanoparticles according to claim 1, further comprising the steps of:
and S4, calculating the geometric parameters of the detected ellipsoidal nanoparticles according to the measured optical spin Hall displacement of the ellipsoidal nanoparticles.
6. The optical spin hall displacement measurement method of three-dimensional nanoparticles of claim 5, wherein step S4 comprises:
s41, calculating the conditions alpha of the ellipsoidal nanoparticles with different geometric parameters 1 ＝β 1 The optical spinning Hall displacement is obtained, and the mapping relation between the geometric parameters of the ellipsoidal nanoparticles and the optical spinning Hall displacement is obtained;
and S42, obtaining the geometric parameters of the detected ellipsoidal nanoparticles according to the mapping relation and the measured optical spin Hall displacement of the detected ellipsoidal nanoparticles.
7. The method according to claim 1, wherein the ellipsoidal nanoparticles are oblate ellipsoids, spheroidal spheroids, or prolate ellipsoids.
8. The method for measuring the optical spin hall displacement of three-dimensional nanoparticles of claim 1, wherein the circularly polarized light is left-handed circularly polarized light or right-handed circularly polarized light.
9. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the steps of the method according to any of claims 1-8 are implemented when the processor executes the program.
10. A computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the steps of the method according to any one of claims 1 to 8.
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