CN111209524A - Method for calculating vortex light scattering characteristics of topological insulator particles - Google Patents

Method for calculating vortex light scattering characteristics of topological insulator particles Download PDF

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CN111209524A
CN111209524A CN202010036763.7A CN202010036763A CN111209524A CN 111209524 A CN111209524 A CN 111209524A CN 202010036763 A CN202010036763 A CN 202010036763A CN 111209524 A CN111209524 A CN 111209524A
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王明军
林妞妞
张佳琳
翟治珠
魏亚飞
张艺伟
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Xian University of Technology
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Abstract

The invention discloses a method for calculating the vortex light scattering characteristic of topological insulator particles, which specifically comprises the following steps: step 1, expanding Laguerre-Gaussian beams by a plane angle spectrum method to respectively obtain electric field intensity and magnetic field intensity in x, y and z directions, and obtaining radial components of the electric field and the magnetic field in a spherical coordinate system by using a local approximation method; step 2, solving a beam factor; step 3, the Laguerre-Gaussian beam is incident to the incident field of the TI sphere, and the scattering field and the internal field of the spherical particles are expanded by the vector spherical harmonic function and the scattering coefficient to obtain Einc、Esca、Eint、Hinc、Hsca、Hint(ii) a Step 4, solving the scattering coefficient of the Laguerre-Gaussian beam incident TI sphere; step 5, solving the scattering electric field component of the Laguerre-Gaussian beam incident TI sphere far field region; and 6, solving a scattering efficiency factor, an extinction efficiency factor and an absorption efficiency factor. The invention providesThe method enables the topological insulator particles to have good application prospects in the aspects of design and production of electronic equipment and optical equipment.

Description

Method for calculating vortex light scattering characteristics of topological insulator particles
Technical Field
The invention belongs to the technical field of wireless laser communication, and relates to a method for calculating vortex light scattering characteristics of topological insulator particles.
Background
Topological insulator materials have unusual quantum states with an insulator-like band structure between its internal conduction and valence bands and topologically protected, energy-gap-free surface states at its outer or edge. On the energy level structure, the surface states connect the valence band and the conduction band, are caused by the topological property of the energy band structure, are protected by time reversal symmetry, and can exist very stably. The existence of topological magnetoelectric coupling terms in the topological insulator enables the Maxwell effect to be modified as follows:
Figure BDA0002366308650000011
wherein epsilon and mu are respectively dielectric constant and permeability, E and BETA are respectively electric field intensity and magnetic induction intensity, α is fine structure constant, d is3xdt is a spatio-temporal volume element, Θ is an axion angle describing TI, i.e. topological magnetic polarizability (TMEP), and the constitutive relation of topological insulators is modified by D ═ e ∈ - (Θ α/pi) Ρ, Η ═ Η/μ + (Θ α/pi) Ε, where D is electric displacement, Η is magnetic field strength.
Experts and scholars at home and abroad deeply research the scattering problem of spherical particles from a single sphere to a plurality of spheres, from a single-layer to a multi-layer medium sphere, from plane waves to incident of shaped beams, from common medium spheres to manual medium spheres and the like. However, scattering studies of spherical particles by laguerre gaussian vortex beams are still in the initial stage. Koxizhen et al studied the scattering properties of high-order LGBs with orbital angular momentum on single-sphere particles; zhao, Ou Jun et al studied the scattering properties of spherical and ellipsoidal particles on focused high-order LGB; kiselev et al studied the near-field scattering properties of isotropic spherical particles on high-order LGB using a T matrix method; the scattering properties of uniaxial anisotropic spheres and doublespheres and chiral medium spheres on LGB were systematically studied by drosanto, wu zhenseng et al; xuehao, Hanyi et al studied the scattering properties of LGB vector far-field single-sphere particles.
Due to the appearance of the topological magnetoelectric effect, the scattering problem of the topological insulator causes the research enthusiasm of researchers at home and abroad. Zelungwu et al have studied the scattering characteristic of TI spherical and TI ellipsoidal particle to the plane electromagnetic wave, according to TI constitutive relation and boundary condition, corrected the analytic expression of internal field and scattered field, utilized and deducted the scattered electromagnetic field; geritin et al studied the electromagnetic scattering properties of TI cylinders and spherical particles, and under Rayleigh approximation, derived an expression for estimating TMEP; akhlesh Lakhtakia et al study the electromagnetic scattering properties of a topological insulating sphere characterized by surface admittance gamma, and it is found that for larger values of gamma, no matter whether the sphere is composed of dissipative or non-dissipative materials, and no matter whether the materials support plane wave transmission of positive phase velocity or negative phase velocity, the scattering properties of TI approach the scattering properties of a perfect conductive sphere; faheem Ashraf et al studied the scattering of TI cylinders in chiral media and compared them to the scattering properties of chiral media chiral cylinders, and found that the topologically cylindrical cross-polarized field components in chiral media behave more strongly than chiral media cylinders.
Disclosure of Invention
The invention aims to provide a method for calculating the vortex light scattering characteristics of topological insulator particles, which researches the scattering characteristics of the topological insulator particles on Laguerre-Gaussian beams by using an electromagnetic wave theory and a generalized Mie scattering theory, so that the topological insulator particles have good application prospects in the aspects of design and production of electronic equipment and optical equipment.
The technical scheme adopted by the invention is that the method for calculating the vortex light scattering characteristic of the topological insulator particles specifically comprises the following steps:
step 1, expanding Laguerre-Gaussian beams by a plane angle spectroscopy method to obtain electric field intensity E in x, y and z directions respectivelyx、Ey、EzAnd magnetic field strength and Hx、Hy、HzAnd obtaining the electric field E in the spherical coordinate system by using a local approximation methodrAnd a magnetic fieldRadial component sum Hr；
Step 2, the radial component E of the electric field and the magnetic field in the spherical coordinate system obtained in the step 1r and HrSubstituting into integral expression of beam factor in transverse magnetic transverse electric mode to obtain beam factor
Figure BDA0002366308650000031
And
Figure BDA0002366308650000032
step 3, the beam factor obtained according to the step 2
Figure BDA0002366308650000033
And
Figure BDA0002366308650000034
utilizing vector spherical harmonics and scattering coefficients to expand an incident field, a scattering field and an internal field of spherical particles of a Laguerre-Gaussian beam incident TI sphere to obtain Eeinc、Εsca、Εint、Hinc、Hsca、Hint；
Step 4, solving the scattering coefficient of the Laguerre-Gaussian beam incident TI sphere according to the result obtained in the step 3;
step 5, based on the scattering coefficient obtained in the step 4, obtaining the theta component sum of the scattering electric field of the Laguerre-Gaussian beam incident TI sphere far-field region
Figure BDA0002366308650000035
A component;
step 6, based on the theta component sum of the scattering electric field of the far field region obtained in step 5
Figure BDA0002366308650000036
Component, finding the scattering efficiency factor Q of the Laguerre-Gauss beam incident TI spherescaExtinction efficiency factor QextAnd absorption efficiency factor Qabs。
The present invention is also characterized in that,
the specific process of step 1 is as follows:
in a spherical coordinate system, a beam of LGB linearly polarized in the X-axis direction is incident on a uniform spherical particle along the Z-axis, and the electric field expression of the incident low-order LGB at Z ═ 0 is:
Figure BDA0002366308650000037
wherein E0Is the electric field amplitude, x, y are rectangular coordinates, k is the wave number, ω is the beam waist radius, l is the topological charge;
based on a vector angle spectrum method, the electromagnetic field distribution of the LGB is expanded along the directions of x, y and z to respectively:
Figure BDA0002366308650000041
Figure BDA0002366308650000042
wherein ,
Figure BDA0002366308650000043
Ex、Ey、Ez and Hx、Hy、HzThe electric field strength and the magnetic field strength in the x, y and z directions respectively.
Converting the expression in the rectangular coordinate system into the expression of each component in the spherical coordinate system:
Figure BDA0002366308650000044
(4) (ii) a Wherein r, theta,
Figure BDA0002366308650000045
Are the coordinates of a spherical coordinate system.
The specific process of step 2 is as follows:
substituting the radial components of the electric field and the magnetic field in the spherical coordinate system obtained in the step 1 into an integral expression of the beam factor in the transverse magnetic transverse electric mode, as follows:
Figure BDA0002366308650000051
wherein, when m is 0, the normalization factor is compounded
Figure BDA0002366308650000052
When m is not equal to 0, a normalization factor is compounded
Figure BDA0002366308650000053
Substituting the formula (4) into the formula (5), and calculating to obtain a beam factor expression of the LGB incident on the axis by utilizing the orthogonality of the exponential function and the trigonometric function:
Figure BDA0002366308650000054
the beam is incident on the axis, and m is + -1-l.
The specific process of step 3 is as follows:
let the dielectric constant and permeability of TI sphere and air be respectively epsilon1,μ1 and ε2,μ2(ii) a The radius of the sphere is a; the LGB wave beam enters a TI sphere on the axis, when an incident electromagnetic field is TE (TM) wave, a scattering electric field and a transmission electric field are both TE wave, in a topological insulator, due to magnetoelectric response, the scattering electromagnetic field is cross-polarized, a Laguerre-Gaussian beam enters an incident field of the TI sphere, and the scattering electric field and an internal field of spherical particles are expanded into a vector spherical harmonic function M and a vector spherical harmonic function N:
Figure BDA0002366308650000061
Figure BDA0002366308650000062
Figure BDA0002366308650000063
wherein ,An，BnIs the scattering coefficient of the TI spherical particles, Cn and DnIs the scattering coefficient inside the TI sphere,
Figure BDA0002366308650000064
and
Figure BDA0002366308650000065
is the cross scatter coefficient due to the TME effect of the TI spheres.
The specific process of step 4 is as follows:
combining the continuous boundary conditions of the electromagnetic field tangential component of the spherical particle surface: r × (E)inc+Esca-Eint)＝0；
Figure BDA0002366308650000066
Then according to
Figure BDA0002366308650000067
And
Figure BDA0002366308650000068
is solved with respect to the scattering coefficient an、Bn、Cn、Dn、
Figure BDA0002366308650000069
And
Figure BDA00023663086500000610
the linear independent equation of (a) yields the scattering coefficient, specifically:
Figure BDA00023663086500000611
Figure BDA00023663086500000612
wherein ,
Figure BDA00023663086500000613
Figure BDA0002366308650000071
Figure BDA0002366308650000072
Figure BDA0002366308650000073
Figure BDA0002366308650000074
Figure BDA0002366308650000075
wherein ,jn and hnThe first ball Bessel function and the Hankel function are respectively adopted; x is a size parameter;
Figure BDA0002366308650000076
is the relative refractive index of a sphere β1 and β2Is a function of the axis angle α of the spherical particles of the topological insulator, respectively
Figure BDA0002366308650000077
Figure BDA0002366308650000078
When Θ is equal to 0,
Figure BDA0002366308650000079
an、bn、cn and dnWill degrade into the scattering coefficient and sphere internal coefficient of a common dielectric sphere.
The specific process of step 5 is as follows:
the theta component of the scattering electric field of the Laguerre-Gaussian beam incident on the TI spherical far-field region is obtained according to the following formula
Figure BDA00023663086500000710
And
Figure BDA00023663086500000711
component(s) of
Figure BDA00023663086500000712
Figure BDA0002366308650000081
When in use
Figure BDA0002366308650000082
Degenerates into the scattering field of the ordinary medium sphere to the LGB;
an and bnIs the scattering coefficient of spherical particles for plane waves,
Figure BDA0002366308650000083
and
Figure BDA0002366308650000084
is a function of the angle of scattering,
Figure BDA0002366308650000085
is a first order n-th legendre function of the first kind.
The specific process of step 6 is as follows:
the scattering efficiency factor Q is obtained by the following formulascaExtinction efficiency factor QextAnd absorption efficiency factor Qabs：
Figure BDA0002366308650000086
Figure BDA0002366308650000087
Qabs＝Qext-Qsca；
Wherein, the lambda is the wavelength,
Figure BDA0002366308650000088
and
Figure BDA0002366308650000089
is the sum of the theta components of the scattered energy density in a spherical coordinate system
Figure BDA00023663086500000810
The components of the first and second images are,
Figure BDA00023663086500000811
and
Figure BDA00023663086500000812
is the theta component under the spherical coordinate system of the incident electric field and the scattered electric field respectively,
Figure BDA00023663086500000813
and
Figure BDA00023663086500000814
respectively under incident electric field and scattered electric field spherical coordinate system
Figure BDA00023663086500000815
The components of the first and second images are,
Figure BDA00023663086500000816
and
Figure BDA00023663086500000817
is the theta component under the spherical coordinate system of the incident magnetic field and the scattered magnetic field respectively,
Figure BDA00023663086500000818
and
Figure BDA00023663086500000819
are respectively provided withIs under the spherical coordinate system of incident magnetic field and scattered magnetic field
Figure BDA0002366308650000091
And (4) components.
The method for calculating the vortex light scattering characteristics of the topological insulator particles has the advantages that theoretical bases can be provided for target stealth, electromagnetic target scattering calculation, parameter inversion and the like, the quantum communication field based on photon angular momentum can be expanded, and a new thought can be provided for the deep research of the optical characteristics of topological materials.
Drawings
FIG. 1 is a schematic diagram of a topological insulator sphere with Laguerre-Gaussian vortex beam incident on an axis in a calculation method of the scattering characteristics of topological insulator particles on vortex light.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention discloses a method for calculating the vortex light scattering characteristic of topological insulator particles, which specifically comprises the following steps:
step 1, expanding Laguerre-Gaussian beams by a plane angle spectroscopy method to obtain electric field intensity E in x, y and z directions respectivelyx、Ey、EzAnd magnetic field strength and Hx、Hy、HzAnd obtaining the electric field E in the spherical coordinate system by using a local approximation methodrAnd the radial component sum H of the magnetic fieldr；
The specific process of the step 1 is as follows:
in a spherical coordinate system, a beam of X-axis linearly polarized LGB is incident on a uniform spherical particle along the Z-axis as shown in fig. 1, and the electric field expression of the incident low-order LGB at Z ═ 0 is:
Figure BDA0002366308650000092
wherein E0Is the amplitude of the electric field, x and y are rectangular coordinates, k is the wave number, omega is the radius of the beam waist, l is the topological charge number, and the time factor exp (-i)ω t) is ignored;
based on a vector angle spectrum method, the electromagnetic field distribution of the LGB is expanded along the directions of x, y and z to respectively:
Figure BDA0002366308650000101
Figure BDA0002366308650000102
wherein ,
Figure BDA0002366308650000103
Ex、Ey、Ez and Hx、Hy、HzThe electric field strength and the magnetic field strength in the x, y and z directions respectively.
Converting the expression in the rectangular coordinate system into the expression of each component in the spherical coordinate system:
Figure BDA0002366308650000104
(4) (ii) a Wherein r, theta,
Figure BDA0002366308650000105
Are the coordinates of a spherical coordinate system.
Step 2, the radial component E of the electric field and the magnetic field in the spherical coordinate system obtained in the step 1r and HrSubstituting into integral expression of beam factor in transverse magnetic transverse electric mode to obtain beam factor
Figure BDA0002366308650000106
And
Figure BDA0002366308650000107
the specific process of step 2 is as follows:
Figure BDA0002366308650000111
wherein, when m is 0, the normalization factor is compounded
Figure BDA0002366308650000112
When m is not equal to 0, a normalization factor is compounded
Figure BDA0002366308650000113
Substituting the formula (4) into the formula (5), and calculating to obtain a beam factor expression of the LGB incident on the axis by utilizing the orthogonality of the exponential function and the trigonometric function:
Figure BDA0002366308650000114
the beam is incident on the axis, and m is + -1-l.
Step 3, the beam factor obtained according to the step 2
Figure BDA0002366308650000115
And
Figure BDA0002366308650000116
utilizing vector spherical harmonics and scattering coefficients to expand an incident field, a scattering field and an internal field of spherical particles of a Laguerre-Gaussian beam incident TI sphere to obtain Eeinc、Εsca、Εint、Hinc、Hsca、Hint；
Let the dielectric constant and permeability of TI sphere and air be respectively epsilon1,μ1 and ε2,μ2(ii) a The radius of the sphere is a; the LGB beam is incident on the axis into the TI sphere, and the electric field of the incident field is EincElectric field of fringe field EscaElectric field of internal fields eintMagnetic field H of incident fieldincMagnetic field H of the scattered fieldscaMagnetic field H of internal fieldint. In general, when the incident electromagnetic field is te (tm) waves, the scattering electric field and the transmission electric field are both te (tm) waves. In topological insulators, the scattered electromagnetic field is cross-polarized due to the magnetoelectric response, and a Laguerre-Gaussian beam enters the TI ballThe scattered electric field and the internal field of the spherical particle are developed with vector spherical harmonics M and N as:
Figure BDA0002366308650000121
Figure BDA0002366308650000122
Figure BDA0002366308650000123
wherein ,An，BnIs the scattering coefficient of the TI spherical particles, Cn and DnIs the scattering coefficient inside the TI sphere.
Figure BDA0002366308650000124
And
Figure BDA0002366308650000125
is the cross scatter coefficient due to the TME effect of the TI spheres.
Step 4, solving the scattering coefficient of the Laguerre-Gaussian beam incident TI sphere according to the result obtained in the step 3;
combining the continuous boundary conditions of the electromagnetic field tangential component of the spherical particle surface: r × (E)inc+Esca-Eint)＝0；
Figure BDA0002366308650000126
r is a, then according to
Figure BDA0002366308650000127
And
Figure BDA0002366308650000128
is solved with respect to the scattering coefficient an，Bn，Cn，Dn，
Figure BDA0002366308650000129
Figure BDA00023663086500001210
And
Figure BDA00023663086500001211
the scattering coefficient can be obtained from the linearly independent equation of (1):
Figure BDA00023663086500001212
Figure BDA00023663086500001213
wherein
Figure BDA00023663086500001214
Figure BDA0002366308650000131
Figure BDA0002366308650000132
Figure BDA0002366308650000133
Figure BDA0002366308650000134
Figure BDA0002366308650000135
wherein ,jn and hnThe first ball Bessel function and the Hankel function are respectively adopted; x is a size parameter;
Figure BDA0002366308650000136
is the relative refractive index of a sphere β1 and β2Is a function of the axion angle α for the spherical particles of the topological insulator,they are respectively represented as
Figure BDA0002366308650000137
Figure BDA0002366308650000138
It is clear that, when Θ is 0,
Figure BDA0002366308650000139
an，bn，cn and dnWill degrade into the scattering coefficient and sphere internal coefficient of a common dielectric sphere.
Step 5, based on the scattering coefficient obtained in the step 4, the theta component sum of the scattering electric field of the Laguerre-Gaussian beam incident TI sphere far-field region can be obtained
Figure BDA00023663086500001310
And (4) components.
Figure BDA00023663086500001311
When in use
Figure BDA0002366308650000141
Degenerates into the scattering field of the ordinary medium sphere to the LGB;
an and bnIs the scattering coefficient of spherical particles for plane waves,
Figure BDA0002366308650000142
and
Figure BDA0002366308650000143
is a function of the angle of scattering,
Figure BDA0002366308650000144
is a first order n-th legendre function of the first kind.
Step 6, based on the theta component sum of the scattering electric field of the far field region obtained in step 5
Figure BDA0002366308650000145
Component, scattering efficiency factor Q of Laguerre-Gaussian beam incident TI sphere can be obtainedscaExtinction efficiency factor QextAnd absorption efficiency factor QabsComprises the following steps:
Figure BDA0002366308650000146
Figure BDA0002366308650000147
Qabs＝Qext-Qsca
wherein, the lambda is the wavelength,
Figure BDA0002366308650000148
and
Figure BDA0002366308650000149
is the sum of the theta components of the scattered energy density in a spherical coordinate system
Figure BDA00023663086500001410
The components of the first and second images are,
Figure BDA00023663086500001411
and
Figure BDA00023663086500001412
is the theta component under the spherical coordinate system of the incident electric field and the scattered electric field respectively,
Figure BDA00023663086500001413
and
Figure BDA00023663086500001414
respectively under incident electric field and scattered electric field spherical coordinate system
Figure BDA00023663086500001415
The components of the first and second images are,
Figure BDA00023663086500001416
and
Figure BDA00023663086500001417
is the theta component under the spherical coordinate system of the incident magnetic field and the scattered magnetic field respectively,
Figure BDA00023663086500001418
and
Figure BDA00023663086500001419
respectively under incident magnetic field and scattered magnetic field spherical coordinate system
Figure BDA00023663086500001420
And (4) components.

Claims (7)

1. A method for calculating the vortex light scattering characteristics of topological insulator particles is characterized by comprising the following steps: the method specifically comprises the following steps:
step 1, expanding Laguerre-Gaussian beams by a plane angle spectroscopy method to obtain electric field intensity E in x, y and z directions respectivelyx、Ey、EzAnd magnetic field strength and Hx、Hy、HzAnd obtaining the electric field E in the spherical coordinate system by using a local approximation methodrAnd the radial component sum H of the magnetic fieldr；
Step 2, the radial component E of the electric field and the magnetic field in the spherical coordinate system obtained in the step 1r and HrSubstituting into integral expression of beam factor in transverse magnetic transverse electric mode to obtain beam factor
Figure FDA0002366308640000011
And
Figure FDA0002366308640000012
step 3, the beam factor obtained according to the step 2
Figure FDA0002366308640000013
And
Figure FDA0002366308640000014
expanding an incident field, a scattering field and an internal field of spherical particles of the Laguerre-Gaussian beam incident TI sphere by using a vector spherical harmonic function and a scattering coefficient to obtain Einc、Esca、Eint、Hinc、Hsca、Hint；
Step 4, solving the scattering coefficient of the Laguerre-Gaussian beam incident TI sphere according to the result obtained in the step 3;
step 5, based on the scattering coefficient obtained in the step 4, obtaining the theta component sum of the scattering electric field of the Laguerre-Gaussian beam incident TI sphere far-field region
Figure FDA0002366308640000016
A component;
step 6, based on the theta component sum of the scattering electric field of the far field region obtained in step 5
Figure FDA0002366308640000017
Component, finding the scattering efficiency factor Q of the Laguerre-Gauss beam incident TI spherescaExtinction efficiency factor QextAnd absorption efficiency factor Qabs。
2. The method for calculating the vortex light scattering property of the topological insulating particles according to claim 1, wherein the specific process of the step 1 is as follows:
in a spherical coordinate system, a beam of LGB linearly polarized in the X-axis direction is incident on a uniform spherical particle along the Z-axis, and the electric field expression of the incident low-order LGB at Z ═ 0 is:
Figure FDA0002366308640000015
wherein E0Is the electric field amplitude, x, y are rectangular coordinates, k is the wave number, ω is the beam waist radius, l is the topological charge;
based on a vector angle spectrum method, the electromagnetic field distribution of the LGB is expanded along the directions of x, y and z to respectively:
Figure FDA0002366308640000021
Figure FDA0002366308640000022
wherein ,
Figure FDA0002366308640000023
Ex、Ey、Ez and Hx、Hy、HzThe electric field strength and the magnetic field strength in the x, y and z directions respectively.
Converting the expression in the rectangular coordinate system into the expression of each component in the spherical coordinate system:
Figure FDA0002366308640000024
wherein r, theta,
Figure FDA0002366308640000025
Are the coordinates of a spherical coordinate system.
3. The method for calculating the vortex light scattering property of the topological insulating particles according to claim 2, wherein the specific process of the step 2 is as follows:
substituting the radial components of the electric field and the magnetic field in the spherical coordinate system obtained in the step 1 into an integral expression of the beam factor in the transverse magnetic transverse electric mode, as follows:
Figure FDA0002366308640000031
wherein, when m is 0, the normalization factor is compounded
Figure FDA0002366308640000032
When m is not equal to 0, a normalization factor is compounded
Figure FDA0002366308640000033
Substituting the formula (4) into the formula (5), and calculating to obtain a beam factor expression of the LGB incident on the axis by utilizing the orthogonality of the exponential function and the trigonometric function:
Figure FDA0002366308640000034
the beam is incident on the axis, and m is + -1-l.
4. The method for calculating the vortex light scattering property of the topological insulating particles according to claim 3, wherein the specific process of the step 3 is as follows:
let the dielectric constant and permeability of TI sphere and air be respectively epsilon1,μ1 and ε2,μ2(ii) a The radius of the sphere is a; the LGB wave beam enters a TI sphere on the axis, when an incident electromagnetic field is TE (TM) wave, a scattering electric field and a transmission electric field are both TE wave, in a topological insulator, due to magnetoelectric response, the scattering electromagnetic field is cross-polarized, a Laguerre-Gaussian beam enters an incident field of the TI sphere, and the scattering electric field and an internal field of spherical particles are expanded into a vector spherical harmonic function M and a vector spherical harmonic function N:
Figure FDA0002366308640000041
Figure FDA0002366308640000042
Figure FDA0002366308640000043
wherein ,An，BnIs the scattering coefficient of the TI spherical particles, Cn and DnIs the scattering coefficient inside the TI sphere,
Figure FDA0002366308640000044
and
Figure FDA0002366308640000045
is the cross scatter coefficient due to the TME effect of the TI spheres.
5. The method for calculating the vortex light scattering property of the topological insulating particles according to claim 4, wherein the specific process of the step 4 is as follows:
combining the continuous boundary conditions of the electromagnetic field tangential component of the spherical particle surface:
r×(Einc+Esca-Eint)＝0；
Figure FDA0002366308640000046
r＝a,
then according to
Figure FDA0002366308640000047
And
Figure FDA0002366308640000048
is solved with respect to the scattering coefficient an、Bn、Cn、Dn、
Figure FDA0002366308640000049
Figure FDA00023663086400000410
And
Figure FDA00023663086400000411
the linear independent equation of (a) yields the scattering coefficient, specifically:
Figure FDA00023663086400000412
Figure FDA00023663086400000413
wherein ,
Figure FDA00023663086400000414
Figure FDA00023663086400000415
Figure FDA0002366308640000051
Figure FDA0002366308640000052
Figure FDA0002366308640000053
Figure FDA0002366308640000054
wherein ,jn and hnThe first ball Bessel function and the Hankel function are respectively adopted; x is a size parameter;
Figure FDA0002366308640000055
is the relative refractive index of a sphere β1 and β2Is a function of the axis angle α of the spherical particles of the topological insulator, respectively
Figure FDA0002366308640000056
Figure FDA0002366308640000057
When Θ is equal to 0,
Figure FDA0002366308640000058
an、bn、cn and dnWill degrade into the scattering coefficient and sphere internal coefficient of a common dielectric sphere.
6. The method for calculating the vortex light scattering property of the topological insulating particles according to claim 5, wherein the specific process of the step 5 is as follows:
the theta component of the scattering electric field of the Laguerre-Gaussian beam incident on the TI spherical far-field region is obtained according to the following formula
Figure FDA0002366308640000059
And
Figure FDA00023663086400000510
component(s) of
Figure FDA00023663086400000511
Figure FDA00023663086400000512
When in use
Figure FDA00023663086400000513
Degenerates into the scattering field of the ordinary medium sphere to the LGB;
an and bnIs the scattering coefficient of spherical particles for plane waves,
Figure FDA0002366308640000061
and
Figure FDA0002366308640000062
is a function of the angle of scattering,
Figure FDA0002366308640000063
is a first order n-th legendre function of the first kind.
7. The method for calculating the vortex light scattering property of the topological insulating particles according to claim 6, wherein the specific process of the step 6 is as follows:
the scattering efficiency factor Q is obtained by the following formulascaExtinction efficiency factor QextAnd absorption efficiency factor Qabs：
Figure FDA0002366308640000064
Figure FDA0002366308640000065
Qabs＝Qext-Qsca；
Wherein, the lambda is the wavelength,
Figure FDA0002366308640000066
and
Figure FDA0002366308640000067
is the sum of the theta components of the scattered energy density in a spherical coordinate system
Figure FDA0002366308640000068
The components of the first and second images are,
Figure FDA0002366308640000069
and
Figure FDA00023663086400000610
is the theta component under the spherical coordinate system of the incident electric field and the scattered electric field respectively,
Figure FDA00023663086400000611
and
Figure FDA00023663086400000612
respectively under incident electric field and scattered electric field spherical coordinate system
Figure FDA00023663086400000613
The components of the first and second images are,
Figure FDA00023663086400000614
and
Figure FDA00023663086400000615
is the theta component under the spherical coordinate system of the incident magnetic field and the scattered magnetic field respectively,
Figure FDA00023663086400000616
and
Figure FDA00023663086400000617
respectively under incident magnetic field and scattered magnetic field spherical coordinate system
Figure FDA00023663086400000618
And (4) components.
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