CN109948266B - Kerr polarization deflection analysis method based on aged insulator-chiral medium interface - Google Patents

Kerr polarization deflection analysis method based on aged insulator-chiral medium interface Download PDF

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CN109948266B
CN109948266B CN201910226828.1A CN201910226828A CN109948266B CN 109948266 B CN109948266 B CN 109948266B CN 201910226828 A CN201910226828 A CN 201910226828A CN 109948266 B CN109948266 B CN 109948266B
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曾然
张明月
陈芳芳
王驰
胡淼
李浩珍
欧军
李齐良
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Hangzhou Dianzi University
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Abstract

The invention provides a Kerr polarization deflection analysis method based on an aged insulator-chiral medium interface, which comprises the following steps of: s1: establishing a model of an aged insulator-chiral medium interface; s2: determining the electromagnetic characteristics of electromagnetic waves at an insulator-chiral medium interface; s3: determining boundaries and initial conditions; s4: solving a transmission matrix by using the boundary and the initial condition; s5: obtaining the reflection coefficient of the electromagnetic wave from the common medium to the interface of the aged insulator-chiral medium by using a transmission matrix method; s6: the Kerr angle, polarization deflection rate and reflected light phase difference under this model were found. The method can accurately analyze the Kerr polarization deflection characteristic of the aged insulator-chiral medium interface, and can accurately reflect the influence of the incident angle, the chiral characteristic and the CI topological characteristic on the Kerr polarization deflection of the aged insulator-chiral medium interface, so that the polarization deflection of the electromagnetic wave is controlled.

Description

Kerr polarization deflection analysis method based on aged insulator-chiral medium interface
Technical Field
The invention belongs to the technical field of optical information, and particularly relates to a method for solving a reflection coefficient of a surface of a aged insulator-chiral medium by a transmission matrix and analyzing Kerr polarization deflection of the surface of the aged insulator-chiral medium according to a Kerr angle, polarization deflection rate and reflected light phase difference.
Background
Polarization of an electromagnetic wave refers to the manner in which the magnitude and direction of the electromagnetic wave changes over time at any given point in space. The shapes generated according to the trajectory change can be classified as: linearly polarized waves, circularly polarized waves, and elliptically polarized waves. Kerr polarization deflection is the change in polarization state of the reflected wave compared to the incident wave. The devices for generating polarized light generally use optical wave plates, utilize optical path difference and phase difference of optical waves in the devices to generate optical wave delay, and finally synthesize optical waves in different polarization states, and utilize the special properties of novel materials to generate different polarized light, so that the novel materials are more convenient and have great application potential, and become the research hotspots at present, such as nano ferromagnetic specific materials, magnetic plasma crystals, topological insulators, chiral specific materials and the like.
Cross-coupling exists between the electric field and the magnetic field of the chiral metamaterial, so that light is transmitted in the chiral metamaterial and is split into right-handed (RCP) and left-handed (LCP) polarized light with different phase velocities. The topological properties of two-dimensional insulators can be studied by observing the optical properties caused by surface currents. The optical properties of chiral metamaterials have been studied mainly for optical activity, circular dichroism and light transmission, and the optical properties of chiral metamaterials for reflected light and aged insulators have been studied less.
Disclosure of Invention
The invention provides a Kerr polarization deflection analysis method based on an aged insulator-chiral medium interface. The aged insulator and the chiral medium are closer to the actual theoretical models of the aged insulator and the chiral medium, and have application value when being used as test models; meanwhile, a new way is provided for controlling Kerr polarization deflection, and an optical method is provided for analyzing polarization properties.
In order to achieve the purpose of the invention, the invention adopts the following technical scheme:
the Kerr polarization deflection analysis method based on the aged insulator-chiral medium interface utilizes a transmission matrix to obtain the reflection coefficient of the aged insulator-chiral medium interface, and then analyzes the Kerr polarization deflection of the aged insulator-chiral medium interface according to the polarization deflection rate, and comprises the following steps:
s1: and establishing a model of the aged insulator-chiral medium interface.
Light propagating along the Z-axis from the medium (. Epsilon.) 1 ,μ 1 ) Oblique incidence CI-CMM (ε) 2 ,μ 2 κ) interface xoy plane, ∈ 1 、ε 2 Is dielectric constant, mu 1 、μ 2 For permeability, κ is a chiral parameter. The insulator (called "corner insulator" for short, CI) is a two-dimensional interface, and the medium and the Chiral meta-material (called "CMM") are semi-infinite interfaces.
S2: the electromagnetic properties of the electromagnetic wave at the surface of the aged insulator-chiral material interface are determined.
The electromagnetic properties of the obtained electromagnetic wave at the interface of the aged insulator-chiral material are as follows: the effect of CI on light is described by the area current: j is a unit of s ＝4πσ s E/c. c is the vacuum speed of light, σ s Surface conductivity in the x0y plane:
Figure GDA0004027267000000021
/>
the CI and CMM in the model are lossless and transparent, the electromagnetic wave is in a time harmonic field, and the constitutive equation of the chiral specific material is as follows:
D＝ε 2 E+iκH (2)
B＝μ 2 H-iκE (3)
s3: boundaries and initial conditions are determined.
Dielectric (ε) 1 ,μ 1 ) The components of the electric and magnetic fields of medium incidence and reflection are:
Figure GDA0004027267000000022
Figure GDA0004027267000000023
Figure GDA0004027267000000031
Figure GDA0004027267000000032
CMM(ε 2 ,μ 2 κ) the transmitted electric and magnetic field components are:
Figure GDA0004027267000000033
Figure GDA0004027267000000034
Figure GDA0004027267000000035
Figure GDA0004027267000000036
the wavevectors of the incident, reflected and transmitted light are:
Figure GDA0004027267000000037
wherein
Figure GDA0004027267000000038
Beta is the angle of incidence, gamma ± Two transmission angles. The electric field of linearly polarized light is divided into perpendicular (subscript s) and parallel (subscript p) components. Subscripts-, + in the CMM denote the LCP and RCP light, respectively, that transmit light.
The above expression is an initial condition, and the boundary conditions are: n × H = J s And n × E =0. The electric field components in the perpendicular and parallel directions being equal, i.e. taken separately
Figure GDA0004027267000000039
S4: the transmission matrix is obtained by using the boundary and the initial condition.
According to the CMM modified constitutive equations (2) and (3) modified Maxwell equation and boundary conditions: n × H = J s And n × E =0, a transmission matrix (13) is obtained.
Figure GDA00040272670000000310
S5: and (3) calculating the reflection coefficient of the electromagnetic wave incident to the interface of the aged insulator-chiral medium from the common medium by using a transmission matrix method.
The reflection and transmission coefficients are obtained from the relationship between the incident light and the reflected and transmitted light, as shown in equations (14) and (15).
Figure GDA0004027267000000041
Figure GDA0004027267000000042
Wherein χ = m 11 m 22 -m 12 m 21 And further modifying the transmission coefficient to obtain a left-handed transmission coefficient and a right-handed transmission coefficient, wherein RCP:
Figure GDA0004027267000000043
LCP：/>
Figure GDA0004027267000000044
other transmission coefficients do not change to
Figure GDA0004027267000000045
Calculating by using a transmission matrix method, wherein the obtained Fresnel coefficients of the reflected light and the transmitted light of the RCP and the LCP are as follows:
Figure GDA0004027267000000046
Figure GDA0004027267000000047
Figure GDA0004027267000000048
Figure GDA0004027267000000049
wherein
Figure GDA00040272670000000410
In the formula
Figure GDA0004027267000000051
r i,j Is a reflection coefficient>
Figure GDA0004027267000000052
The transmission coefficients of RCP and LCP, respectively, where i represents the polarization state of reflected or transmitted light and j represents the polarization state of incident light, and may be s (perpendicular) or p (parallel). />
S6: the Kerr angle, polarization deflection rate and reflected light phase difference under this model were obtained.
The angle between the polarization of the reflected wave and the polarization of the incident wave is called the Kerr angle. Assuming that the incident wave is a TE wave, according to the model of fig. 2, the Kerr angle is the included angle between the polarization state direction of the reflected wave and the y-axis, i.e. the tangent value of the Kerr angle when the incident wave is a TE wave is:
Figure GDA0004027267000000053
similarly, the tangent of the Kerr angle when the incident wave is a TM wave is:
Figure GDA0004027267000000054
the reflected electric field component can again be described as:
Figure GDA0004027267000000055
the phase difference is:
Figure GDA0004027267000000056
when TE polarized light is incident, the polarization deflection rate is:
Figure GDA0004027267000000057
and (5) substituting the calculation results of S4 and S5 into (21), (22), (23) and (24) to obtain the Kerr angle, the polarization deflection rate and the reflected light phase difference, thereby analyzing the Kerr polarization deflection characteristic of the interface of the aged insulator-chiral medium.
Compared with the prior art, the invention has the following beneficial effects:
1. the Kerr polarization deflection method for the aged insulator-chiral medium interface can accurately analyze the Kerr polarization deflection characteristic of the aged insulator-chiral medium interface according to the Kerr polarization deflection method for analyzing the aged insulator-chiral medium interface according to the polarization deflection rate.
2. The method can accurately reflect the influence of the chiral characteristic and the CI topological characteristic on Kerr polarization deflection of the Chen insulator-chiral medium interface.
3. The method can accurately reflect the influence of the incident angle on Kerr polarization deflection of the aged insulator-chiral medium interface.
Drawings
FIG. 1 is an analytical flow chart of the present invention.
FIG. 2 is a schematic diagram of an insulator-chiral media interface model according to the present invention.
FIG. 3 is a schematic diagram of system input and output.
FIG. 4 (a) is a simulation graph of the variation curve of the vertical reflectivity with the incident angle when TE polarized light is incident into the CMM under different chiral parameters;
FIG. 4 (b) is a simulation graph of the change curve of the parallel reflectivity with the incident angle when TE polarized light is incident into the CMM under different chiral parameters;
FIG. 4 (c) is a simulation graph of the variation curve of the PCR value with the incident angle when TE polarized light is incident into the CMM under different chiral parameters;
FIG. 4 (d) is a simulation graph of the variation curve of the phase difference of the reflected light with the incident angle when TE polarized light is incident into the CMM under different chiral parameters;
FIG. 5 (a) is a simulation diagram of the variation curve of the vertical reflectivity with the incident angle when TE polarized light is incident into the CI interface with k =0 at different frequencies;
FIG. 5 (b) is a simulation diagram of the parallel reflectance curve with the incident angle when TE polarized light is incident into the CI interface with κ =0 at different frequencies;
FIG. 5 (c) is a simulation diagram of the variation curve of PCR value with the incident angle when TE polarized light is incident into the CI interface with k =0 at different frequencies;
FIG. 5 (d) is a simulation diagram of the variation curve of the phase difference of the reflected light with the incident angle when TE polarized light is incident into the CI interface with k =0 at different frequencies;
FIG. 6 (a) is a simulation graph of the vertical reflectivity as a function of the incident angle when TE polarized light with different display numbers is incident on the CI and CMM interfaces with kappa =1.3;
FIG. 6 (b) is a simulation graph of the parallel reflectance with the incident angle when TE polarized light with different display numbers is incident on the CI and CMM interfaces with k =1.3;
FIG. 6 (c) is a simulation graph of the variation curve of the PCR value with the incidence angle when TE polarized light is incident into the CI and CMM interfaces with k =1.3 at different ages;
fig. 6 (d) is a simulation diagram of the variation of the phase difference of the reflected light with the incidence angle when TE polarized light is incident on the CI and CMM interfaces with k =1.3 at different display numbers.
Detailed Description
The following describes embodiments of the present invention in detail with reference to the accompanying drawings.
FIG. 1 is an analytical flow chart of the present invention. The method comprises the steps of calculating a reflection coefficient of an aged insulator-chiral medium interface by using a transmission matrix, and analyzing Kerr polarization deflection of the aged insulator-chiral medium interface according to a Kerr angle, a polarization deflection rate and a reflected light phase difference, wherein the method comprises the following steps:
s1: and (3) establishing a model of the aged insulator-chiral medium interface, wherein the space of the negative half axis of the z axis is vacuum, and the space of the positive half axis of the z axis is aged insulator and chiral medium material as shown in FIG. 2.
Light propagating along the Z-axis from the medium (. Epsilon.) 1 ,μ 1 ) Oblique incidence CI-CMM (ε) 2 ,μ 2 κ) interface xoy plane,. Epsilon 1 、ε 2 Is dielectric constant, mu 1 、μ 2 Is the permeability and κ is a chiral parameter. The insulator (called "corner insulator" for short, CI) is a two-dimensional interface, and the medium and the Chiral meta-material (called "CMM") are semi-infinite interfaces.
S2: the electromagnetic properties of the electromagnetic wave at the surface of the aged insulator-chiral material interface are determined.
The electromagnetic properties of the obtained electromagnetic wave at the interface of the aged insulator-chiral material are as follows: the effect of CI on light is described by the area current: j. the design is a square s ＝4πσ s E/c. c is the vacuum speed of light, σ s Surface conductivity in the x0y plane:
Figure GDA0004027267000000081
the CI and CMM in the model are lossless and transparent, the electromagnetic wave is in a time harmonic field, and the constitutive equation of the chiral specific material is as follows:
D＝ε 2 E+iκH (2)
B＝μ 2 H-iκE。 (3)
s3: boundaries and initial conditions are determined.
Dielectric (ε) 1 ,μ 1 ) The medium incident, reflected electric and magnetic field components are:
Figure GDA0004027267000000082
Figure GDA0004027267000000083
Figure GDA0004027267000000084
Figure GDA0004027267000000085
CMM(ε 2 ,μ 2 κ) the transmitted electric and magnetic field components are:
Figure GDA0004027267000000086
Figure GDA0004027267000000087
Figure GDA0004027267000000088
Figure GDA0004027267000000089
the wavevectors of the incident, reflected and transmitted light are:
Figure GDA00040272670000000810
wherein
Figure GDA00040272670000000811
Beta is the angle of incidence, gamma ± Two transmission angles. The electric field of linearly polarized light is divided into perpendicular (subscript s) and parallel (subscript p) components. Subscripts-, + in the CMM denote the LCP and RCP light, respectively, that transmits light.
The above expression is an initial condition, and the boundary conditions are: n × H = J s And n × E =0. The electric field components in the perpendicular and parallel directions being equal, i.e. taken separately
Figure GDA0004027267000000091
S4: the transmission matrix is obtained by using the boundary and the initial condition.
According to the CMM modified constitutive equations (2) and (3) modified Maxwell equation and boundary conditions: n × H = J s And n × E =0, a transmission matrix (13) is obtained.
Figure GDA0004027267000000092
S5: and (3) calculating the reflection coefficient of the electromagnetic wave incident to the interface of the aged insulator-chiral medium from the common medium by using a transmission matrix method.
The reflection and transmission coefficients are obtained from the relationship between the incident light and the reflected and transmitted light, as shown in equations (14) and (15).
Figure GDA0004027267000000093
Figure GDA0004027267000000094
Wherein χ = m 11 m 22 -m 12 m 21 And further modifying the transmission coefficient to obtain a left-handed transmission coefficient and a right-handed transmission coefficient, wherein RCP:
Figure GDA0004027267000000095
LCP：/>
Figure GDA0004027267000000096
other transmission coefficients do not change to
Figure GDA0004027267000000097
Calculating by using a transmission matrix method, wherein the obtained Fresnel coefficients of the reflected light and the transmitted light of the RCP and the LCP are as follows:
Figure GDA0004027267000000101
Figure GDA0004027267000000102
Figure GDA0004027267000000103
Figure GDA0004027267000000104
wherein
Figure GDA0004027267000000105
In the formula
Figure GDA0004027267000000106
r i,j Is a reflection coefficient>
Figure GDA0004027267000000107
The transmission coefficients of RCP and LCP, respectively, where i represents the polarization state of reflected or transmitted light and j represents the polarization state of incident light, and may be s (perpendicular) or p (parallel).
S6: the Kerr angle, polarization deflection rate and reflected light phase difference under this model were obtained.
The angle between the polarization of the reflected wave and the polarization of the incident wave is called the Kerr angle. Assuming that the incident wave is a TE wave, according to the model of fig. 2, the Kerr angle is the included angle between the polarization state direction of the reflected wave and the y-axis, i.e. the tangent value of the Kerr angle when the incident wave is a TE wave is:
Figure GDA0004027267000000111
similarly, the tangent of the Kerr angle when the incident wave is a TM wave is:
Figure GDA0004027267000000112
the reflected electric field component can again be described as:
Figure GDA0004027267000000113
the phase difference is:
Figure GDA0004027267000000114
when TE polarized light is incident, the polarization deflection rate is:
Figure GDA0004027267000000115
and (5) substituting the calculation results of S4 and S5 into (21), (22), (23) and (24) to obtain a Kerr angle, a polarization deflection rate and a reflected light phase difference, thereby analyzing the Kerr polarization deflection characteristic of the aged insulator-chiral medium interface.
In this embodiment, as shown in fig. 3: the chiral coefficients are input at the A port, the dependent parameters of the aged insulator, such as frequency and aged number, are input at the B port, and the incident angle is input at the C port. The vertical reflectivity and the parallel reflectivity are output at the D port, the PCR value is output at the E port, and the reflected light phase difference is output at the F port. By selecting the permutation and combination of the input ports and different values, specific polarization deflection characteristics under different conditions can be obtained, and then the needed polarization deflection is selected according to actual conditions, so that the method has flexibility and practicability.
The vertical reflectance, parallel reflectance, PCR, and reflected light phase difference are shown in fig. 4 (a) -4 (d) in consideration of the influence of the chiral property alone on the Kerr polarization deflection. The vertical reflectance, parallel reflectance, PCR, and reflected light phase difference are shown in fig. 5 (a) -5 (d) considering only the effect of CI topology on Kerr polarization deflection.
Assume that the chiral parameter κ =1.3 is input at the a port; inputting a count C =0, C =1, C =3, and C =5 at a B port; input at C portThe angle of incidence beta ranges from 0 to pi/2. The vertical reflectance and the parallel reflectance were obtained at the D port, the PCR value was obtained at the E port, and the reflected light phase difference was obtained at the F port, and the change curves of the vertical reflectance, the parallel reflectance, the PCR, and the reflected light phase difference with the incident angle are shown in fig. 6 (a) -6 (D). This scenario considers the combined effects of the chiral nature and the CI topological nature. When the normal incidence is carried out on the CI-CMM surface with the chiral parameter and the display number being not 0, the larger the display number is, the larger the value is, | r ss | 2 The larger the PCR, the smaller the PCR. C =0, the reflected light cannot achieve full polarization deflection, and in this case, the reflected light is elliptically polarized light when the incident angle is on the left of the critical angle. With C =1, PCR can take 1,ci to change the angle of polarization of the plane of polarization of the reflected light as well as the polarization mode.
The method for analyzing the Kerr polarization deflection of the aged insulator-chiral medium interface according to the Kerr angle, the polarization deflection rate and the reflected light phase difference can accurately analyze the Kerr polarization deflection characteristic of the aged insulator-chiral medium interface, and can accurately reflect the influence of the incident angle, the chiral characteristic and the CI topological characteristic on the Kerr polarization deflection of the aged insulator-chiral medium interface, so that the polarization deflection of electromagnetic waves is controlled.
While the preferred embodiments and principles of this invention have been described in detail, it will be apparent to those skilled in the art that variations may be made in the embodiments based on the teachings of the invention and such variations are considered to be within the scope of the invention.

Claims (7)

1. The Kerr polarization deflection analysis method based on the aged insulator-chiral medium interface is characterized by comprising the following steps of: the method comprises the following steps:
s1: establishing a model of an aged insulator-chiral medium interface;
s2: determining the electromagnetic characteristics of the electromagnetic waves at the surface of the aged insulator-chiral medium;
s3: determining boundaries and initial conditions;
s4: solving a transmission matrix by using the boundary and the initial condition;
s5: obtaining the reflection coefficient of the electromagnetic wave from the common medium to the interface of the aged insulator-chiral medium by using a transmission matrix method;
s6: and solving the Kerr angle, the polarization deflection rate and the reflected light phase difference under the aged insulator-chiral medium interface model.
2. The assay of claim 1, wherein:
the insulator is denoted by CI, the medium and the chiral metamaterial by CMM,
the step S1 is specifically as follows:
light propagating along the Z-axis from the medium (. Epsilon.) 1 ,μ 1 ) Oblique incidence CI-CMM (ε) 2 ,μ 2 κ) interface xoy plane, ∈ 1 、ε 2 Is dielectric constant, mu 1 、μ 2 Is the magnetic permeability, and κ is the chiral parameter; CI is a two-dimensional interface and CMM is a semi-infinite interface.
3. The analytical method of claim 2, wherein:
step S2 is specifically as follows:
the effect of CI on light is described in terms of area current: j. the design is a square s ＝4πσ s E/c, c is the vacuum speed of light, σ s Surface conductivity in the x0y plane:
Figure FDA0003929834910000011
the CI and CMM in the model are lossless and transparent, the electromagnetic wave is in a time harmonic field, and the constitutive equation of the chiral specific material is as follows:
D＝ε 2 E+iκH (2)
B＝μ 2 H-iκE (3)。
4. the method of claim 3, wherein: step S3 is specifically as follows:
the initial conditions were:
dielectric substance (. Epsilon.) 1 ,μ 1 ) The components of the electric and magnetic fields of medium incidence and reflection are:
Figure FDA0003929834910000021
Figure FDA0003929834910000022
Figure FDA0003929834910000023
Figure FDA0003929834910000024
CMM(ε 2 ,μ 2 and κ) the electric and magnetic field components transmitted are:
Figure FDA0003929834910000025
Figure FDA0003929834910000026
/>
Figure FDA0003929834910000027
Figure FDA0003929834910000028
the wavevectors of the incident, reflected and transmitted light are:
Figure FDA0003929834910000029
wherein
Figure FDA00039298349100000210
Beta is the angle of incidence, gamma ± Two transmission angles; the electric field of the linearly polarized light is divided into perpendicular and parallel components; subscripts-, + in the CMM denote the LCP and RCP light, respectively, that transmit light;
the boundary conditions are as follows: n × H = J s And n × E =0;
the electric field components in the perpendicular and parallel directions being equal, i.e. taken separately
Figure FDA00039298349100000211
Figure FDA0003929834910000031
5. The method of claim 4, wherein step S4 is embodied as follows:
according to the CMM modified constitutive equations (2) and (3) modified Maxwell equation and boundary conditions: n × H = J s And n × E =0, and finds a transmission matrix (13):
Figure FDA0003929834910000032
6. the method of claim 5, wherein step S5 is embodied as follows:
from the relationship between the incident light and the reflected and transmitted light, the reflection and transmission coefficients are obtained as shown in equations (14) and (15):
Figure FDA0003929834910000033
Figure FDA0003929834910000034
wherein χ = m 11 m 22 -m 12 m 21 And further modifying the transmission coefficient to obtain a left-handed transmission coefficient and a right-handed transmission coefficient, wherein RCP:
Figure FDA0003929834910000035
LCP：/>
Figure FDA0003929834910000036
7. the method according to claim 6, wherein step S6 is as follows:
let the incident wave be TE wave, the Kerr angle be the included angle between the polarization direction of the reflected wave and the y-axis, i.e. the tangent value of Kerr angle when the incident wave is TE wave is:
Figure FDA0003929834910000037
the tangent of the Kerr angle when the incident wave is a TM wave is:
Figure FDA0003929834910000041
the reflected electric field component is described as:
Figure FDA0003929834910000042
wherein the phase difference is:
Figure FDA0003929834910000043
when TE polarized light enters, the polarization deflection rate is as follows:
Figure FDA0003929834910000044
and (5) substituting the calculation results of the steps S4 and S5 into the steps (16), (17), (18) and (19) to obtain a Kerr angle, a polarization deflection rate and a reflected light phase difference so as to analyze the Kerr polarization deflection characteristic of the aged insulator-chiral medium interface.
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