CN109948266A - Based on old insulator-chiral soliton interface Kerr polarization rotation analysis method - Google Patents
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Abstract
The present invention proposes a kind of based on old insulator-chiral soliton interface Kerr polarization rotation analysis method, carries out as follows: S1: establishing old insulator-chiral soliton interface model；S2: determine electromagnetic wave in old insulator-chiral soliton interface electromagnetic property；S3: boundary and primary condition are determined；S4: transmission matrix is acquired using boundary and primary condition；S5: electromagnetic wave is acquired using transfer matrix method and is incident on old insulator-chiral soliton interface reflection coefficient from generic media；S6: ask the angle Kerr under this model, polarization rotation rate and reflective phase poor.The method of the invention, old insulator-chiral soliton interface Kerr polarization rotation characteristic can accurately be analyzed, it can accurately reflect the influence of incidence angle, chirality and CI topological property to old insulator-chiral soliton interface Kerr polarization rotation, to control polarization of electromagnetic wave deflection.
Description
Technical field
The invention belongs to optical information technology fields, and in particular to a kind of transmission matrix seeks old insulator-chiral soliton circle
Face reflection coefficient analyses old insulator-chiral soliton interface further according to the angle Kerr, polarization rotation rate and reflective phase difference
The method of Kerr polarization rotation.
Background technique
Polarization of electromagnetic wave refers to the mode that the size and Orientation of the electromagnetic wave on any given point in space changes over time.
It can be divided into according to the shape that trail change generates: line polarization wave, circularly polarised wave and elliptically polarised wave.Kerr polarization rotation is
Change of the back wave compared to the polarized state of incidence wave.Generate polarised light device generally use wave plate, using optical path difference with
And the phase difference of light wave generates light wave delay, the final light wave for synthesizing different polarization states in device, and utilize new material
Different polarization light is more convenient, has huge application potential generating for special nature, so new material becomes present research
Hot spot, such as nanometer ferromagnetism metamaterials, magnetic plasma crystal, topological insulator, chiral metamaterials etc..
There are cross-couplings between chiral metamaterials electric and magnetic fields, therefore light transmits difference in chiral metamaterials
Can split into different phase velocities dextrorotation (RCP) and left-handed (LCP) polarised light.The topological property of the old insulator of two dimension, Ke Yitong
Optical characteristics caused by observation surface current is crossed to study.Have at present main to the research of the optical characteristics of chiral metamaterials
It is optical activity and circular dichroism and transmission light characteristic, chiral metamaterials reflected light and old insulator optical property is ground
Study carefully less.
Summary of the invention
The present invention provides a kind of based on old insulator-chiral soliton interface Kerr polarization rotation analysis method.This hair
Bright old insulator and chiral soliton are comparatively close to the theoretical model of actual old insulator and chiral soliton, as test mould
Type relatively has application value；New way is provided for control Kerr polarization rotation simultaneously, provides one kind for analysis polarization property
Optical means.
In order to reach the purpose of the present invention, the present invention is adopted the following technical scheme that:
Based on old insulator-chiral soliton interface Kerr polarization rotation analysis method, sought using transmission matrix old exhausted
Edge body-chiral soliton interface reflection coefficients analyzes old insulator-chiral soliton interface Kerr polarization further according to polarization rotation rate
Deflection carries out as follows:
S1: old insulator-chiral soliton interface model is established.
The light propagated along Z axis is from medium (ε1,μ1) oblique it is mapped to CI-CMM (ε2,μ2, κ) and interface xoy plane, ε1、ε2For
Dielectric constant, μ1、μ2For magnetic conductivity, κ is chiral parameter.Old insulator (Chern insulator, be abbreviated as CI), is two-dimentional boundary
Face, medium and chiral metamaterials (Chiral metamaterial, be abbreviated as CMM) are all semo-infinite interfaces.
S2: determine electromagnetic wave in old insulator-chiral material interface electromagnetic property.
Obtained electromagnetic wave is as follows in old insulator-chiral material interface electromagnetic property: influence face of the CI for light
Electric current description: Js=4 π σsE/c.C is vacuum light speed, σsFor the surface conductivity in x0y plane:
CI and CMM is lossless and transparent in model, humorous field when electromagnetic wave is, chiral metamaterials constitutive equation
Are as follows:
D=ε2E+iκH (2)
B=μ2H-iκE (3)
S3: boundary and primary condition are determined.
Dielectric (ε1,μ1) in incident, reflection electric and magnetic fields component are as follows:
CMM(ε2,μ2, κ) in transmit electric and magnetic fields component are as follows:
The wave vector of incident, reflection and transmitted light is respectively as follows:
Whereinβ is
Incidence angle, γ±For two angle of transmission.The electric field of linearly polarized photon is divided into vertical (subscript s) and parallel (subscript p) component.In CMM
Subscript-,+respectively indicate the LCP and RCP light of transmitted light.
The above expression formula is primary condition, boundary condition are as follows: n × H=JsWith n × E=0.The electricity in vertical and parallel direction
Field component is equal, i.e., takes respectively
S4: transmission matrix is acquired using boundary and primary condition.
According to the revised constitutive equation of CMM (2) and (3) modified Maxwell equation and boundary condition: n × H=Js
With n × E=0, transmission matrix (13) are acquired.
S5: acquiring electromagnetic wave using transfer matrix method, from generic media to be incident on old insulator-chiral soliton interface anti-
Penetrate coefficient.
According to the relationship between incident light and reflection and transmitted light, obtain reflection and transmission coefficients, such as formula (14) and
(15) shown in.
Wherein χ=m11m22-m12m21, transmission coefficient is further modified and obtains left-handed and right-handed transmissive coefficient, RCP:LCP:Other transmission coefficients do not become
It is calculated using transfer matrix method, the Fresnel coefficient of obtained reflected light and RCP, LCP transmitted light are as follows:
Wherein
In formulari,jFor reflection coefficient,Respectively RCP and LCP transmission coefficient,
Middle i represents reflection or transmission polarization state, j represent incident light polarization state, can use s (vertical) or p (parallel).
S6: it is poor that the angle Kerr under this model, polarization rotation rate and reflective phase are acquired.
The angle in back wave polarization state direction and incidence wave polarization state direction is known as the angle Kerr.Assuming that incidence wave is TE wave,
Model according to fig. 2, the angle Kerr are back wave polarization state direction and y-axis angle, i.e., Kerr tangent of an angle value when incidence wave is TE wave
Are as follows:
Similarly, Kerr tangent of an angle value when incidence wave is TM wave are as follows:
Reflected field component can be described as again:Its phase difference are as follows:
When TE polarised light incidence, polarization rotation rate are as follows:
By the calculated result of S4, S5, substitution (21), (22), (23), (24) can be obtained by the angle Kerr, polarization rotation rate
It is poor with reflective phase, to analyze old insulator-chiral soliton interface Kerr polarization rotation characteristic.
Compared with the prior art, the invention has the following beneficial effects:
1, the method that the present invention analyzes old insulator-chiral soliton interface Kerr polarization rotation according to polarization rotation rate,
Old insulator-chiral soliton interface Kerr polarization rotation characteristic can accurately be analyzed.
2, the present invention can accurately reflect chirality and CI topological property to old insulator-chiral soliton interface
The influence of Kerr polarization rotation.
3, the present invention can accurately reflect incidence angle to old insulator-chiral soliton interface Kerr polarization rotation
It influences.
Detailed description of the invention
Fig. 1 is analysis flow chart diagram of the invention.
Fig. 2 is old insulator-chiral soliton INTERFACE MODEL schematic diagram in the present invention.
Fig. 3 is system input and output schematic diagram.
Fig. 4 (a) is that TE polarised light is incident in CMM when taking different chiral parameters, vertical reflectivity with incidence angle variation
Curve analogous diagram；
Fig. 4 (b) is that TE polarised light is incident in CMM when taking different chiral parameters, reflected in parallel rate with incidence angle variation
Curve analogous diagram；
Fig. 4 (c) is that TE polarised light is incident in CMM when taking different chiral parameters, and PCR value is imitative with the change curve of incidence angle
True figure；
Fig. 4 (d) is that TE polarised light is incident in CMM when taking different chiral parameters, reflective phase difference with incidence angle change
Change curve analogous diagram；
Fig. 5 (a) is that TE polarised light is incident in the CI interface of κ=0 when taking different frequency, and vertical reflectivity is with incidence angle
Change curve analogous diagram；
Fig. 5 (b) is that TE polarised light is incident in the CI interface of κ=0 when taking different frequency, and reflected in parallel rate is with incidence angle
Change curve analogous diagram；
Fig. 5 (c) is that TE polarised light is incident in the CI interface of κ=0 when taking different frequency, PCR value with incidence angle change
Change curve analogous diagram；
Fig. 5 (d) is that TE polarised light is incident in the CI interface of κ=0 when taking different frequency, and reflective phase difference is with incidence
The change curve analogous diagram at angle；
Fig. 6 (a) is that TE polarised light is incident in CI the and CMM interface of κ=1.3 when taking different old several, vertical reflectivity
With the change curve analogous diagram of incidence angle；
Fig. 6 (b) is that TE polarised light is incident in CI the and CMM interface of κ=1.3 when taking different old several, reflected in parallel rate
With the change curve analogous diagram of incidence angle；
Fig. 6 (c) is that TE polarised light is incident in CI the and CMM interface of κ=1.3 when taking different old several, and PCR value is with incidence
The change curve analogous diagram at angle；
Fig. 6 (d) is that TE polarised light is incident in CI the and CMM interface of κ=1.3 when taking different old several, reflective phase
Difference with incidence angle change curve analogous diagram.
Specific embodiment
It elaborates with reference to the accompanying drawing to the embodiment of the present invention.
Fig. 1 is analysis flow chart diagram of the invention.Old insulator-chiral soliton interface reflection system is sought using transmission matrix
It is inclined to analyse old insulator-chiral soliton interface Kerr polarization further according to the angle Kerr, polarization rotation rate and reflective phase difference for number
The method turned, the method carry out as follows:
S1: establishing old insulator-chiral soliton interface model, as shown in Fig. 2, the space where the negative semiaxis of z-axis is true
Sky, the space where z positive axis are old insulator and chiral soliton material.
The light propagated along Z axis is from medium (ε1,μ1) oblique it is mapped to CI-CMM (ε2,μ2, κ) and interface xoy plane, ε1、ε2For
Dielectric constant, μ1、μ2For magnetic conductivity, κ is chiral parameter.Old insulator (Chern insulator, be abbreviated as CI), is two-dimentional boundary
Face, medium and chiral metamaterials (Chiral metamaterial, be abbreviated as CMM) are all semo-infinite interfaces.
S2: determine electromagnetic wave in old insulator-chiral material interface electromagnetic property.
Obtained electromagnetic wave is as follows in old insulator-chiral material interface electromagnetic property: influence face of the CI for light
Electric current description: Js=4 π σsE/c.C is vacuum light speed, σsFor the surface conductivity in x0y plane:
CI and CMM is lossless and transparent in model, humorous field when electromagnetic wave is, chiral metamaterials constitutive equation
Are as follows:
D=ε2E+iκH (2)
B=μ2H-iκE。 (3)
S3: boundary and primary condition are determined.
Dielectric (ε1,μ1) in incident, reflection electric and magnetic fields component are as follows:
CMM(ε2,μ2, κ) in transmit electric and magnetic fields component are as follows:
The wave vector of incident, reflection and transmitted light is respectively as follows:
Whereinβ is
Incidence angle, γ±For two angle of transmission.The electric field of linearly polarized photon is divided into vertical (subscript s) and parallel (subscript p) component.In CMM
Subscript-,+respectively indicate the LCP and RCP light of transmitted light.
The above expression formula is primary condition, boundary condition are as follows: n × H=JsWith n × E=0.The electricity in vertical and parallel direction
Field component is equal, i.e., takes respectively
S4: transmission matrix is acquired using boundary and primary condition.
According to the revised constitutive equation of CMM (2) and (3) modified Maxwell equation and boundary condition: n × H=Js
With n × E=0, transmission matrix (13) are acquired.
S5: acquiring electromagnetic wave using transfer matrix method, from generic media to be incident on old insulator-chiral soliton interface anti-
Penetrate coefficient.
According to the relationship between incident light and reflection and transmitted light, obtain reflection and transmission coefficients, such as formula (14) and
(15) shown in.
Wherein χ=m11m22-m12m21, transmission coefficient is further modified and obtains left-handed and right-handed transmissive coefficient, RCP:LCP:Other transmission coefficients do not become
It is calculated using transfer matrix method, the Fresnel coefficient of obtained reflected light and RCP, LCP transmitted light are as follows:
Wherein
In formulari,jFor reflection coefficient,Respectively RCP and LCP transmission coefficient,
Middle i represents reflection or transmission polarization state, j represent incident light polarization state, can use s (vertical) or p (parallel).
S6: it is poor that the angle Kerr under this model, polarization rotation rate and reflective phase are acquired.
The angle in back wave polarization state direction and incidence wave polarization state direction is known as the angle Kerr.Assuming that incidence wave is TE wave,
Model according to fig. 2, the angle Kerr are back wave polarization state direction and y-axis angle, i.e., Kerr tangent of an angle value when incidence wave is TE wave
Are as follows:
Similarly, Kerr tangent of an angle value when incidence wave is TM wave are as follows:
Reflected field component can be described as again:Its phase difference are as follows:
When TE polarised light incidence, polarization rotation rate are as follows:
By the calculated result of S4, S5, substitution (21), (22), (23), (24) can be obtained by the angle Kerr, polarization rotation rate
It is poor with reflective phase, to analyze old insulator-chiral soliton interface Kerr polarization rotation characteristic.
In the present embodiment, as shown in Figure 3: inputting chiral coefficient in the port A, input old insulator correlation ginseng in the port B
Number, such as frequency, old number input incidence angle in C port.Vertical reflectivity and parallel reflectivity are exported in the port D, it is defeated in the port E
PCR value out, in the port F, output reflection light phase is poor.By the permutation and combination and different values that select input port, so that it may
The specific polarization rotation characteristic under different situations is obtained, then selects the polarization rotation needed according to the actual situation, is had flexible
Property and practicability.
Under the influence of only considering chirality to Kerr polarization rotation, vertical reflectivity, reflected in parallel rate, PCR, reflection
Shown in light phase difference such as Fig. 4 (a) -4 (d).It is vertical to reflect under the influence of only considering CI topological property to Kerr polarization rotation
Shown in rate, reflected in parallel rate, PCR, reflective phase difference such as Fig. 5 (a) -5 (d).
Assuming that inputting chiral parameter κ=1.3 in the port A；Old several C=0, C=1, C=3, C=5 are inputted in the port B；In C
Port inputs 0-pi/2 of incident angle β range.Vertical reflectivity and parallel reflectivity are obtained in the port D, obtains PCR value in the port E,
Obtain that reflective phase is poor in the port F, vertical reflectivity, reflected in parallel rate, PCR, reflective phase difference with incidence angle variation
Shown in curve such as Fig. 6 (a) -6 (d).This scene is the combined influence for considering chirality and CI topological property.Vertical incidence is in one's hands
When sign parameter and old number are not 0 surface CI-CMM, old number is bigger, | rss|2Bigger, PCR is smaller.When C=0, reflected light cannot
Realize perfact polarization deflection, for incidence angle value in the case where the critical angle left side, reflected light is elliptically polarized light at this time.C=1
When, PCR can get 1, CI and change reflected light plane of polarization deflection angle and polarization mode.
The present invention analyses old insulator-chiral soliton interface according to the angle Kerr, polarization rotation rate and reflective phase difference
The method of Kerr polarization rotation can accurately analyze old insulator-chiral soliton interface Kerr polarization rotation characteristic, Neng Gouzhun
Really reflect incidence angle, chirality and CI topological property to old insulator-chiral soliton interface Kerr polarization rotation
It influences, to control polarization of electromagnetic wave deflection.
The preferred embodiment of the present invention and principle are described in detail above, to those skilled in the art
Speech, the thought provided according to the present invention will change in specific embodiment, and these changes also should be regarded as the present invention
Protection scope.
Claims (7)
1. based on old insulator-chiral soliton interface Kerr polarization rotation analysis method, it is characterised in that: as follows into
Row:
S1: old insulator-chiral soliton interface model is established；
S2: determine electromagnetic wave in old insulator-chiral soliton interface electromagnetic property；
S3: boundary and primary condition are determined；
S4: transmission matrix is acquired using boundary and primary condition；
S5: electromagnetic wave is acquired using transfer matrix method and is incident on old insulator-chiral soliton interface reflection system from generic media
Number；
S6: it is poor that the angle Kerr under old insulator-chiral soliton INTERFACE MODEL, polarization rotation rate and reflective phase are solved.
2. analysis method as described in claim 1, it is characterised in that:
Old insulator indicates that medium and chiral metamaterials are indicated with CMM with CI,
Step S1 is specific as follows:
The light propagated along Z axis is from medium (ε1,μ1) oblique it is mapped to CI-CMM (ε2,μ2, κ) and interface xoy plane, ε1、ε2For dielectric
Constant, μ1、μ2For magnetic conductivity, κ is chiral parameter；CI is two-dimentional interface, and CMM is semo-infinite interface.
3. analysis method as claimed in claim 2, it is characterised in that:
Step S2 is specific as follows:
Influence of the CI for light is described with surface current: Js=4 π σsE/c, c are vacuum light speed, σsFor the surface conductance in x0y plane
Rate:
CI and CMM is lossless and transparent in model, humorous field when electromagnetic wave is, chiral metamaterials constitutive equation are as follows:
D=ε2E+iκH (2)
B=μ2H-iκE。 (3)
4. method as claimed in claim 3, it is characterised in that: step S3 is specific as follows:
Primary condition are as follows:
Dielectric (ε1,μ1) in incident, reflection electric and magnetic fields component are as follows:
CMM(ε2,μ2, κ) in transmit electric and magnetic fields component are as follows:
The wave vector of incident, reflection and transmitted light is respectively as follows:
Whereinβ is incidence angle,
γ±For two angle of transmission；The electric field of linearly polarized photon is divided into vertical and parallel component；Subscript-in CMM ,+respectively indicate transmitted light
LCP and RCP light；
Boundary condition are as follows: n × H=JsWith n × E=0；
The electric field component in vertical and parallel direction is equal, i.e., takes respectively
5. method as claimed in claim 4, characterized in that step S4 is specific as follows:
According to the revised constitutive equation of CMM (2) and (3) modified Maxwell equation and boundary condition: n × H=JsWith n ×
E=0 acquires transmission matrix (13):
6. method as claimed in claim 5, characterized in that step S5 is specific as follows:
According to the relationship between incident light and reflection and transmitted light, reflection and transmission coefficients are obtained, such as formula (14) and (15) institute
Show:
Wherein χ=m11m22-m12m21, transmission coefficient is further modified and obtains left-handed and right-handed transmissive coefficient, RCP:LCP:
7. method as claimed in claim 6, characterized in that step S6 is specific as follows:
If incidence wave is TE wave, the angle Kerr is back wave polarization state direction and y-axis angle, i.e., the angle Kerr when incidence wave is TE wave
Tangent value are as follows:
Kerr tangent of an angle value when incidence wave is TM wave are as follows:
Reflected field component statement are as follows:Wherein phase difference are as follows:
When TE polarised light incidence, polarization rotation rate are as follows:
By the calculated result of step S4, S5, substitution (16), (17), (18), (19) obtain the angle Kerr, polarization rotation rate and reflection
Light phase is poor, to analyze old insulator-chiral soliton interface Kerr polarization rotation characteristic.
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111897126A (en) * | 2020-07-31 | 2020-11-06 | 杭州电子科技大学 | Finite thickness chiral atomic medium-based Faraday polarization conversion analysis method |
| CN111950141A (en) * | 2020-07-30 | 2020-11-17 | 杭州电子科技大学 | Kerr polarization deflection analysis method based on vacuum and chiral atomic medium interface |
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| WO2018068249A1 (en) * | 2016-10-13 | 2018-04-19 | Yonggang Zhang | Algorithms of resonance wave reflectivity through interface of the transition zone |
| CN108614911A (en) * | 2018-03-09 | 2018-10-02 | 杭州电子科技大学 | Material interface light beam IF displacement systems based on limited surface band gap topological insulator |
| CN109273057A (en) * | 2018-09-11 | 2019-01-25 | 杭州电子科技大学 | Trapped ion the spontaneous emission rate calculation method near a kind of chiral metamaterials interface |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| WO2018068249A1 (en) * | 2016-10-13 | 2018-04-19 | Yonggang Zhang | Algorithms of resonance wave reflectivity through interface of the transition zone |
| CN108614911A (en) * | 2018-03-09 | 2018-10-02 | 杭州电子科技大学 | Material interface light beam IF displacement systems based on limited surface band gap topological insulator |
| CN109273057A (en) * | 2018-09-11 | 2019-01-25 | 杭州电子科技大学 | Trapped ion the spontaneous emission rate calculation method near a kind of chiral metamaterials interface |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN111950141A (en) * | 2020-07-30 | 2020-11-17 | 杭州电子科技大学 | Kerr polarization deflection analysis method based on vacuum and chiral atomic medium interface |
| CN111897126A (en) * | 2020-07-31 | 2020-11-06 | 杭州电子科技大学 | Finite thickness chiral atomic medium-based Faraday polarization conversion analysis method |
| CN111897126B (en) * | 2020-07-31 | 2022-05-31 | 杭州电子科技大学 | Finite thickness chiral atomic medium-based Faraday polarization conversion analysis method |
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