CN116755264B - graphene-VO-based 2 Magneto-optical-thermo-optical regulating and controlling method for waveguide - Google Patents
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Abstract
The invention discloses a graphene-VO-based liquid crystal display device 2 A magneto-optical-thermo-optical regulation method of a waveguide relates to the field of IF displacement regulation, and comprises the following steps S1: introducing a Laguerre-Gaussian beam; s2: when the linear polarized light beam is refracted and reflected at the interface of the medium, the left-handed and right-handed circular polarization components of the linear polarized light beam are separated from each other; s3: calculating an angular spectrum component of the linearly polarized Laguerre-Gaussian beam; s4: establishing a relation between angular spectrum components of an incident light beam and a reflected light beam by a plane wave angular spectrum analysis method; s5: calculating left-handed and right-handed polarization angle spectrum components of the actual light beam; s6: graphene and VO of terahertz wave band are described through Drude model 2 A dielectric tensor matrix; s7: calculating the reflection coefficient of the structure; s8: the method is substituted into an IF displacement formula to realize the IF displacement simulation of the Laguerre-Gaussian beam, and the method is adopted to realize the effective modulation of the magnetic field and the temperature to the IF displacement, thereby providing a new way for developing high-sensitivity optical sensors and sensitive detection of parameters.
Description
Technical Field
The invention relates to the technical field of IF displacement regulation, in particular to a graphene-VO-based liquid crystal display device 2 A magneto-optic-thermo-optic regulation method of a waveguide.
Background
The optical spin hall effect (Photonic spin Hall effect, PSHE) refers to the fact that linearly polarized light, when passing through a non-uniform medium, under the action of an external field acting on the refractive index gradient of the medium, photons of opposite spin are separated in opposite directions along a direction perpendicular to the refractive index gradient, resulting in splitting of the light beam into two circularly polarized light beams, including left circularly polarized Light (LHCP) and right circularly polarized light (RHCP), which are split on both sides of a cross section perpendicular to the incident plane. Also known as the Imbert-Fedorov (IF) effect, is essentially a physical phenomenon related to photon spin trajectories caused by spin-orbit interactions.
IF shift is usually only a fraction of a wavelength, and the control and amplification of which is the current focus research direction. On the one hand, amplification of IF shift can be achieved by changing the material and structure of the medium. On the other hand, the IF displacement can be flexibly regulated and controlled by changing the external fields such as a magnetic field, an electric field, temperature and the like. For example, by utilizing the excellent magneto-optical characteristics of single-layer graphene in the terahertz wave band, the magnetic field regulation and control of the IF displacement can be realized. And VO is 2 As a typical phase change material, under the action of external light excitation, thermal excitation or electric excitation, the phase change material can be subjected to structural transformation from monoclinic phase to tetragonal phase, namely from an insulating state to a metal state, and the phase change temperature is about 68 ℃ (340K), so that the efficient regulation and control of IF displacement can be realized. Currently, many researchers have utilized graphene or VO 2 Many related works are done. But combine graphene with VO 2 Studies in combination with IF shift have not been reported.
In addition to external field modulation, different incident beam modes can also have a large impact on IF shift. The beam mode related to the prior IF displacement research is mainly a traditional Gaussian beam, and compared with the traditional Gaussian beam, the Laguerre-Gaussian beam (LG beam) carries a spiral phase, which influences the angular momentum of photons, so that the IF displacement is changed. In 2019, long et al demonstrate weak value amplification of IF and GH displacements caused by micro OAM at the air prism interface and demonstrate linear changes in amplified beam offset with incident OAM by careful selection of pre-and post-selection states. In 2019, lin et al studied the IF shift of the high-order lager-gaussian (LG) beam when the LMR was excited in a prismatic, indium tin oxide structure. In 2021, liu systematically investigated the asymmetric IF shift of the first order LG beam at the PT symmetric metamaterial interface. The above research is only to analyze the influence of the intrinsic characteristics of the optical materials or structures on the IF displacement of the LG beam, and does not additionally apply physical fields such as magnetic fields, thermal fields and the like to dynamically modulate, and related physical mechanisms and regulation effects are still to be explored.
Accordingly, a graphene-VO-based solution is provided 2 The above problems are solved by a method for magneto-optical-thermo-optical modulation of a waveguide.
Disclosure of Invention
The invention aims to provide a graphene-VO-based liquid crystal display device 2 The magneto-optical-thermo-optical regulation method of the waveguide realizes the effective modulation of the IF displacement by the magnetic field and the temperature, VO in the structure 2 The unique phase change characteristic realizes the effective regulation and control of the temperature to the IF displacement, and provides a new way for developing high-sensitivity optical sensors and realizing the sensitive detection of parameters such as magnetic field, temperature and the like.
In order to achieve the above object, the present invention provides a graphene-VO-based liquid crystal display device 2 Magneto-optical-thermo-optical regulation method of waveguide, comprising graphene layer and VO 2 A layer, wherein the graphene layer is with VO 2 The layer is clung, the LG beam is incident from the graphene layer direction, and the method specifically comprises the following steps:
s1: introducing Laguerre-Gaussian beams which are the superposition of plane waves of different angular spectrum components, wherein each angular spectrum component forms an included angle with a transmission axis of light;
s2: when the linear polarized light beam is refracted and reflected at the interface of the medium, the phases and the polarizations of different angular spectrum components are changed differently, so that the left-handed circular polarization component and the right-handed circular polarization component of the linear polarized light beam are separated from each other;
s3: calculating an angular spectrum component of the linearly polarized Laguerre-Gaussian beam; in step S3, the angular spectrum components of the linearly polarized lager-gaussian beam are:
wherein l represents orbital angular momentum of incident light, s l =sign (l) denotes the sign function of l, with values "+" and "-", ω 0 For beam waist radius, k x And k y Representing the wave vector components of the incident beam in the x and y directions, respectively.
S4: establishing a relation between angular spectrum components of an incident beam and a reflected beam through a boundary continuous condition by a plane wave angular spectrum analysis method; in step S4, the relation between the angular spectrum components of the incident beam and the reflected beam is:
wherein,and->Incident angle spectrum and reflection angle spectrum of H polarized light respectively,>and->The transmission matrix is used for respectively representing the incident angle spectrum and the reflection angle spectrum of the V polarized light, and R is used for representing the relationship between the incident angle spectrum and the reflection angle spectrum;
in the above, r pp 、r ss 、r sp 、r ps Representing the reflection coefficient, theta i For incident angle, r' pp Is r pp Is the first derivative of r' ss Is r ss Is the first derivative of r' sp Is r sp Is the first derivative of r' ps Is r ps Is a first derivative of (a).
S5: calculating left-hand and right-hand polarization angular spectrum components of an actual light beam, integrating the angular spectrum components of the reflected light, performing Fourier transform to obtain a reflected light beam electric field distribution expression, and obtaining the center of gravity of a light field by utilizing a geometrical optics principle to obtain the transverse displacement of spin components in the reflected light; in step S5, the left-hand and right-hand polarization angle spectrum components of the actual light beam are expressed as follows:
lateral displacement delta of spin component in reflected light ± Expressed as:
in the method, in the process of the invention,dxdy, which is a conjugate expression of the light field distribution, represents the double integral of x and y.
S6: graphene and VO of terahertz wave band are described through Drude model 2 A dielectric tensor matrix; in step S6, the graphene dielectric tensor matrix is expressed as:
wherein ε xx Represents the effective dielectric constant diagonal element, epsilon of graphene xy Representing the effective dielectric constant off-diagonal element of graphene;
in the above formula, ω is the angular frequency of the incident beam ε 0 Is the dielectric constant of vacuum, t g Diagonal photoconductive tensor sigma of graphene, which is the thickness of graphene in a structure xx Non-diagonal element photoconductive tensor sigma xy The definition is as follows:
wherein E is f Is the effective fermi level of graphene,for a reduced planck constant, τ=0.2×10 - 9 s is the relaxation time, e=1.6x10 -19 C is the value of unit cell charge, ω c A gyratory frequency at which the particles revolve around the magnetic lines of force;
wherein v is f ＝9.5×10 5 m/s is fermi speed, B is magnetic field strength;
VO 2 the dielectric constant ε (ω) is described by the Drude model;
wherein the dielectric constant at high frequency limit value epsilon ∞ =12, plasma frequency ω p ＝1.4×10 15 S -1 Collision frequency omega d ＝5.75×10 13 S -1 ，σ 0 ＝3×10 5 S/m, VO in insulating state 2 Conductivity σ=200s/m, VO in metallic state 2 σ=200000S/m.
S7: establishing transmission modes of light beams in the same medium and among different mediums through a transfer matrix method, and calculating reflection coefficients of the structure;
s8: substituting the IF shift formula to realize the IF shift simulation of the Laguerre-Gaussian beam.
Therefore, the invention adopts the graphene-VO-based material 2 The magneto-optical-thermo-optical regulation method of the waveguide realizes the effective modulation of the IF displacement by the magnetic field and the temperature, VO in the structure 2 The unique phase change characteristic realizes the effective regulation and control of the temperature to the IF displacement, and provides a new way for developing high-sensitivity optical sensors and realizing the sensitive detection of parameters such as magnetic field, temperature and the like.
The technical scheme of the invention is further described in detail through the drawings and the embodiments.
Drawings
FIG. 1 is a graphene-VO of the present invention 2 Is a structural schematic diagram of (a);
FIG. 2 is a graph showing the variation of the IF displacement of LHCP at different orbital angular momentums in accordance with one embodiment of the present invention;
FIG. 3 is a graph showing the IF shift of LHCP at different magnetic field strengths, incident frequencies, fermi levels in a second embodiment of the present invention;
FIG. 4 is a schematic diagram of the magneto-optical Kerr effect and the IF shift diagram of the LHCP at different magneto-optical Kerr effects in the third embodiment of the present invention;
FIG. 5 is a graph showing the IF shift of LHCP at different frequencies with a varying magnetic field B in accordance with the third embodiment of the present invention;
FIG. 6 shows the Fresnel reflection coefficient r in the fourth embodiment of the present invention s And r p Schematic diagram changing with incidence angle theta;
FIG. 7 is an IF shift diagram of LHCP and RHCP in embodiment five of the present invention;
FIG. 8 shows the insulating and metallic VO in a sixth embodiment of the invention 2 Schematic diagram of structural reflection coefficient;
FIG. 9 shows the different magnetic field B in the insulating and metallic VO states according to the sixth embodiment of the present invention 2 An IF shift map of LHCP in the structure;
Detailed Description
The technical scheme of the invention is further described below through the attached drawings and the embodiments.
Unless defined otherwise, technical or scientific terms used herein should be given the ordinary meaning as understood by one of ordinary skill in the art to which this invention belongs. The terms "first," "second," and the like, as used herein, do not denote any order, quantity, or importance, but rather are used to distinguish one element from another. The word "comprising" or "comprises", and the like, means that elements or items preceding the word are included in the element or item listed after the word and equivalents thereof, but does not exclude other elements or items. The terms "connected" or "connected," and the like, are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "upper", "lower", "left", "right", etc. are used merely to indicate relative positional relationships, which may also be changed when the absolute position of the object to be described is changed.
Examples
As shown in FIG. 1, the invention provides a graphene-VO-based liquid crystal display device 2 Magneto-optic thermo-optic of waveguideRegulating method comprising graphene layer and VO 2 A layer, wherein the graphene layer is with VO 2 The layer is clung, the LG beam is incident from the graphene layer direction, and the method specifically comprises the following steps:
s1: introducing Laguerre-Gaussian beams which are the superposition of plane waves of different angular spectrum components, wherein each angular spectrum component forms an included angle with a transmission axis of light;
s2: when the linear polarized light beam is refracted and reflected at the interface of the medium, the phases and the polarizations of different angular spectrum components are changed differently, so that the left-handed circular polarization component and the right-handed circular polarization component of the linear polarized light beam are separated from each other;
s3: calculating an angular spectrum component of the linearly polarized Laguerre-Gaussian beam; in step S3, the angular spectrum components of the linearly polarized lager-gaussian beam are:
wherein l represents orbital angular momentum of incident light, s l =sign (l) denotes the sign function of l, with values "+" and "-", ω 0 For beam waist radius, k x And k y Representing the wave vector components of the incident beam in the x and y directions, respectively.
S4: establishing a relation between angular spectrum components of an incident beam and a reflected beam through a boundary continuous condition by a plane wave angular spectrum analysis method; in step S4, the relation between the angular spectrum components of the incident beam and the reflected beam is:
wherein,and->Incident angle spectrum and reflection angle spectrum of H polarized light respectively,>and->The transmission matrix is used for respectively representing the incident angle spectrum and the reflection angle spectrum of the V polarized light, and R is used for representing the relationship between the incident angle spectrum and the reflection angle spectrum;
in the above, r pp 、r ss 、r sp 、r ps Representing the reflection coefficient, theta i For incident angle, r' pp Is r pp Is the first derivative of r' ss Is r ss Is the first derivative of r' sp Is r sp Is the first derivative of r' ps Is r ps Is a first derivative of (a).
S5: calculating left-hand and right-hand polarization angular spectrum components of an actual light beam, integrating the angular spectrum components of the reflected light, performing Fourier transform to obtain a reflected light beam electric field distribution expression, and obtaining the center of gravity of a light field by utilizing a geometrical optics principle to obtain the transverse displacement of spin components in the reflected light; in step S5, the left-hand and right-hand polarization angle spectrum components of the actual light beam are expressed as follows:
lateral displacement delta of spin component in reflected light ± Expressed as:
in the method, in the process of the invention,dxdy, which is a conjugate expression of the light field distribution, represents the double integral of x and y.
S6: graphene and VO of terahertz wave band are described through Drude model 2 A dielectric tensor matrix; in step S6, the graphene dielectric tensor matrix is expressed as:
wherein ε xx Represents the effective dielectric constant diagonal element, epsilon of graphene xy Representing the effective dielectric constant off-diagonal element of graphene;
in the above formula, ω is the angular frequency of the incident beam ε 0 Is the dielectric constant of vacuum, t g Diagonal photoconductive tensor sigma of graphene, which is the thickness of graphene in a structure xx Non-diagonal element photoconductive tensor sigma xy The definition is as follows:
wherein E is f Is the effective fermi level of graphene,for a reduced planck constant, τ=0.2×10 - 9 s is the relaxation time, e=1.6x10 -19 C is the value of unit cell charge, ω c A gyratory frequency at which the particles revolve around the magnetic lines of force;
wherein v is f ＝9.5×10 5 m/s is fermi speed, B is magnetic field strength;
VO 2 the dielectric constant ε (ω) is described by the Drude model;
wherein the dielectric constant at high frequency limit value epsilon ∞ =12, plasma frequency ω p ＝1.4×10 15 S -1 Collision frequency omega d ＝5.75×10 13 S -1 ，σ 0 ＝3×10 5 S/m, VO in insulating state 2 Conductivity σ=200s/m, VO in metallic state 2 σ=200000S/m.
S7: establishing transmission modes of light beams in the same medium and among different mediums through a transfer matrix method, and calculating reflection coefficients of the structure;
s8: substituting the IF shift formula to realize the IF shift simulation of the Laguerre-Gaussian beam.
Example 1
Graphene layer thickness of 0.5nm and VO 2 The thickness of the layer is 20nm, the bottom layer is a substrate with refractive index n=1.48, and VO 2 Is a thermally induced phase-change material, VO when the temperature is lower than 68 DEG C 2 The structure is in a monoclinic system structure, has higher resistivity and is in an insulating state; VO at a temperature above 68 DEG C 2 In tetragonal structure, resistivity is reduced by four to five orders of magnitude, VO 2 Switching to the metallic phase;
researching the influence of the magnitude of orbital angular momentum OAml on IF displacement; taking the H polarization incidence as an example, IF shift in the case of l=0, 1,2,3 is simulated, and the structural parameters are set as follows: magnetic field strength b=2t, incidence frequency v=1thz, relaxation time τ=0.2 ps, graphene fermi level E f =0.2 eV. As shown in fig. 2, IF shift increases with an increase in l.
Approximating the case of l=0 as the case of gaussian beam incidence, the IF shift is 41.89 μm at θ=78.4°; when l=1, the IF displacement reaches a maximum 150.52 μm at θ=81°, and when l=2, the IF displacement reaches a maximum 406.71 μm at θ=82.5°; when l=3, the IF shift reaches a peak at θ=84°, the peak is 756.43 μm, which is increased by a factor of ten or more compared to the gaussian beam. The principle is that the LG beam carries orbital angular momentum itself, and its IF displacement is caused by both spin-orbital angular momentum interaction and orbital-orbital interaction, and when l becomes large, a complex vortex structure is coupled with angular spin splitting, so that the IF displacement is significantly increased.
Example two
Under the same structure as the embodiment one, the magnetic field intensity B, the incidence frequency v and the graphene Fermi level E are changed f IF displacement when l=0 and l=3 is simulated, the incident beam when l=0 is similar to the incident condition of the traditional gaussian beam, and the simulation result is shown in fig. 3 by comparing the incident beam with the high-order lager beam when l=3; wherein (a), (b) and (c) are three-dimensional diagrams of IF displacement under different magnetic field intensity, incidence frequency and fermi energy level and change along with incidence angle when l=0 respectively; (d) And (e) and (f) are simulation results when l=3.
As can be seen from fig. 3, under the control of different parameters, the higher-order laguerre beam produces an IF shift that is much larger than that of the gaussian beam. When b=2t, the gaussian beam IF shift peak is 88 μm and the lager-gaussian beam peak reaches 780 μm, and similarly, at v=1.5 THz, the gaussian beam IF shift peak85.5 μm, a Laguerre-Gaussian beam peak of 785 μm, E f At =0.1 eV, the peak of the gaussian beam IF shift is 68 μm, and the peak of the lager-gaussian beam reaches 775 μm, which is ten times greater than the IF shift of the gaussian beam.
Example III
The kerr effect is divided into: the transverse kerr effect (TMOKE), the longitudinal kerr effect (LMOKE) and the polar kerr effect (PMOKE), as shown in fig. 4 (b). The simulation content is carried out on the basis of TMOKE, and the previous research on the traditional Gaussian beam shows that the regulation of the external magnetic field is more obvious under the condition of PMOKE, and the result is shown as (a) in FIG. 4, and is consistent with the existing research conclusion. Therefore, to study the effect of other external physical fields such as magnetic field, temperature on the optical spin hall effect displacement of the lager-gaussian beam, we selected LG beam with orbital angular momentum OAM l=1, exploring its IF displacement in PMOKEs.
The IF shift trend at different incident frequencies is shown in fig. 5 when the magnetic field B is changed from-2T to 2T. The peak of the IF shift tends to increase and decrease with increasing magnetic field, and the corresponding angle of incidence decreases with increasing magnetic field. When the direction of the magnetic field changes, IF displacement under PMOKE shows non-reciprocity, and when v=1.4THz, B= -2T, the peak value is 331.9 μm, and the corresponding incident angle is 72.7 degrees; b=2t, at an incident angle θ=75.8°, the IF shift peak is 170.1 μm. It can be seen that the magnitude and direction of the magnetic field can regulate the peak value and incidence angle of the IF shift.
Example IV
In FIG. 6, (a) and (b) are Fresnel reflection coefficients r when the magnetic field changes from-4T to 4T, respectively s And r p A three-dimensional plot as a function of angle of incidence θ; when the direction of the magnetic field changes, r s And r p Exhibit symmetry, and thus infer that cross polarization, i.e., change or cross of polarization of incident light, occurs in the case of PMOKE, which is manifested by reflection of incident light of parallel polarization while simultaneously producing parallel polarization component r pp And a perpendicular polarization component r sp The method comprises the steps of carrying out a first treatment on the surface of the Similarly, reflection of normally polarized incident light will also simultaneously produce a normally polarized component r ss And parallel polarization component r ps . Cross polarization component r sp And r ps The presence of (c) ultimately results in non-reciprocity of IF shift.
Example five
Researching the regulation and control effects of the magnetic field on the left-handed circular polarization and the right-handed circular polarization; in fig. 7 (a) and (b) represent IF shifts of LHCP and PHCP, respectively. As can be seen from the figure, the IF shifts of RHCP and LHCP are asymmetrically distributed with the change of magnetic field. At b=3t, the peak of IF shift and the corresponding angle of incidence are different. The magnitude of spin splitting caused by the optical spin Hall effect depends on the intrinsic parameters of the medium and the polarization state of the light, so that the tiny changes of the polarization state caused by the magneto-optical Kerr effect can lead the distribution of LHCP and RHCP component fields to be different, thereby leading the spin splitting of the left and right optical rotation to be obviously changed, and leading the IF displacement distribution of the RHCP and the LCHP to be asymmetric.
Example six
Studying the influence of temperature under a constant magnetic field on IF displacement; VO (VO) 2 The conductivity of (2) can be greatly changed along with the change of temperature, a magnetic field of B= -1T is applied to PMOKE, terahertz waves of v=1 THz are incident, and VO in the structure is changed 2 And realizes the simulation of temperature regulation. FIG. 8 is a graph showing the VO in the insulating state and the VO in the metal state 2 Reflection coefficient r of corresponding structure s And r p As can be seen from the figure, when VO 2 After the phase change, the reflection coefficient is changed greatly, and the rapid change of the reflection coefficient can cause the change of the IF displacement.
In the case where (a) in fig. 9 represents b= -3T without changing the structural parameters, VO 2 A curve of IF shift before and after phase transition as a function of the incident angle θ; in FIG. 9 (B) represents B= -1T, VO 2 A curve of IF shift before and after phase transition as a function of the incident angle θ; in fig. 9 (c) represents b=1t, VO 2 A curve of IF shift before and after phase transition as a function of the incident angle θ; in fig. 9, (d) represents b=3t, VO 2 A curve of IF shift before and after phase transition as a function of the incident angle θ; the IF shift difference before and after phase transition is defined as Δh. At different positionsVO caused by temperature under the condition of magnetic field intensity 2 The phase change of the (B) can be regulated and controlled on the IF shift, and the IF shift has sensitive temperature characteristics. As can be seen from FIG. 8, the reflection coefficient of p-polarized light at Brewster's angle tends to be 0, while the magnitude of the IF shift depends on r s /r p Is regulated by the common regulation of magnetic field and temperature 2 The transition from the insulating-metallic state results in a change in dielectric properties while interacting with the graphene film such that the reflection coefficient r is near the brewster angle p And r s The difference changes, causing a large change in IF shift.
Conclusion: IF displacement increases with the increase of orbital angular momentum OAM, when topological charge l=3, IF displacement can reach 756.43 μm under TMOKE condition, 10 times of the increase compared with the traditional gaussian beam; under the condition of PMOKE, the effective modulation of a magnetic field and temperature on IF displacement is realized, the magneto-optical effect and the cross polarization effect of graphene in a terahertz wave band are realized, the size and the direction of the magnetic field have obvious influence on the IF displacement, and the left-handed polarized light and the right-handed polarized light show asymmetry and non-reciprocity, and in addition, the frequency of the incident polarized light and the parameters of the graphene, such as the Fermi level, have regulation and control effects on the IF displacement; VO in structure 2 The unique phase change characteristic realizes the effective regulation and control of the temperature to the IF shift.
Therefore, the invention adopts the graphene-VO-based material 2 The magneto-optical-thermo-optical regulation method of the waveguide realizes the effective modulation of the IF displacement by the magnetic field and the temperature, VO in the structure 2 The unique phase change characteristic realizes the effective regulation and control of the temperature to the IF shift. Provides a new way for developing high-sensitivity optical sensors and realizing the sensitive detection of parameters such as magnetic field, temperature and the like.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention and not for limiting it, and although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that: the technical scheme of the invention can be modified or replaced by the same, and the modified technical scheme cannot deviate from the spirit and scope of the technical scheme of the invention.
Claims (1)
1. graphene-VO-based 2 The magneto-optical-thermo-optical regulation method of the waveguide is characterized in that: comprises a graphene layer and VO 2 A layer, wherein the graphene layer is with VO 2 The layer is clung, the LG beam is incident from the graphene layer direction, and the method specifically comprises the following steps:
s1: introducing Laguerre-Gaussian beams which are the superposition of plane waves of different angular spectrum components, wherein each angular spectrum component forms an included angle with a transmission axis of light;
s2: when the linear polarized light beam is refracted and reflected at the interface of the medium, the phases and the polarizations of different angular spectrum components are changed differently, so that the left-handed circular polarization component and the right-handed circular polarization component of the linear polarized light beam are separated from each other;
s3: calculating an angular spectrum component of the linearly polarized Laguerre-Gaussian beam; in step S3, the angular spectrum components of the linearly polarized lager-gaussian beam are:
wherein l represents orbital angular momentum of incident light, s l =sign (l) denotes the sign function of l, with values "+" and "-", ω 0 For beam waist radius, k x And k y Representing wave vector components of the incident beam in the x and y directions, respectively;
s4: establishing a relation between angular spectrum components of an incident beam and a reflected beam through a boundary continuous condition by a plane wave angular spectrum analysis method; in step S4, the relation between the angular spectrum components of the incident beam and the reflected beam is:
wherein,and->Incident angle spectrum and reflection angle spectrum of H polarized light respectively,>and->The transmission matrix is used for respectively representing the incident angle spectrum and the reflection angle spectrum of the V polarized light, and R is used for representing the relationship between the incident angle spectrum and the reflection angle spectrum;
in the above, r pp 、r ss 、r sp 、r ps Representing the reflection coefficient, theta i For incident angle, r' pp Is r pp Is the first derivative of r' ss Is r ss Is the first derivative of r' sp Is r sp Is the first derivative of r' ps Is r ps Is the first derivative of (a);
s5: calculating left-hand and right-hand polarization angular spectrum components of an actual light beam, integrating the angular spectrum components of the reflected light, performing Fourier transform to obtain a reflected light beam electric field distribution expression, and obtaining the center of gravity of a light field by utilizing a geometrical optics principle to obtain the transverse displacement of spin components in the reflected light; in step S5, the left-hand and right-hand polarization angle spectrum components of the actual light beam are expressed as follows:
lateral displacement delta of spin component in reflected light ± Expressed as:
in the method, in the process of the invention,for the conjugate expression of the light field distribution, dxdy represents the double integral of x and y;
s6: graphene and VO of terahertz wave band are described through Drude model 2 A dielectric tensor matrix;
in step S6, the graphene dielectric tensor matrix is expressed as:
wherein ε xx Represents the effective dielectric constant diagonal element, epsilon of graphene xy Representing the effective dielectric constant off-diagonal element of graphene;
in the above formula, ω is the angular frequency of the incident beam ε 0 Is the dielectric constant of vacuum, t g Is a knotThickness of graphene in structure, diagonal photoconductive tensor sigma of graphene xx Non-diagonal element photoconductive tensor sigma xy The definition is as follows:
wherein E is f Is the effective fermi level of graphene,for a reduced planck constant, τ=0.2×10 -9 s is the relaxation time, e=1.6x10 -19 C is the value of unit cell charge, ω c A gyratory frequency at which the particles revolve around the magnetic lines of force;
wherein v is f ＝9.5×10 5 m/s is fermi speed, B is magnetic field strength;
VO 2 the dielectric constant ε (ω) is described by the Drude model;
wherein the dielectric constant at high frequency limit value epsilon ∞ =12, plasma frequency ω p ＝1.4×10 15 S -1 Collision frequency omega d ＝5.75×10 13 S -1 ，σ 0 ＝3×10 5 S/m, VO in insulating state 2 Conductivity σ=200s/m, VO in metallic state 2 σ=200000S/m;
s7: establishing transmission modes of light beams in the same medium and among different mediums through a transfer matrix method, and calculating reflection coefficients of the structure;
s8: substituting the IF shift formula to realize the IF shift simulation of the Laguerre-Gaussian beam.
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| CN102230986A (en) * | 2011-05-20 | 2011-11-02 | 北京航空航天大学 | Optical phase device as well as application method and system thereof |
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| CN115793295A (en) * | 2022-11-25 | 2023-03-14 | 成都信息工程大学 | Magneto-optical spin Hall effect experimental device and method under terahertz frequency |
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| CN102230986A (en) * | 2011-05-20 | 2011-11-02 | 北京航空航天大学 | Optical phase device as well as application method and system thereof |
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