CN115793295A - Magneto-optical spin Hall effect experimental device and method under terahertz frequency - Google Patents
Magneto-optical spin Hall effect experimental device and method under terahertz frequency Download PDFInfo
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Abstract
The invention discloses a magneto-optic optical spin Hall effect experimental device and method under terahertz frequency, which comprises a prism and a graphene-metal heterojunction arranged below the prism, wherein the graphene-metal heterojunction is obtained by periodically and alternately superposing a graphene layer and a metal layer, and the substrate material of the graphene-metal heterojunction is SiO 2 (ii) a After being coupled by a prism, the linearly polarized Gaussian beam is incident into the graphene-metal heterojunction at an angle theta, and is reflected at the interface of the graphene-metal heterojunction under the action of an external magnetic field to generate a light spinning Hall effect, so that the beam is split into left circularly polarized light and right circularly polarized light. The magneto-optical spin Hall effect experimental device and method under the terahertz frequency can greatly enhance the left-handed circularly polarized light and the right-handed circularly polarized lightThe asymmetric splitting is carried out, so that under the terahertz magnetic field, the possibility is provided for enhancing the transverse displacement of the optical spin Hall effect and effectively regulating and controlling.
Description
Technical Field
The invention relates to the technical field of Hall elements, in particular to a magneto-optic light spin Hall effect experimental device and method under terahertz frequency.
Background
When the linearly Polarized Light is reflected in the direction perpendicular to the incident plane, a micro-motion occurs, that is, a Left-handed circular Polarized component and a Right-handed circular Polarized component of the reflected Light at the interface of the waveguide layer are subjected to a micro-transverse splitting perpendicular to the incident plane, so as to be divided into a Left-handed circular Polarized component (LHCP) and a Right-handed circular Polarized component (RHCP), which is called a Spin Hall Effect (Light, sheath).
In general, the beam splitting in the SHEL is small, only a fraction of the wavelength, and direct measurement through experiments is difficult. To this end, weak measurement techniques were introduced to observe beam splitting in the SHEL, while many structures, especially artificially designed nano-and metamaterial waveguides, were designed to increase the lateral splitting of the circularly polarized beam.
And it is known from the common general knowledge in the art that the terahertz (THz) range is widely defined as the portion of the electromagnetic spectrum from 0.1 to 10 THz. The spectrum of the electromagnetic wave corresponding to a vacuum wavelength of 3000 to 30 μm lies between the photonic and electronic range.
Graphene is a novel two-dimensional material with a single sp2 hybridized atomic layer, has very high electron mobility, and can observe the integer quantum hall effect even at room temperature.
In a terahertz frequency band, a light beam is incident on a graphene layer to cause a remarkable Magneto-Optical kerr Effect, namely a Magneto-Optical kerr Effect (MOKE) which is a phenomenon that linearly polarized light rotates after being reflected to the surface of a magnetized medium. At the same time the metal layer will generate Surface plasmons (SPP), which are nanoparticles of electromagnetic waves at the interface between materials with positive and negative dielectric constants, typically dielectric and metal, and in the collective oscillatory coupling of free electron gas. It is known that it can only propagate when the resonance condition with the incident light is satisfied and allows the diffraction limit to be broken to localize the light to the subwavelength dimension, thereby achieving an increase in the field strength.
However, few studies and reports are currently made on graphene layers. Therefore, the waveguide structure based on the graphene layer has great practical significance, research value and application potential.
Disclosure of Invention
In order to solve the problems, the invention provides a magneto-optical spin Hall effect experimental device and method under terahertz frequency, the change gradient of the refractive index between waveguide layers is larger, the interaction between spin and orbit is stronger, and the SHEL (magneto-optical spin Hall effect) can be effectively enhanced.
In order to achieve the purpose, the invention provides a magneto-optic optical spin Hall effect experimental device under terahertz frequency, which comprises a prism and a graphene-metal heterojunction arranged below the prism, wherein the graphene-metal heterojunction is obtained by periodically and alternately superposing a graphene layer and a metal layer, and a substrate material of the graphene-metal heterojunction is SiO 2 ；
After being coupled by a prism, the linearly polarized Gaussian beam is incident into the graphene-metal heterojunction at an angle theta, and is reflected at the interface of the graphene-metal heterojunction under the action of an external magnetic field to generate a light spinning Hall effect, so that the beam is split into left circularly polarized light and right circularly polarized light.
Preferably, the metal in the graphene-metal heterojunction is gold, and the thickness of the single-layer metal layer is 50nm;
the thickness of a single-layer graphene layer in the graphene-metal heterojunction is 0.5nm, the Fermi level is 0.2eV, and the Fermi speed v is f ＝9.5×10 -5 。
Preferably, the external magnetic field is a transverse magnetic field, and the magnetic induction intensity is B =10T.
Preferably, the incident angle theta is 55-60 degrees, and the frequency of the incident terahertz wave is 0.8-1.8 THz.
Preferably, the incident angle θ is 58 ° and the frequency of the incident terahertz is 1.2THz.
A magneto-optical spin Hall effect experimental method under terahertz frequency comprises the following steps:
s1, determining basic parameters
Determining a dielectric tensor matrix of a graphene layer of the graphene-metal heterojunction at a terahertz frequency:
in the formula, the diagonal elements of the effective dielectric constant of graphene
Non-diagonal elements of effective dielectric constant of graphene
i is the imaginary unit, ω is the angular frequency of the incident beam, ε 0 Is a vacuum dielectric constant, and t g The thickness of a single graphene layer in the graphene-metal heterojunction is adopted;
photoconductive tensor σ of graphene diagonal xx Calculated by the following formula:
photoconductive tensor sigma of graphene non-diagonal elements xy Calculated by the following formula:
in formulae (2) and (3), E f Is the effective fermi level of the graphene layer,
is reduced Planck constant, where h =6.626 × 10 -34 J · s is planck constant, τ =0.2 × 10 -9 s is relaxation time, e =1.6 × 10 -19 C is the value of the unit charge;
the cyclotron frequency omega at which the particles revolve around the magnetic field lines c Calculated by the following formula:
in the formula, B is magnetic induction intensity; v. of f ＝9.5×10 5 m/s is the Fermi velocity;
s2, calculating the reflection coefficients of incident light and reflected light in the multilayer dielectric film structure by using a nonlinear magneto-optical transfer matrix method;
and S3, calculating the optical spin Hall effect displacement of the whole structure.
Preferably, step S2 specifically includes the following steps:
s21, calculating a dynamic matrix D of elements according to a nonlinear magneto-optical transfer matrix method (2) ：
Under the precondition of generating transverse Kerr effect by applying transverse magnetic field, in the formula, D 11 ＝D 12 ＝11，D21＝-D 22 ＝N z1 ，
D 43 ＝-(N y ε zy +N z3 ε zz )，D 44 ＝-(N y ε zy +N z4 ε zz ) And the others are all 0;
under the premise of adding a poloidal magnetic field to generate a poloidal Kerr effect, in the formula,
j＝1,2,3,4，
s22, calculating the transmission matrix of the isotropic layer on the premise that the magnetization direction M = 0:
s23, calculating an anisotropic layer transmission matrix D and a magneto-optical layer transmission matrix P of the transmission matrix:
in formulae (6) and (7), d (n) Is the thickness of the nth layer; in the case of the anisotropic layer(s),
j＝1,2,3,4，
and is
In the magneto-optical layer N zi Wherein i =1,2,3,4
This is obtained from the following equation:
in the formula (I), the compound is shown in the specification,
s24, calculating a total transmission matrix Q:
preferably, step S3 specifically includes the following steps:
s31, calculating the reflection coefficient of the multilayer structure:
in the formula, r ij Is the reflection coefficient, i, j = s or p; i denotes the incident beam is s-polarized or p-polarized; j represents the reflected beam as s-polarized or p-polarized;
s32, obtaining a reflected light field through angle spectrum operation of the incident light field:
where E represents the amplitude of the light field, subscripts i, r represent the incident and reflected light fields, respectively, superscripts H and V represent the horizontal and vertical polarization components, respectively, of the light field, k 0 For propagating wave vector, k ry A y-axis component representing a reflected wave vector;
s33, defining transverse displacement of the reflected light:
in the formula, the plus or minus signs respectively represent the right-left circularly polarized light part and the right-hand circularly polarized light part of the optical spin Hall effect displacement.
Preferably, step S4 is further included after step S3: simulation contrast analysis
S41, determining the direction of an external magnetic field, and analyzing the influence of the thickness of the gold layer in the visible light band on the spin splitting value
Respectively changing the thickness change of a metal layer in the graphene-metal heterojunction and analyzing the influence of a spin splitting value on the premise of a polar magnetic field and a transverse magnetic field to obtain that the thickness of the metal layer of the graphene-metal heterojunction is 50nm and the Fermi level of the graphene is E when incident light is in a visible light wave band in the transverse magnetic field f =0.2eV, relaxation time τ =0.2ps, magnetic induction B =10T, fermi velocity ν f ＝9.5×10 -5 The spin splitting value is the largest, reaches 546nm and is 1.65 times of the extreme value under the polar magnetic field, so that a transverse magnetic field mode is selected for simulation subsequently;
s42, analyzing a terahertz wave band and spin splitting value in the same graphene-metal heterojunction structure
In a transverse magnetic field mode, when incident light is a terahertz waveband, and other calculation parameters are the same as those of a visible light waveband, the change trend of a spin splitting value along with an incident angle and terahertz frequency is analyzed, and when the obtained terahertz frequency is 1.2THz, the spin splitting value reaches an extreme value of 498 mu m, which is 10 microns larger than that of the visible light waveband 3 Magnitude;
s43, changing the external magnetic induction intensity and the graphene Fermi level, and analyzing the change trend of the spin split value;
and S44, analyzing the influence of the periodicity of the graphene-metal heterojunction on the displacement of the optical spin Hall effect.
Therefore, the invention has the following beneficial effects:
1. the gradient of the change of the refractive index between the waveguide layers is larger, the interaction between spin and orbit is stronger, and the SHEL (magneto-optical light spin Hall effect) can be effectively enhanced;
2. through research, under the terahertz frequency of 1.2THz, the maximum value of the centroid transverse movement of the optical spin Hall effect under the designed structure is determined by changing the parameters of the terahertz frequency, the thickness of the metal layer, the graphene Fermi level and the like, the spin splitting value of a light beam can reach 498 mu m at most, and is increased by 10 compared with the visible light wave band 3 And the graphene shows a great magneto-optical effect at the moment, so that asymmetric splitting of LHCP (left-handed circularly polarized light) and RHCP (right-handed circularly polarized light) is greatly enhanced, and a new application approach is provided for the novel terahertz device.
The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.
Drawings
FIG. 1 is a schematic structural view of the present invention;
FIG. 2 is a schematic view of the shift of the SHEL according to the present invention;
FIG. 3 is a diagram illustrating the magneto-optical Kerr effect under a poloidal magnetic field in accordance with the present invention;
FIG. 4 is a diagram illustrating the magneto-optical Kerr effect under a transverse magnetic field in accordance with the present invention;
FIG. 5 shows the Fermi level E of graphene under the poloidal magnetic field of the present invention, when the incident beam wavelength is 632.8nm, the magnetic induction intensity is B =10T, the thickness of single-layer graphene is tg =0.5nm, and Au is used as the metal layer f Simulation result diagram of left-handed circularly polarized light when =0.2eV and relaxation time τ =0.2 ps;
fig. 6 is a graph of simulation results of right-handed circularly polarized light when the incident beam wavelength is 632.8nm, the magnetic induction B =10T, the thickness of single-layer graphene is tg =0.5nm, au is used as a metal layer, the fermi level Ef =0.2eV of the graphene, and the relaxation time τ =0.2ps under the poloidal magnetic field of the present invention;
FIG. 7 is a SHEL distribution graph of circularly polarized light under a poloidal magnetic field according to the present invention;
FIG. 8 is a graph of the theoretical distribution of the reflection coefficient of incident light under a polar magnetic field according to the present invention;
fig. 9 is a graph of simulation results of left-handed circularly polarized light when the incident beam wavelength is 632.8nm, the magnetic induction B =10T, the thickness of single-layer graphene is tg =0.5nm, au is used as a metal layer, the fermi level Ef =0.2eV of the graphene, and the relaxation time τ =0.2ps under the transverse magnetic field of the present invention;
fig. 10 is a graph of simulation results of right-handed circularly polarized light in a transverse magnetic field according to the present invention, when the wavelength of an incident light beam is 632.8nm, the magnetic induction B =10T, the thickness of single-layer graphene is tg =0.5nm, au is used as a metal layer, the fermi level Ef =0.2eV of graphene, and the relaxation time τ =0.2 ps;
FIG. 11 is a graph showing the result of the theoretical reflection coefficient of incident light varying with the incident angle under the lateral magnetic field and different gold layer thicknesses according to the present invention;
FIG. 12 is a color intensity plot of SHEL of the present invention as a function of incident angle and terahertz frequency;
FIG. 13 is an in-plane intensity projection of the xOy of the present invention;
FIG. 14 shows a schematic view of the invention E f Shift plot of SHEL with incident angle at =0.1 eV;
FIG. 15 shows a schematic view of the invention E f Shift plot of SHEL with incident angle at =0.2 eV;
FIG. 16 shows a schematic view of E of the present invention f Shift plot of SHEL with incident angle at =0.3 eV;
FIG. 17 shows a schematic view of E of the present invention f Shift plot of SHEL with incident angle at =0.4 eV;
fig. 18 is a graph of a graphene and gold layer periodicity distribution of the invention;
FIG. 19 is a simulation graph of the change of the LHPC and RHCP components of the SHEL splitting value with incident light when the number of cycles of the graphene and gold layers is 1 according to the present invention;
FIG. 20 is a simulation graph of the change of the LHPC and RHCP components of the SHEL splitting value with incident light when the number of periods of the graphene and gold layers is 3 according to the present invention;
FIG. 21 is a simulation graph of the change of the LHPC and RHCP components of the SHEL splitting value with incident light when the number of cycles of the graphene and gold layers is 7 according to the present invention;
FIG. 22 is a simulation graph of the variation of the LHPC and RHCP components of the SHEL splitting values with incident light for a graphene and gold periodicity of 11 in accordance with the present invention;
FIG. 23 is a simulation graph of simulated SHEL with different incident terahertz wave frequencies according to the present invention when the number of cycles of the graphene and gold layers is 7;
FIG. 24 is a graph of the fragmentation value of the SHEL of the present invention as a function of cycle number.
Detailed Description
The present invention will be further described with reference to the accompanying drawings, and it should be noted that the present embodiment is based on the technical solution, and the detailed implementation and the specific operation process are provided, but the protection scope of the present invention is not limited to the present embodiment.
As shown in fig. 1 to 4, the magneto-optical spin hall effect experimental device under terahertz frequency disclosed by the invention comprises a prism and a graphene-metal heterojunction arranged below the prism, wherein the graphene-metal heterojunction is obtained by periodically and alternately superposing a graphene layer and a metal layer, and a substrate material of the graphene-metal heterojunction is SiO 2 (ii) a Under the structure, after being coupled by a prism, a linearly polarized Gaussian beam is incident to the graphene-metal heterojunction at an angle theta, and is reflected at the interface of the graphene-metal heterojunction under the action of an external magnetic field to generate a light spinning Hall effect, so that the beam is split into left-handed circularly polarized light and right-handed circularly polarized light.
Preferably, the metal in the graphene-metal heterojunction is gold, and the thickness of the single-layer metal layer is 50nm; the thickness of a single-layer graphene layer in the graphene-metal heterojunction is 0.5nm, the Fermi level is 0.2eV, and the Fermi speed v is f ＝9.5×10 -5 . Preferably, the external magnetic field is a transverse magnetic field, and the magnetic induction intensity B =10T. Preferably, the incident angle theta is 55-60 degrees, and the frequency of the incident terahertz wave is 0.8-1.8 THz. Preferably, the incident angle θ isThe frequency of 58 ° incident terahertz is 1.2THz.
A magneto-optical spin Hall effect experimental method under terahertz frequency comprises the following steps:
s1, determining basic parameters
Determining a dielectric tensor matrix of a graphene layer of the graphene-metal heterojunction at a terahertz frequency:
in the formula, the diagonal elements of the effective dielectric constant of graphene
Non-diagonal elements of effective dielectric constant of graphene
i is the unit of imaginary number, ω is the angular frequency of the incident beam, ε 0 Is a vacuum dielectric constant, and t g The thickness of a single graphene layer in the graphene-metal heterojunction is taken as the thickness;
photoconductive tensor σ of graphene diagonal xx Calculated by the following formula:
photoconductive tensor sigma of graphene non-diagonal elements xy Calculated by the following formula:
in formulae (2) and (3), E f Is the effective fermi level of the graphene layer,
is reduced planck constant, where h =6.626 × 10 -34 J · s is planck constant, τ =0.2 × 10 -9 s is relaxation time, e =1.6 × 10 -19 C is the value of the unit cell charge;
the cyclotron frequency omega of the revolution of the particles around the magnetic field lines c Calculated by the following formula:
wherein B is magnetic induction intensity; v. of f ＝9.5×10 5 m/s is the Fermi velocity;
s2, calculating the reflection coefficients of incident light and reflected light in the multilayer dielectric film structure by using a nonlinear magneto-optical transfer matrix method;
preferably, step S2 specifically includes the following steps:
s21, calculating a dynamic matrix D of elements according to a nonlinear magneto-optical transfer matrix method (2) ：
Under the precondition of generating transverse Kerr effect by applying transverse magnetic field, in the formula, D 11 ＝D 12 ＝11，D21＝-D 22 ＝N z1 ，
D 43 ＝-(N y ε zy +N z3 ε zz )，D 44 ＝-(N y ε zy +N z4 ε zz ) And the others are all 0;
under the premise of adding a polar magnetic field to generate a polar Kerr effect, in the formula,
j＝1,2,3,4，
s22, on the premise that the magnetization direction M =0, calculating a transmission matrix of the isotropic layer, where M =0 indicates that the layer medium is not affected by a magnetic field:
s23, calculating an anisotropic layer transmission matrix D and a magneto-optical layer transmission matrix P of the transmission matrix:
in formulae (6) and (7), d (n) Is the thickness of the nth layer; in the case of the anisotropic layer(s),
j＝1,2,3,4，
and is provided with
In the magneto-optical layer N zi Wherein i =1,2,3,4
Obtained from the following equation:
in the formula (I), the compound is shown in the specification,
s24, calculating a total transmission matrix Q:
since the jones reflection matrix is the complex electric field amplitude of the vertical polarized wave(s) and the horizontal polarized wave (p) in which the incident wave (i) and the reflected wave (r) are linearly polarized with respect to the plane of the incident wave, it can be seen that the Q matrix contains all the information of the incident and reflected optical field distributions.
And S3, calculating the optical spin Hall effect displacement of the whole structure.
Preferably, step S3 specifically includes the following steps:
s31, calculating the reflection coefficient of the multilayer structure:
in the formula, r ij Is the reflection coefficient, i, j = s or p; i denotes the incident beam as s-polarized or p-polarized; j denotes the reflected beam is s-polarized or p-polarized;
s32, obtaining reflected light by an incident light field through angular spectrum operation:
where E represents the amplitude of the light field, subscripts i, r represent the incident and reflected light fields, respectively, superscripts H and V represent the horizontal and vertical polarization components, respectively, of the light field, and k represents the horizontal and vertical polarization components of the light field 0 For propagating wave vector, k ry A y-axis component representing a reflected wave vector;
s33, defining the transverse displacement of the reflected light:
in the formula, the plus or minus signs respectively represent the right-left circularly polarized light part and the right-hand circularly polarized light part of the optical spin Hall effect displacement.
Preferably, step S3 is followed by step S4: simulation comparative analysis
S41, determining the direction of an external magnetic field, and analyzing the influence of the thickness of the gold layer in the visible light band on the spin splitting value
Respectively changing the thickness change of a metal layer in the graphene-metal heterojunction and analyzing the influence of a spin splitting value on the premise of a polar magnetic field and a transverse magnetic field to obtain that the thickness of the metal layer of the graphene-metal heterojunction is 50nm and the Fermi level of the graphene is E when incident light is in a visible light wave band under the transverse magnetic field f =0.2eV, relaxation time τ =0.2ps, magnetic induction B =10T, fermi velocity ν f ＝9.5×10 -5 The spin splitting value is the largest and reaches 546nm, which is 1.65 times of the lower extreme value of the poloidal magnetic field, so that a transverse magnetic field mode is selected for simulation subsequently;
in step S41, both magnetic field magnitudes affect the magnitude of the reflected beam optical spin hall effect splitting.
The method specifically comprises the following steps:
when a poloidal magnetic field, namely PMOKE, is applied firstly, the wavelength of an incident beam is 632.8nm, the magnetic induction intensity is B =10T, and the thickness of single-layer graphene is T g (ii) =0.5nm, and Fermi level E of graphene when Au is used as the metal layer f As shown in fig. 5, it is understood that the calculation results are shown when the relaxation time τ =0.2ps and 0.2eV are satisfied, and that the linearly polarized light enters the designed structureAnd when the thickness of the gold layer is increased from 30nm to 70nm, the spin splitting value of the left-handed circularly polarized light tends to increase first and then decrease, and reaches the maximum when the thickness is 50 nm. Meanwhile, as can be seen from fig. 6, the simulation curves of the right-handed circularly polarized light RHCP and the LHCP are symmetrically distributed, so the variation trend is similar to that of fig. 5.
When the gold layer thickness was 50nm, the SHEL distribution of the circularly polarized light was 330nm at the maximum, as shown in FIG. 7. As shown in fig. 8, the theoretical distribution of the reflection coefficient of the incident light shows that the p-wave reflection coefficient is minimum at an incident angle of 72 °, rpp approaches 0, and the splitting value corresponding to the SHEL is maximum.
And then, changing the direction of the external magnetic field to be transverse, namely selecting the same structural parameters as PMOKE under TMOKE. The results of the curves of the she splitting values of the LHCP and RHCP along with the change of the incident angle are shown in fig. 9 and fig. 10, respectively, and it can be known that, similar to PMOKE, the she splitting value shows a trend of increasing first and then decreasing along with the increase of the thickness of the gold layer, and when the thickness of the gold layer is 50nm, the spin splitting value of the she is the largest, which reaches 546nm and is 1.65 times of the extreme value under PMOKE, so that the TMOKE mode is selected in the subsequent simulation calculation.
The theoretical value of the reflection coefficient of incident light varying with the incident angle under different gold layer thicknesses is shown in fig. 11, and it can be seen that the lowest values of the reflection coefficients are 0.41, 0.11, 0.002, 0.16 and 0.42 from 30nm to 70nm, respectively. At an Au layer thickness of 50nm, the theoretical value curve of the reflection coefficient of p-wave is the lowest at the trough (around 72 °), where Rpp approaches 0 and the splitting value corresponding to the SHEL is the largest.
S42, analyzing a terahertz waveband and spin splitting value in the same graphene-metal heterojunction structure
In a transverse magnetic field mode, when incident light is a terahertz waveband, and other calculation parameters are the same as those of a visible light waveband, the change trend of a spin splitting value along with an incident angle and terahertz frequency is analyzed, and when the obtained terahertz frequency is 1.2THz, the spin splitting value reaches an extreme value of 498 mu m, which is 10 microns larger than that of the visible light waveband 3 Magnitude;
due to the fact that the graphene has high magnetic field response, the graphene shows a large magneto-optical effect in a terahertz waveband. Calculating the surface, the splitting value of the SHEL jumps from nanometer magnitude to micrometer magnitude, as can be seen from FIG. 12, the SHEL peak value is close to 500 μm, and is increased by 1000 times compared with that of the visible light wave band. As can be seen from fig. 13, the peak region of the sel is located in the incident angle range of 55 to 60 °, and the frequency of the incident terahertz wave is in the range of 0.8 to 1.8THz, and the spin splitting of the sel in this region is significant. And when the incident angle is about 58 degrees, larger amplitude distribution appears.
Meanwhile, as shown in fig. 13, under different terahertz frequencies, the variation curve of the SHEL splitting value with the incident angle is not too large, but the splitting value of the SHEL tends to increase first and then decrease with the increase of the frequency f, and when the frequency is 1.2THz, the splitting value of the SHEL is the largest and reaches 498 μm.
S43, changing the external magnetic induction intensity and the graphene Fermi level, and analyzing the change trend of the spin split value;
as can be seen from fig. 14, the magnitude of the magnetic induction shows different effects on the splitting value of the sel in the case of different graphene fermi levels. With E f At the SHEL extreme, the trend is first increasing and then decreasing, at E f The spin-splitting value of SHEL is maximal at 0.2eV, which is close to 500 μm. As can be seen from FIG. 15, when E f At a constant value, e.g. when E f When =0.1eV, the sel gradually decreases as the magnetic induction B increases. As shown in fig. 15-17, when E thereafter f And the SHEL is distributed irregularly along with the change of the magnetic induction intensity.
And S44, analyzing the influence of the periodicity of the graphene-metal heterojunction on the displacement of the optical spin Hall effect.
Setting specific parameters as d Au ＝50nm，B＝10T，E f =0.2eV, υ =1.2THz, τ =0.2ps, and then the influence of the periodic graphene-gold structure on the optical spin hall effect displacement of the system was analyzed.
As shown in fig. 18, since the graphene and the gold layer are periodically and alternately stacked to form the metamaterial, the metamaterial is an artificial structure in nature, has a size much larger than that of a conventional atom and much smaller than the wavelength of incident light, so that the metamaterial has the required optical properties, can generate a new degree of freedom to manipulate light waves,
simulation calculations were performed at cycle numbers 1, 3, 7 and 11, and simulations of the change of LHPC and RHCP components with incident light for the she split values are shown in fig. 19-22, and it can be seen that the maximum values of the she split values are 498 μm, 218 μm, 276 μm and 80.5 μm, respectively, and show a tendency of oscillation that decreases from the maximum value to increase and then decrease.
At the cycle number n =7, the simulation curve of the simulated SHEL with the incident angle at different incident terahertz wave frequencies is shown in fig. 23, where the maximum value of the splitting value of the SHEL is around 61 ° at the incident angle, corresponding to the terahertz frequency v =1.2THz, and is consistent with the above discussion. The variation of the split value of the SHEL with the number of cycles is shown at 24, and it can be seen that the value of the SHEL increases from maximum to decrease as the number of cycles n increases. When n exceeds 7, the value of SHEL is gradually decreased. Thus, in this configuration, when the number of cycles n is equal to or less than 10, the value of the sel oscillates with the increase of the number of cycles, and when n is greater than 10, the value of the sel gradually decreases. This is because although the anisotropy of the multi-layer periodic metamaterial structure can significantly increase the lateral displacement of left-handed circularly polarized light and right-handed circularly polarized light, the multiple absorption of light between layers is increased with the increase of the skin depth, which leads to the gradual decrease of the SHEL effect, so that the splitting value of the light beam is also reduced, and the SHEL value is gradually reduced, but still in the order of μm.
Therefore, the magneto-optical spin Hall effect experimental device and method under the terahertz frequency can greatly enhance the asymmetric splitting of the left-handed circularly polarized light and the right-handed circularly polarized light, thereby providing possibility for enhancing the transverse displacement and effectively regulating and controlling the optical spin Hall effect under the terahertz magnetic field.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention is described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that: modifications and equivalents may be made to the disclosed embodiments without departing from the spirit and scope of the present invention.
Claims (9)
1. The magneto-optical spin Hall effect experimental device under the terahertz frequency is characterized in that: the graphene-metal heterojunction structure comprises a prism and a graphene-metal heterojunction arranged below the prism, wherein the graphene-metal heterojunction is obtained by periodically and alternately superposing a graphene layer and a metal layer, and a substrate material of the graphene-metal heterojunction is SiO 2 ；
After being coupled by a prism, the linearly polarized Gaussian beam is incident into the graphene-metal heterojunction at an angle theta, and is reflected at the interface of the graphene-metal heterojunction under the action of an external magnetic field to generate a light spinning Hall effect, so that the beam is split into left circularly polarized light and right circularly polarized light.
2. The magneto-optical spin hall effect experimental device at terahertz frequency according to claim 1, characterized in that: the metal in the graphene-metal heterojunction is gold, and the thickness of a single-layer metal layer is 50nm;
the thickness of a single-layer graphene layer in the graphene-metal heterojunction is 0.5nm, the Fermi level is 0.2eV, and the Fermi speed v is f ＝9.5×10 -5 。
3. The magneto-optical spin hall effect experimental device at terahertz frequency according to claim 1, characterized in that: the external magnetic field is a transverse magnetic field, and the magnetic induction intensity B =10T.
4. The magneto-optical spin hall effect experimental device at thz frequency according to claim 1, characterized in that: the incident angle theta is 55-60 degrees, and the frequency of the incident terahertz wave is 0.8-1.8 THz.
5. The magneto-optical spin Hall effect experimental apparatus at terahertz frequency according to claim 4, characterized in that: the incident angle θ is 58 ° and the frequency of incident terahertz is 1.2THz.
6. A magneto-optical spin Hall effect experimental method under terahertz frequency is characterized in that: the method comprises the following steps:
s1, determining basic parameters
Determining a dielectric tensor matrix of a graphene layer of the graphene-metal heterojunction at the terahertz frequency:
in the formula, diagonal elements of effective dielectric constant of graphene
Non-diagonal elements of effective dielectric constant of graphene
i is the unit of imaginary number, ω is the angular frequency of the incident beam, ε 0 Is a vacuum dielectric constant, and t g The thickness of a single graphene layer in the graphene-metal heterojunction is adopted;
photoconductive tensor σ of graphene diagonal xx Calculated by the following formula:
photoconductive tensor sigma of graphene non-diagonal elements xy Calculated by the following formula:
in formulae (2) and (3), E f Is the effective fermi level of the graphene layer,
is reduced to Planck constant, where h =6.626×10 -34 J · s is planck constant, τ =0.2 × 10 -9 s is relaxation time, e =1.6 × 10 -19 C is the value of the unit cell charge;
the cyclotron frequency omega of the revolution of the particles around the magnetic field lines c Calculated by the following formula:
in the formula, B is magnetic induction intensity; v. of f ＝9.5×10 5 m/s is the Fermi velocity;
s2, calculating the reflection coefficients of incident light and reflected light in the multilayer dielectric film structure by using a nonlinear magneto-optical transfer matrix method;
and S3, calculating the optical spin Hall effect displacement of the whole structure.
7. The assay method of claim 6, wherein: the step S2 specifically includes the following steps:
s21, calculating a dynamic matrix D of elements according to a nonlinear magneto-optical transfer matrix method (2) ：
Under the precondition of applying a transverse magnetic field to generate a transverse Kerr effect, in the formula, D 11 ＝D 12 ＝11，D21＝-D 22 ＝N z1 ，
D 43 ＝-(N y ε zy +N z3 ε zz )，D 44 ＝-(N y ε zy +N z4 ε zz ) And the others are all 0;
under the premise of adding a polar magnetic field to generate a polar Kerr effect, in the formula,
s22, calculating the transmission matrix of the isotropic layer on the premise that the magnetization direction M = 0:
s23, calculating an anisotropic layer transmission matrix D and a magneto-optical layer transmission matrix P of the transmission matrix:
in formulae (6) and (7), d (n) Is the thickness of the nth layer; in the case of the anisotropic layer(s),
and is provided with
In the magneto-optical layer N zi Wherein i =1,2,3,4
Obtained from the following equation:
in the formula (I), the compound is shown in the specification,
s24, calculating a total transmission matrix Q:
Q＝D (1)-1 D (2) P (2) D (2)-1 D (3) P (3) D (3)-1 D (4) (10)。
8. the assay method of claim 7, wherein: the step S3 specifically includes the following steps:
s31, calculating the reflection coefficient of the multilayer structure:
in the formula, r ij Is the reflection coefficient, i, j = s or p; i denotes the incident beam as s-polarized or p-polarized; j represents the reflected beam as s-polarized or p-polarized;
s32, obtaining a reflected light field through angle spectrum operation of the incident light field:
where E represents the amplitude of the light field, subscripts i, r represent the incident and reflected light fields, respectively, superscripts H and V represent the horizontal and vertical polarization components, respectively, of the light field, k 0 To propagate wave vectors, k ry A y-axis component representing a reflected wave vector;
s33, defining transverse displacement of the reflected light:
in the formula, the +/-symbols respectively represent a right-left circularly polarized light part and a right-circular polarized light part of the optical spin Hall effect displacement.
9. The assay method of claim 8, wherein: step S3 is followed by step S4: simulation comparative analysis
S41, determining the direction of an external magnetic field, and analyzing the influence of the thickness of the gold layer in the visible light band on the spin splitting value
Respectively changing the thickness change of a metal layer in the graphene-metal heterojunction and analyzing the influence of a spin splitting value on the premise of a polar magnetic field and a transverse magnetic field to obtain that the thickness of the metal layer of the graphene-metal heterojunction is 50nm and the Fermi level of the graphene is E when incident light is in a visible light wave band in the transverse magnetic field f =0.2eV, relaxation time τ =0.2ps, magnetic induction B =10T, fermi velocity ν f ＝9.5×10 -5 The spin splitting value is the largest, reaches 546nm and is 1.65 times of the extreme value under the polar magnetic field, so that a transverse magnetic field mode is selected for simulation subsequently;
s42, analyzing a terahertz waveband and spin splitting value in the same graphene-metal heterojunction structure
In a transverse magnetic field mode, when the incident light is in a terahertz waveband, and other calculation parameters are the same as those in a visible light waveband, spin splitting is analyzedThe value is along with the variation trend of the incident angle and the terahertz frequency, when the terahertz frequency is 1.2THz, the spin splitting reaches an extreme value of 498 mu m, and is increased by 10 compared with the visible light wave band 3 Magnitude;
s43, changing the external magnetic induction intensity and the graphene Fermi level, and analyzing the change trend of the spin split value;
and S44, analyzing the influence of the periodicity of the graphene-metal heterojunction on the displacement of the optical spin Hall effect.
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