Goos-Hanchen displacement sensor based on graphene-dielectric hyperbolic metamaterial

Abstract

The utility model provides a Goos-Hanchen displacement sensor based on a graphene-dielectric hyperbolic metamaterial, and belongs to the technical field of optical sensors. Graphene sheets and dielectric sheets are alternately arranged to form a periodic photonic crystal structure, and in a near-infrared band, for a given incident wavelength, in a photonic crystal composed of graphene and a dielectric, a dispersion space presents a hyperbolic dispersion characteristic by modulating the Fermi level of electrons in the graphene. Furthermore, by changing the Fermi level, the number of layers of the graphene and the thickness of the medium, large GH displacement can be achieved at the phase change position from hyperbolic dispersion to elliptic dispersion, and the maximum GH displacement reaches up to 300 times of incident wavelength. GH displacement is very sensitive to wavelength response, and based on the effect, a hyperbolic metamaterial high-sensitivity dielectric thickness and light wave incident angle sensor is provided.

Description

TECHNICAL FIELD

[0001] The utility model belongs to optical sensor technical field relates to a kind of based on graphene-dielectric doubly curved metamaterial Goos-Ha nchin displacement sensor. BACKGROUND

[0002] Goos-Ha nchin (GH) displacement refers to the lateral deviation of the actual reflected light beam from the geometrically predicted position when the light beam is reflected at an interface. Material properties and structural parameters have a significant impact on GH displacement, which in turn allows for the sensing of material structure and physical parameters by monitoring GH displacement. GH displacement-based sensors have high precision and sensitivity and are widely used in precision measurement, medicine and optical sensing. GH) displacement is the lateral deviation of the actual reflected light beam from the geometrically predicted position when the light beam is reflected at an interface. Material properties and structural parameters have a significant impact on GH displacement, which in turn allows for the sensing of material structure and physical parameters by monitoring GH displacement. GH displacement-based sensors have high precision and sensitivity and are widely used in precision measurement, medicine and optical sensing.

[0003] Doubly curved dispersion characteristics generally refer to the sign of one principal component being opposite to that of the other two principal components in the dielectric constant or magnetic permeability tensor of a material, resulting in a hyperbolic curve of the equal-frequency curve of the material, and thus exhibiting strong anisotropy. Materials or structures with doubly curved dispersion characteristics are called doubly curved metamaterials, which have exhibited many unique electromagnetic properties in the fields of negative refraction, subwavelength imaging, photonic crystals, etc.

[0004] Graphene is a hexagonal honeycomb lattice-like two-dimensional structural material composed of a single layer of carbon atoms. The optical response of graphene is mostly controlled by its surface conductivity, which can be flexibly regulated by a gate voltage. The unique electronic structure and optoelectronic properties of graphene make it a practical plasmonic optical material in the THz to infrared band, widely used in micro-nano photonics, optical super-materials, etc.

[0005] In the composite doubly curved metamaterial of graphene and dielectric, it has been found that a larger GH displacement occurs at the Brewster angle [Applied Physics B (2018) 124:115],

[0006] The combination of graphene and dielectric to form a doubly curved metamaterial results in a dramatic change in the reflection coefficient phase due to the weak loss of graphene and the phase transition characteristics of the doubly curved metamaterial, thereby achieving significant GH displacement. Therefore, it is of great physical significance and application value to study the GH displacement in doubly curved metamaterials and to utilize the GH displacement to detect the physical parameter sensitivity of the structure and material, as well as the dependence on the surface conductivity of graphene. UTILITY MODEL CONTENT

[0007] The utility model discloses a gus -hankin displacement sensor based on graphene -dielectric hyperbolic metamaterial for solving the technical problem of the utility model is the sensitivity of GH displacement to wavelength response, and a hyperbolic metamaterial high sensitivity dielectric thickness and light wave incidence angle sensor is prepared.

[0008] The utility model discloses a gus -hankin displacement sensor based on graphene -dielectric hyperbolic metamaterial can realize the GH displacement of several times of incident wavelength through the change of the fermi level of the electron in graphene, the layer number of graphene sheet and the thickness of dielectric sheet at the phase transition of hyperbolic dispersion to elliptical dispersion.

[0009] Further, the graphene sheet is single layer or multilayer graphene.

[0010] Further, the dielectric sheet is polyimide material.

[0011] Further, the thickness of the dielectric sheet is greater than the thickness of the graphene sheet.

[0012] The graphene sheet and the dielectric sheet (polyimide) are alternately arranged to form a periodic photonic crystal structure: N =(AB) N Wherein N (N = 1, 2, 3,...) is the space period number. In the near infrared wave band, for a given incident wavelength, the dispersion space presents hyperbolic dispersion characteristics in the photonic crystal composed of graphene and dielectric by modulating the fermi level of the electron in graphene. Further, by changing the fermi level, the number of graphene layers and the thickness of the dielectric, a large GH displacement (Gus -Hankin displacement) can be achieved at the phase transition from hyperbolic dispersion to elliptical dispersion, and the maximum GH displacement is up to 300 times the incident wavelength. GH displacement is very sensitive to wavelength, and based on this effect, hyperbolic metamaterial can be used for high sensitivity dielectric thickness and light wave incidence angle sensor. BRIEF DESCRIPTION OF DRAWINGS

[0013] Figure 1 Is the periodic photonic crystal structure schematic diagram when the period number is 6.

[0014] Figure 2 The (a) graph in (a) is the real part of the relative dielectric constant component in the direction of parallel graphene layers under different fermi levels as a function of wavelength. Figure 2Fig. (b) in the figure is the real part of the relative dielectric constant component of the vertical graphene layer direction at different Fermi energy levels as a function of wavelength.

[0015] Figure 3 Fig. (a) in the figure is the reflectivity corresponding to different Fermi energy levels; Figure 3 Fig. (b) in the figure is the local reflectivity amplification corresponding to different Fermi energy levels; Figure 3 Fig. (c) in the figure is the reflection phase corresponding to different Fermi energy levels; Figure 3 Fig. (d) in the figure is the GH displacement corresponding to different Fermi energy levels.

[0016] Figure 4 Fig. (a) in the figure is the reflectivity corresponding to different medium thicknesses; Figure 4 Fig. (b) in the figure is the local reflectivity amplification corresponding to different medium thicknesses; Figure 4 Fig. (c) in the figure is the reflection phase corresponding to different medium thicknesses; Figure 4 Fig. (d) in the figure is the GH displacement corresponding to different medium thicknesses.

[0017] Figure 5 Fig. (a) in the figure is the reflectivity corresponding to different numbers of graphene layers; Figure 5 Fig. (b) in the figure is the local reflectivity amplification corresponding to different numbers of graphene layers; Figure 5 Fig. (c) in the figure is the reflection phase corresponding to different numbers of graphene layers; Figure 5 Fig. (d) in the figure is the GH displacement corresponding to different numbers of graphene layers.

[0018] In the figure, A, graphene sheet; B, dielectric sheet. DETAILED DESCRIPTION

[0019] The following is a specific embodiment of the present application and further describes the technical scheme of the present application in combination with the drawings, but the present application is not limited to these embodiments.

[0020] Two graphene sheets A and dielectric sheets B with different thicknesses are alternately arranged to form a periodic photonic crystal structure: S N =(AB) N , where N (N=1, 2, 3,...) is the number of spatial periods, as shown in Figure 1 . Where 1 is the incident light beam, 2 is the position of the reflected light beam predicted by geometric optics when the light beam is completely reflected at the interface, and 3 is the actual reflected light beam. The selected dielectric sheet B is polyimide, and the structure period number N is set to 6, at which time the structure is ABABABABABAB. The optical properties of graphene can be described by the optical function. Using the random phase approximation, the surface conductivity of graphene is obtained in the absence of an external magnetic field, represented as

[0021]

[0022] where the first term is the intra-graphene band conductivity and the second term is the inter-graphene band conductivity. In the equation, ω is the angular frequency of the incident electromagnetic wave, e is the electronic charge, is the reduced Planck constant, K B is the Boltzmann constant, E F is the Fermi energy of graphene, τ is the relaxation time, and T is the temperature.

[0023] Without considering the influence of the external electric field, a TM polarized light is incident from the air. In the figure, θ is the incident angle of the light, and S is the GH displacement. The effective dielectric constant of the graphene sheet can be expressed as

[0024]

[0025] where ε0is the vacuum dielectric constant, and the monolayer thickness of graphene is t g . The thickness and dielectric constant of the medium are t d and ε d , respectively. Under the subwavelength condition, when the structure period is much smaller than the incident wavelength, i.e., t g +t d << λ0, the graphene / medium periodic structure can be regarded as an effective homogeneous uniaxial anisotropic medium. The direction perpendicular to the graphene layer is defined as the Z axis, and the dielectric constant tensor has a diagonal form, which can be expressed as

[0026] [ε] = diag[ε xx , ε yy , ε zz ], (3)

[0027] where ε xx = ε yy = ε || , ε zz = ε ⊥ , ε || and ε ⊥ represent the dielectric constants parallel and perpendicular to the graphene layer, respectively, and are expressed as follows

[0028] The effective thickness of graphene can be ignored compared with the thickness of the medium layer. For the propagation of transverse magnetic (TM) waves, the dispersion surface can be expressed as:

[0029]

[0030] where k x and k z are the wave vectors of the structure in the X and Z directions, respectively, k0is the wave vector of free space, and ε xx · εzz <0, then the dispersion curve is hyperbolic, in which case the structure is also referred to as a Graphene-based hyperbolic metamaterial (GHMM). If ε xx > 0, then the dispersion curve is elliptic. zz > 0, then the dispersion curve is elliptic.

[0031] For photonic crystals or multilayer structures, the transfer matrix method is used to analyze the reflection phase and reflectivity of the structure. For a given medium layer i, when an electromagnetic wave is incident into the structure, the transfer matrix can be expressed as

[0032] Here,

[0033]

[0034] where n d and n g are the refractive indices of the dielectric and graphene, respectively, and λ is the wavelength of the incident light. η i (i = d, g) are the effective optical admittances in the dielectric and graphene. The transfer matrix of a multilayer material can be obtained by multiplying the transfer matrices of each layer, i.e.

[0035]

[0036] The reflection coefficient of the structure can then be calculated as

[0037]

[0038] The reflectivity R = |r| of the structure can be obtained from the reflection coefficient, as well as the reflection phase Φ 2 r According to the static phase method, the GH shift can be obtained as

[0039]

[0040] In the calculation, the temperature T = 300 K, the relaxation time τ = 0.5 ps, the thickness of the dielectric t d = 50 nm, the dielectric constant ε d = 2.88, and the thickness of single-layer graphene t g = 0.5 nm.

[0041] When the transverse magnetic wave is vertically incident, at different Fermi levels (E F = 0.6, 0.7, 0.8, 0.9, 1.0 eV), the reflectivity R and the reflection phase Φ Figure 2 (a) The horizontal axis represents the dielectric constant component ε xx ​of the real part of ε xx of the real part of ε xx of the real part of ε xx of the real part of ε

[0042] Figure 2 (b) shows the real part of the dielectric constant component ε zz of the real part of ε zz of the real part of ε zz of the real part of ε zz of the real part of ε F of the real part of ε zz of the real part of ε zz of the real part of ε Figure 2 (a) shows the real part of the dielectric constant component ε xx of the real part of ε xx of the real part of ε zz of the real part of ε

[0043] Figure 3 (a) shows the reflectivity curve with the change of the incident angle, the horizontal axis of the incident angle ranges from 40° to 70°. It can be seen that the reflectivity appears obvious troughs with the change of the incident angle. Figure 3 (b) is a local magnification of the reflectivity[ Figure 3 (a) rectangular dotted frame]. Here the reflectivity of the Fermi level E = 0.6eV, 0.7eV, 0.8eV, 0.9eV, 1.0eV is respectively zoomed in. It can be seen that the incident angle corresponding to the extreme value of the reflectivity is affected by the Fermi level, when the Fermi level increases, the incident angle corresponding to the minimum reflectivity first increases and then decreases.

[0044] Figure 3 (c) shows the change of the reflection phase with the incident angle at different Fermi levels, it can be seen that with the increase of the Fermi level, the slope of the reflection phase curve gradually decreases, when E F= 0.6 eV, the reflection phase curve is the steepest. It is worth noting that, according to formula (12), a larger GH displacement requires a larger reflection phase slope. The slope of the reflection phase curve in the figure is always positive, which will result in a negative GH displacement.

[0045] Figure 3 (d) shows the variation of GH displacement with the incident angle at different Fermi energy levels. It can be seen that, with the increase of the Fermi energy level, the negative GH displacement gradually decreases. At E F = 0.6 eV, the negative GH displacement can reach 300 times the incident wavelength, and the maximum GH displacement is located at the phase transition point from hyperbolic dispersion to elliptical dispersion. Therefore, the size of the GH displacement of the reflected light beam can be flexibly adjusted by changing the Fermi energy level.

[0046] Figure 4 (a) shows the variation of reflectivity R with the incident angle at different medium thicknesses. It can be seen that, with the change of the incident angle, the reflectivity shows obvious troughs. Figure 4 (b) is a partial enlargement of the reflectivity [ Figure 4 (a) rectangular dashed box]. Here, the reflectivity of the medium thickness t d = 50 nm, 55 nm, 60 nm, and 65 nm is respectively zoomed in. It can be seen that the troughs of the reflectivity curve gradually move to the right with the increase of the medium thickness. For the incident light, the best incident angle region of the structure is affected by the medium thickness.

[0047] Figure 4 (c) shows the variation of the reflection phase with the incident angle at different medium thicknesses. It can be seen that, with the increase of the medium thickness, the slope of the reflection phase gradually decreases. And the slope of the curve corresponding to the reflection phase is always positive, which will result in a negative GH displacement.

[0048] Figure 4 (d) shows the variation of GH displacement with the incident angle at different medium thicknesses. It can be seen that, with the increase of the medium thickness, the negative GH displacement gradually decreases. When the medium thickness t d = 50 nm is selected, a negative GH displacement of about 300 times the wavelength can be obtained. Therefore, the size of the GH displacement on the surface of the structure can also be flexibly adjusted by changing the medium thickness.

[0049] Figure 5 (a) shows the variation of reflectivity R with the incident angle at different numbers of graphene layers. In the calculation, the Fermi energy level E F = 0.6 eV is set. It can be seen that, with the change of the incident angle (the incident angle ranges from 30° to 70°), the reflectivity shows obvious troughs. Figure 5 (b) is a partial enlargement of the reflectivity [ Figure 5(a) rectangular dashed box]. Here the reflectivity of graphene layers N g =1, 2, 3, 4 are shown in close-up. It can be seen that with the increase of the number of graphene layers, the trough of the reflectivity curve gradually moves to the left with the increase of the number of graphene layers. For the incident light, the best absorption incident angle region of the structure is affected by the number of graphene layers.

[0050] Figure 5 (c) shows the change curve of the reflection phase with the incident angle under different number of graphene layers. It can be seen that the slope of the reflection phase gradually decreases with the increase of the number of graphene layers. And the slope of the curve corresponding to the reflection phase is always positive, which will get a negative GH shift. Figure 5 (d) shows the GH shift corresponding to different number of graphene layers. The GH shift always shows a negative value, and gradually decreases with the increase of the number of graphene layers. The maximum negative GH shift of 300 times the wavelength can be obtained when the number of graphene layers is 1.

[0051] In summary, the graphene sheets A and the dielectric sheets B (polyimide) with two different thicknesses are arranged alternately to form a periodic photonic crystal structure. In the near-infrared waveband, by adjusting the Fermi energy level of graphene, the hyperbolic dispersion characteristics of the composite structure can be realized. Further, by changing the Fermi energy level, the number of graphene layers and the dielectric thickness, at the phase transition from hyperbolic dispersion to elliptical dispersion, the GH shift can be effectively controlled and the GH shift of up to 300 times the incident wavelength can be obtained. This effect can be used for high-sensitivity dielectric thickness and light wave incident angle sensors based on GH shift effect in hyperbolic metamaterials.

[0052] The specific embodiments described herein are merely illustrative of the spirit of the present application. Those skilled in the art of the present application can make various modifications or supplements to the described specific embodiments or use similar ways to replace them, but will not deviate from the spirit of the present application or exceed the scope defined by the appended claims.

Claims

1. A Goos-Ha nchen shift sensor based on graphene-dielectric hyperbolic metamaterials, characterized in that, comprise the same number of graphene sheets (A) and dielectric sheets (B) alternately stacked to form a periodic photonic crystal multilayer structure.

2. The graphene-dielectric hyperbolic metamaterial based Goos-Haunchn shift sensor according to claim 1, wherein, The graphene sheets (A) are single or multiple layers of graphene.

3. The graphene-dielectric hyperbolic metamaterial based Goos-Haunchn shift sensor according to claim 1, wherein, The dielectric sheets (B) are polyimide materials.

4. The graphene-dielectric hyperbolic metamaterial based Goos-Haunchn shift sensor according to claim 1, wherein, The dielectric sheets (B) have a thickness greater than that of the graphene sheets (A).

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