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

Abstract

The invention 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 invention belongs to the technical field of optical sensors and relates to a Goos-Hanchen displacement sensor based on graphene-dielectric hyperbolic metamaterial. Background Art

[0002] Goos-Hanchen GH displacement refers to the lateral displacement of the actual reflected light beam from the geometric optical predicted position when the light beam is reflected at the interface. Material properties and structural parameters have a significant impact on GH displacement. Conversely, the material structure and physical parameters can be perceived by monitoring GH displacement. Sensors based on GH displacement have high accuracy and sensitivity and are widely used in precision measurement, medicine, optical sensing and other fields.

[0003] Hyperbolic dispersion usually refers to the fact that the sign of one principal component in the dielectric constant or permeability tensor of a material is opposite to the signs of the other two principal components, making the equal frequency curve of the material hyperbolic, thereby showing strong anisotropy. Materials or structures with hyperbolic dispersion properties are called hyperbolic metamaterials. Hyperbolic metamaterials have demonstrated many unique electromagnetic properties in the fields of negative refraction, subwavelength imaging, photonic crystals, etc.

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

[0005] In composite hyperbolic metamaterials of graphene and dielectrics, it has been found that large GH shifts occur at the Brewster angle [Applied Physics B (2018) 124: 115].

[0006] The composite of graphene and dielectric to form a hyperbolic metamaterial, due to the weak loss of graphene, combined with the phase change characteristics of the hyperbolic metamaterial, will inevitably lead to a drastic change in the phase of the reflection coefficient, thereby achieving a significant GH shift. Therefore, studying the GH shift in hyperbolic metamaterials and using the GH shift to detect the sensitivity of the physical parameters of the structure and material, as well as the dependence on the conductivity of the graphene surface, has important physical significance and application value. Summary of the invention

[0007] The purpose of the present invention is to provide a Goos-Hanchen shift sensor based on graphene-dielectric hyperbolic metamaterial in view of the above-mentioned problems existing in the prior art. The technical problem to be solved by the present invention is to utilize the sensitivity of GH shift response to wavelength to obtain a hyperbolic metamaterial high-sensitivity dielectric thickness and light wave incident angle sensor.

[0008] The objective of the present invention can be achieved through the following technical solutions: a Goos-Hanchen shift sensor based on graphene-dielectric hyperbolic metamaterial, characterized in that it comprises the same number of graphene sheets and dielectric sheets, and the graphene sheets and dielectric sheets are alternately stacked to form a periodic photonic crystal multilayer structure; in the near-infrared band, the periodic photonic crystal multilayer structure exhibits hyperbolic dispersion characteristics in the dispersion space, and by changing the Fermi level of electrons in the graphene, the number of graphene sheets and the thickness of the dielectric sheets, a Goos-Hanchen shift several times the incident wavelength is achieved at the phase transition from hyperbolic dispersion to elliptical dispersion.

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

[0010] Furthermore, the dielectric sheet is made of polyimide material.

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

[0012] Alternately arrange graphene sheets and dielectric sheets (polyimide) to form a periodic photonic crystal structure: S N =(AB) N , where N (N = 1, 2, 3, ...) is the number of spatial periods. In the near-infrared band, for a given incident wavelength, in a photonic crystal composed of graphene and dielectrics, by modulating the Fermi level of electrons in graphene, the dispersion space exhibits hyperbolic dispersion characteristics. Further, by changing the Fermi level, the number of graphene layers and the thickness of the dielectric, a larger GH shift (Goose-Hanchen shift) can be achieved at the phase transition from hyperbolic dispersion to elliptical dispersion, with a maximum GH shift of up to 300 times the incident wavelength. The GH shift is very sensitive to wavelength response. Based on this effect, hyperbolic metamaterials can be used for highly sensitive dielectric thickness and light wave incident angle sensors. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0014] Figure 2 (a) shows the real part of the relative dielectric constant component parallel to the graphene layer at different Fermi levels as a function of wavelength; Figure 2 Figure (b) shows the variation of the real part of the relative dielectric constant component perpendicular to the graphene layer with wavelength at different Fermi levels.

[0015] Figure 3 Figure (a) shows the reflectivity corresponding to different Fermi levels; Figure 3 (b) is the local reflectivity amplification corresponding to different Fermi levels; Figure 3 Figure (c) shows the reflection phase corresponding to different Fermi levels; Figure 3 Figure (d) shows the GH shift corresponding to different Fermi levels.

[0016] Figure 4 Figure (a) shows the reflectivity corresponding to different medium thicknesses; Figure 4 Figure (b) is the magnified local reflectivity corresponding to different medium thicknesses; Figure 4 Figure (c) shows the reflection phase corresponding to different medium thicknesses; Figure 4 Figure (d) shows the GH displacement corresponding to different dielectric thicknesses.

[0017] Figure 5 Figure (a) shows the reflectivity corresponding to different numbers of graphene layers; Figure 5 Figure (b) is the magnified local reflectivity corresponding to different numbers of graphene layers; Figure 5 Figure (c) shows the reflection phase corresponding to different numbers of graphene layers; Figure 5 Figure (d) shows the GH shift corresponding to different numbers of graphene layers.

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

[0019] The following are specific embodiments of the present invention and the accompanying drawings to further describe the technical solution of the present invention, but the present invention is not limited to these embodiments.

[0020] Two graphene sheets A and dielectric sheets B with different thicknesses are arranged alternately to form a periodic photonic crystal structure: S N =(AB) N , where N (N = 1, 2, 3, ...) is the number of spatial periods, such as Figure 1 As shown. 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 dielectric sheet B selected is polyimide, and the number of structural periods N is set to 6. At this time, the structure is ABABABABABAB. The optical properties of graphene can be described by light functions. Using the random phase approximation in the absence of an external magnetic field, the surface conductivity of graphene is obtained, which is expressed as

[0021]

[0022] The first term is the conductivity within the graphene band, and the second term is the conductivity between graphene bands. In the formula, ω is the angular frequency of the incident electromagnetic wave, e is the electron charge, is the reduced Planck constant, K B is the Boltzmann constant, E F is the Fermi level of graphene, τ is the relaxation time, and T is the temperature.

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

[0024]

[0025] Where ε0 is the dielectric constant of vacuum and the single layer thickness of graphene is t g The thickness and dielectric constant of the medium are t d and ε d Under sub-wavelength conditions, when the structural period is much smaller than the incident wavelength, that is, t g +t d <<λ0, the graphene / medium periodic structure can be regarded as an effectively uniform 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 and 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 ⊥ The dielectric constants parallel to and perpendicular to the graphene layer are expressed as follows:

[0028]

[0029] The effective thickness of graphene can be ignored compared to the thickness of the dielectric layer. For the propagation of transverse magnetic waves (TM), its dispersion surface can be expressed as:

[0030]

[0031] where k x and k z are the wave vectors of the structure in the X and Z directions respectively, k0 is the wave vector of free space, if ε xx ·ε zz<0, the dispersion curve is hyperbolic, and the structure is also called (Graphene-based hyperbolicmetamaterials, GHMM). xx ·ε zz >0, the dispersion curve is elliptical.

[0032] For photonic crystals or multilayer structures, the transmission matrix method is used to analyze the reflection phase and reflectivity of the structure. For a given dielectric layer i, when an electromagnetic wave is incident on the structure, the transmission matrix can be expressed as

[0033]

[0034] here,

[0035]

[0036] Where n d and n g are the refractive indices of dielectric and graphene respectively, and λ is the wavelength of the incident light wave. i (i = d, g) is the effective optical admittance in the dielectric and graphene. The transmission matrix of the multilayer material can be obtained by multiplying the transmission matrices of each layer, that is,

[0037]

[0038] Then the reflection coefficient of the structure can be calculated as

[0039]

[0040] The reflectivity of the structure can be obtained through the reflection coefficient R = |r| 2 and the reflected phase Φ r According to the static phase method, the GH displacement can be obtained as

[0041]

[0042] In the calculation, set the temperature T = 300K, the relaxation time τ = 0.5ps, and the thickness of the medium to t d =50nm, dielectric constant is ε d =2.88, the thickness of a single layer of graphene is t g =0.5nm.

[0043] When the transverse magnetic wave is incident vertically, at different Fermi levels (E F =0.6, 0.7, 0.8, 0.9, 1.0 eV), Figure 2 (a) The vertical axis represents the dielectric constant component ε parallel to the graphene layer direction. xxThe real part of , the horizontal axis represents the incident wavelength. It can be seen that different Fermi levels correspond to different ε xx Real part curve. As the incident wavelength increases, ε xx The real part of ε gradually decreases, and xx The real part of is positive for all wavelengths. The angle of incidence is set to 0°.

[0044] Figure 2 (b) The vertical axis represents the dielectric constant component ε perpendicular to the graphene layer. zz It can be seen that different Fermi levels correspond to different ε zz Real part curve. ε zz The incident wavelength corresponding to the change in the real part is obviously different. As the Fermi level gradually increases, ε zz When the real part changes from positive to negative, the corresponding incident wavelength gradually decreases. F = 0.6eV. When the wavelength λ is around 1300nm, ε zz The real part of changes dramatically, from negative to positive. In a small incident wavelength region on the left side of λ=1299.4nm, ε zz The real part of is negative. In this case, we can get Figure 2 (a) Find the ε corresponding to the incident wavelength xx The real part of is positive, then ε xx and ε zz The opposite signs make the periodic structure composed of graphene and medium show hyperbolic dispersion characteristics. In the subsequent study, the incident wavelength λ=1299.4nm is selected.

[0045] Figure 3 (a) shows the curve of reflectivity changing with the incident angle, and the incident angle range of the horizontal axis is 40°-70°. It can be seen that with the change of the incident angle, the reflectivity has an obvious trough. Figure 3 (b) is a local enlarged view of the reflectivity [ Figure 3 (a) Rectangular dotted box]. Here, the reflectivity at Fermi levels of E = 0.6eV, 0.7eV, 0.8eV, 0.9eV, and 1.0eV is shown in close-up. 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 increases first and then decreases.

[0046] Figure 3 (c) shows the curve of reflection phase changing with incident angle at different Fermi levels. It can be seen that with the increase of Fermi level, the slope of reflection phase curve decreases gradually. F=0.6eV, the reflection phase curve is the steepest. It is worth noting that, from formula (12), in order to obtain a larger GH shift, a larger reflection phase slope is required. The slope of the reflection phase curve in the figure is always positive, which will result in a negative GH shift.

[0047] Figure 3 (d) shows the change of GH shift with incident angle at different Fermi levels. It can be seen that with the increase of Fermi level, the negative GH shift gradually decreases. F =0.6eV, the negative GH shift can reach 300 times the incident wavelength, and the maximum GH shift is located exactly at the phase transition point from hyperbolic dispersion to elliptical dispersion. Therefore, the magnitude of the reflected beam GH shift can be flexibly controlled by changing the Fermi level.

[0048] Figure 4 (a) shows the curve of reflectivity R changing with the incident angle under different dielectric thicknesses. It can be seen that with the change of the incident angle, the reflectivity has an obvious trough. Figure 4 (b) is a local enlarged view of the reflectivity [ Figure 4 (a) Rectangular dotted box]. Here the dielectric thickness is t d =50nm, 55nm, 60nm, 65nm reflectivity are shown in close-up. It can be seen that the trough of the reflectivity curve gradually shifts to the right as the thickness of the medium increases. For incident light, the optimal incident angle area of ​​the structure is affected by the thickness of the medium.

[0049] Figure 4 (c) shows the curve of the reflection phase changing with the incident angle under different dielectric thicknesses. It can be seen that with the increase of dielectric 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 shift.

[0050] Figure 4 (d) shows the change of GH displacement with incident angle under different dielectric thickness. It can be seen that with the increase of dielectric thickness, the negative displacement of GH gradually decreases. d =50nm, a negative GH shift of about 300 times the wavelength can be obtained. Therefore, the magnitude of the GH shift on the surface of the structure can be flexibly controlled by changing the thickness of the medium.

[0051] Figure 5 (a) shows the curve of reflectivity R changing with the incident angle under different graphene layer numbers. The Fermi level E is set in the calculation F =0.6eV. It can be seen that with the change of the incident angle (the incident angle range is 30°-70°), the reflectivity has an obvious trough. Figure 5 (b) is a local enlarged view of the reflectivity [ Figure 5(a) Rectangular dashed box]. Here, the number of graphene layers N g =1, 2, 3, 4 are shown in close-up. It can be seen that as the number of graphene layers increases, the trough of the reflectivity curve gradually shifts to the left. For incident light, the optimal absorption incident angle region of the structure is affected by the number of graphene layers.

[0052] Figure 5 (c) shows the curve of the reflection phase changing with the incident angle under different graphene layer numbers. It can be seen that the slope of the reflection phase gradually decreases with the increase of graphene layer numbers. And the slope of the curve corresponding to the reflection phase is always positive, which will result in a negative GH shift. Figure 5 (d) shows the GH shift corresponding to different numbers of graphene layers. The GH shift is always negative and gradually decreases with the increase of the number of graphene layers. When the number of graphene layers is 1, the maximum negative GH shift of 300 times the wavelength can be obtained.

[0053] In summary, two graphene sheets A and dielectric sheets B (polyimide) of different thicknesses are arranged alternately to form a periodic photonic crystal structure. In the near-infrared band, the Fermi level of graphene can be adjusted to achieve the hyperbolic dispersion characteristics of the composite structure. Further, by changing the Fermi level, the number of graphene layers and the thickness of the dielectric, the GH shift can be effectively controlled at the phase transition from hyperbolic dispersion to elliptical dispersion and a 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 the GH shift effect in hyperbolic metamaterials.

[0054] The specific embodiments described herein are merely examples of the spirit of the present invention. Those skilled in the art may make various modifications or additions to the specific embodiments described or replace them in similar ways, but they will not deviate from the spirit of the present invention or exceed the scope defined by the appended claims.

Claims

1. A Goos-Hanchen displacement sensor based on graphene-dielectric hyperbolic metamaterial, characterized in that: The invention comprises the same number of graphene sheets (A) and dielectric sheets (B), wherein the graphene sheets (A) and dielectric sheets (B) are alternately stacked to form a periodic photonic crystal multilayer structure; in the near-infrared band, the periodic photonic crystal structure exhibits hyperbolic dispersion characteristics in the dispersion space; by changing the Fermi level of electrons in the graphene, the number of graphene sheets (A) layers and the thickness of the dielectric sheets (B), a Goos-Hanchen shift up to 300 times the incident wavelength is achieved at the phase transition from hyperbolic dispersion to elliptical dispersion; the Goos-Hanchen shift is used for high-sensitivity dielectric thickness and light wave incident angle sensors.

2. The Goos-Hanchen displacement sensor based on graphene-dielectric hyperbolic metamaterial according to claim 1, characterized in that: The graphene sheet (A) is a graphene single layer or multilayer.

3. The Goos-Hanchen displacement sensor based on graphene-dielectric hyperbolic metamaterial according to claim 1, characterized in that: The dielectric sheet (B) is made of polyimide material.

4. The Goos-Hanchen displacement sensor based on graphene-dielectric hyperbolic metamaterial according to claim 1, characterized in that: The thickness of the dielectric sheet (B) is greater than the thickness of the graphene sheet (A).

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