An optical bistable device based on a ternary photonic crystal structure of graphene

Abstract

The application discloses a kind of optical bistable devices based on ternary photonic crystal structure of graphene to terahertz wave band optical bistable device technical field, comprising: the composite structure suitable for terahertz wave band, it is characterized in that: the composite structure is by ternary photonic crystal structure, defect layer C and graphene layer G arrangement combination is formed;The ternary photonic crystal structure is by three dielectric constant different dielectric layer A, B and P alternately arranged composition, the ternary photonic crystal structure is embedded in two layers of defect layer C in the middle, two layers of graphene layer G are embedded in the middle of the defect layer C, the composite structure is Air / (ABP) N1 CG M C(ABP) N2 / Air, the dielectric layer A is made of ZrO2 Material, the dielectric layer B is made of Si material, the dielectric layer P is made of anisotropic plasmon material, the present application has low threshold value, can be used for the parameter multiple of optical bistable control, and the advantages, such as stable working performance, have broad application prospect in terahertz wave band equipment.

Description

Technical Field

[0001] This invention relates to the field of terahertz optical bistable device technology, specifically to an optical bistable device based on a ternary photonic crystal structure of graphene. Background Technology

[0002] Optical bistableness is a nonlinear effect produced when light of a certain intensity interacts with a medium, resulting in two output states for a single input state. It possesses two highly resolvable steady states that can be controlled by an optical signal. Optical bistableness is considered a form of feedback control of light by a nonlinear medium.

[0003] Optical bistable devices are widely used in all-optical switches, photodiodes, sensors, and memories. One approach is to achieve a lower threshold to reduce power consumption. Another method is to maintain a larger threshold gap to avoid malfunctions. Due to their operating principle, lowering the excitation threshold of optical bistable devices helps reduce the laser power required to excite the bistable phenomenon, thereby reducing power consumption; more distinct high and low states and a wider threshold width help avoid malfunctions.

[0004] To design low-threshold optical bistable devices, two common approaches are structure-localized field enhancement and the use of strongly nonlinear dielectric materials. In recent years, researchers have focused on the unique properties of graphene, discovering that it exhibits stronger third-order nonlinear effects compared to traditional nonlinear Kerr dielectric materials. Graphene also possesses ultrafast optical response, variable gate conductivity, and small size, making it a promising new material for fabricating tunable, low-threshold optical devices. For example, graphene can be used to create deeply tunable metamaterial modulators. Current research includes numerous studies on optical bistable devices based on photonic crystal structures, offering more possibilities for designing optical bistable devices. While there are many research results on optical bistable devices, existing devices still need improvement towards practicality, low threshold performance, and the ability to control multiple parameters. Summary of the Invention

[0005] The purpose of this invention is to provide an optical bistable device based on a ternary photonic crystal structure of graphene, so as to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution: an optical bistable device based on a ternary photonic crystal structure of graphene, comprising: a composite structure suitable for the terahertz band, characterized in that: the composite structure is composed of a ternary photonic crystal structure, a defect layer C, and a graphene layer G arranged and combined.

[0007] The ternary photonic crystal structure is a periodic photonic crystal structure composed of three dielectric layers A, B and P with different dielectric constants arranged alternately. Two defect layers C are embedded in the middle of the ternary photonic crystal structure, and a graphene layer G is embedded between the two defect layers C.

[0008] The composite structure is Air / (ABP). N1 CG M C(ABP) N2 / Air, M, N1, N2 are spatial period numbers, the dielectric layer A is made of ZrO2 material, the dielectric layer B is made of Si material, and the dielectric layer P is made of anisotropic plasma material.

[0009] Preferably, the defect layer C is filled with air and has a refractive index of n0 = 1.

[0010] Preferably, the relative permittivity of the dielectric layer A is ε. a =4.21, the relative permittivity of the dielectric layer B is ε b =7.95, the relative permittivity of the dielectric layer P is

[0011] In the formula, i is the imaginary unit, and i 2 = -1, ω is the incident angular frequency, It is the plasma frequency, where n e Here, ρ is the plasma density, e is the electron charge, m is the electron mass, ε0 is the vacuum permittivity, and v is the plasma density. c It is the plasma collision frequency. is the electron cyclotron frequency, and B is the magnetic field strength.

[0012] Preferably, the thickness of each layer in the composite structure is d. a =30um, d b =21.28um, d p =60um, d c =30um and d g =0.33nm;

[0013] Wherein, the number of spatial cycles is M = 1, N1 = 2, and N2 = 3.

[0014] Preferably, the threshold and threshold width of the bistable device are controlled by the Fermi level, relaxation time and number of layers of the graphene layer G.

[0015] Preferably, the threshold and threshold width of the bistable device are modulated by the plasma electron density of the dielectric layer P.

[0016] Preferably, the threshold and threshold width of the bistable device are controlled by the incident angle of the electromagnetic wave.

[0017] Compared with the prior art, the beneficial effects of the present invention are as follows: The present application is composed of a ternary photonic crystal structure with a defect layer embedded with a graphene layer in the middle. Through the defect mode of the above-mentioned composite structure and the strong third-order nonlinear effect of graphene, a lower threshold optical bistable state is achieved. The two metamaterials, plasma and graphene, in the composite structure provide more control parameters for the tuning of the optical bistable state, thereby realizing the tuning of the optical bistable state by using plasma physical parameters, graphene physical parameters, and electromagnetic wave incident angle, etc. It has the advantages of low threshold and many parameters that can be used to control the optical bistable state. It has stable working performance and has broad application prospects in terahertz band equipment. Attached Figure Description

[0018] Figure 1 This is a schematic diagram of the optical bistable device structure of the present invention;

[0019] Figure 2 (a) is a photonic bandgap diagram of the periodic structure of the one-dimensional ternary photonic crystal of the present invention;

[0020] Figure 2 (b) is a photonic bandgap diagram of the periodic structure of the one-dimensional ternary photonic crystal of the present invention after the addition of a defect layer;

[0021] Figure 2 (c) is a photonic bandgap diagram of the optical bistable device structure of the present invention;

[0022] Figure 3 This is an electric field distribution diagram of the ternary photonic crystal composite structure of the present invention;

[0023] Figure 4 (a) is a graph showing the relationship between the transmission electric field and the incident electric field corresponding to different Fermi levels of graphene in this invention.

[0024] Figure 4 (b) is a graph showing the relationship between reflectivity and incident electric field for different Fermi levels of graphene in this invention;

[0025] Figure 5 (a) is a graph showing the relationship between the transmission electric field and the incident electric field for different graphene relaxation times according to the present invention.

[0026] Figure 5 (b) is a graph showing the relationship between reflectivity and incident electric field for different graphene relaxation times according to the present invention;

[0027] Figure 6 (a) is a graph showing the relationship between the transmitted electric field and the incident electric field for different numbers of graphene film layers in this invention;

[0028] Figure 6 (b) is a graph showing the relationship between reflectivity and incident electric field for different numbers of graphene film layers in this invention;

[0029] Figure 7 (a) is a graph showing the relationship between the transmitted electric field and the incident electric field for different plasma electron densities according to the present invention;

[0030] Figure 7 (b) is a graph showing the relationship between reflectivity and incident electric field for different plasma electron densities according to the present invention;

[0031] Figure 8 (a) is a graph showing the relationship between the transmitted electric field and the incident electric field at different incident angles according to the present invention;

[0032] Figure 8 (b) is a graph showing the relationship between reflectivity and incident electric field at different incident angles according to the present invention. Detailed Implementation

[0033] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0034] Example 1

[0035] Please see Figure 1 An optical bistable device based on a graphene-based ternary photonic crystal structure is disclosed, comprising: a ternary photonic crystal structure, a defect layer C, and a graphene layer G; the ternary photonic crystal structure is a periodic photonic crystal structure composed of alternating dielectric layers A, B, and P with different dielectric constants, wherein dielectric layer A is made of ZrO2, dielectric layer B is made of Si, and dielectric layer P is made of anisotropic plasmonic material; two defect layers C are embedded in the ternary photonic crystal structure, and a graphene layer G (graphene thin film layer) is coated between the two defect layers C, forming a composite structure Air / (ABP). N1 CG M C(ABP) N2 / Air, suitable for the terahertz band;

[0036] Where M, N1, and N2 are the spatial period numbers, and are positive integers, (ABP) NIt is a ternary photonic crystal structure. The spatial period number of the ternary photonic crystal to the left of the defect layer C is N1=2, and the spatial period number of the ternary photonic crystal to the right of the defect layer C is N2=3, M=1; the thickness of the dielectric layer A is 30μm, the thickness of the dielectric layer B is 21.28μm, and the thickness of the dielectric layer P is 60μm; the thickness of the defect layer C is 30μm, the thickness of the graphene layer G is 0.33nm, the defect layer C is filled with air, and the refractive index is n0=1.

[0037] It should be noted that when the above composite structure is placed in air, electromagnetic waves are incident from the left side of the composite structure, with an incident frequency of 0.91 THz; the ambient temperature is set to 300 K, the Fermi level of the graphene layer G is set to 0.04 eV, the relaxation time is 0.6 ps, and the initial graphene layer G is a single layer of graphene; the plasma electron density of the dielectric layer P is 1e19 m. －3 The plasma collision frequency is 0 GHz, and the external magnetic field is set to 0 T.

[0038] It should also be noted that the relative permittivity of dielectric layer A is ε. a =4.21, the relative permittivity of dielectric layer B is ε b =7.95, the relative permittivity of dielectric layer P is .

[0039] in,

[0040]

[0041] Finally, the dielectric constant of the plasma layer can be expressed as:

[0042] In the formula, i is the imaginary unit, and i 2 = -1, ω is the incident angular frequency, It is the plasma frequency, where n e Here, e is the plasma density, e is the electron charge, m is the electron mass, ε0 is the vacuum permittivity, and v is the plasma density. c It is the plasma collision frequency. is the electron cyclotron frequency, and B is the magnetic field strength.

[0043] Figure 2 (a) The one-dimensional ternary photonic crystal (ABP) in this application when electromagnetic waves are incident perpendicularly. N Photonic bandgap diagram in the terahertz band; the incident wave enters from the left side of the composite structure. There are four band gaps in the terahertz band, and there is a short passband region a in the middle of each band gap.

[0044] Figure 2 (b) is a post-modal composite structure (ABP) of a one-dimensional ternary photonic crystal with embedded defects. N1 CC(ABP)N2 The photonic bandgap diagram shows that a defect mode transmission peak is formed on both the left and right sides of region a in the photonic bandgap diagram. In each bandgap, the peak value of the transmission peak on the left side of region a is higher than that on the right side. Among the four bandgap regions, the peak value of the transmission peak on the left side of region a increases with the increase of the number of bandgap regions, while the peak value of the transmission peak on the right side of region a decreases with the increase of the number of bandgap regions.

[0045] Figure 2 (c) is the composite structure (ABP) designed in this application. N1 CG M C(ABP) N2 The photonic bandgap diagram is shown; the black dotted line represents the calculation result of the transfer matrix method, and the gray dashed line represents the simulation result of the above structure in COMSOL software; it can be observed from the figure that the two curves are in good agreement, and the COMSOL simulation results verify the correctness of the transfer matrix method used in this paper; the absorption rate of graphene reduces the transmittance of the entire photonic bandgap diagram, and the peak value of the transmission peak on the left side of the first bandgap region a is significantly reduced.

[0046] like Figure 3 As shown, the vertical axis represents the normalized electric field strength; the graphene film is located at the point where the local electric field is strongest, according to the graphene conductivity formula σ=σ0+σ3|E| 2 The third-order nonlinear effect of graphene is enhanced by the increase of the local electric field.

[0047] It should be noted that, without considering the changes in graphene under an applied magnetic field, the electrical conductivity of graphene consists of linear conductivity and nonlinear conductivity, σ = σ0 + σ3|E|. 2 In the formula, E is the field value of the parallel electric field parallel to the graphene interface, σ0 is the linear conductivity, and σ3 is the nonlinear conductivity; the linear conductivity of graphene is equal to the interband conductivity plus the intraband conductivity, i.e., σ0 = σ inter +σ intra .

[0048] Its interband conductivity and intraband conductivity are expressed as follows:

[0049]

[0050] Where i is the imaginary unit, i 2 =-1, π is the constant of pi, e is the electron charge, ω is the incident angular frequency, E F τ is the Fermi level of graphene, τ is the relaxation time of graphene, and k is the energy level of graphene. B Here, T is Boltzmann's constant, h is temperature, and h is Planck's constant. is the reduced Planck constant.

[0051] When the number of graphene layers is small, the number of layers directly and proportionally affects the strength of the nonlinear effect. The third-order nonlinear conductivity of graphene is... The Fermi velocity v of an electron F ≈10 6 m / s.

[0052] It should also be noted that in the graphene-plasma photonic crystal composite structure, the electromagnetic wave expression in the plasma layer and ordinary dielectric layer regions is as follows:

[0053]

[0054]

[0055]

[0056] The z-axis was chosen as the propagation direction, H j,y E is the magnetic field strength of the y-direction component of the TM wave in the medium. j,x E is the electric field intensity of the x-direction component of the TM wave in the medium. j,z It is the electric field intensity of the z-direction component of the TM wave in the medium. Where A j B j These are the amplitudes of the incident electric field and the reflected electric field within the j-th dielectric layer, respectively. l = 0, d a ,d b +d a ,……(d a +d b +d p )×N+2×d c This indicates the position of the electromagnetic wave at the interface between two media, starting from the first interface z = 0 and ending at the last interface z = (d a +d b +d p )×N+2×d c N is the spatial period number of the one-dimensional ternary photonic crystal. x = 0 represents the position of the electromagnetic wave in the x-direction. Here, ω is the incident angular frequency, ε0 ​​is the vacuum permittivity, and the z-component of the wave vector in each layer of the medium is expressed as: Where ε j μ j Let be the relative permittivity and permeability of the j-th layer dielectric material, respectively; ω be the incident angular frequency; c be the speed of light in vacuum; and θ0 be the incident angle of the electromagnetic wave.

[0057] In the above structure, at the ordinary interface of the dielectric layer, there exists a boundary condition E. j,x =E j+1,x H j,y =H j+1,y The boundary condition for the interface containing the two-dimensional material graphene is E. j,x =E j+1,x Hj+1,y -H j,y =-σ g E j+1,x Based on the boundary conditions, the electric field relationships at different interfaces are obtained as follows:

[0058]

[0059] In the above formula These represent the amplitudes of the incident and reflected electric fields in the j-th dielectric layer, respectively, where ω is the incident angular frequency, and k is the amplitude of the incident electric field. j,z Let εj be the z-component of the electromagnetic wave vector in the j-th dielectric layer, and ε0 be the vacuum permittivity. j Let σ be the relative permittivity of the j-th layer dielectric material, and σ be the conductivity at the interface between the two dielectric materials. For ordinary dielectric materials, σ = 0, and for two-dimensional graphene, the conductivity at the interface is σ = σ0 + σ3|E|. 2 E is the electric field value at the interface where the graphene is located.

[0060] The wave propagates a distance d inside the j-th layer of medium j When a wave propagates, only the phase magnitude changes, which can be determined by a propagation matrix M. j to indicate Where i is the imaginary unit, i 2 =-1, e is the natural constant, k j,z Let z be the wave vector z-component of the electromagnetic wave in the j-th layer of the medium. The relationship between the electric field at the graphene interface and the transmitted electric field can then be derived. Where M a M b M p and M c These are the propagation matrices of electromagnetic waves in dielectric layers A, B, P, and C, respectively, and D. a,b It is the propagation matrix of electromagnetic waves at the interface from dielectric layer A to dielectric layer B, and similarly, D b,p and D p,a It is also the propagation matrix of the interface between the two media in the structure, D p,0 This represents the propagation matrix of electromagnetic waves from the P-layer dielectric to the air interface. E is the electric field value at the interface where the graphene is located. t + The transmission electric field is for the composite structure.

[0061] The electric field E at the location of graphene can be determined using the boundary conditions and inverse transport matrix of two-dimensional materials. g Based on other boundary conditions, the transmission electric field E can be determined. t The reflectivity R is related to the incident electric field E. i The relational expression.

[0062] Please see Figure 4 Changing the Fermi level of graphene Figure 4 (a) Figure 4 (b) is the E obtained through calculation, analysis, and simulation when the Fermi levels of graphene are 0.04 eV, 0.05 eV, and 0.06 eV. t R and E respectively i The optical bistable hysteresis loop between; the solid line in the figure is the result of calculation and analysis, and the dashed line is the result of COMSOL simulation; as the Fermi level of graphene increases, both the bistable excitation threshold and the shut-off threshold increase, but the increase in the shut-off threshold is less than the increase in the excitation threshold, and the bistable threshold width increases.

[0063] Please see Figure 5 Changing the relaxation time of graphene Figure 5 (a) Figure 5 (b) E is the calculated value obtained after analysis when the graphene relaxation times are 0.6 ps, 0.8 ps, and 1.0 ps. t R and E respectively i The optical bistable curves between the graphene relaxation time and the bistable threshold increase slightly with increasing graphene relaxation time, while the bistable threshold decreases and the bistable threshold width increases significantly. Figure 5 In (a), the increase in the transmitted electric field value is relatively small. Figure 5 (b) The reflectivity of the optical bistable phenomenon excited by the structure gradually decreases.

[0064] Please see Figure 6 By changing the number of graphene film layers, the thickness of a single graphene layer is 0.33 nm. When the number of graphene film layers N < 6, its conductivity can be approximated as σ ≈ Nσ0. Figure 6 The E values ​​obtained through calculation and analysis are for graphene films with one, two, and three layers, respectively. t R and E respectively i Optical bistability curves between; as the number of graphene layers increases, the excited optical bistability phenomenon... Figure 6 (a) The transmitted electric field intensity gradually decreases, and Figure 6 (b) The reflectivity value increases; with the increase of the number of graphene film layers, both the bistable excitation threshold and the bistable shut-off threshold increase, but the increase of the excitation threshold is greater than the increase of the shut-off threshold, which leads to an increase in the optical bistable threshold width and a larger optical bistable working range; as can be seen from the above analysis, the bistable threshold and threshold width can be controlled by the Fermi level, relaxation time and number of layers of graphene layer G.

[0065] Please see Figure 7 Changing the plasma electron density of dielectric layer P Figure 7 The plasma electron densities are n e =1e19m -3 ne =1e20m -3 n e =2e20m -3 At that time, E was obtained through calculation and analysis. t R and E respectively i Optical bistable curves between [aspects]; with increasing electron density, both the bistable excitation threshold and the shut-off threshold increase; the threshold widths calculated from the results are 0.30 × 10 [units]. 5 V / m, 0.33×10 5 V / m, 0.36×10 5 V / m; it can be seen that as the electron density increases, the increase in the bistable excitation threshold is greater than the increase in the shutdown threshold, thus widening the range between the switching thresholds; therefore, the bistable threshold and threshold width can be controlled by the plasma electron density of the dielectric layer P.

[0066] Please see Figure 8 By changing the incident angle of the electromagnetic wave to 0°, 5°, and 10°, the E obtained through calculation and analysis is... t R and E respectively i Optical bistability curves between; as the incident angle increases, the optical bistability phenomenon of the excited state... Figure 8 (a) The transmitted electric field intensity gradually increases, and Figure 8 (b) The reflectivity value decreases; as the incident angle increases, both the bistable excitation threshold and the bistable shut-off threshold increase, but the increase in the excitation threshold is significantly greater than the increase in the shut-off threshold, which leads to an increase in the bistable threshold width and a larger optical bistable operating range; therefore, the bistable threshold and threshold width can be controlled by the incident angle of the electromagnetic wave.

[0067] In summary, the composite structure of this invention achieves a lower threshold by leveraging the localized field enhancement of defect modes and the strong nonlinear effect of graphene. By incorporating two metamaterials, plasma and graphene, into the composite structure, it is possible to tune optical bistable states using plasma physical parameters, graphene physical parameters, and the incident angle of electromagnetic waves. Furthermore, the defect modes employed in the ternary photonic crystal structure further reduce the excitation threshold of the optical bistable device. This invention possesses advantages such as a low threshold and a wide range of parameters that can be used to control optical bistable states. It also exhibits stable performance and has broad application prospects in terahertz band devices.

[0068] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. An optical bistable device based on a ternary photonic crystal structure of graphene, comprising: A composite structure suitable for the terahertz band, characterized in that: the composite structure is composed of a ternary photonic crystal structure, a defect layer C, and a graphene layer G arranged in combination; The ternary photonic crystal structure is a periodic photonic crystal structure composed of three dielectric layers A, B and P with different dielectric constants arranged alternately. Two defect layers C are embedded in the middle of the ternary photonic crystal structure, and a graphene layer G is embedded between the two defect layers C. The composite structure is as follows: M, N1, and N2 are spatial period numbers. The dielectric layer A is made of ZrO2 material, the dielectric layer B is made of Si material, and the dielectric layer P is made of anisotropic plasma material.

2. The optical bistable device based on a ternary photonic crystal structure of graphene according to claim 1, characterized in that: The defect layer C is filled with air and has a refractive index of .

3. The optical bistable device based on a ternary photonic crystal structure of graphene according to claim 1, characterized in that: The relative permittivity of the dielectric layer A is The relative permittivity of the dielectric layer B is The relative permittivity of the dielectric layer P is ; In the formula, For imaginary units, there is , It is the incident angular frequency. It is the plasma frequency, where It is plasma density. It is the amount of electron charge. It is electronic quality. It is the vacuum permittivity. It is the plasma collision frequency. It is the electron cyclotron frequency. denoted as , where is the magnetic field strength.

4. The optical bistable device based on a ternary photonic crystal structure of graphene according to claim 1, characterized in that: The thicknesses of each layer in the composite structure are respectively , , , as well as ; Wherein, the number of spatial periods , , .

5. The optical bistable device based on a ternary photonic crystal structure of graphene according to claim 1, characterized in that: The threshold and threshold width of the bistable device are controlled by the Fermi level, relaxation time, and number of layers of the graphene layer G.

6. The optical bistable device based on a ternary photonic crystal structure of graphene according to claim 1, characterized in that: The threshold and threshold width of the bistable device are modulated by the plasma electron density of the dielectric layer P.

7. The optical bistable device based on a ternary photonic crystal structure of graphene according to claim 1, characterized in that: The threshold and threshold width of the bistable device are controlled by the incident angle of the electromagnetic wave.

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