CN109669227B - Photonic crystal with enhanced reflectivity to defect mode - Google Patents
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- 230000007547 defect Effects 0.000 title claims abstract description 79
- 239000004038 photonic crystal Substances 0.000 title claims abstract description 37
- 238000002310 reflectometry Methods 0.000 title claims abstract description 36
- OKTJSMMVPCPJKN-UHFFFAOYSA-N Carbon Chemical compound [C] OKTJSMMVPCPJKN-UHFFFAOYSA-N 0.000 claims abstract description 38
- 229910021389 graphene Inorganic materials 0.000 claims abstract description 38
- 239000013078 crystal Substances 0.000 claims abstract description 5
- 239000000463 material Substances 0.000 claims description 4
- 239000005083 Zinc sulfide Substances 0.000 claims description 2
- ORUIBWPALBXDOA-UHFFFAOYSA-L magnesium fluoride Chemical compound [F-].[F-].[Mg+2] ORUIBWPALBXDOA-UHFFFAOYSA-L 0.000 claims description 2
- 229910001635 magnesium fluoride Inorganic materials 0.000 claims description 2
- 229910052984 zinc sulfide Inorganic materials 0.000 claims description 2
- DRDVZXDWVBGGMH-UHFFFAOYSA-N zinc;sulfide Chemical compound [S-2].[Zn+2] DRDVZXDWVBGGMH-UHFFFAOYSA-N 0.000 claims description 2
- 238000006073 displacement reaction Methods 0.000 abstract description 27
- 230000005622 photoelectricity Effects 0.000 abstract 1
- 239000010410 layer Substances 0.000 description 73
- 230000002950 deficient Effects 0.000 description 13
- 230000005540 biological transmission Effects 0.000 description 9
- 239000011159 matrix material Substances 0.000 description 6
- 230000005672 electromagnetic field Effects 0.000 description 4
- 238000000034 method Methods 0.000 description 3
- 238000002834 transmittance Methods 0.000 description 3
- 230000000694 effects Effects 0.000 description 2
- 239000002245 particle Substances 0.000 description 2
- 230000001902 propagating effect Effects 0.000 description 2
- 239000002356 single layer Substances 0.000 description 2
- 238000001228 spectrum Methods 0.000 description 2
- 239000000126 substance Substances 0.000 description 2
- 238000007792 addition Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 239000003989 dielectric material Substances 0.000 description 1
- 238000009472 formulation Methods 0.000 description 1
- 239000000203 mixture Substances 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 230000003287 optical effect Effects 0.000 description 1
- 230000005693 optoelectronics Effects 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
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- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B5/00—Optical elements other than lenses
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- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B1/00—Optical elements characterised by the material of which they are made; Optical coatings for optical elements
- G02B1/002—Optical elements characterised by the material of which they are made; Optical coatings for optical elements made of materials engineered to provide properties not available in nature, e.g. metamaterials
- G02B1/005—Optical elements characterised by the material of which they are made; Optical coatings for optical elements made of materials engineered to provide properties not available in nature, e.g. metamaterials made of photonic crystals or photonic band gap materials
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- Crystallography & Structural Chemistry (AREA)
- Optical Integrated Circuits (AREA)
- Optical Modulation, Optical Deflection, Nonlinear Optics, Optical Demodulation, Optical Logic Elements (AREA)
Abstract
The invention provides a photonic crystal with enhanced reflectivity to a defect mode, and belongs to the technical field of photoelectricity. The photonic crystal comprises a first dielectric layer, a second dielectric layer, a defect layer and a graphene layer, wherein the defect layer is positioned in the middle of the electronic crystal; the distribution rule of the first dielectric layer and the second dielectric layer is as follows: a plurality of first dielectric layers and a plurality of second dielectric layers are alternately arranged on two sides of the defect layer, the first dielectric layers are arranged on two outer side surfaces of the photonic crystal, and the second dielectric layers are arranged on two sides close to the defect layer; the graphene layer is embedded within the defect layer. The invention has the advantages of improving the reflectivity of a defect mode, causing the severe change of the phase of the reflection coefficient, large transverse displacement of the reflected light beam and the like by doping the graphene into the defect layer of the photonic crystal.
Description
Technical Field
The invention belongs to the technical field of optoelectronics, and relates to a photonic crystal with enhanced reflectivity to a defect mode.
Background
The band gap exists in the photonic crystal. When light impinges on the photonic crystal, if the frequency of the light is within the band gap, no light will be transmitted through the photonic crystal and total reflection of the light beam will occur. However, if a defect layer is added to the photonic crystal, there is one defect mode in the band gap of the energy band. When the frequency of the incident light is equal to the frequency of the defect mode, the light beam will pass through the photonic crystal entirely without reflection, and the reflectivity at this time is zero, so the defect mode is also called a transmission mode. The energy of the defect mode is mainly distributed in the defect layer, and the energy distribution at the center point of the defect layer is strongest. The energy distribution of the defect mode decays exponentially extending from the center of the defect layer to both sides of the photonic crystal.
The lateral displacement of the reflected light beam can be widely applied to high-sensitivity sensors, optical switches and the like. However, in general, the lateral displacement of the reflected light beam is small, typically several wavelengths or several tens of wavelengths, and thus it is very difficult to experimentally detect the lateral displacement of the light beam and to actually apply the same. One enhances the lateral displacement of the reflected beam by a variety of methods, such as utilizing the bandgap edge of photonic crystals, weakly lossy materials, graphene, and the like to achieve a larger lateral displacement.
The lateral displacement of the reflected beam is proportional to the derivative of the reflection coefficient phase with respect to the wave vector, and there is uncertainty in the reflection coefficient phase of the defective mode due to the zero reflectivity of the defective mode, so that there may be a large lateral displacement of the reflected beam of the defective mode. However, for a photonic crystal without gain and loss, the reflectance of the defective mode is zero, and even if there is a large lateral displacement at this time, it is practically meaningless.
Disclosure of Invention
The present invention is directed to solving the above-mentioned problems of the prior art, and provides a photonic crystal with high reflectivity, and the technical problem to be solved by the present invention is how to increase the reflectivity by doping graphene into a defect layer of the photonic crystal.
The aim of the invention can be achieved by the following technical scheme: the photonic crystal with high reflectivity is characterized by comprising a first dielectric layer, a second dielectric layer, a defect layer and a graphene layer, wherein the defect layer is positioned in the middle of the electronic crystal; the distribution rule of the first dielectric layer and the second dielectric layer is as follows: a plurality of first dielectric layers and a plurality of second dielectric layers are alternately arranged on two sides of the defect layer, the first dielectric layers are arranged on two outer side surfaces of the photonic crystal, and the second dielectric layers are arranged on two sides close to the defect layer; the graphene layer is embedded within the defect layer.
The first and second dielectric layers may be dielectrics common in the art, such as magnesium fluoride, zinc sulfide, and the like.
The graphene is doped into a defect layer of the photonic crystal, and the weak loss of the graphene is utilized to weaken the transmittance of the photonic crystal to a defect mode, so that the reflectivity of a light beam is improved. Meanwhile, weak loss of graphene also causes abrupt changes in the reflection coefficient phase. According to the fact that the lateral displacement of the reflected light beam is proportional to the phase change rate of the reflection coefficient, when the incidence frequency of light is located near the defect mode, larger lateral displacement of the reflected light beam can be obtained.
The refractive index of the first dielectric layer, the second dielectric layer and the defect layer is n a ＝1.38、n b =2.35 and n c =2.35, the thicknesses of the first dielectric layer, the second dielectric layer and the defect layer are d a ＝0.281μm、d b =0.165 μm and d c =0.33 μm. The incident light is denoted as 1, the reflected light is denoted as 2, and the transmitted light is denoted as 3. The lateral displacement of the reflected light with respect to the point of incidence is noted as delta.
The single-layer graphene is doped in the middle of the defect layer, namely at the 0-point position of the z-axis of the photonic crystal. Single layer graphene is a two-dimensional material of no thickness, whose surface conductivity can be described by the nine-bauer formula (Kubo formula), as follows:
wherein f d ＝1/(1+exp[(ε-μ c )/(k B T)]) For the fermi-dirac statistics, epsilon is the particle energy, mu c Is a graphene chemical potential (also known as fermi level E F ) T is the temperature, e is the electron charge, τ is the momentum relaxation time, k B Is the boltzmann constant.
The graphene layer is considered as an equivalent dielectric with a thickness, and when the equivalent thickness is below 1nm, the effect of this equivalent method on the calculated reflectivity and transmittance is negligible. We take the thickness of the graphene layer to be 0.34nm. Graphene having an equivalent dielectric constant of ε g ＝1+iσ g η 0 /(kd g ) Where k is incident ofWave vector, eta 0 Is the vacuum impedance. Temperature t=27 ℃, momentum relaxation time τ=0.5 ps, μ c ＝0.15eV。
The whole structure is (AB) N CGC(BA) N (assuming a first dielectric layer is a, B second dielectric layer is B, C for the defect layer, G for the graphene layer), where the number of bragg periods n=5.
Let the incident light be a TM wave, propagating along the z-axis. The electromagnetic fields across each layer of dielectric may be related by a transmission matrix. For example, the electromagnetic fields across the first layer dielectric may be related by the following relationship
Wherein M is l The transmission matrix of layer I, where eta l ＝ε l (ε 0 /μ 0 ) 1/2 /(ε l -sin 2 θ) 1/2 ，θ is the incident angle of light, here θ=20°. The transmission matrix of the whole system is
Where n is the total number of layers of the structure. The reflection coefficient is
Wherein eta 1 ＝η N+1 ＝(ε 0 /μ 0 ) 1/2 (1-sin 2 θ) 1/2 The impedance of the incident end and the emergent end respectively, and the reflectivity is r=rr. The band gap of the photonic crystal is omega gap ＝4ω 0 arcsin│(n b -n a )/(n b +n a )│ 2 Pi, wherein omega 0 ＝2πc/λ 0 ，λ 0 ＝1.55μm。
If the graphene layer is undoped, it can be seen that the reflectivity is a function of the frequency of the incident light. There is a band gap in the middle of the reflection spectrum, and light within this band gap will be totally reflected. However, the reflectivity of the defect mode is zero at the x position, and the light of the defect mode is totally transmitted, so that the defect mode is also called a transmission mode.
Based on the relationship between the lateral displacement of the reflected beam and the phase of the reflection coefficient
It is known that the lateral displacement of the reflected beam in the vicinity of the defective mode is large. But now the reflectivity is smaller, so we have doped graphene into the defect layer, resulting in a larger reflectivity.
After doping the graphene layer, the reflectivity of the defect mode at the x position is not zero, and r=0.212. The phase at the defective mode does not jump but changes more strongly. Thus, a reflected beam having a reflectivity other than zero and a large lateral displacement can be obtained.
When the frequency of the incident light is at the defect mode, the lateral displacement of the reflected light beam is maximum, and the maximum value thereof is Δ=124 λ.
The invention has the advantages that: graphene is doped in the defect photonic crystal, so that the reflectivity of a defect mode can be greatly improved, and in the case, the maximum reflectivity of the defect mode can reach R=0.212; the maximum value of the lateral displacement of the reflected light beam can reach 124 lambda, which is an order of magnitude higher than the lateral displacement in the general structure.
Drawings
Fig. 1 is a schematic structural diagram of the present electronic crystal.
Fig. 2 is a graph of reflectance and reflectance phase of a defect mode of undoped graphene.
Fig. 3 is a graph of reflectivity and reflectance phase of a defect mode doped graphene.
Fig. 4 is a lateral displacement of a reflected beam in a graphene-doped defective photonic crystal.
In the figure, A, a first dielectric layer; B. a second dielectric layer; C. a defect layer; G. and a graphene layer.
Detailed Description
The following are specific embodiments of the present invention and the technical solutions of the present invention will be further described with reference to the accompanying drawings, but the present invention is not limited to these embodiments.
The photonic crystal comprises a first dielectric layer A, a second dielectric layer B, a defect layer C and a graphene layer G, wherein the defect layer C is positioned in the middle of the electronic crystal; the distribution rule of the first dielectric layer A and the second dielectric layer B is as follows: a plurality of first dielectric layers A and a plurality of second dielectric layers B are alternately arranged on two sides of the defect layer C, the first dielectric layers A are arranged on two outer side surfaces of the photonic crystal, and the second dielectric layers B are arranged on two sides close to the defect layer C; the graphene layer G is embedded within the defect layer C.
As shown in fig. 1, the refractive index of the first dielectric layer a, the second dielectric layer B and the defect layer C are n a ＝1.38，n b =2.35 and n c =2.35, the thicknesses of the first dielectric layer a, the second dielectric layer B and the defect layer C are d a ＝0.281，d b =0.165 and d c =0.33 μm. The incident light is 1, the reflected light is 2, and the transmitted light is 3. The reflected light has a lateral displacement delta with respect to the point of incidence.
Graphene is doped in the middle of the defect layer, i.e., at the 0-point position of the z-axis. Graphene is a two-dimensional material without thickness, whose surface conductivity can be described by the nine-bauer formula (Kubo formulation), as follows:
wherein f d ＝1/(1+exp[(ε-μ c )/(k B T)]) For the fermi-dirac statistics, epsilon is the particle energy, mu c Is a graphene chemical potential (also known as fermi level E F ) T is the temperature, e is the electron charge, τ is the momentum relaxation time, k B Is the boltzmann constant.
Graphene is considered as an equivalent dielectric with a thickness, and when the equivalent thickness is below 1nm, the effect of this equivalent method on the calculated reflectivity and transmittance is negligible. Here we take the thickness of graphene to be 0.34nm. Graphene having an equivalent dielectric constant of ε g ＝1+iσ g η 0 /(kd g ) Where k is the incident wave vector, η 0 Is the vacuum impedance. Temperature t=27 ℃, momentum relaxation time τ=0.5 ps, μ c ＝0.15eV。
The whole structure is (AB) N CGC(BA) N Where the number of bragg periods n=5.
Let the incident light be a TM wave, propagating along the z-axis. The electromagnetic fields across each layer of dielectric may be related by a transmission matrix. For example, the electromagnetic fields across the first layer dielectric may be related by the following relationship
Wherein M is l The transmission matrix of layer I, where eta l ＝ε l (ε 0 /μ 0 ) 1/2 /(ε l -sin 2 θ) 1/2 ，θ is the incident angle of light, here θ=20°. The transmission matrix of the whole system is
Where n is the total number of layers of the structure. The reflection coefficient is
Wherein eta 1 ＝η N+1 ＝(ε 0 /μ 0 ) 1/2 (1-sin 2 θ) 1/2 The impedance of the incident end and the emergent end respectively, and the reflectivity is r=rr. The band gap of the photonic crystal is omega gap ＝4ω 0 arcsin│(n b -n a )/(n b +n a )│ 2 Pi, wherein omega 0 ＝2πc/λ 0 ，λ 0 ＝1.55μm。
Fig. 2 (a) shows the reflectance of a defect mode in a defective photonic crystal of undoped graphene. It can be seen that the reflectivity is a function of the frequency of the incident light. There is a band gap in the middle of the reflection spectrum, and light within this band gap will be totally reflected. However, the reflectivity of the defect mode is zero at the x position, and the light of the defect mode is totally transmitted, so that the defect mode is also called a transmission mode. Writing the reflection coefficient in the form of an indexWherein->Is the phase of the reflection coefficient. In fig. 2 (b), the reflection coefficient phase of the defect mode in the defect photonic crystal of undoped graphene, it can be seen that there is a pi phase jump at the position of the defect mode. Because the reflectivity of the defective mode is zero, there is uncertainty in the phase where the reflection coefficient exists. Meanwhile, near the defective mode, the reflection coefficient phase change is relatively severe. Based on the relationship between the lateral displacement of the reflected beam and the phase of the reflection coefficient
It is known that the lateral displacement of the reflected beam in the vicinity of the defective mode is large. But now the reflectivity is smaller, so we have doped graphene into the defect layer, resulting in a larger reflectivity.
Fig. 3 (a) is the reflectivity of the defect mode in a graphene-doped defect photonic crystal. It can be seen that the reflectivity of the defect mode at the x position is not zero, in this case, the maximum reflectivity r=0.212 of the defect mode. Fig. 3 (b) is the reflectance phase of the defect mode in the graphene-doped defect photonic crystal. It can be seen that the phase at the defective mode does not jump but changes more strongly, so that a reflected beam with a reflectivity other than zero and a large lateral displacement can be obtained.
Fig. 4 is a lateral displacement of a reflected beam in a graphene-doped defective photonic crystal. It can be seen that when the frequency of the incident light is at the defect mode, the lateral displacement of the reflected beam is maximum, with a maximum of Δ=124 λ.
This can be seen as follows: graphene is doped in the defect photonic crystal, so that the reflectivity of a defect mode can be greatly improved, and in the case, the maximum reflectivity of the defect mode can reach R=0.212; the maximum value of the lateral displacement of the reflected light beam can reach 124 lambda, which is an order of magnitude higher than the lateral displacement in the general structure.
The specific embodiments described herein are offered by way of example only to illustrate the spirit of the invention. Those skilled in the art may make various modifications or additions to the described embodiments or substitutions thereof without departing from the spirit of the invention or exceeding the scope of the invention as defined in the accompanying claims.
Claims (1)
1. A photonic crystal with enhanced reflectivity to a defect mode, characterized in that the photonic crystal comprises a first dielectric layer (a), a second dielectric layer (B), a defect layer (C) and a graphene layer (G), wherein the defect layer (C) is positioned in the middle of an electronic crystal; the distribution rule of the first dielectric layer (A) and the second dielectric layer (B) is as follows: a plurality of first dielectric layers (A) and a plurality of second dielectric layers (B) are alternately arranged on two sides of the defect layer (C), the first dielectric layers (A) are arranged on two outer side surfaces of the photonic crystal, and the second dielectric layers (B) are arranged on two sides close to the defect layer (C); the graphene layer (G) is embedded within the defect layer (C);
refractive indexes of the first dielectric layer (a), the second dielectric layer (B) and the defect layer (C) are na=1.38, nb=2.35 and nc=2.35, respectively, and thicknesses of the first dielectric layer (a), the second dielectric layer (B) and the defect layer (C) are da=0.281 μm, db=0.165 μm and dc=0.33 μm, respectively;
the materials of the first dielectric layer (A) and the second dielectric layer (B) are magnesium fluoride or zinc sulfide.
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