CN113534505A

CN113534505A - Non-periodic photon multilayer structure for phase modulation coding

Info

Publication number: CN113534505A
Application number: CN202110985777.8A
Authority: CN
Inventors: 倪浩; 刘芳华
Original assignee: Hubei University of Science and Technology
Current assignee: Hubei University of Science and Technology
Priority date: 2021-08-26
Filing date: 2021-08-26
Publication date: 2021-10-22

Abstract

The invention provides a non-periodic photon multilayer structure for phase modulation coding, and belongs to the technical field of phase modulation coders. The aperiodic photonic multilayer structure comprises two Yue-Morse sequences which are distributed in an astronomical-time symmetry manner, and the Thue-Morse sequence S_NThe iteration rule of (1) is: when N is 1, S₂When N is not less than 2, S_N＝S_N‑1(S_N‑1Wherein A is replaced by AB and S_N‑1B in (B) is replaced by BA), a is a first dielectric layer; b is a second dielectric layer; wherein subscript N is the ordinal number of the sequence, the first dielectric layer and the second dielectric layer are two uniform dielectric sheets with different refractive indexes, and two layers of stones are also present in the sequence of true-MorseAnd the graphene sheets are respectively embedded between two adjacent second dielectric layers. The invention can form phase jump for numerical value coding.

Description

Non-periodic photon multilayer structure for phase modulation coding

Technical Field

The invention belongs to the technical field of phase modulation encoders, and relates to a non-periodic photon multilayer structure for phase modulation encoding.

Background

An encoder is a device that compiles, converts, and formats signals (e.g., bitstreams) or data into a form of signals that can be communicated, transmitted, and stored. In the optical fiber sensor, the phases of the pump light and the probe light can be periodically and rapidly encoded by using a phase modulation technique. The faster the phase modulation speed, the higher the spatial resolution of the phase modulation technology, and meanwhile, by changing the width of the phase code, the positions of the correlation peaks except the zero-order correlation peak in the optical fiber can be moved, thereby realizing distributed measurement. Compared with the amplitude modulation and frequency modulation coding technology, the phase modulation coding has no problem of mutual restriction between the spatial resolution and the measurement range, and the scanning of the correlation peak in the optical fiber to be measured can be realized by changing the width of the phase coding, so that distributed measurement is carried out.

In the process of phase modulation encoding, the phase change of the optical wave is closely related to the optical system structure of the material. A space-time (PT) symmetric structure can implement regular changes in phase. A PT symmetric optical system is a special non-hermitian structure that enhances resonance. The research shows that: the maximum point of the transmittance of the light waves incident on the PT symmetrical structure in different directions and the minimum point of the reflectance are not overlapped; the light waves incident in the positive direction and the reverse direction of the PT structure have the same transmission characteristic, but the reflection characteristics are different. The phase of the reflection coefficient has a phase jump at a zero reflection point, and the nonreciprocal of reflection causes the positions of the phase jumps of the left and right inverse coefficients to be not coincident, so that the effect can be applied to phase modulation coding. Non-photonic crystals have more defect cavities and transmissive films than periodic and quasi-periodic photonic crystals. Therefore, PT symmetrical and non-periodic photonic crystals can be combined to realize multi-value phase coding.

Graphene is an ultrathin two-dimensional material, has excellent conductivity, and the surface conductivity of the graphene can be flexibly adjusted through chemical potential. The graphene is embedded into the photonic crystal, and the zero position of the reflectivity is influenced by the graphene, so that the phase jump position of the reflection coefficient can be regulated and controlled through the chemical potential of the graphene, and the phase modulation coding is controlled.

Disclosure of Invention

The present invention is directed to provide an aperiodic photonic multilayer structure for phase modulation coding, which is capable of solving the above problems of the prior art, and how to make the multilayer structure form phase jump of reflection coefficient for application in numerical coding.

The purpose of the invention can be realized by the following technical scheme: aperiodic photonic multilayer structure usable for phase modulation coding, characterized in that it comprises two symmetrically distributed Thue-Morse sequences S_NThe iteration rule of (1) is: s₁＝A，N＝1；S₂＝AB，N＝2；S_N＝S_N-1(A → AB, B → BA), N.gtoreq.3, wherein S_N-1Wherein A → AB indicates that A is replaced by AB, B → BA indicates that B is replaced by BA, N indicates the sequence number, S_NThe Nth term representing the sequence; a is a first dielectric layer; b is a second dielectric layer; the first dielectric layer and the second dielectric layer are two uniform dielectric sheets with different refractive indexes, a graphene sheet layer also exists in the true-Morse sequence, and the graphene sheet layer is embedded between two adjacent second dielectric layers;

the first dielectric layer on the side of the symmetry center of the aperiodic photonic multilayer structure is called the first loss dielectric layer, and the refractive index in the light-passing state is expressed as n_a(ii) a The first dielectric layer on the other side of the symmetry center of the aperiodic photonic multilayer structure is called the first gain dielectric layer, and the refractive index in the light-passing state is represented as n_a'(ii) a The second dielectric layer on the same side as the first gain dielectric layer is called a second gain dielectric layer, and the refractive index in the light-transmitting state is represented by n_b(ii) a The second dielectric layer on the same side as the first lossy dielectric layer is called the second lossy dielectric layer, and the refractive index in the light-transmitting state is represented by n_b'；

n_a＝n_A+0.01qi，n_a'＝n_A–0.01qi，n_b＝n_B–0.01qi，n_b'＝n_B+0.01qi, where i is an imaginary unit, q is a gain-loss factor, n_AIs the real part of the refractive index of the first dielectric layer, n_BIs the real part of the refractive index of the second dielectric layer; 1/4 optical layers with the thicknesses of the first dielectric layer and the second dielectric layer corresponding to the respective refractive indexesA wavelength; the loss can be realized by doping metal ions such as iron ions, the gain is obtained by nonlinear two-wave mixing, and incident light is transverse magnetic wave and vertically incident from any side of the multi-layer dielectric medium structure;

when incident light of a certain wavelength value is incident in the forward and backward directions, the 0 reflectivity (EP) point trajectory curve is split. The location of these EP points on the normalized frequency axis is a function of the gain loss factor, and each EP point is the critical point at which the photonic multilayer interconverts between the PT symmetric phase and the PT asymmetric phase. At these transition critical points, the phase of the reflection coefficient

The jump of + -pi/2 is generated at all times, and can be used for phase encoding. Meanwhile, the wavelength of the invisible incident light can be adjusted by changing the gain-loss factor or the chemical potential of the graphene.

Further, the first dielectric layer is silicon dioxide, and the second dielectric layer is silicon.

Further, the thickness of the graphene flake layer is 0.001 μm.

Four dielectrics with different refractive indexes are sequentially stacked layer by layer according to a true-Morse sequence, so that the refractive indexes of the dielectrics meet the condition n (z) ═ n (-z) in space, and a PT symmetrical photon multilayer is formed. The PT symmetry of the structure results in the forward and backward reflected light waves being non-reciprocal. This nonreciprocal reflection characteristic splits the 0-reflectivity point, the ep (extrinsic point), of the trace curve generated by the photonic multilayer at normal and reverse incidence. At the same time, the phase of the reflection coefficient

At each EP a jump of + -pi/2 is generated, wherein

And

the phases of the reflection coefficients corresponding to the normal incidence and the reverse incidence respectively. This regular variation of the phase in the EP provides good conditions for phase modulation encoding. In addition, the position of the EP, that is, the position where the phase jumps, can be flexibly controlled by adjusting the gain-loss factor, and accordingly, the width of the phase code is adjusted, thereby realizing distributed measurement.

The invention compounds graphene and non-photonic crystal: the four dielectric sheets are regularly arranged according to a Thue-Morse sequence, and then graphene is embedded into a Thue-Morse sequence photon multilayer meeting PT symmetry. The phase curves of the reflected light are not coincident when the light waves are incident in the forward direction and the reverse direction due to the nonreciprocity of the photonic multilayer on the reflection of the light waves, so that the phase of the reflected light is caused

In EP, in which mutations occur

And

respectively representing the forward and backward reflected light phases. This regular change in phase can be exploited for phase modulation encoding. Meanwhile, the width of phase encoding can be changed by adjusting the gain-loss factor or the chemical potential of graphene, and the method is used for distributed measurement.

Drawings

FIG. 1 is a schematic diagram of a Thue-Morse sequence PT symmetrical photonic multilayer structure embedded in graphene.

FIG. 2 is the Thue-Morse sequence TM without graphene intercalation₄The PT symmetrical photon multilayer structure of (1) has electric field intensity distribution.

FIG. 3(a) is a graph showing reflectance according to forward incident light; FIG. 3 (b) is a graph showing reflectance corresponding to backward incident light; the graph (c) in fig. 3 shows the EP variation with the gain-loss factor at the forward and backward incidence.

Fig. 4(a) is a graph of the real part of the characteristic value of the hamiltonian quantity versus the normalized frequency when the gain-loss factor q is 5; the graph (b) in fig. 4 shows the relationship between the imaginary part of the characteristic value of the hamiltonian and the normalized frequency when the gain-loss factor q is 5.

In fig. 5, (a) is a phase when the gain-loss factor q is 5

A relationship to normalized frequency; fig. 5(b) shows the correspondence between the position of the phase jump and the code value when the gain-loss factor q is 5.

Fig. 6 is a graph of the width of the phase encoding as a function of gain-loss factor and graphene chemical potential.

In the figure, a first gain dielectric layer; a', a first lossy dielectric layer; B. a second gain dielectric layer; b', a second lossy dielectric layer.

Detailed Description

The following are specific embodiments of the present invention and are further described with reference to the drawings, but the present invention is not limited to these embodiments.

Here by S_NShows the sequence number N (N ═ 1,2,3, … …) due to Thue-Morse, TM_NThe representation follows the corresponding S_NArranged space-time symmetric photonic multilayer structures. S_NComprising A, B two homogeneous dielectrics with different refractive indices. Mathematically, the iteration rule for the T-M sequence is: s₁A, N is 1; when S is present_N＝S_N-1(A—>AB,B—>BA), N is more than or equal to 1, wherein the symbol is->"denotes a combination of S_N-1Wherein A and B are replaced by AB and BA, respectively, to form S_N. From this can be obtained S₂＝AB，S₃＝ABBA,S₄＝ABBABAAB，S₅＝ABBABAABBAABABBA，……。

The corresponding astronomical-time symmetric photonic multilayer structure is TM_N＝S_NS’_NOf which is S'_NAnd S_NAstronomical-time symmetry about the origin, the TM can be obtained₂＝ABB’A’，TM₃＝ABBAA’B’B’A’,TM₄Abbababb 'a' B 'a', … …. FIG. 1 shows a fourth Thue-Morse sequence S satisfying PT symmetry₄The photonic multilayer structure of (a), ABBAABB ' A ' A ' B ' A ' B ' B ' B ' A '. A. Refractive indices of A ', B and B' are n_a＝3.53+0.01qi，n_a'＝3.53-0.01qi，n_b＝1.46-0.01qi，n_b'1.46+0.01 qi. Q in the dashed portion is the introduced gain-loss factor, representing gain or loss. When the imaginary part is positive, it indicates that loss is introduced, and when the imaginary part is negative, it indicates that gain is introduced. The loss can be realized by doping metal ions such as iron ions, and the gain is obtained by nonlinear two-wave mixing. These four dielectric thicknesses are all 1/4 optical wavelengths, i.e., A and A' thicknesses are 0.1098 μm (μm means microns) and 0.2654 μm.

Two graphene sheet layers each having a thickness of 0.001 μm are embedded in the photonic multilayer structure, one layer being placed between the dielectric layers B and B on the left side of the photonic multilayer, and the other layer being placed between the dielectric layers B 'and B' on the right side. The incident light is transverse magnetic wave and enters the photonic multilayer in a vertical incidence mode. In the figure I_ifAnd I_ibRespectively representing normal and reverse normal incident light waves. Because PT symmetrical structure has identical transmitted light, the transmitted light wave when it is vertically incident in forward and backward directions is I_tAnd (4) showing.

FIG. 2 shows the electric field intensity distribution of a PT-symmetric Thue-Morse series photonic multilayer without graphene intercalation. The abscissa Z-axis is the direction of the dielectric layer stack, which is also the direction of light propagation, and the ordinate Normalized | E²To normalize the electric field strength. It can be seen that the strongest electric field strength exists near these two locations in the middle of the dielectric layers B and B, B 'and B'. Therefore, the graphene sheet is placed at the two places with the strongest electric field intensity, so that the third-order nonlinear effect of the structure can be enhanced.

Fig. 3(a) and (b) show the reflectances of the forward and backward incident lights, and both the transmittances and reflectances are logarithmic for the convenience of observation. Abscissa (ω - ω)₀)/ω_gapDenotes a normalized angular frequency, where ω is 2 π c/λ, ω₀＝2πc/λ₀And ω_gap＝4ω₀arcsin│[Re(n_a)-Re(n_b)]/[Re(n_a)+Re(n_b)]|²The/pi represents incident light angular frequency, incident light central angular frequency and angular frequency band gap respectively, c is light speed in vacuum, arcsin is inverse sine function, and Re isAnd extracting a real part function of the complex refractive index. The specific locations of EPs of EP are indicated by white dashed lines between normalized frequency bands (-0.12,0.02) in the parameter space for both the forward and reflectance spectra₁And EPs₂. EPs from FIG. 3(c)₁And EPs₂Drawn in the same coordinate axis to facilitate observation, two intersection points of the two 0-reflectivity track lines are located on the normalized frequency axis, and the specific position is (omega-omega)₀)/ω _gap0 and-0.094. The EP trace varies with gain-loss factor and normalized frequency: the cleavage occurs from one intersection point and then converges to another intersection point again. EPs₁And EPs₂The parameter space is divided into three parts, labeled I, II, and III, respectively, where I and III are PT symmetric phases and II is non-PT symmetric phase. If the gain-loss factor is set to q 5, as shown by the dashed line, the dashed line is aligned with the two 0-reflectivity trace points EPs₁There are 4 intersections with the EPs2, i.e., 4 EPs are generated. When the normalized frequency is gradually increased and the corresponding incident light wavelength is decreased, the generated EP is EP₁～EP₄. That is, when the normalized frequency is gradually increased in the (-0.12,0.02) region, the photonic multilayer is applied to EP under the action of the backward incident light₁From symmetric phase I to asymmetric phase II, and then in EP under the action of forward incident light₂From asymmetric phase II to symmetric phase III, and then in EP under the action of incident light in the reverse direction₃From symmetric phase III to asymmetric phase II and finally in EP under the action of forward incident light₄Returning to the symmetric phase I from the asymmetric phase II. The conversion process of the PT symmetrical phase and the non-PT symmetrical phase inevitably causes the jump of the phase of the reflected light, and provides a necessary condition for phase encoding.

The PT symmetrical structure designed by the invention is a special non-Hermite structure, and the scattering matrix of the PT symmetrical structure can be expressed as S ═ t, r_f,r_b,t]Where t, rf and rb denote the transmission coefficient, the reflection coefficient for forward and backward incidence, respectively. Its characteristic value and characteristic vector are respectively beta 1,2 ═ t + - (rfrb)^1/2And (rf)^1/2,±rb^1/2). When (rfrb)^1/2At 0, eigenvalues merge at the EP, while the eigenvectors degenerate. Therefore, the temperature of the molten metal is controlled,in addition to this important feature of 0 reflectivity, EP corresponds to two characteristic values β_1,2The real part of (a) will produce an anti-crossover and the imaginary part will produce a crossover. Fig. 4(a) (b) shows the relationship between the real part and imaginary part of the characteristic value of the system hamiltonian and the normalized frequency when the gain-loss factor q is 5. By beta in graph (a)_1,2The crossing relation between the real part and the imaginary part in the graph (b) can judge that the positions of the four EPs are respectively EP₁～EP₄Corresponding to the four epss in fig. 3(d), one for one. At the same time, EP can be calculated₁～EP₄Corresponding normalized frequencies are respectively omega_1～4-0.1049, -0.0627, -0.0075 and-0.0056.

The reflection coefficient of a photonic multilayer can be expressed as

Wherein

And

complex-valued reflection coefficients r at normal and reverse incidence, respectively_fAnd r_bThe phase of (c). Fig. 5(a) shows the phase of the reflection coefficient when the gain loss factor q is 5

The variation with normalized frequency can also be considered as the gradual decrease of the wavelength of the incident light from left to right

The phase spectrum of (1). It can be seen that when the solutions characteristic of the scattering matrix S are combined over four EPs, there is a jump of ± pi/2 for each EP corresponding to the phase of the reflection coefficient. The set of phase jumps is applied to Q in FIG. 5(b)₁Q₀Numerical value encoding: omega<ω₁Corresponds to Q₁Q₀00, PT symmetric phase I of the system in fig. 3 (d); omega₁<ω<ω₂Corresponds to Q₁Q₀Entering asymmetry, 01Phase II, omega₂<ω<ω₃Corresponds to Q₁Q₀10, switch to PT symmetry phase III, ω₂<ω<ω₃Corresponds to Q₁Q₀Re-enter the asymmetric phase II, ω, 11>ω₄Corresponds to Q₁Q₀Go back to asymmetric phase I at 00. This is the main idea for implementing phase encoding by using the photonic multilayer designed by the present invention.

Further, when the gain loss factor q changes, the position of the intersection of the dashed line and the dashed line in fig. 3(d) also changes, i.e., the corresponding normalized frequency of each EP point changes. Fig. 6 shows a comparison of the widths of the phase codes when the gain-loss factors are different. If the chemical potential mu of graphene is kept_cWhen the gain loss factor q increases from 5 to 6, the widths of

codes

01 and 11 increase and the width of code 10 decreases, 0eV being constant. On the other hand, when the chemical potential of graphene is μ_cWhen varied, EPs with 0 reflectivity are represented in FIG. 3(d)₁And EPs₂The shape of the curve will change. When the graphene chemical potential increases from 0eV to 0.2eV, the widths of

codes

00 and 10 increase and the width of code 01 decreases, keeping the gain loss factor q equal to 5. This shows that the width of the phase code can be flexibly adjusted by changing the gain loss factor or the chemical potential of the graphene, and distributed measurement is realized. .

In summary, the forward and backward reflected light waves of a photonic multilayer that follows the Thue-Morse sequence and satisfies PT symmetry are non-reciprocal, and the 0-reflectivity (EP) point trace curves generated at the forward and backward incidence are split. The position of these EPs on the normalized frequency axis is a function of the gain loss factor, each EP being the critical point at which the photonic multilayer interconverts between the PT symmetric phase and the asymmetric phase. At these transition critical points, the phase of the reflection coefficient

The jump of + -pi/2 is generated at all times, and can be used for phase encoding. Meanwhile, the width of phase coding can be flexibly controlled by adjusting the gain-loss factor, and distributed measurement is realized. The effect can be applied to manufacturing optical fiber sensors.

The method can be implemented as follows:

(1) and (4) selecting materials. Two dielectrics with silicon dioxide and silicon as substrates are selected, four dielectrics A, A ', B and B' are formed by introducing gain or loss through doping or nonlinear double-wave mixing, the refractive indexes of the dielectrics are 3.53+0.01qi, 1.46-0.01qi, 3.53-0.01qi and 1.46+0.01qi in sequence, wherein q is a gain-loss factor, and the gain and the loss are introduced through doping or nonlinear double-wave mixing respectively.

(2) And (5) structural design. The four dielectrics are subjected to a Thue-Morse sequence, and different sequence numbering types S are selected_NThe photonic multilayer stacked to conform to the space-time symmetry is TM, for example, when N is 4₄Abbababab ' a ' B ' a ' and then two graphene sheets with a thickness of 0.001 μm were embedded between B, B and B ', respectively (as in fig. 1).

(3) Detecting reflection coefficient phase

The phase jump of (2). The gain-loss factor q is chosen to be 5, and the wavelength of the incident light is changed, i.e. the incident light frequency ω is changed within a normalized frequency range of (-0.12, 0.02). The incident light is firstly vertically incident into the photonic multilayer from the front direction and is in omega₂-0.0627 and ω₃Two positions-0.0075 detected

Phase jumps of-pi/2 and pi/2 occur, respectively. Then the incident light enters the photonic multilayer from the reverse vertical incidence, and is in omega₁-0.1049 and ω₄Two positions-0.0056 detected

A phase jump of pi/2 occurs (see fig. 3-5).

(4) Phase hopping is applied to the numerical code. Combining the two sets of phase jumps described above for application to Q₁Q₀Numerical value encoding: omega<ω₁Corresponds to Q₁Q₀＝00，ω₁<ω<ω₂Corresponds to Q₁Q₀＝01，ω₂<ω<ω₃Corresponds to Q₁Q₀＝10，ω₂<ω<ω₃Corresponds to Q₁Q₀＝11，ω>ω₄Corresponds to Q₁Q₀00 (as in fig. 5).

Adjusting the gain-loss factor changes the phase encoding width. By adjusting the gain-loss factor of the dielectric medium, the normalized frequency position of the EP on the reflection spectrum can be adjusted, thereby controlling the width of phase encoding and realizing distributed measurement. For example, increasing q from 5 to 6, the dashed line representing the gain-loss factor in fig. 3(c) is shifted to the right, and the resulting phase-encoding width changes accordingly: the widths of

codes

01 and 11 increase while the width of code 10 decreases. (see fig. 6).

The specific embodiments described herein are merely illustrative of the spirit of the invention. Various modifications or additions may be made to the described embodiments or alternatives may be employed by those skilled in the art without departing from the spirit or ambit of the invention as defined in the appended claims.

Although the terms … … 1, … … 2, etc. are used more herein, the possibility of using other terms is not excluded. These terms are used merely to more conveniently describe and explain the nature of the present invention; they are to be construed as being without limitation to any additional limitations that may be imposed by the spirit of the present invention.

Claims

1. An aperiodic photonic multilayer structure for phase modulation coding, characterized in that the aperiodic photonic multilayer structure comprises two Yue-Morse sequences distributed in an astronomical-time symmetry manner, the Thue-Morse sequences S_NThe iteration rule of (1) is: when N is 1, S₂When N is not less than 2, S_N＝S_N-1(S_N-1Wherein A is replaced by AB and S_N-1B in (B) is replaced by BA), a is a first dielectric layer; b is a second dielectric layer; wherein subscript N is a sequential number, and the first dielectric layer and the second dielectric layer are two uniform dielectric sheets having different refractive indicesTwo graphene sheet layers also exist in the Thue-Morse sequence, and are respectively embedded between two adjacent second dielectric layers;

n_a＝n_A+0.01qi，n_a'＝n_A-0.01qi，n_b＝n_B-0.01qi，n_b'＝n_B+0.01qi，

Where i is an imaginary unit, q is a gain-loss factor, n_AIs the real part of the refractive index of the first dielectric layer, n_BIs the real part of the refractive index of the second dielectric layer; the thicknesses of the first dielectric layer and the second electrolyte layer are both at the respective 1/4 optical wavelengths; the loss can be realized by doping metal ions such as iron ions, the gain is obtained by nonlinear two-wave mixing, and incident light is transverse magnetic wave and vertically incident from any side of the multi-layer dielectric medium structure;

when incident light with a certain wavelength value is incident in the positive direction and the negative direction, a track curve of a 0 reflectivity (EP) point is split, the positions of the EP points on a normalized frequency axis are functions of gain loss factors, and each EP point is a critical point of the mutual conversion of the photon multilayer between a PT symmetrical phase and a PT asymmetrical phase; at the critical points of the conversion, the reflection coefficient phase (phi rf + phi rb)/2 generates jump of +/-pi/2 and can be used for phase encoding; meanwhile, the wavelength of the invisible incident light can be adjusted by changing the gain-loss factor or the chemical potential of the graphene.

2. The aperiodic photonic multilayer structure for phase modulation encoding as recited in claim 1, wherein the first dielectric layer is silicon dioxide and the second dielectric layer is silicon.

3. The aperiodic photonic multilayer structure usable for phase modulation coding according to claim 1 or 2, characterized in that the graphene platelet layer has a thickness of 0.001 μm.