CN216013718U

CN216013718U - anti-PT symmetrical photon multilayer capable of realizing directional regulation and control of reflectivity

Info

Publication number: CN216013718U
Application number: CN202122025175.6U
Authority: CN
Inventors: 刘芳华; 张巍
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: 2022-03-11
Anticipated expiration: 2031-08-26

Abstract

The utility model provides an inverse PT symmetrical photon multilayer capable of realizing directional regulation and control of reflectivity, and belongs to the technical field of optics. The anti-PT symmetrical photon multilayer comprises two symmetrically distributed Thue-Morse sequences, wherein one 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 (1) is replaced by BA); another of the Thue-Morse sequences S_NThe iteration rule of' is: when N is 1, S₂'As A', when N ≧ 2S_N'＝S_N‑1'(S_N‑1In 'A' is replaced by A 'B', S_N‑1In 'B' is replaced by B 'A'). The utility model can realize the directional regulation and control of the reflectivity.

Description

anti-PT symmetrical photon multilayer capable of realizing directional regulation and control of reflectivity

Technical Field

The utility model belongs to the technical field of optics, and relates to an inverse PT symmetrical photon multilayer capable of realizing directional regulation and control of reflectivity.

Background

When gain or loss exists in the material, the refractive index of the dielectric medium is complex, and reflection spectrums obtained when the light waves enter from the forward direction and the reverse direction are not overlapped. The optical waves incident in the positive direction and the reverse direction in a space-time (PT) symmetrical structure have the same transmission characteristic, but the reflection spectrums of the optical waves do not coincide, namely, the reflectivity is nonreciprocal. This nonreciprocity provides conditions for the directional control of the light wave reflectivity. For example, the characteristic that the incident light frequency is different corresponding to the PT symmetrical structure with the positive and negative reflectivities of 0 is utilized, and the PT symmetrical structure can be used for optical directional stealth of specific wavelength.

PT symmetric optical system whose refractive index spatially satisfies the condition n (z) ═ n × z, where z is the position coordinate. The PT symmetry condition can be decomposed into: n is_r(z)＝n_r(-z) and n_i(z) ＝-n_i(-z), i.e. the real part of the refractive index n_rEven symmetry, n_iThe imaginary part is odd symmetric and the letter i denotes the imaginary unit. In studying the lateral shift of the reflected beam, it is necessary to use a partial reflectivity reflection light, and near the resonance state, the lateral shift effect of the beam is the largest, while the resonance mode reflectivity of the PT symmetric system is zero, which is very disadvantageous for detecting the lateral shift of the reflected beam. In addition, in exploring the spatial nonreciprocal of the lateral displacement of the light beam, the difference in the reflectivity of the device for the normal and reverse incident lights is also an important research content of the spatial nonreciprocal.

SUMMERY OF THE UTILITY MODEL

The utility model aims to provide an anti-PT symmetrical photon multilayer capable of realizing the directional regulation and control of reflectivity aiming at the problems in the prior art, and the technical problem to be solved by the utility model is how to realize the directional regulation and control of the reflectivity.

The purpose of the utility model can be realized by the following technical scheme: the anti-PT symmetrical photon multilayer capable of realizing directional regulation and control of reflectivity is characterized by comprising two symmetrically distributed Thue-Morse sequences, wherein one Thue-Morse sequence 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 and B → BA indicates that B is replaced by BA, to form a new sequence S_N；

Another of the Thue-Morse sequencesS_N' iteration rule and S_NSame, S_N' and S_NIs anti-PT symmetric about the origin;

a is a first dielectric layer; b is a second dielectric layer; a' is a third dielectric layer; b' is a fourth dielectric layer; wherein subscript N is the ordinal number of the sequence;

the refractive index of the first dielectric layer is denoted as n_a(ii) a The refractive index of the third dielectric layer is denoted as n_a'(ii) a The refractive index of the second dielectric layer is denoted as n_b(ii) a The refractive index of the fourth dielectric layer is represented as 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; n is_A'Is the real part of the refractive index of the third dielectric layer, n_B'Is the real part of the refractive index of the fourth dielectric layer;

the real parts of the refractive indexes of the first dielectric layer and the fourth dielectric layer are the same, and the real parts of the refractive indexes of the second dielectric layer and the third dielectric layer are the same; light waves are normally incident from either the forward or reverse direction of the inverse PT symmetric photonic multilayer.

Furthermore, the first dielectric layer and the fourth dielectric layer are both silicon dioxide, and the second dielectric layer and the third dielectric layer are both lithium niobate.

And compounding the two Thue-Morse sequence photons in a multilayer manner to form an inverse PT symmetrical structure. The inverse PT symmetric system is formed by sequentially stacking two dielectric sheets having different refractive indexes. When the gain-loss factor of the material is not zero, the reflection of the incident light in the positive direction and the reverse direction by the structure is different, and the reflectivity of a resonant mode is not zero. The gain-loss factor is increased, the reflection of the structure to the forward incident light is firstly inhibited and then enhanced, and the reflectivity of the structure to the backward incident light is continuously enhanced. This effect can be used as a directional suppression or enhancement of the reflectivity of light waves.

The inverse PT symmetrical system can better overcomeThe problem of transverse displacement of light beams near a resonance state can realize nonreciprocal reflectivity of forward and backward incident light under the condition of not changing the position of a defect mode, namely the left and backward reflectivities at the position of the defect mode are different. The refractive index of an optical system with inverse PT symmetry spatially satisfies the condition n (z) ═ -n × z, i.e., the real part and the imaginary part of the refractive index satisfy the condition n, respectively_r(z)＝-n_r(-z) and n_i(z)＝n_i(-z), i.e., odd real and even imaginary symmetry. The gain-loss system in the inverse PT symmetrical system is regulated and controlled, and the inhibition or enhancement of the left and right light wave reflectivity can be respectively realized.

Drawings

FIG. 1 is an inverse PT symmetric Thue-Morse sequence TM₃Photonic multilayer structure diagram.

Fig. 2 shows the corresponding transmission spectrum and reflection spectrum when the gain-loss factor q is 0.

Fig. 3 shows the reflectance for the forward and backward incident light.

FIG. 4 is a graph (a) of normal incidence reflectance spectra for different gain-loss factors; FIG. 4(b) is a view of (. omega. -omega.) diagram₀)/ω_gap1.5227, the corresponding forward reflectivity is a function of the gain-loss factor.

FIG. 5(a) is a plot of the retro-incident reflectance spectra for different gain-loss factors; FIG. 5 (b) is a view of (. omega. -omega.) diagram₀)/ω_gap1.5227, the corresponding retroreflectance varies with the gain-loss factor.

In the figure, a first dielectric layer; a', a third dielectric layer; B. a second gain dielectric layer; b', a fourth 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 refractive indexesThe same uniform dielectric. Mathematically, the iteration rule for the T-M sequence 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 and B → BA indicates that B is replaced by BA, to form a new sequence S_N. From this can be obtained S₃＝ABBA,S₄＝ ABBABAAB，……。

The corresponding inverse PT symmetric photonic multilayer structure is TM_N＝S_NS_N', wherein S_N' and S_NReverse PT symmetry about the origin, obtaining TM₂＝ABB’A’，TM₃＝ABBAA’B’B’A’, TM₄Abbababb 'a' B 'a', … …. FIG. 1 shows a third Thue-Morse sequence S satisfying inverse PT symmetry with respect to the origin₃Photonic crystals of, i.e. TM₃. Dielectric sheet A is silicon dioxide, and the matrix material of A' is lithium niobate with refractive index n_a3.6+0.01qi and n_a'3.0+0.01qi, where i is an imaginary unit and q is a gain-loss factor; dielectric sheets A and A' having a thickness d_a＝d_a'0.05 μm (μm means μm); the matrix material of the dielectric sheet B is lithium niobate, the matrix material of B' is silicon dioxide, and the refractive index is n_b3.0+0.01qi and n_b'3.6+0.01 qi. Parameter q>0, representing loss, q<0, represents the gain. The loss can be realized by doping metal ions such as iron ions, and the gain is obtained by nonlinear two-wave mixing. Only the case of losses is considered here. Dielectric sheets B and B' having a thickness d_b＝d_b'0.1 μm. The refractive index of the material of the whole structure satisfies n (z) ═ -n (-z), wherein x represents the complex conjugate.

N if the dielectric refractive index is written in the form of real part + imaginary part_r0+n_r1+in_iThen the four refractive indices of the dielectric are written as n_a＝3.3+0.3+0.01qi，n_a'＝ 3.3-0.3+0.01qi，n_b＝3.3-0.3+0.01qi，n_b'3.3+0.3+0.01 qi. The real part of the refractive index n can be seen_r1(z) odd symmetry about point 0, imaginary part n_i(z) about point 0Is even symmetrical.

The transmission and reflection of the inversely PT symmetric true-Morse sequence photonic multilayer is shown in figure 2, with the frequency of incidence of the light being varied. Given a gain-loss factor q of 0, there is no gain and no loss in the dielectric material.

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 respectively represents incident light angular frequency, incident light central angular frequency and angular frequency band gap, c is light speed in vacuum, and parameter lambda₀1.55 μm, arcsin is the inverse sine function. The letter T denotes transmittance, and R denotes reflectance. When the gain-loss factor q is 0, the transmission spectrum and the reflection spectrum corresponding to the forward incidence and the backward incidence are respectively overlapped.

In particular, the normalized frequency (ω - ω)₀)/ω_gapWhen the corresponding incident wavelength λ is 1.3175 μm, 1.5227, the transmittance shows a distinct resonance peak, corresponding to a maximum point T of the transmittance of 0.9836. Moreover, this formant corresponds to exactly the limit point R of the reflectance of 0.0164.

When the gain-loss factor is not zero, the reflection spectra of the forward and backward incident light are not coincident. Fig. 3 shows the corresponding reflection spectrum of the system when q is 1. Wherein the letter R_fDenotes the reflectance, R, corresponding to normal incidence_bIndicating the reflectivity corresponding to reverse incidence. It can be seen that R_fAnd R_bAre not coincident and are all in (omega-omega)₀)/ω_gapThere is a minimum reflectivity at 1.5227, respectively. That is, when (ω - ω)₀)/ω_gapWhen q is 0, R corresponds to 1 when q is 1.5227_fDecrease and R_bAnd (4) enhancing. Thus, when losses are introduced in an inverse PT symmetric system, the reflectivity of the forward incident light is reduced and the reflectivity of the backward incident light is enhanced relative to a non-gain and loss-free dielectric. This effect can be used for directional suppression or enhancement of reflected light.

When the light wave is normally incident, FIG. 4(a) showsThe reflection spectra corresponding to different gain-loss factors are shown. Ordinate log₁₀(R_f) The logarithm is taken of the reflectivity. It can be seen that the normalized frequency is in (omega-omega)₀)/ω_gap1.5227, there are 1 trough in the reflectance spectrum. When q is 0,1,2, the corresponding reflectance decreases in order, and when q is 3, the reflectance increases again. FIG. 4(b) shows the signal at (ω - ω)₀)/ω_gapReflectivity R when 1.5227_fAs a function of gain-loss factor. It can be seen that when q.ltoreq.2, R_fDecreases with increasing gain-loss factor, indicating that the forward reflectivity is suppressed, and when q is greater>At 2 time, R_fIncreasing with increasing gain-loss factor indicates that the forward reflectivity is enhanced.

When the light wave is incident perpendicularly in the opposite direction, fig. 5(a) shows the reflection spectrum corresponding to different gain-loss factors. Ordinate log₁₀(R_b) The logarithm is taken of the reflectivity. It can be seen that the normalized frequency is in (omega-omega)₀)/ω_gap1.5227, there are 1 trough in the reflectance spectrum, when R is_bIncreasing with increasing gain-loss gain. The larger q, the larger the loss in the dielectric, and thus the reflectivity of the resonant mode can be enhanced by increasing the loss.

In summary, when the loss is not zero, the forward and backward reflection spectra in the inverse PT symmetric system composed of two Thue-Morse sequence photon multilayer do not coincide. At a resonant mode, the system has the effect of inhibiting or enhancing the forward incident light wave, and can be specifically regulated and controlled by a gain-loss factor; for a backward incident light wave, the system only enhances the reflection, and the reflectivity increases with the gain-loss factor. This effect can be used for directional suppression or enhancement of light wave reflections.

Alternative embodiments:

(1) and (4) selecting materials. Two dielectrics of silicon dioxide and lithium niobate are selected, gain is introduced by doping to form A, A ', B and B', the refractive indexes of the dielectric materials are 3.6+0.01qi, 3.0+0.01qi, 3.0+0.01qi and 3.6+0.01qi in sequence, wherein q is a gain-loss factor. Here, q >0 is taken, i.e. only losses are taken into account.

(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 in accordance with the inverse-time symmetry is ABBAA ' B ' a ', for example, when N ═ 3. The thickness of A and A 'was set to 0.05. mu.m, and the thickness of B and B' was set to 0.1. mu.m (see FIG. 1).

(3) The positive and negative reflectivities are not coincident after the loss is introduced. Taking q to 0, there is a peak in transmittance, which corresponds exactly to the valley of the reflectance spectrum (see fig. 2), at the normalized frequency (ω - ω)₀)/ω_gap1.5227, corresponding to a wavelength λ 1.3175 μm. The introduced loss is q equal to 1, the positive and negative transmittances are overlapped, the reflectivities are not overlapped, and the positions of the valleys of the reflection spectrum are not changed. In (omega-omega)₀)/ω_gapAt 1.5227, the forward reflectivity decreases and the reverse reflectivity increases (fig. 3). This provides conditions for directional control of the reflectivity.

(4) The gain-loss factor is increased, and the forward reflectivity is suppressed or enhanced. When the light is normally and vertically incident, the gain-loss factor is changed, and the position of the reflection spectrum valley is unchanged. At normalized frequency (omega-omega)₀)/ω_gapWhen the gain-loss factor of 0 is introduced at 1.5227<q is less than or equal to 2, the position of a forward reflectance spectrum wave trough is unchanged, and the reflectivity is reduced along with the increase of q; if 2<q<The forward reflectance increases with increasing q (fig. 4) 16. Thus, when light is incident in the forward direction at the wavelength λ, the forward reflectance can be suppressed or enhanced by the gain-loss factor.

(5) The gain-loss factor is increased and the reverse reflectivity is enhanced. When the light is reversely and vertically incident, the gain-loss factor is changed, and the position of the reflection spectrum valley is unchanged. At normalized frequency (omega-omega)₀)/ω_gapWhen the gain-loss factor of 0 is introduced at 1.5227<q.ltoreq.16, the retroreflectivity increases with increasing q (FIG. 5). Thus, when light is reversely incident at the wavelength λ, the reverse reflectance can be enhanced by the gain-loss factor.

The specific embodiments described herein are merely illustrative of the spirit of the utility model. 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 utility model as defined in the appended claims.

Claims

1. The anti-PT symmetrical photon multilayer capable of realizing directional regulation and control of reflectivity is characterized by comprising two symmetrically distributed Thue-Morse sequences, wherein one Thue-Morse sequence S_NThe iteration rule of (1) is: when N is 1, S₁A is ═ a; when N is greater than or equal to 2, S_N＝S_N-1In which S is_N-1Wherein A is replaced by AB and S_N-1B in (1) is replaced by BA;

another of the Thue-Morse sequences S_NThe iteration rule of' is: when N is 1, S₁'As A', when N ≧ 2S_N'＝S_N-1In which S is_N-1In 'A' is replaced by A 'B', S_N-1In 'B' is replaced by B 'A';

2. The multilayer of claim 1, wherein the first and fourth dielectric layers are silicon dioxide, and the second and third dielectric layers are lithium niobate.