A parity-time symmetric Thue-Morse photonic crystal composite structure

Abstract

The present invention provides a parity-time symmetric Thue-Morse photonic crystal composite structure, which belongs to the field of optical technology. It includes a non-periodic photonic crystal and two periodic photonic multilayers symmetrically distributed on both sides of the non-periodic photonic crystal; the non-periodic photonic crystal structure includes two symmetrically distributed Thue-Morse sequences, the Thue-Morse sequence S N The iteration rules are: S1 = A, N = 1; S2 = AB, N = 2; S N =S N‑1 (A→AB, B→BA), N≥3, where S N‑1 A→AB means A is replaced by AB, B→BA means B is replaced by BA, N is the sequence number, S N represents the Nth item of the sequence; A is the first dielectric layer; B is the second dielectric layer; the first dielectric layer and the second dielectric layer are two uniform dielectric sheets with different refractive indices. The present invention has the advantages of being able to realize a high-sensitivity sensor and a small-size laser.

Description

Technical Field

[0001] The invention belongs to the field of optical technology and relates to a Thue-Morse photonic crystal based on parity-time symmetry. Background Art

[0002] Coherent perfect absorption (CPA) produces the interaction of optical absorption and optical interference, and is a new method for manipulating light waves and their absorption. The CPA system has some anti-laser characteristics, such as a time-reversal relationship with a general optical amplification laser in the optical process, and can completely absorb coherent incident light. It can be widely used in many aspects such as optical modulation, optical switching, and optical detection. In particular, the CPA effect can be realized in extremely simple structural devices such as a single silicon chip, which can promote the design of silicon-based integrated photonic devices and has important research value in the fields of optical communications and computing.

[0003] In a non-Hermitian system, if gain or loss (or both gain and loss) is introduced into the dielectric, the system can exchange energy with the outside world. At this time, the refractive index of the dielectric is complex, and after introducing gain-loss, it can be written as n = n r ±iq, where n r is the real part of the refractive index, and i represents the imaginary unit. q is the gain-loss factor, which is the imaginary part of the refractive index. + and - respectively represent the introduced loss and gain. By adjusting the real and imaginary parts of the dielectric refractive index, the multilayer dielectric photonic crystal can satisfy n(z)=n*(–z) in space, where * represents the complex conjugate and z is the position coordinate. The resulting photonic crystal is a parity-time symmetric structure. Parity-time symmetry is a special non-Hermitian structure. In the parity-time symmetric photonic crystal, a point with both the reflectivity and transmittance being the maximum can be found, which is called the coherent perfect absorption laser point (CPA-LP). The corresponding photonic crystal can be applied to high-precision sensors and lasers. However, affected by the number of dielectric layers, this type of laser has high requirements for the manufacturing process and it is difficult to control the size of the sensor well. Summary of the invention

[0004] The purpose of the present invention is to provide a parity-time symmetric Thue-Morse photonic crystal composite structure in view of the above-mentioned problems existing in the prior art. The technical problem to be solved by the present invention is how to obtain a coherent perfect absorption laser point at the point where both the reflectivity and the transmittance are maximum.

[0005] The object of the present invention can be achieved by the following technical solutions: A parity-time symmetric Thue-Morse photonic crystal composite structure, characterized by comprising a non-periodic photonic crystal and two periodic photonic multilayers symmetrically distributed on both sides of the non-periodic photonic crystal;

[0006] The non-periodic photonic crystal structure includes two symmetrically distributed Thue-Morse sequences, wherein the Thue-Morse sequence S N The iteration rules are: S1 = A, N = 1; S2 = AB, N = 2; S N =S N-1 (A→AB, B→BA), N≥3, where S N-1 A→AB means A is replaced by AB, B→BA means B is replaced by BA, N is the sequence number, S N represents the Nth item of the sequence; A is the first dielectric layer; B is the second dielectric layer; the first dielectric layer and the second dielectric layer are two uniform dielectric sheets with different refractive indices;

[0007] The first dielectric layer located on one side of the symmetry center of the non-periodic photonic crystal structure is called the first lossy dielectric layer (A), and its refractive index in the light-transmitting state is expressed as n a The first dielectric layer located on the other side of the symmetry center of the non-periodic photonic crystal structure is called the first gain dielectric layer (A'), and its refractive index in the light-transmitting state is expressed as n a' The second dielectric layer on the same side as the first gain dielectric layer is called the second gain dielectric layer (B), and its refractive index in the light-transmitting state is expressed as n b The second dielectric layer on the same side as the first lossy dielectric layer is called the second lossy dielectric layer (B'), and its refractive index in the light-transmitting state is expressed as n b' ;

[0008] n a =n A +0.01qi,n a' =n A -0.01qi,n b =n B -0.01qi,n b' =n B +0.01qi,

[0009] where i is the imaginary unit, q is the gain-loss factor, and n A is the real part of the refractive index of the first dielectric layer, n B is the real part of the refractive index of the second dielectric layer; the thickness of the first dielectric layer and the second dielectric layer are both 1 / 4 optical wavelength corresponding to their respective refractive indices; the loss can be achieved by doping metal ions such as iron ions, and the gain is obtained by nonlinear two-wave mixing.

[0010] The periodic photonic crystal comprises a first dielectric sheet and a second dielectric sheet, and the first dielectric sheet and the second dielectric sheet are periodically arranged alternately.

[0011] Furthermore, the first dielectric sheet is titanium dioxide, the second dielectric sheet is lithium niobate, the first dielectric layer is silicon dioxide, and the second dielectric layer is silicon.

[0012] The above-mentioned dielectric layers A, A', B and B' are selected, and these four layers of dielectrics are stacked in sequence according to the Thue-Mose sequence rule to form a non-periodic photonic crystal that satisfies parity-time symmetry, in which A and A', B and B' respectively satisfy the equal complex refractive index conjugation. . This photonic crystal is placed in the middle of the photonic multilayer composed of dielectric sheets C and D as a defect to form a composite multilayer structure. This composite structure has stronger electric field localization than periodic and non-periodic photonic crystals, and can make the resonant cavity produce stronger resonance. By changing the wavelength of the incident light, a coherent perfect absorption laser point (CPA-LP) can be obtained at the maximum reflectivity and transmittance. At the same time, the position of the CPA-LP in the parameter space can also be adjusted by the gain-loss factor of the material. Therefore, after this coherent perfect absorber is applied to the sensor, its resolution is 1 to 2 orders of magnitude higher than that of ordinary optical sensors, and the sensor size is reduced to the micron level, which is suitable for making small-sized high-resolution sensors and lasers.

[0013] When defects are introduced into a periodic structure, defect states will appear in the band gap. For a periodic structure with defects and a finite number of periods, the defect state causes a transmission peak to appear in the high reflection band of the structure's reflection spectrum. Compared with periodic photonic crystals and quasi-photonic crystals, the electric field in non-photonic crystals is more localized, that is, more resonant. Stronger resonance in the resonant cavity can better stimulate emission of the doped medium in the cavity, achieve light amplification, and thus generate lasers. Therefore, if periodic and non-periodic structures are combined in a photonic crystal, a laser spot with higher intensity can be achieved, or the sensor size can be reduced at a given amplification factor.

[0014] Here, the Thue-Morse sequence numbered S4 is selected to form a photonic crystal multilayer material. By adjusting the complex refractive index of each dielectric layer, it satisfies parity-time symmetry. This parity-time symmetric structure is then placed in the photonic crystal as a defect to form a composite structure. By changing the incident angle and wavelength of light, a laser point that satisfies the resonance condition can be found. The position of the laser point in the parameter space can also be controlled by the gain-loss coefficient of the material. When this coherent perfect absorber is applied to sensors and lasers, the detection limit can reach 2×10 -9The resolution is 1 to 2 orders of magnitude higher than that of surface plasmon resonance devices on the market, while the sensor size is reduced to the micron level. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a Thue-Morse sequence composite photon multilayer that satisfies parity-time symmetry.

[0016] Figure 2 Figure (a) shows the relationship between transmittance and gain loss factor and normalized frequency. Figure 2 (b) is the three-dimensional parameter space transmission spectrum after taking the logarithm and the position of CPA-LP in the transmission spectrum.

[0017] Figure 3 The middle figure (a) shows the relationship between the reflectivity, gain loss factor and normalized frequency when the incident light enters from the left; Figure 3 The middle (b) figure shows the transmission spectra R corresponding to the left and right when the light is incident vertically. l and R r , gain-loss factor q=11.1.

[0018] Figure 4 Figure (a) shows the relationship between the transmittance and the incident angle and the normalized frequency when the gain-loss factor q = 12; Figure 4 The middle figure (b) shows the relationship between the left-input reflectivity and the incident angle and normalized frequency when the gain-loss factor q=12.

[0019] In the figure, A is the first lossy dielectric layer; A' is the first gain dielectric layer; B is the second gain dielectric layer; B' is the second lossy dielectric layer; C is the first dielectric sheet; and D is the second dielectric sheet. DETAILED DESCRIPTION

[0020] The following are specific embodiments of the present invention and the accompanying drawings to further describe the technical solution of the present invention, but the present invention is not limited to these embodiments.

[0021] Here we use S N represents the Thue-Morse sequence numbered N (N = 1, 2, 3, ...), TM N Indicates that the corresponding S N Arranged parity-time symmetric photonic multilayer structure. N The TM sequence contains two uniform dielectrics with different refractive indices, A and B. Mathematically, the iteration rule of the TM sequence is: when N = 1, S1 = A; when N = 2, S2 = AB; when N ≥ 3, S N =S N-1(A—>AB, B—>BA), where the symbol “—>” indicates that S N-1 In the formula, A and B are replaced by AB and BA respectively to form S N . From this we can get S2 = AB, S3 = ABBA, S4 = ABBABAAB, ….

[0022] The corresponding parity-time symmetric photon multilayer structure is TM N =S N S' N , where S' N With S N Parity-time symmetry is present about the origin, so TM2=ABB'A', TM3=ABBAA'B'B'A', TM4=ABBABAABB'A'A'B'A'B'B'A', …. Figure 1 The third photonic crystal of Thue-Morse sequence TM3, ABBAA'B'B'A', which satisfies parity-time symmetry, is given. This non-periodic photonic crystal is used as a defect in a periodic photonic crystal composed of C and D, and the composite photonic multilayer CDCDABBAA'B'B'A'DCDC is obtained.

[0023] The matrix material of dielectric sheets A and A' is silicon dioxide, and the refractive index is n a =3.53+0.01qi,n a' =3.53-0.01qi, where i is the imaginary unit, and q in the imaginary part is the introduced gain-loss factor, indicating gain or loss. When the imaginary part is positive, it indicates the introduction of loss, and when the imaginary part is negative, it indicates the introduction of gain. Loss can be achieved by doping metal ions such as iron ions, and gain can be obtained by nonlinear two-wave mixing. The thickness of the dielectric sheets A and A' is 1 / 4 of the optical wavelength, that is, d a =d a' =λ0 / 4 / Re(n a )=0.1098μm (μm means micrometer), where λ0=1.55μm is the center wavelength, Re(n a ) represents the refractive index n a The real part of the dielectric sheets B and B' is made of silicon with refractive indices n b =1.46-0.01qi, n b' =1.46+0.01qi, the thickness of dielectric sheets B and B' is d b =d b' =λ0 / 4 / Re(n b)=0.2654μm. The refractive index of the material of the Thue-Morse structure satisfies parity-time symmetry, that is, the real part of the refractive index of each dielectric layer is even symmetric about the zero point, and the imaginary part is odd symmetric about the zero point. The dielectric sheet C is titanium dioxide, and D is lithium niobate. The refractive index is divided into n c =2.3 and n d =3.0. The thickness of C is d c =0.05μm, and the thickness of D is 0.1μm. C and D are stacked alternately to form 8 layers of photon multilayers. Then the above-mentioned parity-time symmetric Thue-Morse structure is embedded in the middle of the photon multilayer to form a composite photon multilayer. The solid line and dotted line in the figure respectively represent the light incident from the left and right into the photonic crystal, and the arrows point to the direction of the incident light and the outgoing light. Here, the transverse magnetic (TM) wave is taken as an example to discuss and prove the effectiveness of the present invention.

[0024] First, when the light is incident vertically, that is, the incident angle θ = 0°, Figure 2 (a) shows the transmittance of the parity-time symmetric Thue-Morse sequence photonic crystal when the light is incident vertically (left and right). The vertical axis q is the gain loss factor; the horizontal axis (ω-ω0) / ω gap represents the normalized angular frequency, where ω = 2πc / λ, ω0 = 2πc / λ0 and ω gap =4ω0arcsin│[Re(n a )-Re(n b )] / [Re(n a )+Re(n b )]| 2 / π represent the incident light angular frequency, the incident light center angular frequency and the angular frequency band gap, c is the speed of light in a vacuum, and arcsin is the inverse sine function. 10 (T) for easy observation. It can be seen that changing the wavelength of the incident light changes the normalized frequency accordingly, and the transmittance is a function of the normalized frequency. There is a maximum transmittance point in the parameter space, called the coherent perfect absorption laser point (CPA-LP). The position coordinates of the CPA-LP are (-0.0754, 11.1), and the transmittance of this point is T LP =7.02×10 3 .exist Figure 2 (b) The exact location of CPA-LP can be seen in the logarithmic three-dimensional parameter space transmission spectrum, which is located at (ω-ω0) / ω gap =-0.0754,q=11.1,log 10 (T) = 3.85. Here the normalized frequency is (ω-ω0) / ω gap=-0.0754 corresponds to an incident light wavelength of 1.6164 μm, log 10 (T) = 3.85 corresponds to a transmittance of T LP =7.02×10 3 When the gain-loss factor is 11.1, the vertical incident light wavelength for CPA-LP is 1.6164 μm, which can be used to make lasers corresponding to specific wavelengths.

[0025] To prove that the point (-0.0754, 11.1) is a laser point, Figure 3 (a) gives the reflectivity of the incident light wave in parameter space, log 10 (R l ) represents the logarithm of the reflectivity. It can be seen that with the change of the incident angle and the normalized frequency, the left-input reflectivity R l There is also a maximum point in the parameter space, which is located at (-0.0754, 11.1). l The maximum value of Figure 2 The positions of the T maximum points in (a) are completely coincident, and it can be judged that CPA-LP is located at the coordinates (-0.0754, 11.1). In order to more vividly demonstrate the CPA-LP in reflectivity, Figure 3 (b) shows the corresponding reflection spectrum when the light is incident vertically and the gain-loss factor is q = 11.1. When the wavelength of the incident light changes, the normalized frequency changes accordingly, and the reflectivity is a function of the normalized frequency. It can be seen that there is a maximum reflection peak in both the left-input reflection spectrum and the right-input reflection spectrum, and both reflection peaks are located at (ω-ω0) / ω gap =-0.0754. Under the combined effect of the parity-time symmetry structure and the localization of the electric field, the extreme values ​​of the reflection peaks are different when the light enters from the left and right, which are 2.14×10 3 and 2.32×10 4 , the reflection peak when entering from the right is one order of magnitude larger than that when entering from the left.

[0026] Secondly, the gain-loss factor is set to a fixed value, and the incident angle and wavelength of the light are changed. When the gain-loss factor q changes, the transmittance in the parameter space changes. When q = 0 to 11, no matter how the incident angle is changed, CPA-LP will not appear in the normalized frequency interval [-1, 1]. However, when q = 12, CPA-LP will appear in the parameter space, such as Figure 4 (a) As shown. For a clear contrast, the transmittance T is taken as log 10 (T), the vertical axis unit is the incident angle. It can be seen that in the parameter space, there is a maximum transmittance point, which is a coherent perfect absorption laser point (CPA-LP). The position coordinates of LP are [θ=13.6°, (ω-ω0) / ωgap =-0.062], the transmittance of this point is T LP =2.46×10 4 In order to prove that the point [θ=13.6°, (ω-ω0) / ω gap =-0.062] is the laser point, Figure 4 (b) The reflectivity of the given light wave in parameter space when it enters from the left. 10 (R l ) represents the logarithm of the reflectivity. It can be seen that with the change of the incident angle and the normalized frequency, the reflectivity R l There is also a maximum point in the parameter space, which is located at [θ=13.6°, (ω-ω0) / ω gap =-0.062]. Therefore, this point is the extreme point of both transmittance and reflectance, so this point is CAP-LP. The reflectance value at this point is R LP =7.8×10 4 . (ω-ω0) / ω gap =-0.062 corresponds to a wavelength of 1.6046μm, that is, after being applied to the laser, the operating wavelength of the laser is 1.6046μm. It can be seen that when the gain loss-factor changes, the position of the coherent perfect absorption laser point also changes, and the corresponding normalized frequency changes. In this way, after applying this composite photon multilayer to the laser, the loss-factor can be changed to realize lasers with different operating wavelengths.

[0027] In summary, CPA-LP can be realized by embedding the parity-time symmetric Thue-Morse sequence as a defect into a periodic structure to form a composite photonic multilayer. CPA-LP is the maximum point of reflection and transmittance. Therefore, this coherent perfect absorption point can be used for lasers, and the operating wavelength of the laser can be flexibly adjusted by the loss-factor.

[0028] Possible implementation methods:

[0029] (1) Material selection. Select four dielectric materials A, A', B and B' with refractive indices of 3.53+0.01qi, 1.46-0.01qi, 3.53-0.01qi and 1.46+0.01qi, respectively. A and A' are silicon dioxide, B and B' are silicon, q is the gain-loss factor, and gain and loss are introduced by doping or nonlinear two-wave mixing, respectively. Select two dielectric materials C and D with refractive indices of 3.6 and 3.0, respectively.

[0030] (2) Structural design. The four dielectrics A, A', B and B' are stacked into photonic crystals with different numbers of layers according to Thue-Morse sequences with different sequence numbers. The refractive index of each layer of this photonic crystal satisfies n(z) = n*(-z) in space, which conforms to the parity-time symmetric structure. For example, the parity-time symmetric photonic crystal corresponding to the Thue-Morse sequence numbered S3 is TM3 = ABBAA'B'B'A'. This photonic crystal is then embedded as a defect in the middle of the periodic structure CDCDDCDC to form a composite structure photonic multilayer CDCDABBAA'B'B'A'DCDC (such as Figure 1 ).

[0031] (3) Realize a coherent perfect absorber. Take the gain-loss factor as q = 11.1, the light is incident vertically along the z axis into the parity-time symmetric photon multilayer, and the normalized frequency is (ω-ω0) / ω gap = -0.0754, the left-entry reflectivity is R l =2.14×10 3 , the right-input reflectivity is R r =2.32×10 4 , the transmittance is T LP =7.02×10 3 ( Figure 2-3 ). This coherent perfect absorber is applied to the laser, and the photon multilayer is stimulated to emit laser, with a normalized frequency of (ω-ω0) / ω gap =-0.0754 corresponds to a wavelength of λ=1.6164μm, which is the output wavelength of the laser.

[0032] Change the loss factor and adjust the wavelength corresponding to the CPA-LP point. Change the gain-loss factor to q=12, the incident angle of the light to 13.6°, and the normalized frequency to (ω-ω0) / ω gap = -0.062, the left-entry reflectivity is R l =7.8×10 4 , the transmittance is T LP =2.46×10 4 ( Figure 2-3 ). This coherent perfect absorber is applied to the laser, and the photon multilayer is stimulated to emit laser, with a normalized frequency of (ω-ω0) / ω gap =-0.062 corresponds to λ=1.6046μm, which is the output wavelength of the laser.

[0033] The specific embodiments described herein are merely examples of the spirit of the present invention. Those skilled in the art may make various modifications or additions to the specific embodiments described or replace them in similar ways, but they will not deviate from the spirit of the present invention or exceed the scope defined by the appended claims.

Claims

1. A parity-time symmetric Thue-Morse photonic crystal composite structure, characterized in that: It includes a non-periodic photonic crystal structure and periodic photonic multilayers distributed on both sides of the non-periodic photonic crystal; The non-periodic photonic crystal structure includes two Thue-Morse sequences with parity-time symmetric distribution, wherein the Thue-Morse sequence S N The iteration rules are: S1 = A, N = 1; S2 = AB, N = 2; S N =S N-1 (A→AB, B→BA), N≥3, where SN -1 A→AB means A is replaced by AB, B→BA means B is replaced by BA, N is the sequence number, S N represents the Nth item of the sequence; A is the first dielectric layer; B is the second dielectric layer; the first dielectric layer and the second dielectric layer are two uniform dielectric sheets with different refractive indices; The first dielectric layer located on one side of the symmetry center of the non-periodic photonic crystal structure is called the first lossy dielectric layer (A), and its refractive index in the light-transmitting state is expressed as n a The first dielectric layer located on the other side of the symmetry center of the non-periodic photonic crystal structure is called the first gain dielectric layer (A'), and its refractive index in the light-transmitting state is expressed as n a' The second dielectric layer on the same side as the first gain dielectric layer is called the second gain dielectric layer (B), and its refractive index in the light-transmitting state is expressed as n b The second dielectric layer on the same side as the first lossy dielectric layer is called the second lossy dielectric layer (B'), and its refractive index in the light-transmitting state is expressed as n b' ; <h2 style=";text-align:left;direction:ltr">n<h2 style=";text-align:left;direction:ltr"> a <h2 style=";text-align:left;direction:ltr"> =n<h2 style=";text-align:left;direction:ltr"> A <h2 style=";text-align:left;direction:ltr"> +0.01qi,n<h2 style=";text-align:left;direction:ltr"> a' <h2 style=";text-align:left;direction:ltr"> =n<h2 style=";text-align:left;direction:ltr"> A <h2 style=";text-align:left;direction:ltr"> -0.01qi,n<h2 style=";text-align:left;direction:ltr"> b <h2 style=";text-align:left;direction:ltr"> =n<h2 style=";text-align:left;direction:ltr"> B <h2 style=";text-align:left;direction:ltr"> -0.01qi,n<h2 style=";text-align:left;direction:ltr"> b' <h2 style=";text-align:left;direction:ltr"> =n<h2 style=";text-align:left;direction:ltr"> B <h2 style=";text-align:left;direction:ltr"> +0.01qi, where i is the imaginary unit, q is the gain-loss factor, and n A is the real part of the refractive index of the first dielectric layer, n B is the real part of the refractive index of the second dielectric layer; the thickness of the first dielectric layer and the second dielectric layer are both 1 / 4 of the optical wavelength corresponding to their respective refractive indices; the loss is achieved by doping iron ions, and the gain is obtained by nonlinear two-wave mixing; The periodic photon multilayer comprises a dielectric sheet 1 (C) and a dielectric sheet 2 (D), wherein the dielectric sheet 1 and the dielectric sheet 2 are periodically arranged alternately; The dielectric sheet 1 (C) is titanium dioxide, and the dielectric sheet 2 (D) is lithium niobate.

2. The parity-time symmetric Thue-Morse photonic crystal composite structure according to claim 1, characterized in that: The first dielectric layer (A) is silicon dioxide, and the second dielectric layer is silicon (B).

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