CN113534299B - Multichannel non-periodic photonic crystal structure based on optical fractal - Google Patents
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- 239000004038 photonic crystal Substances 0.000 title claims abstract description 62
- 230000000737 periodic effect Effects 0.000 title claims abstract description 27
- 230000003287 optical effect Effects 0.000 title claims abstract description 25
- 239000013078 crystal Substances 0.000 claims abstract description 6
- VYPSYNLAJGMNEJ-UHFFFAOYSA-N Silicium dioxide Chemical group O=[Si]=O VYPSYNLAJGMNEJ-UHFFFAOYSA-N 0.000 claims description 8
- 235000012239 silicon dioxide Nutrition 0.000 claims description 4
- 239000000377 silicon dioxide Substances 0.000 claims description 4
- XEEYBQQBJWHFJM-UHFFFAOYSA-N iron Substances [Fe] XEEYBQQBJWHFJM-UHFFFAOYSA-N 0.000 claims description 3
- 229910052742 iron Inorganic materials 0.000 claims description 3
- -1 iron ions Chemical class 0.000 claims description 3
- 230000005540 biological transmission Effects 0.000 description 18
- 230000007547 defect Effects 0.000 description 17
- 238000000411 transmission spectrum Methods 0.000 description 16
- 238000002834 transmittance Methods 0.000 description 9
- 230000001105 regulatory effect Effects 0.000 description 5
- 230000002950 deficient Effects 0.000 description 4
- 230000000694 effects Effects 0.000 description 4
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Abstract
The invention provides a multichannel non-periodic photonic crystal structure based on optical fractal, and belongs to the technical field of multichannel photonic filters. The multi-channel non-periodic photonic crystal structure comprises two symmetrically distributed Thue-Morse sequences, and the iteration rule of Thue-Morse sequence S N is as follows: s 1＝A,N＝1;S2＝AB,N＝2;SN＝SN‑1 (A.fwdarw.AB, B.fwdarw.BA), N.gtoreq.3, wherein A.fwdarw.AB in S N‑1 represents that A is replaced by AB, B.fwdarw.BA represents that B is replaced by BA, N represents the sequence number of the sequence, and S N represents the nth item of 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. The invention combines the space-time symmetry and Thue-Morse sequence photon crystal to realize the multi-channel tunable photon filter.
Description
Technical Field
The invention belongs to the technical field of multi-channel photon filters, and relates to a multi-channel non-periodic photon crystal structure based on optical fractal.
Background
While conventional photonic devices can be classified into bandpass, bandstop, lowpass and highpass elements according to frequency characteristics, single-channel devices can only transmit light waves around a single frequency. In all-optical communications, there is a strong demand for the development of wavelength division multiplexing devices, which puts higher demands on channel capacity. The photon filter can be applied to a wavelength division multiplexer/demultiplexer, noise suppression, a wavelength converter, a dispersion compensator, a delay, a semiconductor laser, a wavelength selector, and the like. Thus, photonic filters offer an alternative solution to wavelength division multiplexed transmission of optical signals.
Photonic crystals are an emerging structure in photonic filters, which are the focus and focus of research for photonic filters. Photonic crystals are periodic structures formed by alternating arrangements of dielectrics having different refractive indices. A defect mode is formed in the forbidden band of the photonic crystal when the photonic crystal is inserted into the defect. The transmittance at the defective mode is extremely high, and when the wavelength of the incident light is equal to the transmission wavelength, the light wave resonates to be output. The more the defect layers of the photonic crystal are, the more the number of defect modes are. With this principle, a multi-channel photon filter can be fabricated.
The defect mode has stronger locality to the electric field, the stronger the electric field locality, the higher the quality factor of the channel. But in general, once a defective photonic crystal is formed, it is difficult to control the quality factor of the channel. The non-periodic photonic crystal generally has stronger electric field locality than the periodic and quasiperiodic photonic crystals, so that a channel with a high quality factor can be obtained.
Optical fractal may be formed in the non-periodic photonic crystal because of the presence of natural defect layers in the non-periodic photonic crystal. Optical fractal is a phenomenon of splitting based on a defective mode, which is also a resonant state. Because the number of defect modes exhibits an increasing geometric progression as the number of non-periodic photonic crystals increases, these defect states are referred to as optical morphologies. The optical fractal has self-similar properties, and the reason for this phenomenon is the iterative principle of non-periodic sequences. So as the number of layers of the non-periodic photonic crystal increases, the number of defect cavities and the number of defect modes also increase. This optical fractal effect can be used for multi-channel communications, as well as for spreading of channels.
Disclosure of Invention
The invention aims to solve the problems existing in the prior art and provide a multichannel non-periodic photonic crystal structure based on optical fractal, and the technical problem to be solved by the invention is to combine space-time (PT) symmetry with Thue-Morse (T-M) sequence photonic crystals to realize a multichannel tunable photonic filter.
The aim of the invention can be achieved by the following technical scheme: the multichannel non-periodic photonic crystal structure based on optical fractal is characterized by comprising two T-M sequences distributed in PT symmetry, wherein the iteration rule of the T-M sequences S N is as follows: s 1＝A,N＝1;S2＝AB,N＝2;SN＝SN-1 (A.fwdarw.AB, B.fwdarw.BA), N.gtoreq.3, wherein A.fwdarw.AB in S N-1 represents that A is replaced by AB, B.fwdarw.BA represents that B is replaced by BA, N represents the sequence number of the sequence, and S N represents the nth item of 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;
The first dielectric layer positioned on one side of the symmetry center of the multi-channel non-periodic photonic crystal structure close to the incident direction is called a first loss dielectric layer, and the refractive index in the light-on state is expressed as n a; the first dielectric layer positioned on one side of the symmetry center of the multi-channel non-periodic photonic crystal structure close to the emergent direction is called a first gain dielectric layer, and the refractive index in the light-on state is expressed as n a'; the second dielectric layer positioned on one side of the symmetry center of the multi-channel non-periodic photonic crystal structure close to the incident direction is called a second gain dielectric layer, and the refractive index in the light-on state is expressed as n b; the second dielectric layer positioned on one side of the symmetry center of the multi-channel non-periodic photonic crystal structure near the emergent direction is called a second loss dielectric layer, and the refractive index in the light-on state is denoted as n b'. ;
na＝nA+0.01qi,na'＝nA-0.01qi,nb＝nB-0.01qi,nb'＝nB+0.01qi, Where i is the imaginary unit, q is the gain-loss factor, n A is the real part of the refractive index of the first dielectric layer, and n B is the real part of the refractive index of the second dielectric layer; the thicknesses of the first dielectric layer and the second dielectric layer are 1/4 optical wavelength corresponding to the respective refractive indexes; the loss can be realized by doping metal ions such as iron ions, the gain is obtained by nonlinear two-wave mixing, the incident light is transverse magnetic wave, and the incident light is vertically incident from the incident side of the multichannel non-periodic photonic crystal structure.
Further, the first dielectric layer is silicon dioxide and the second dielectric layer is silicon.
The two dielectric sheets are sequentially arranged according to a T-M sequence, and the real part and the imaginary part of the refractive index of the dielectric are regulated and controlled at the same time, so that the PT symmetry is spatially satisfied: n (z) =n (-z), where x represents complex conjugate and z is the position coordinate. There are a plurality of tunable optical fractal states in this structure, corresponding to a series of transmission modes. The number of transmission modes is geometrically split as the number of T-M sequences increases. These split transmission modes can be used for photon filters in multi-channel communications. In addition, the quality factor of the transmission mode can be flexibly regulated by the gain-loss factor in the PT symmetrical system.
Drawings
FIG. 1 is a schematic diagram of a TM 3 photonic crystal structure that satisfies PT symmetry.
FIG. 2 (a) is a graph of TM 3 photonic crystal transmission spectrum; (b) FIG. TM 4 photon crystal transmission spectrum; (c) The graph shows the transmission spectrum of the TM 5 photonic crystal.
Fig. 3 is the effect of gain-loss factor q on transmission spectra in PT symmetric photon polycrystal TM 4.
FIG. 4 is an optical fractal effect in a T-M sequence photonic crystal.
In the figure, A, 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 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 T-M sequence is an aperiodic sequence. The two dielectric thin plates are regularly arranged according to Thue-Morse sequence, so that an aperiodic photon crystal can be formed. Thus, the photonic crystal has a plurality of defect cavities, and a plurality of defect modes exist in the same defect cavity, so that the photonic crystal can be used for manufacturing a multi-channel device. Here, S N denotes the T-M sequence with the sequence number N (n=1, 2,3, … …), and TM N denotes the structure of a parity-time symmetric photonic crystal following the corresponding S N arrangement. S N contains A, B homogeneous dielectrics with different refractive indices. Mathematically, the iteration rule for the T-M sequence is: s 1＝A,N＝1;S2＝AB,N＝2;SN＝SN-1 (A.fwdarw.AB, B.fwdarw.BA), N.gtoreq.3, wherein A.fwdarw.AB in S N-1 represents A replaced by AB and B.fwdarw.BA represents B replaced by BA, forms a new sequence S N. Thereby, S 3＝ABBA,S4＝ABBABAAB,S5 = ABBABAABBAABABBA, … … can be obtained.
In the photonic crystal meeting the PT symmetry, the electric field locality of the defect mode can be further enhanced by regulating and controlling the gain-loss factor in the PT symmetry system, so that the quality factor of the defect mode is regulated and controlled. Therefore, it is contemplated to combine PT symmetry with T-M sequence photonic crystals to implement a multi-channel, tunable photonic filter. The spatially-temporally symmetric photonic crystal structure corresponding to S N is TM N＝SNS'N, where S' N and S N are spatially-temporally symmetric about the origin, TM 2＝ABB'A',TM3＝ABBAA'B'B'A',TM4 = ABBABAABB 'a' B 'a' … … is available. The corresponding TM 3 parity-time symmetric photonic crystal structure of S 3 is given as figure 1. Wherein, the matrix A and the matrix A' are silicon dioxide, and the refractive indexes are n a＝3.53+0.01qi,na' =3.53-0.01 qi respectively; the B and B' substrates are both silicon and have refractive indices n b＝1.46-0.01qi,nb' = 1.46+0.01qi, respectively. q in the imaginary part is the gain-loss factor introduced, representing the gain or loss. Loss is indicated when the imaginary part is positive and gain is indicated when the imaginary part is negative. The loss can be realized by doping metal ions such as iron ions, and the gain is obtained by nonlinear two-wave mixing. The incident light is a transverse magnetic wave, perpendicularly incident from the left, and the incident angle is θ=0°. A. A ', B and B ' each have a thickness of 1/4 of the optical wavelength, i.e. A, A ' each have a thickness d a＝da'＝λ0/4/Re(na) = 0.1098 μm (μm represents micrometers), where λ 0 =1.55 μm is the center wavelength, re (n a) represents the real part of the refractive index n a, The thicknesses of the dielectric sheets B and B' are d b＝db'＝λ0/4/Re(nb) = 0.2654 μm, respectively.
When transverse magnetic waves are vertically incident, corresponding transmission spectrums can be obtained by changing the sequence number N of the T-M sequence, and the transmission spectrums of the PT symmetrical photonic crystals TM 3 corresponding to the sequence number N=3 are shown in fig. 2 (a). The ordinate T represents the transmittance, the abscissa (ω - ω 0)/ωgap represents the normalized angular frequency, where ω=2pi c/λ, ω 0＝2πc/λ0 and ωgap＝4ω0arcsin│[Re(na)-Re(nb)]/[Re(na)+Re(nb)]|2/π represent the incident light angular frequency, the incident light center angular frequency and the angular frequency band gap, respectively, c is the light velocity in vacuum, arcsin is an arcsine function, and Re is a function for extracting the real part of complex refractive index. it can be seen that there are and only 1 formant, corresponding to 1 channel, within the normalized frequency (-1, 1) interval. The central transmittance of this channel is t=1, the corresponding central frequency is: (ω - ω 0)/ωgap =0, near the center frequency of the incident light when n=4, the number of photonic crystal layers increases to 16 layers, and the transmission spectrum thereof is as in fig. 2 (b). The increase of the defect mode causes a significant increase of formants in the interval (-1, 1) to 7 formants, and the channels correspondingly expand to 7. The central transmittance of the 7 channels is t= [1,0.9981,1,1,1,0.9981,1] from left to right, and the corresponding central frequencies are (ω - ω 0)/ωgap = [ -0.9573, -0.4087, -0.0940,0,0.0940,0.4087,0.9573]. When the sequence number continues to increase to n=5, the number of photonic crystal layers increases to 32, the transmission spectrum increases to 9 as in the interval of fig. 2 (c) (-1, 1), and the channel number further expands. The central transmittance of these 9 channels is, in turn, t= [0.0982,0.9987,0.9998,0.8002,1,0.8002,0.9998,0.9987,0.0982] from left to right, and their corresponding central frequencies are, in turn, (ω - ω 0)/ωgap = [ -0.8620, -0.4087, -0.1373, -0.0647,0,0.0647,0.1373,0.4087,0.8620]. It can be seen that as the number N of the T-M sequences increases, the transmission spectrum formants increase continuously, and the number of channels can be expanded after the transmission spectrum formants are applied to the photon filter.
When the gain-loss factor of the PT symmetric photonic crystal structure is changed, the transmission spectrum is also changed. Fig. 3 shows the effect of the gain-loss factor q on the transmission spectrum. It can be seen that as the gain-loss factor increases, the transmittance corresponding to each transmission peak increases except at the incident light center frequency ω 0. In particular two transmission peaks on the left and right of ω 0, whose corresponding peak transmission is quite sensitive to changes in q. When q=10, the transmission peak at ω 0 disappears due to the sharp increase of the left and right transmission peaks. In order to better observe the center frequency corresponding to the transmission peak, the transmission spectrum between the frequency ranges (-0.15, 0) is taken as an example, and amplified into a subgraph for analysis. It can be seen that as the gain-loss factor increases, the normalized frequency corresponding to the transmission peak dashed line increases in the sub-graph, and (ω - ω 0)/ωgap = [ -0.0940, -0.0900, -0.0787] and the peak transmittance corresponding to the peak transmittance is t= [1,1.5558, 28.5748] respectively from left to right.
The variation in the number, position and peak transmittance of the transmission peaks due to the variation in the number of the T-M sequences and the gain-loss factor is typical of the optical fractal phenomenon. Fig. 4 summarizes the optical morphologies, and shows the positions of the resonance modes on the normalized frequency axis when the transverse magnetic mode is perpendicularly incident from the left, the gain-loss factor is q=0 and 10 when the sequence numbers are n=3, 4,5, and 6. When gain-loss is not added, i.e., q=0, as the sequence number N increases, the defect mode corresponding to the transmission peak is split, so that more formants are generated, and the positions of the formants are basically symmetrical about the center frequency ω=ω 0 of the incident light. When q=10, it can be seen that, under the influence of gain or loss, the defective mode is degenerated while splitting occurs, and the number of formants increases slowly. At the same time, the symmetry about the formant ω=ω 0 is broken.
The number of channels in the photonic crystal of different sequence numbers T-M is given in table 1, corresponding to the splitting of the number of channels at q=0 and 10 in fig. 4. The transmission spectrum of the photonic crystal shows the characteristic of optical fractal, namely, with the increase of the serial number (dielectric layer number), the transmission mode in the transmission spectrum of the photonic crystal is split to form an optical split form, and different transmission spectrums have the characteristics of self similarity and the like.
In summary, T-M sequence PT symmetrical photonic crystals have multiple resonant transmission modes and optical fractal phenomenon. As the number of series numbers increases, the number of resonant modes increases. Both the center frequency of the channel and the number of channels can be regulated by changing the gain-loss factor. These transmission modes can be used for multi-channel communications and can also expand the number of channels in the photonic crystal by increasing the sequence number of the T-M sequence.
TABLE 1 number of channels in T-M Photonic Crystal of different sequence numbers
The specific modes can be as follows:
(1) And (5) selecting materials. Two dielectric matrixes A, A ', B and B' are selected, wherein the refractive indexes of the two dielectric matrixes are 3.53+0.01qi,1.46-0.01qi,3.53-0.01qi and 1.46+0.01qi respectively, the matrixes of A and A 'are silicon dioxide, the matrixes of B and B' are silicon, q is a gain-loss factor, and the gain and the loss are respectively introduced through doping or nonlinear frequency mixing.
(2) And (3) structural design. The two dielectric matrixes are stacked according to a T-M sequence by selecting different sequence numbers N to form a photonic crystal conforming to a space-time symmetrical structure, wherein the photonic crystal is TM 3 = ABBAA 'B' B 'A' (shown in figure 1) when N=3.
(3) Realizing multichannel photonic crystal. The input light is selected as transverse magnetic wave and vertically enters the photonic crystal from left to right as shown in fig. 1. When n=3, the single-channel photonic crystal can be used as a single-channel photonic crystal in the range of normalized center frequency-1 to 1, and the normalized center frequency of the channel is 0; n=4, and each channel has a normalized center frequency of-0.9573, -0.4087, -0.0940,0,0.0940,0.4087, and 0.9573 (see fig. 2 (a)); n=5, forming a 9-channel photonic crystal in the range of normalized center frequencies-1 to 1, each channel normalized center frequency being-0.8620, -0.4087, -0.1373, -0.0647,0,0.0647,0.1373,0.4087, and 0.8620, respectively (as in fig. 2 (b)); n=6, a photonic crystal of 18 channels is formed (see fig. 2 (c), fig. 4)) in the range of the normalized center frequencies-1 to 1. This means that the larger the sequence number, the more photonic crystal channels, and the more filter channels are available after use in a photonic crystal filter.
(4) The optical fractal is used for adjusting the channel number and the channel center frequency. Increasing the gain-loss factor q from 0 to 10, and slowing down the increase in the number of photonic crystal channels, and when n=3, 4,5, and 6 in the range of normalized center frequencies-1 to 1, the corresponding channel numbers are 1,6, and 7, respectively, and the channel center frequency also shifts blue as q increases (as shown in fig. 3). It can be seen that the gain-loss factor is increased, the number of photon crystal channels is increased and slowed down, and the channel frequency is adjustable.
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 (2)
1. The multi-channel non-periodic photonic crystal structure based on optical fractal is characterized by comprising two Thue-Morse sequences distributed in a space-time symmetrical manner, wherein the iteration rule of the Thue-Morse sequence S N is as follows: s 1＝A,N＝1;S2＝AB,N＝2;SN＝SN-1 (A.fwdarw.AB, B.fwdarw.BA), N.gtoreq.3, wherein A.fwdarw.AB in S N-1 represents that A is replaced by AB, B.fwdarw.BA represents that B is replaced by BA, N represents the sequence number of the sequence, and S N represents the nth item of 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;
The first dielectric layer positioned on one side of the symmetry center of the multi-channel non-periodic photonic crystal structure close to the incident direction is called a first loss dielectric layer, and the refractive index in the light-on state is expressed as n a; the first dielectric layer positioned on one side of the symmetry center of the multi-channel non-periodic photonic crystal structure close to the emergent direction is called a first gain dielectric layer, and the refractive index in the light-on state is expressed as n a'; the second dielectric layer positioned on one side of the symmetry center of the multi-channel non-periodic photonic crystal structure close to the incident direction is called a second gain dielectric layer, and the refractive index in the light-on state is expressed as n b; the second dielectric layer positioned on one side of the symmetry center of the multi-channel non-periodic photonic crystal structure close to the emergent direction is called a second loss dielectric layer (B'), and the refractive index in the light-on state is expressed as n b';
na＝nA+0.01qi,na'＝nA-0.01qi,nb＝nB-0.01qi,nb'＝nB+0.01qi,
Where i is the imaginary unit, q is the gain-loss factor, n A is the real part of the refractive index of the first dielectric layer, and n B is the real part of the refractive index of the second dielectric layer; the thicknesses of the first dielectric layer and the second dielectric layer are 1/4 optical wavelength corresponding to the respective refractive indexes; the incident light is transverse magnetic wave and vertically enters from the incident side of the multi-channel non-periodic photon crystal structure;
The first dielectric layer is silicon dioxide.
2. The optical fractal-based multi-channel non-periodic photonic crystal structure according to claim 1, wherein the loss values of the first and second loss dielectric layers are adjusted by doping with iron ions, and the gain values of the first and second gain dielectric layers are adjusted by nonlinear two-wave mixing.
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