CN215415969U

CN215415969U - Photon band stop filter structure based on quaternary Rudin-Shapiro photonic crystal

Info

Publication number: CN215415969U
Application number: CN202122075524.5U
Authority: CN
Inventors: 张亚平
Original assignee: Hubei University of Science and Technology
Current assignee: Hubei University of Science and Technology
Priority date: 2021-08-30
Filing date: 2021-08-30
Publication date: 2022-01-04
Anticipated expiration: 2031-08-30

Abstract

The utility model provides a photonic band-stop filter structure based on quaternary Rudin-Shapiro photonic crystals, and belongs to the technical field of optics. It has solved technical problem such as current … …. The iteration rule of Rudin-Shapiro sequences in the quaternary Rudin-Shapiro photonic crystal is as follows: s₀＝A，S₁＝AB，S₂＝ABAC，S₃＝ABACABDB，S₄＝ABACABDBABACDCAC，……，S_N＝S_N‑1(A → AB, B → AC, C → DB, D → DC), … …, wherein N is the sequence number of Rudin-Shapiro sequence, S_NRepresenting Rudin-Shapiro sequencesItem N, A → AB denotes S_N‑1A in (1) is replaced by AB, B → AC represents S_N‑1B in (1) is replaced by AC, and C → DB represents S_N‑1C in (1) is replaced by DB, D → DC represents S_N‑1D in (a) is replaced with DC, and the letters A, B, C and D denote four uniform dielectric sheets having different refractive indices, a first dielectric layer, a second dielectric layer, a third dielectric layer, and a fourth dielectric layer, respectively. The photonic band gap structure in the photonic crystal can be utilized, so that the photonic band gap structure is applied to the photonic band-stop filter.

Description

Photon band stop filter structure based on quaternary Rudin-Shapiro photonic crystal

Technical Field

The utility model belongs to the technical field of optics, and relates to a photonic band-stop filter structure based on a quaternary Rudin-Shapiro photonic crystal.

Background

The filter can be divided into four types of band-pass, band-stop, low-pass and high-pass according to the amplitude-frequency characteristic. In the field of optical communication, the communication wavelength is in the near infrared band, so that a band-pass or band-stop filter is required. Fiber gratings have been used to make filters, and the presence of artificial photonic crystals has made possible the implementation of photonic filters.

The dielectric substances with different refractive indexes are arranged periodically in space, and one-dimensional, two-dimensional or three-dimensional photonic crystals can be formed. The photonic crystal has an energy band structure, and can totally reflect light waves in a band gap. This characteristic can be applied to photonic band-stop filters. It is generally believed that defects have a destructive effect on the band structure of a photonic crystal because a single defect transmission mode exists in the bandgap of a defective photonic crystal. Defects enhance the locality of the optical field, thereby enhancing the resonance of the optical wave. The transmission of the defect mode is extremely large and the reflection is extremely small.

Quasi-periodic photonic crystals, also called quasi-photonic crystals, have a natural defect layer in the structure, often used for defect mode output. The quasiperiodic photonic crystal has an order between that of the periodic photonic crystal and that of the aperiodic photonic crystal. In addition, the number and position of the defect modes in the quasi-periodic photonic crystal can be expanded by increasing the number of the crystal. These defect modes have self-similar characteristics, which is called optical fractal effect, and the corresponding resonance modes are also called optical fractal.

Can defect layers in quasi-photonic crystals be disordered into order? Therefore, a photonic band structure in the quasi-photonic crystal is realized, a photonic band gap is obtained between two adjacent energy bands, and then the photonic band-stop filter based on the quasi-photonic crystal is realized.

SUMMERY OF THE UTILITY MODEL

The utility model aims to provide a photonic band-stop filter structure based on a quaternary Rudin-Shapiro photonic crystal aiming at the problems in the prior art, and the technical problem to be solved by the utility model is how to utilize a photonic band-gap structure in a quasi-photonic crystal to be used for a photonic band-stop filter.

The purpose of the utility model can be realized by the following technical scheme: a photonic band rejection filter structure based on a quaternary Rudin-Shapiro photonic crystal is characterized in that an iteration rule of Rudin-Shapiro sequences in the quaternary Rudin-Shapiro photonic crystal is as follows: s₀＝A，S₁＝AB，S₂＝ABAC，S₃＝ABACABDB，S₄＝ABACABDBABACDCAC，……，S_N＝S_N-1(A → AB, B → AC, C → DB, D → DC), … …, wherein N is the sequence number of Rudin-Shapiro sequence, S_NItem N representing Rudin-Shapiro sequence, A → AB represents S_N-1A in (1) is replaced by AB, B → AC represents S_N-1B in (1) is replaced by AC, and C → DB represents S_N-1C in (1) is replaced by DB, D → DC represents S_N-1D in (a) is replaced with DC, and the letters A, B, C and D denote four uniform dielectric sheets having different refractive indices, a first dielectric layer, a second dielectric layer, a third dielectric layer, and a fourth dielectric layer, respectively.

When N is greater than or equal to 3, the Rudin-Shapiro sequence forms a quaternary photonic crystal structure.

Furthermore, the thicknesses of the first dielectric layer, the second dielectric layer, the third dielectric layer and the fourth dielectric layer are 1/4 optical wavelengths corresponding to the respective refractive indexes.

Further, the first dielectric layer is titanium dioxide, the second dielectric layer is silicon dioxide, the third dielectric layer is cryolite, and the fourth dielectric layer is lead telluride.

Mathematically, a quaternary luding-schpino (Rudin-Shapiro: RS) sequence is a quasi-periodic sequence whose corresponding RS photonic crystal is a quasi-photonic crystal. In quaternary RS photonic crystals, there are photonic band gap structures that can be used for photonic band stop filters. The width of the stop band is controlled by the serial number of the RS sequence, and the position of the stop band can be flexibly regulated and controlled by the incident angle of the light wave.

Drawings

Fig. 1 is a structural diagram of quaternary RS-sequence photonic crystals corresponding to different numbers (numbers N ═ 0, 1, 2, and 3).

Fig. 2 shows a transmission spectrum and a reflection spectrum (No. N4) corresponding to the RS photonic crystal.

Fig. 3(a) is a transmission spectrum corresponding to N ═ 2, 3, 4, and 5; the (b) diagram in fig. 3 shows reflection spectra corresponding to N ═ 2, 3, 4, and 5.

In fig. 4, (a) shows transmission spectra corresponding to different incident angles when N is 4; in fig. 4, (b) is a graph of transmittance in a parameter space composed of an incident angle and a normalized frequency when N is 4; fig. 4(c) shows reflection spectra corresponding to different incident angles when N is 4; in fig. 4, (d) shows the reflectance in the parameter space composed of the incident angle and the normalized frequency when N is 4.

In the figure, a first dielectric layer; B. a second dielectric layer; C. a third dielectric layer; D. 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.

Mathematically, the iterative rule for the quaternary luding-hopino (Rudin-shariro: RS) sequence is: s₀＝A，S₁＝AB，S₂＝ABAC，S₃＝ABACABDB，S₄＝ABACABDBABACDCAC，……，S_N＝S_N-1(a → AB, B → AC, C → DB, D → DC), … …, where N (N ═ 0, 1, 2, 3, … …) is the sequence number, S_NThe Nth term of the sequence is shown, A → AB indicates S_N-1A in (1) is replaced by AB. In the corresponding quaternary RS photonic crystal, the letters A, B, C and D denote four uniform dielectric sheets with different refractive indices, respectively.

Fig. 1 shows quaternary RS photonic crystal structures with numbers N ═ 0, 1, 2, and 3, respectively, where a is a titanium dioxide flake with refractive index N_A2.1 as a result; b is a silica flake having a refractive index of n_B1.45; c is cryolite flake with refractive index n_C1.35; d is a lead telluride sheet having a refractive index of n_D4.1. The incident light is transverse magnetic wave. A. B, C and D both have a thickness of 1/4 optical wavelengths, i.e., A has a thickness D_A＝λ₀/4/n_A0.1685 μm (μm for micrometers),wherein λ₀1.55 μm as the center wavelength, and B has a thickness d_B＝λ₀/4/n_B0.2672 μm, thickness of C d_C＝λ₀/4/n_C0.287 μm, D has a thickness D_D＝λ₀/4/n_D＝0.0945μm。

In a photonic crystal, there is a band structure with a band gap between the two bands. The light waves in the band gap cannot pass through the photonic crystal and are not totally reflected. The RS photonic crystal is a quasi-photonic crystal, the wave vector space of the RS photonic crystal also has an energy band structure, and a band gap is also arranged between two adjacent band energies.

When transverse magnetic waves are vertically incident, a transmission spectrum and a reflection spectrum corresponding to the quaternary RS photonic crystal with the N-4 are shown in FIG. 2. The ordinate T represents the transmittance, R represents the reflectance, and the abscissa (ω - ω)₀)/ω_gapDenotes a normalized angular frequency, where ω is 2 π c/λ, ω₀＝2πc/λ₀And ω_gap＝4ω₀arcsin│(n_a-n_b)/(n_a+n_b)|²And/pi respectively represents incident light angular frequency, incident light central angular frequency and angular frequency band gap, c is light speed in vacuum, and arcsin is an inverse sine function. It can be seen that: within the normalized frequency range (-1,1), there is a photonic bandgap; the light wave transmittance positioned in the photonic band gap is T-0, and the reflectivity is R-1; the band gap can be used in photon stop band filter, and the stop band interval is the central frequency corresponding to the falling edge to the rising edge of the transmission band gap, and is expressed as [ -0.773, 0.773 ] by normalized frequency](ii) a The stop band width is the absolute value [ omega ] - [ omega ] of the difference between the center frequencies corresponding to the rising edge and the falling edge of the transmission band gap_{On the upper part}-ω_{Lower part}|＝1.546。

The serial number N of the sequence of the RS photonic crystal is changed, and the transverse magnetic wave is still kept incident perpendicularly, and the transmission spectra corresponding to the serial numbers N of 2, 3, 4 and 5 are respectively given in fig. 3 (a). It can be seen that: in the normalized frequency range (-1,1), the transmittance has a minimum value corresponding to the photonic band gap in the transmission spectrum; when N is increased continuously, the transmissivity in the middle of the band gap is closer to 0; also, the larger N, the steeper the upper and lower edges of the band gap, which indicates the better extinction ratio at the band gap edge, but it can also be seen that the width of the stop band becomes slightly narrower as N increases. Specifically, the statistics of stop band parameters of RS photonic crystals with different numbers are shown in table 1.

TABLE 1 RS Photonic Crystal stop band Filter parameters of different numbers

Fig. 3(b) shows reflection spectra corresponding to N ═ 2, 3, 4, and 5, respectively. It can be seen that: in the normalized frequency range of (-1,1), the reflectivity is extremely high, and a photonic band gap exists; as N increases, the reflectivity in the middle of the band gap is closer to 1; when N is more than or equal to 4, the reflectivity of the center of the band gap is 1, and the light wave can be totally reflected; the larger the N, the steeper the rising and falling edges of the band gap, and the better the reflection effect. The reflection spectrum and the transmission spectrum of the photonic crystals corresponding to different index numbers are complementary to each other, i.e. symmetrically distributed about the ordinate axis 0.5.

By changing the incident angle of the transverse magnetic wave, fig. 4(a) shows the transmission spectrum corresponding to different incident angles. It can be seen that: a region with extremely low transmissivity exists in the middle of each spectral line, namely a band gap; as the angle of incidence increases, the spectral line shifts generally to the right. Therefore, the position of the band gap, namely the position of the stop band can be regulated and controlled by changing the size of the incident angle.

Fig. 4(b) shows the transmittance in the parameter space. The parameter space consists of the angle of incidence and the normalized frequency. When the angle of incidence changes, the position of the photonic band gap with zero transmission shifts as viewed by the dark portion sandwiched between the two curved white dashed lines in the figure. In addition, when the frequency of the light wave is located between two vertical white dotted lines, the light wave is totally reflected regardless of the change in the incident angle, i.e., from-90 ° to 90 °, and the transmittance is 0.

Fig. 4(c) shows the reflection spectrum for different incident angles. It can be seen that: a region with extremely high reflectivity exists in the middle of each spectral line, namely a band gap; as the angle of incidence increases, the spectral line shifts generally to the right. Light within the band gap is totally reflected and not transmitted. By varying the angle of incidence, the position of the band gap, i.e. the position of the stop band, can be varied.

Fig. 4(d) shows the reflectivity in the parameter space. When the angle of incidence is changed, the high reflectivity photonic band gap location shifts as viewed by the dark portion sandwiched between the two curved white dashed lines in the figure. In addition, when the frequency of the light wave is located between two vertical white dotted lines, the light wave reflectance is 1 regardless of the change in the incident angle, and no transmission is made.

In conclusion, the quaternary RS photonic crystal has a photonic band gap structure, the reflectivity of light waves in the band gap is extremely high, and the transmissivity is extremely low. This band gap can be used in photonic band stop filters, the stop band width of which decreases slightly as the number of photonic crystals increases. When the number N is not less than 4, the center transmittance of the band gap is 0 and the reflectance is 1. In addition, the position of the stop band can be flexibly regulated and controlled by changing the size of the incident angle. 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. A photonic band rejection filter structure based on a quaternary Rudin-Shapiro photonic crystal is characterized in that an iteration rule of Rudin-Shapiro sequences in the quaternary Rudin-Shapiro photonic crystal is as follows: s₀＝A，S₁＝AB，S₂＝ABAC，S₃＝ABACABDB，S₄＝ABACABDBABACDCAC，……，S_N＝S_N-1(A → AB, B → AC, C → DB, D → DC), … …, wherein N is the sequence number of Rudin-Shapiro sequence, S_NItem N representing Rudin-Shapiro sequence, A → AB represents S_N-1A in (1) is replaced by AB, B → AC represents S_N-1B in (1) is replaced by AC, and C → DB represents S_N-1C in (1) is replaced by DB, D → DC represents S_N-1D in (b) is replaced by DC, and the letters A, B, C and D respectively denote four kinds of uniform dielectric sheets having different refractive indicesA layer, a second dielectric layer, a third dielectric layer, and a fourth dielectric layer.

2. The photonic band stop filter structure based on the quaternary Rudin-Shapiro photonic crystal as claimed in claim 1, wherein the thicknesses of the first dielectric layer, the second dielectric layer, the third dielectric layer and the fourth dielectric layer are all 1/4 optical wavelengths corresponding to respective refractive indexes.

3. The photonic band stop filter structure based on the quaternary Rudin-Shapiro photonic crystal as claimed in claim 1 or 2, wherein the first dielectric layer is titanium dioxide, the second dielectric layer is silicon dioxide, the third dielectric layer is cryolite, and the fourth dielectric layer is lead telluride.

4. The photonic band stop filter structure based on the quaternary Rudin-Shapiro photonic crystal as claimed in claim 1 or 2, wherein the stop band width and extinction ratio of the photonic band stop filter structure are regulated and controlled by the serial number of the photonic crystal; the position of the stop band of the photonic band-stop filter structure is regulated and controlled by an incident angle.