CN113534301B - Photon crystal structure capable of realizing optical fractal - Google Patents
Photon crystal structure capable of realizing optical fractal Download PDFInfo
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- CN113534301B CN113534301B CN202111003135.XA CN202111003135A CN113534301B CN 113534301 B CN113534301 B CN 113534301B CN 202111003135 A CN202111003135 A CN 202111003135A CN 113534301 B CN113534301 B CN 113534301B
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- 230000003287 optical effect Effects 0.000 title claims abstract description 31
- 239000013078 crystal Substances 0.000 title description 3
- 239000004038 photonic crystal Substances 0.000 claims abstract description 49
- 238000001914 filtration Methods 0.000 claims description 8
- 230000001105 regulatory effect Effects 0.000 claims description 7
- VYPSYNLAJGMNEJ-UHFFFAOYSA-N Silicium dioxide Chemical compound O=[Si]=O VYPSYNLAJGMNEJ-UHFFFAOYSA-N 0.000 claims description 6
- GWEVSGVZZGPLCZ-UHFFFAOYSA-N Titan oxide Chemical compound O=[Ti]=O GWEVSGVZZGPLCZ-UHFFFAOYSA-N 0.000 claims description 6
- 239000000377 silicon dioxide Substances 0.000 claims description 3
- 239000004408 titanium dioxide Substances 0.000 claims description 3
- 235000012239 silicon dioxide Nutrition 0.000 claims description 2
- 230000015572 biosynthetic process Effects 0.000 abstract 1
- 230000005540 biological transmission Effects 0.000 description 12
- 238000000411 transmission spectrum Methods 0.000 description 11
- 238000002834 transmittance Methods 0.000 description 8
- 230000007547 defect Effects 0.000 description 6
- 230000000694 effects Effects 0.000 description 4
- 230000007423 decrease Effects 0.000 description 2
- 230000002950 deficient Effects 0.000 description 2
- 230000004807 localization Effects 0.000 description 2
- 239000000463 material Substances 0.000 description 2
- 230000000737 periodic effect Effects 0.000 description 2
- 238000006467 substitution reaction Methods 0.000 description 2
- 238000007792 addition Methods 0.000 description 1
- 230000001276 controlling effect Effects 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 239000003989 dielectric material Substances 0.000 description 1
- 230000005684 electric field Effects 0.000 description 1
- 239000000835 fiber Substances 0.000 description 1
- 238000005194 fractionation Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000000926 separation method Methods 0.000 description 1
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- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B1/00—Optical elements characterised by the material of which they are made; Optical coatings for optical elements
- G02B1/002—Optical elements characterised by the material of which they are made; Optical coatings for optical elements made of materials engineered to provide properties not available in nature, e.g. metamaterials
- G02B1/005—Optical elements characterised by the material of which they are made; Optical coatings for optical elements made of materials engineered to provide properties not available in nature, e.g. metamaterials made of photonic crystals or photonic band gap materials
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- G—PHYSICS
- G02—OPTICS
- G02F—OPTICAL DEVICES OR ARRANGEMENTS FOR THE CONTROL OF LIGHT BY MODIFICATION OF THE OPTICAL PROPERTIES OF THE MEDIA OF THE ELEMENTS INVOLVED THEREIN; NON-LINEAR OPTICS; FREQUENCY-CHANGING OF LIGHT; OPTICAL LOGIC ELEMENTS; OPTICAL ANALOGUE/DIGITAL CONVERTERS
- G02F1/00—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics
- G02F1/01—Devices or arrangements for the control of the intensity, colour, phase, polarisation or direction of light arriving from an independent light source, e.g. switching, gating or modulating; Non-linear optics for the control of the intensity, phase, polarisation or colour
- G02F1/0102—Constructional details, not otherwise provided for in this subclass
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- Optics & Photonics (AREA)
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- Chemical & Material Sciences (AREA)
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Abstract
The invention provides a photonic crystal structure capable of realizing optical fractal, and belongs to the technical field of optics. The multi-layer structure of the photonic crystal structure satisfies a binary Lu Ding-Xia Pinuo (Rudin-shape: RS) sequence arrangement rule, a binary RS sequence is an iterative rule ：S0＝H,S1＝HH,S2＝HHHL,S3＝HHHLHHLH,……,SN＝SN‑1(HH→HHHL,HL→HHLH,LH→LLHL,LL→LLLH),……, in which N (n=0, 1,2,3, … …) sequence numbers, S N represents the nth item of the sequence, hh→ HHHL represents the replacement of HH in S N‑1 with HHHL, hl→ HHLH represents the replacement of HL in S N‑1 with HHLH, lh→llhl represents the replacement of LH in S N‑1 with LLHL, ll→lllh represents the replacement of LL in S N‑1 with LLLH; H. l represents a first dielectric medium and a second dielectric medium with different refractive indexes respectively; the thickness of the first dielectric medium and the second dielectric medium is 1/4 optical wavelength corresponding to the respective refractive indexes. The invention enables the formation of optical morphologies that can be used in multichannel photon filters.
Description
Technical Field
The invention belongs to the technical field of optics, and relates to a photonic crystal structure capable of realizing optical fractal.
Background
The dielectrics with different refractive indexes are periodically arranged in space, and one-dimensional, two-dimensional or three-dimensional photonic crystals can be formed. The photonic crystal has an energy band and a band gap structure, and the characteristic enables the photonic crystal to perform total transmission and total reflection on light waves. A single defect mode, also called a transmission mode, exists in the bandgap of the defective photonic crystal. Defects enhance the localization of the optical field, thereby increasing the resonance of the light wave. Thus, the transmittance of the defective mode is extremely large, and the reflection is extremely small.
The quasiperiodic photonic crystal also has an energy band structure. The quasi-periodic photonic crystal has a natural defect layer with an order between that of the periodic photonic crystal and that of the non-periodic photonic crystal, and is often used to obtain a defect mode output. In addition, the number and the positions of defect modes in the quasi-periodic photonic crystal can be expanded by increasing the sequence number of the crystal, and the defect modes have self-similarity characteristics, so that the phenomenon is called an optical fractal effect, and the corresponding resonance mode is called an optical division form. The optical fractionation can be applied to electric field localization, reflection enhancement, lasers, filters, and the like.
In particular, filters can be classified into four types of bandpass, bandstop, lowpass, and highpass according to the amplitude-frequency characteristics. In wavelength division multiplexing, multiple channels need to be filtered, which requires multiple channel filters. The traditional optical wavelength division multiplexer realizes the filtering and separation of channels by regulating and controlling the space period of the fiber grating. The advent of artificial photonic crystals provides a new choice for the design of multi-channel filters.
In quasiperiodic photonic crystals, there are many transmission modes, corresponding to a series of optical fractal states. The optical fractal state in the quasi-periodic photonic crystal can be applied to the multichannel optical filter, the number of channels can be expanded through serial numbers of sequences, and the positions of the channels can be flexibly regulated and controlled through changing the incidence angle of light waves.
Disclosure of Invention
The present invention is directed to a photonic crystal structure capable of realizing optical fractal, and the technical problem to be solved by the present invention relates to a photonic crystal structure with optical fractal for application in a multichannel optical filter.
The aim of the invention can be achieved by the following technical scheme: a photonic crystal structure capable of realizing optical fractal, characterized in that the multi-layer structure of the photonic crystal structure satisfies a binary Lu Ding-Xia Pinuo (Rudin-shape: RS) sequence arrangement rule, a binary RS sequence is an iterative rule ：S0＝H,S1＝HH,S2＝HHHL,S3＝HHHLHHLH,……,SN＝SN-1(HH→HHHL,HL→HHLH,LH→LLHL,LL→LLLH),……, in which N (n=0, 1,2,3, … …) is a sequence number, S N represents an nth item of the sequence, hh→ HHHL represents replacement of HH in S N-1 with HHHL, hl→ HHLH represents replacement of HL in S N-1 with HHLH, lh→llhl represents replacement of LH in S N-1 with LLHL, ll→lllh represents replacement of LL in S N-1 with LLLH; H. l represents a first dielectric medium and a second dielectric medium with different refractive indexes respectively; the thickness of the first dielectric medium and the second dielectric medium is 1/4 optical wavelength corresponding to the respective refractive indexes.
Further, the first dielectric is titanium dioxide and the second dielectric is silicon dioxide.
Further, the photonic crystal structure can be used for a multi-channel photonic filter, the number of filtered channels is expanded by increasing the sequence number of a binary RS sequence, and the channel center wavelength of the photonic crystal structure is regulated and controlled by an incident angle.
Mathematically, the binary Lu Ding-Xia Pinuo (Rudin-Shapiro: RS) sequence is a quasi-periodic sequence, and its corresponding binary RS photonic crystal is a quasi-periodic photonic crystal, also called quasi-photonic crystal. In binary RS photonic crystals, there are a series of transmission modes, corresponding to a series of optical fractal states. The optical fractal state can be applied to a multichannel optical filter, the number of channels can be controlled by the serial number of a binary RS sequence, and the positions of the channels can be flexibly regulated and controlled by the incident angle of light waves.
Drawings
FIG. 1 is a schematic diagram of a binary RS sequence photonic crystal structure.
Fig. 2 (a) is a transmission spectrum corresponding to the binary RS photonic crystal when n=2; fig. 2 (b) is a transmission spectrum corresponding to the binary RS photonic crystal when n=3; fig. 2 (c) is a transmission spectrum corresponding to the binary RS photonic crystal when n=4; fig. 2 (d) is a transmission spectrum corresponding to the binary RS photonic crystal when n=5.
Fig. 3 is a binary RS photonic crystal transmission spectrum corresponding to different angles of incidence when n=3.
FIG. 4 (a) is a graph showing the transmittance of channel 1 of FIG. 3 as a function of angle of incidence; fig. 4 (b) is a graph showing normalized frequency of channel 1 in fig. 3 as a function of angle of incidence.
In the figure, H is the first dielectric; l, a second dielectric.
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.
Mathematically, the iterative rule for a binary Lu Ding-Xia Pinuo (Rudin-Shapiro: RS) sequence is ：S0＝H,S1＝HH,S2＝HHHL,S3＝HHHLHHLH,……,SN＝SN-1(HH→HHHL,HL→HHLH,LH→LLHL,LL→LLLH),……, where the sequence number of the N (N=0, 1,2,3, … …) sequence, S N represents the nth term of the sequence, HH→ HHHL represents the substitution of HH in S N-1 for HHHL. In the corresponding RS photonic crystal, letters H, L represent two kinds of uniform dielectric sheets having different refractive indexes, respectively.
Fig. 1 shows binary RS photonic crystal structures with numbers n=0, 1,2 and 3, respectively, where H is titanium dioxide, a high refractive index material, and its refractive index is N H =2.1; l is a low refractive index material silica having a refractive index of n L =1.45. The incident light is transverse magnetic waves. The thickness of both H and L is 1/4 of the optical wavelength, i.e. H has a thickness d H＝λ0/4/nH = 0.1685 μm (μm represents micrometers), where λ 0 = 1.55 μm is the central wavelength and L has a thickness d L＝λ0/4/nL = 0.2672 μm.
In a quasi-photonic crystal, there is an optical fractal effect. The optical fractal effect can be used to obtain a multi-channel filter and expand the filtering channels. Fig.2 (a) shows the transmission spectrum corresponding to a binary RS photonic crystal with n=2 when the transverse magnetic wave is perpendicularly incident. The ordinate T represents the transmittance, and the abscissa (ω - ω 0)/ωgap represents the normalized angular frequency, where ω=2ρc/λ, ω 0＝2πc/λ0, and ω gap＝4ω0arcsin│(na-nb)/(na+nb)|2/pi 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, it can be seen that in the normalized frequency interval (-3, 3), the number of transmission peaks is 3, thus the number of filter channels in the structure is 3, FIG.2 (b) shows the transmission spectrum corresponding to a binary RS photonic crystal of N=3, the number of transmission peaks is 7, the number of filter channels in the structure is 7, FIG.2 (c) shows the transmission spectrum corresponding to a binary RS photonic crystal of N=4, the number of transmission peaks is 11, the number of filter channels in the structure is 11, and FIG.2 (d) shows the transmission spectrum corresponding to a binary RS photonic crystal of N=5, the number of transmission peaks is 23.
The optical fractal has self-similar properties. The three fractal patterns in the dashed boxes in fig. 2 (a) are similar to the three fractal patterns in the dashed boxes in fig. 2 (b), 2 (c) and 2 (d) along paths I, II and III, respectively. Whereas the three fractal patterns of the left and right dashed boxes in fig. 2 (c) are similar to the three fractal patterns of the two dashed boxes in fig. 2 (d) along paths IV and V, respectively.
For clarity of comparison, the number of filter channels corresponding to binary RS photonic crystals of different sequence numbers N is given in table 1. The conditions given in the table are: the light wave is vertically incident, and the normalized frequency interval is (-3, 3). As can be seen from the table, as the number N increases, the number of filter channels increases rapidly, and this effect can be used to expand the number of filter channels.
TABLE 1 number of channels of filter pass in binary RS photonic crystals of different sequence numbers
Mention was made in the above: when n=3, the transverse magnetic wave is perpendicularly incident, the number of filtering channels of the binary RS photonic crystal in the normalized frequency interval (-3, 3) is 7. The magnitude of the incident angle of the light wave is changed, so that the center frequency of each filtering channel is regulated. The binary RS photonic crystal structure with the sequence number n=3 is kept unchanged, and the incident angles given in fig. 3 are respectively transmission spectra corresponding to θ=0 °, 15 °, 30 ° and 45 °. It can be seen that the number of filter channels remains unchanged within the interval (-3, 3), despite the variation in the magnitude of the angle of incidence. Only with increasing angle of incidence, the transmission spectrum moves to the right as a whole. Therefore, the center frequency of the filter channel can be changed by adjusting the magnitude of the incident angle. For comparison purposes, a filtered channel at the center position is chosen to quantitatively illustrate, the position of this channel is delineated by an ellipse and labeled with a sign, which is designated channel 1.
The corresponding center transmittance for channel 1 in fig. 3 is denoted T 1 and the corresponding transmission mode center frequency is denoted ω 1. Fig. 4 (a) shows the transmittance T 1 of the channel 1 of fig. 3 as a function of the incident angle θ. It can be seen that as the angle of incidence increases, the transmittance T 1 decreases slightly therewith; when θ rises from=0° to 60 °, the transmittance T 1 decreases from 1 to 0.999996. Fig. 4 (b) shows the variation of the center frequency ω 1 of the transmission mode of the channel 1 in fig. 3 with the incident angle. It can be seen that as the angle of incidence increases, the transmittance ω 1 increases. When θ rises from 0 ° to 60 °, (ω 1-ω0)/ωgap rises from 0 to 0.421).
In summary, there are optical morphologies in the binary RS photonic crystal, corresponding to different transmission modes. These transmission modes can be used for multi-channel photon filtering, the number of filtering channels can be expanded by increasing the sequence number, and the center frequency of each filtering channel can be flexibly regulated by changing the magnitude of the incident angle.
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 (3)
1. The photonic crystal structure capable of realizing optical fractal is characterized in that the multilayer structure of the photonic crystal structure meets the sequence arrangement rule of binary Lu Ding-Xia Pinuo (Rudin-shape: RS), and the binary RS sequence is as follows: s0=h, s1=hh, s2= HHHL, s3= HHHLHHLH, … …, sn=sn-1, i.e. HHHL in SN replaces HH in SN-1, HHLH in SN replaces HL in SN-1, LLHL in SN replaces LH in SN-1, LLLH in SN replaces LL in SN-1, … …, where N is the sequence number, SN represents the nth item of the sequence, n=0, 1,2,3, … …, hh→ HHHL represents replacement of HH in SN-1 with HHHL, hl→ HHLH represents replacement of HL in SN-1 with LH, lh→llhl represents replacement of LH in SN-1 with LLHL, ll→lllh represents replacement of LL in SN-1 with LLLH; H. l represents a first dielectric medium and a second dielectric medium with different refractive indexes respectively; the thickness of the first dielectric medium and the second dielectric medium is 1/4 optical wavelength corresponding to the respective refractive indexes.
2. A photonic crystal structure enabling optical fractal according to claim 1, characterized in that said first dielectric is titanium dioxide and said second dielectric is silicon dioxide.
3. A photonic crystal structure capable of realizing optical fractal according to claim 1 or 2, characterized in that said photonic crystal structure can be used for a multi-channel photonic filter, the number of filtering channels is extended by increasing the sequence number of binary RS sequences, and the channel center wavelength of said photonic crystal structure is regulated by the incidence angle.
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| WO2005104317A1 (en) * | 2004-04-23 | 2005-11-03 | Massachusetts Institute Of Technology | Silicon rich nitride cmos-compatible light sources and si-based laser structures |
| WO2008073601A2 (en) * | 2006-10-31 | 2008-06-19 | Trustees Of Boston University | Deterministic aperiodic patterned dielectric and plasmonic materials for localized electromagnetic field enhancement |
| CN216013719U (en) * | 2021-08-30 | 2022-03-11 | 湖北科技学院 | A Photonic Crystal Structure That Can Realize Optical Fractals |
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| CN113687450A (en) * | 2021-08-16 | 2021-11-23 | 湖北科技学院 | PT symmetrical Octonacci sequence photon multilayer structure capable of realizing optical directional stealth |
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Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2005104317A1 (en) * | 2004-04-23 | 2005-11-03 | Massachusetts Institute Of Technology | Silicon rich nitride cmos-compatible light sources and si-based laser structures |
| WO2008073601A2 (en) * | 2006-10-31 | 2008-06-19 | Trustees Of Boston University | Deterministic aperiodic patterned dielectric and plasmonic materials for localized electromagnetic field enhancement |
| CN216013719U (en) * | 2021-08-30 | 2022-03-11 | 湖北科技学院 | A Photonic Crystal Structure That Can Realize Optical Fractals |
Non-Patent Citations (2)
| Title |
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