CN113066464B - Acousto-optic photonic crystal structure - Google Patents
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- G10K—SOUND-PRODUCING DEVICES; METHODS OR DEVICES FOR PROTECTING AGAINST, OR FOR DAMPING, NOISE OR OTHER ACOUSTIC WAVES IN GENERAL; ACOUSTICS NOT OTHERWISE PROVIDED FOR
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Abstract
The invention discloses an acousto-optic photonic crystal structure, which comprises a body, wherein the body is formed by regularly arranging a plurality of unit cell structures with completely identical structures; each unit cell structure comprises a square silicon, a square hole and four groups of elastic beams, the square hole is arranged in the middle of the inside of the square silicon in an equal-ratio reduced mode according to the outline of the square silicon, and the four groups of elastic beams are arranged on four sides of the square silicon in a cross-shaped distribution mode; each group of elastic beams comprises a first straight line section, a connecting section and a second straight line section which are sequentially connected; the square silicon and the four groups of elastic beams are made of silicon. The invention has the following advantages and effects: the acousto-optic photonic crystal structure has good double band gap broadband characteristics, and can obtain wider phonon and photon complete band gaps through adjustable geometric parameters, so that the acousto-optic photonic crystal structure can be better applied to the engineering field.
Description
Technical Field
The invention relates to the field of structural design of acoustic and optical functional materials, in particular to an acousto-optic photonic crystal structure.
Background
By analogy with photonic crystals, it is found that when an elastic wave propagates in a periodic elastic composite medium, a similar elastic wave band gap is generated, and thus, a photonic crystal concept is proposed. Phonon/photonic crystals are a new type of artificial periodic structure that can inhibit wave propagation in certain frequency ranges (band gaps), while waves in other frequency ranges (pass bands) will continue to propagate and the transmission of classical waves can be artificially regulated by design. The characteristic of the sound/photon crystal structure can lead the sound/photon crystal to have huge utilization value in the scientific application of practical engineering, and also creates a new situation for solving the problems of mechanical structure vibration and electromagnetic wave radiation. In general, current phonon/photonic crystal structure studies have involved: quantum optics, electromagnetism, solid energy band theory, semiconductor device physics, nanometer structure, solid physics, molecular biology, micro-electro-mechanical engineering, material science and other fields.
In the last few years that phononic crystals were proposed, phononic crystals and photonic crystals were developed independently in their respective fields, and there was little interest in research. Although a certain range of phonon and photon forbidden bands may exist in a certain periodic structure, the application in real life is difficult to realize due to the scale problem of the periodic structure and the practical technical problem, so that the problem of presenting the phonon and photon forbidden band characteristics at the same time is stranded by people and is difficult to enter a research front queue. With the progress of nanotechnology, people find that elastic waves and electromagnetic waves can show unique coupling characteristics under the micro-nano scale, and the problem that phonons and photon forbidden bands simultaneously exist in the same periodic structure is a hot research. Based on the concept of phonon and photonic crystal, we name a new material or structure with spatial periodicity and exhibiting both elastic band gap and electromagnetic band gap characteristics as a phonon crystal. In addition, in the acousto-optic photonic crystal, phonon and photonic bandgaps are collectively referred to as a double bandgap. Due to the tunability of the dual band gap, acousto-optic nanocrystals have many potential applications in opto-mechanical and acousto-optic devices, such as acousto-optic crystal sensors, resonators, waveguides, and the like. Theories and experiments verify that double band gaps exist in the acousto-optic photonic crystal, and the acousto-optic photonic crystal can be used for acousto-optic devices, sensors and optical communication. Since the structure of the acousto-photonic crystal is designed for the first time, acousto-photonic crystals with different dimensions and different structural forms are designed successively.
On the basis of the research, the invention provides an acousto-optic photonic crystal structure, which is used for simultaneously obtaining the complete band gap broadband characteristics of phonons and photons, so that the acousto-optic photonic crystal is better applied to the engineering field.
Disclosure of Invention
It is an object of the present invention to provide an acousto-optic photonic crystal structure that solves the problems set forth in the background.
The technical purpose of the invention is realized by the following technical scheme: an acousto-photonic crystal structure characterised by: the body is formed by regularly arranging a plurality of unit cell structures with the same structure;
each unit cell structure comprises a square silicon, a square hole and four groups of elastic beams, wherein the square hole is arranged in the middle of the inside of the square silicon in an equal-ratio reduction mode according to the outline of the square silicon, and the four groups of elastic beams are arranged on four edges of the square silicon in a cross distribution mode;
each group of elastic beams comprises a first straight line section, a connecting section and a second straight line section which are sequentially connected, wherein the first straight line section and the second straight line section are vertically arranged on the edge of the square silicon along the direction far away from the square silicon, a gap is arranged between the first straight line section and the second straight line section, and the tail ends of the first straight line section and the second straight line section are connected through the connecting section;
the square silicon and the four groups of elastic beams are made of silicon.
The further setting is that: the refractive index of the silicon adopted by the square silicon and the four groups of elastic beams is 3.5.
The further setting is that: the lattice constant of the body is a, the side length of the square silicon is b, the side length of the square hole is c, the width of the elastic beam is d, and the widths of the first straight line segment, the connecting segment and the second straight line segment are f;
specifically, a =666nm, b =0.55a, c =0.1a, d =0.1a, and f =0.025 a.
The further setting is that: the unit cell structures are arranged in the transverse direction to form a structural layer, at least two layers are arranged on the structural layer in the longitudinal direction, and the structural layers jointly form the body.
The invention has the beneficial effects that:
the acousto-optic photonic crystal structure has good double band gap broadband characteristics, and can obtain wider phonon and photon complete band gaps through adjustable geometric parameters, so that the acousto-optic photonic crystal structure can be better applied to the engineering field. The advantageous effects are further explained below in conjunction with the detailed description.
Drawings
FIG. 1 is a schematic structural diagram of an embodiment;
FIG. 2 is a first diagram of a unit cell structure according to an embodiment;
FIG. 3 is a diagram of a second embodiment of a unit cell structure;
FIG. 4 is a first irreducible Brillouin zone in an embodiment;
FIG. 5 is a band diagram of the photonic crystal structure of an example (phonon band diagram);
FIG. 6 is a band diagram of the photonic crystal structure of an example (photonic band diagram);
FIG. 7 shows a transmission spectrum (phonon transmission spectrum) of the phononic crystal structure in the example;
FIG. 8 is a transmission spectrum (photon transmission spectrum) of the phononic crystal structure in the example;
FIG. 9 is a band gap variation (variation law of phonon complete band gap) corresponding to the side length c of the square hole in the embodiment;
FIG. 10 is a diagram showing the band gap variation (variation law of complete band gap of photons) corresponding to the side length c of the square hole in the embodiment;
FIG. 11 is a band gap variation (variation law of phonon complete band gap) corresponding to the side length b of square silicon in the example;
FIG. 12 is a band gap variation (variation law of photon complete band gap) corresponding to the side length b of square silicon in the example;
FIG. 13 is a band gap variation (variation law of phonon complete band gap) corresponding to the elastic beam width f in the embodiment;
FIG. 14 is a band gap variation (variation law of photon complete band gap) corresponding to the elastic beam width f in the embodiment;
fig. 15 is a diagram of material properties in the examples.
In the figure: 1. square silicon; 2. a square hole; 3. an elastic beam; 31. a first straight line segment; 32. a second straight line segment; 33. and (4) connecting the sections.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
As shown in fig. 1 to 4, an acousto-optic photonic crystal structure comprises a body, wherein the body is formed by regularly arranging a plurality of unit cell structures with completely identical structures;
each unit cell structure comprises a square silicon 1, a square hole 2 and four groups of elastic beams 3, wherein the square hole 2 is arranged in the middle of the interior of the square silicon 1 in an equal-proportion reduction mode according to the outline of the square silicon 1, and the four groups of elastic beams 3 are arranged on four edges of the square silicon 1 in a cross-shaped distribution mode;
each group of elastic beams 3 comprises a first straight line section 31, a connecting section 33 and a second straight line section 32 which are sequentially connected, the first straight line section 31 and the second straight line section 32 are vertically arranged on the side of the square silicon 1 along the direction far away from the square silicon 1, a space is arranged between the first straight line section 31 and the second straight line section 32, and the tail ends of the first straight line section 31 and the second straight line section 32 are connected through the connecting section 33;
the square silicon 1 and the four groups of elastic beams 3 are made of silicon.
Further, the refractive index of silicon used for the square silicon 1 and the four sets of elastic beams 3 is 3.5.
Specifically, the lattice constant of the body is a, the side length of the square silicon 1 is b, the side length of the square hole 2 is c, the width of the elastic beam 3 is d, and the widths of the first straight line section 31, the connecting section 33 and the second straight line section 32 are f;
specifically, a =666nm, b =0.55a, c =0.1a, d =0.1a, and f =0.025 a.
Specifically, a plurality of unit cell structures are arranged in the transverse direction to form a structural layer, at least two layers are arranged on the structural layer in the longitudinal direction, and the structural layers jointly form the body. In this embodiment, the body is composed of two structural layers.
And calculating the phonon and photonic band gaps of the acousto-optic photonic crystal structure by using a finite element method. The material properties of the materials used in the lattice structure are shown in fig. 15, with the structural dimensional parameters consistent with those described above.
Figures 5 and 6 show calculated phonon and photonic bandgap diagrams. As can be seen, FIGS. 5 and 6 show dimensionless phonon frequenciesωa/2πc tAnd dimensionless photon frequencyωa/2πc tA variation relation of the satellite vector, whereinc tAndcrespectively the shear wave velocity of the silicon material and the vacuum velocity of the light.
As can be seen from fig. 5, the first full band gap (between the fifth and sixth inner bands) and the second full band gap (between the seventh and eighth inner bands) of the phonons are distributed in [0.286,0.73] and [0.748,0.774], and the total bandwidth reaches 0.444 and 0.026, respectively. Further, the relative band gap widths of the first phonon full band gap (2.3 GHz-5.87 GHz) and the second phonon full band gap (6.02 GHz-6.23 GHz), which are defined as the ratio of the band gap width to the band gap center frequency, are 87.4% and 3.4%, respectively. The first bandgap appears to be too narrow compared to the second bandgap, and therefore the second bandgap was chosen as the main subject of investigation.
As can be seen from fig. 6, the solid line and the dotted line represent the TE mode and the TM mode, respectively, wherein the photon complete band gap (between the second TE band and the fourth TM band) is distributed in [0.4, 0.46], and the corresponding band gap width is 0.06 (14% relative to the band gap width). In addition, the wavelength in the photon complete band gap frequency range (180 THz-207 THz) is 1448nm-1665nm, and the photonic complete band gap frequency band gap can be applied to the fields of communication and infrared. Therefore, the acousto-optic photonic crystal structure can simultaneously have wider complete band gaps of phonons and photons, and the relative band gap widths of the acousto-optic photonic crystal structure reach 87.4 percent and 14 percent respectively, so that the acousto-optic photonic crystal structure can be widely applied to acousto-optic devices, sensors, communication engineering and the like.
In order to verify whether the acousto-optic crystal structure has attenuation effects on both acoustic and light waves, the phonon and photon transmission spectra of 20 × 2 finite elements of the structure were calculated, and the results are shown in fig. 7 and 8. In the transmission curve, there is a range of frequencies over which the acoustic or optical attenuation is greatest, referred to as the full band gap, and the peak of the transmission spectrum indicates the degree of attenuation.
In fig. 7 and 8, the grey areas represent the calculated band gap frequency ranges, corresponding to the phonon and photon full band gap frequency ranges in fig. 5 and 6. FIG. 7 shows the phonon transmission spectrum, from which it can be seen that when the dimensionless frequency reaches around 0.286, the transmission coefficients for both in-plane and out-of-plane modes are below 0dB, and then significant attenuation begins, from 0.286 to 0.73 (grey area), with transmission coefficients below 0dB, corresponding to the calculated result for the first complete bandgap of the phonon; when the dimensionless frequency reaches about 0.748, the in-plane and out-of-plane modal transmission coefficients are both lower than 0dB and in the range of 0.748 to 0.774, significant attenuation occurs, corresponding to the calculation result of the phonon second complete band gap.
FIG. 8 shows the photon transmission spectrum, from which it can be seen that the transmission coefficients of both the TE and TM modes are below 0dB when the dimensionless frequency reaches around 0.4, and then the significant attenuation starts, from 0.4 to 0.46 (grey area), the transmission coefficients are below 0dB, corresponding to the calculation result of the photon complete bandgap.
In conclusion, within the complete band gap frequency range (gray region) of phonons and photons, the transmission coefficients are obviously attenuated, the upper and lower boundary frequencies of the band gaps are basically consistent with the gray region result calculated by the band gaps, the correctness and the effectiveness of the band gap calculation method are proved, and the acousto-optic photonic crystal structure can be simultaneously used for attenuating sound waves and light waves.
Then, the influencing factors for generating the dual bandgap characteristics are analyzed.
The band gap is measured mainly by the upper and lower boundary frequencies and the band gap width of the band gap. The influencing factors include: physical parameters and geometric parameters, and only the influence of the geometric parameters is considered when the structure is designed.
(1) Influence of the Square hole 2 on the Dual band gap
The side length c of the square hole 2 defined in fig. 3, the dual band gap as a function of c, and other geometric parameters were kept constant, the material parameters are shown in fig. 15, and the calculation results are shown in fig. 9 and 10. As can be seen from FIG. 9, the phonon full band gap exists in the range of [0.05a, 0.275a ], and as the side length of the square hole 2 increases from 0.05a to 0.275a, the lower boundary frequency of the phonon full band gap slowly increases from 0.285 to 0.323, but the upper boundary frequency is maintained at about 0.732 (0.05 a. ltoreq. c. ltoreq.0.125 a) and then rapidly decreases to 0.368. Therefore, as the square hole 2 becomes larger, the width of the phonon full band gap decreases from 0.447 to 0.
Fig. 10 shows the variation of the photonic complete band gap with the square hole 2. It can be seen from the figure that as the side length of the square hole 2 is increased from 0.05a to 0.3a, the lower boundary and the upper boundary of the complete band gap of the photon show an increasing trend, but the frequency of the lower boundary of the band gap increases faster than that of the upper boundary, so that the complete band gap width of the photon is gradually reduced from 0.0615 to 0.0309.
From the above, as the square hole 2 is enlarged, the complete band gap widths of both phonons and photons are gradually narrowed. Therefore, the smaller the square hole 2 is, the better the wider phonon and photon complete band gap can be obtained at the same time.
(2) Effect of Square silicon 1 on Low frequency bandgap
The square silicon 1 as defined in fig. 3 has a side length of b, the dual band gap is taken as a function of b, other geometrical parameters are kept unchanged, the material parameters are shown in fig. 15, and the calculation results are shown in fig. 11 and 12.
As can be seen from fig. 11, the phonon full bandgap exists in the range of [0.4a, 0.775a ], the lower boundary frequency of the phonon full bandgap slowly decreases from 0.34 to 0.283 as the side length of the square silicon 1 increases from 0.4a to 0.6a, and then, the lower boundary of the bandgap starts to increase rapidly from 0.283 to 0.664 in the range of [0.6a, 0.775a ]. Contrary to the law of variation of the lower boundary frequency, the upper boundary frequency of the band gap is firstly increased from 0.426 to 0.78 (0.4 a ≦ c ≦ 0.575 a), and then decreased from 0.78 to 0.664 (0.575 a ≦ c ≦ 0.575 a). Therefore, as the side length c of the square silicon 1 becomes larger, the width of the phonon full band gap first gradually increases from 0.085 to the maximum bandwidth of 0.78 in [0.4a, 0.575a ], and then gradually decreases in the range of 0.575a to 0.775a until the band gap disappears.
Fig. 12 shows the variation of the photonic full bandgap with square silicon 1. As can be seen from the figure, the complete band gap of the photon exists in the range of [0.425a, 0.675a ], as the side length of the square silicon 1 is increased from 0.425a to 0.675a, the lower boundary frequency of the complete band gap of the photon is reduced from 0.4834 to 0.363, the upper boundary frequency is reduced from 0.3946 to 0.363, but in the range of [0.425a, 0.525a ], the lower boundary frequency of the band gap is reduced faster than the upper boundary frequency, so that the complete band gap width of the photon is gradually increased from 0.01 to reach the maximum bandwidth of 0.383; then, in the range of [0.525a, 0.675a ], the band gap lower boundary frequency is decreased more slowly than the upper boundary frequency, so that the band gap width is gradually decreased until the band gap disappears.
(3) Influence of the width of the elastic beam 3 on the double band gap
The width of the beam 3 defined in fig. 3 is f, the dual band gap is taken as a function of f, other geometrical parameters are kept unchanged, the material parameters are shown in fig. 15, and the calculation results are shown in fig. 13 and 14. As can be seen from fig. 13 and 14, varying the width f of the elastic beam 3 also causes a change in both phonon and photonic bandgap structure. As can be seen from fig. 13, for a phonon full bandgap, when f is increased from 0.015a to 0.03a, the upper boundary frequency of the bandgap increases from 0.469 to 0.748 and the lower boundary frequency increases from 0.228 to 0.368, but the upper boundary frequency of the bandgap increases faster than the lower boundary frequency, thereby increasing the width of the bandgap from 0.241 to 0.455; then, when f is increased from 0.03a to 0.04a, the lower boundary of the phonon complete band gap still gradually increases, but the upper boundary frequency shows a tendency to decrease slowly, thereby gradually decreasing the bandwidth to 0.38.
Fig. 14 shows the variation law of the complete band gap of photons. As can be seen from the figure, as the width of the elastic beam 3 is increased from 0.015a to 0.04a, the frequency of the complete lower band gap boundary of the photon is rapidly reduced from 0.4515 to 0.4 (0.05 a ≦ f ≦ 0.125 a), and then is almost kept unchanged; for a photonic full band gap upper boundary, the band gap upper boundary frequency remains almost at 0.46 as f increases from 0.015a to 0.03a, but begins to decrease gradually as f increases from 0.03a to 0.04 a. Thus, as f increases, the photonic full bandgap width first increases from 0.01 to 0.06, then remains constant, and finally gradually decreases to 0.05.
Based on the above, the side length of the square hole 2, the side length of the square silicon 1 and the width of the elastic beam 3 can be changed to simultaneously adjust the upper and lower boundary frequencies of the complete band gaps of phonons and photons, so that the desired double band gap width is achieved to adapt to engineering application.
The above disclosure is only for the purpose of illustrating the preferred embodiments of the present invention, and it is therefore to be understood that the invention is not limited by the scope of the appended claims.
Claims (4)
1. An acousto-photonic crystal structure characterised by: comprises a body which is formed by regularly arranging a plurality of unit cell structures with the same structure;
each unit cell structure comprises a square silicon (1), a square hole (2) and four groups of elastic beams (3), wherein the square hole (2) is arranged in the middle of the inside of the square silicon (1) in a manner of being reduced in an equal ratio according to the outline of the square silicon (1), and the four groups of elastic beams (3) are arranged on four sides of the square silicon (1) in a cross distribution manner;
each group of elastic beams (3) comprises a first straight line section (31), a connecting section (33) and a second straight line section (32) which are sequentially connected, the first straight line section (31) and the second straight line section (32) are vertically arranged on the side of the square silicon (1) along the direction far away from the square silicon (1), a gap is formed between the first straight line section (31) and the second straight line section (32), and the tail ends of the first straight line section (31) and the second straight line section (32) are connected through the connecting section (33);
the square silicon (1) and the four groups of elastic beams (3) are made of silicon.
2. An acousto-optic photonic crystal structure according to claim 1, characterised in that: the refractive index of the silicon adopted by the square silicon (1) and the four groups of elastic beams (3) is 3.5.
3. An acousto-optic photonic crystal structure according to claim 2, characterised in that: the lattice constant of the body is a, the side length of the square silicon (1) is b, the side length of the square hole (2) is c, the width of the elastic beam (3) is d, and the widths of the first straight line segment (31), the connecting segment (33) and the second straight line segment (32) are all f;
specifically, a =666nm, b =0.55a, c =0.1a, d =0.1a, and f =0.025 a.
4. An acousto-optic photonic crystal structure according to claim 1, 2 or 3, characterised in that: the plurality of unit cell structures are arranged in the transverse direction to form a structural layer, at least two layers are arranged on the structural layer in the longitudinal direction, and the structural layers jointly form the body.
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Application publication date: 20210702 Assignee: TEJI VALVE GROUP Co.,Ltd. Assignor: Wenzhou University Contract record no.: X2023330000105 Denomination of invention: An acoustic photonic crystal structure Granted publication date: 20220524 License type: Common License Record date: 20230311 |