WO2021081697A1 - 二维拓扑光子晶体腔及其设计方法和在激光器中的应用 - Google Patents

二维拓扑光子晶体腔及其设计方法和在激光器中的应用 Download PDF

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WO2021081697A1
WO2021081697A1 PCT/CN2019/113621 CN2019113621W WO2021081697A1 WO 2021081697 A1 WO2021081697 A1 WO 2021081697A1 CN 2019113621 W CN2019113621 W CN 2019113621W WO 2021081697 A1 WO2021081697 A1 WO 2021081697A1
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photonic crystal
cavity
dimensional topological
sub
dimensional
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PCT/CN2019/113621
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French (fr)
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陆凌
杨乐臣
高晓梅
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中国科学院物理研究所
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Priority to IL292531A priority Critical patent/IL292531A/en
Priority to PCT/CN2019/113621 priority patent/WO2021081697A1/zh
Priority to CA3155990A priority patent/CA3155990A1/en
Priority to US17/755,246 priority patent/US20220385038A1/en
Priority to EP19950767.4A priority patent/EP4053607A4/en
Priority to KR1020227017759A priority patent/KR20220118406A/ko
Priority to JP2022524599A priority patent/JP7420416B2/ja
Publication of WO2021081697A1 publication Critical patent/WO2021081697A1/zh

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    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01S—DEVICES USING THE PROCESS OF LIGHT AMPLIFICATION BY STIMULATED EMISSION OF RADIATION [LASER] TO AMPLIFY OR GENERATE LIGHT; DEVICES USING STIMULATED EMISSION OF ELECTROMAGNETIC RADIATION IN WAVE RANGES OTHER THAN OPTICAL
    • H01S5/00—Semiconductor lasers
    • H01S5/10—Construction or shape of the optical resonator, e.g. extended or external cavity, coupled cavities, bent-guide, varying width, thickness or composition of the active region
    • H01S5/18—Surface-emitting [SE] lasers, e.g. having both horizontal and vertical cavities
    • H01S5/185—Surface-emitting [SE] lasers, e.g. having both horizontal and vertical cavities having only horizontal cavities, e.g. horizontal cavity surface-emitting lasers [HCSEL]
    • 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
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
    • G02B6/10—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings of the optical waveguide type
    • G02B6/12—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings of the optical waveguide type of the integrated circuit kind
    • G02B6/122—Basic optical elements, e.g. light-guiding paths
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B6/00—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings
    • G02B6/10—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings of the optical waveguide type
    • G02B6/12—Light guides; Structural details of arrangements comprising light guides and other optical elements, e.g. couplings of the optical waveguide type of the integrated circuit kind
    • G02B6/122—Basic optical elements, e.g. light-guiding paths
    • G02B6/1225—Basic optical elements, e.g. light-guiding paths comprising photonic band-gap structures or photonic lattices
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01S—DEVICES USING THE PROCESS OF LIGHT AMPLIFICATION BY STIMULATED EMISSION OF RADIATION [LASER] TO AMPLIFY OR GENERATE LIGHT; DEVICES USING STIMULATED EMISSION OF ELECTROMAGNETIC RADIATION IN WAVE RANGES OTHER THAN OPTICAL
    • H01S5/00—Semiconductor lasers
    • H01S5/10—Construction or shape of the optical resonator, e.g. extended or external cavity, coupled cavities, bent-guide, varying width, thickness or composition of the active region
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01S—DEVICES USING THE PROCESS OF LIGHT AMPLIFICATION BY STIMULATED EMISSION OF RADIATION [LASER] TO AMPLIFY OR GENERATE LIGHT; DEVICES USING STIMULATED EMISSION OF ELECTROMAGNETIC RADIATION IN WAVE RANGES OTHER THAN OPTICAL
    • H01S5/00—Semiconductor lasers
    • H01S5/10—Construction or shape of the optical resonator, e.g. extended or external cavity, coupled cavities, bent-guide, varying width, thickness or composition of the active region
    • H01S5/11—Comprising a photonic bandgap structure
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01S—DEVICES USING THE PROCESS OF LIGHT AMPLIFICATION BY STIMULATED EMISSION OF RADIATION [LASER] TO AMPLIFY OR GENERATE LIGHT; DEVICES USING STIMULATED EMISSION OF ELECTROMAGNETIC RADIATION IN WAVE RANGES OTHER THAN OPTICAL
    • H01S5/00—Semiconductor lasers
    • H01S5/04—Processes or apparatus for excitation, e.g. pumping, e.g. by electron beams
    • H01S5/042—Electrical excitation ; Circuits therefor
    • H01S5/0425—Electrodes, e.g. characterised by the structure
    • H01S5/04256—Electrodes, e.g. characterised by the structure characterised by the configuration
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01S—DEVICES USING THE PROCESS OF LIGHT AMPLIFICATION BY STIMULATED EMISSION OF RADIATION [LASER] TO AMPLIFY OR GENERATE LIGHT; DEVICES USING STIMULATED EMISSION OF ELECTROMAGNETIC RADIATION IN WAVE RANGES OTHER THAN OPTICAL
    • H01S5/00—Semiconductor lasers
    • H01S5/10—Construction or shape of the optical resonator, e.g. extended or external cavity, coupled cavities, bent-guide, varying width, thickness or composition of the active region
    • H01S5/18—Surface-emitting [SE] lasers, e.g. having both horizontal and vertical cavities
    • H01S5/183—Surface-emitting [SE] lasers, e.g. having both horizontal and vertical cavities having only vertical cavities, e.g. vertical cavity surface-emitting lasers [VCSEL]

Definitions

  • the present disclosure relates to the technical field of a two-dimensional topological photonic crystal cavity, and more specifically, to a two-dimensional topological photonic crystal cavity, a design method thereof, and an application in a laser.
  • Semiconductor lasers have the advantages of high efficiency, long life, small size, wide wavelength range, easy integration and modulation, etc., and are widely used in optical communications, optical processing, medical and military fields.
  • the traditional semiconductor laser has a wide gain spectrum, many modes, large divergence angle, and low power of a single device.
  • Single-mode semiconductor lasers are standard light sources in the fields of optical communications, spectroscopy, metrology and sensing.
  • the uniform one-dimensional Bragg grating distributed feedback laser (DFB) is widely used in long-distance fiber networks with its advantages of narrow linewidth and stable wavelength. However, it has two competing band-edge modes. In order to achieve a stable band Mid-gap mode (mid-gap mode) operates at the Bragg wavelength, and a quarter-wavelength phase shift needs to be introduced in the cavity design.
  • the vertical cavity surface emitting laser (VCSEL) also uses the same one-dimensional defect mode to select a single longitudinal mode output, which is widely used in applications such as near field communication, mouse, laser printer, and face recognition.
  • the two-dimensional photonic crystal surface emitting laser developed in recent years has the advantages of large area, high power, and low divergence angle compared with one-dimensional design.
  • the periodic structure of the two-dimensional photonic crystal surface emitting laser also has at least two high quality factor (Q) band side modes to compete for output. Therefore, there is an urgent need to design a single-mode two-dimensional photonic crystal cavity, especially a two-dimensional cavity with a robust inter-band single-mode.
  • Q quality factor
  • the present disclosure provides a two-dimensional topological photonic crystal cavity, a design method thereof, and an application in a laser.
  • a two-dimensional topological photonic crystal cavity in a first aspect of the present disclosure, includes a plurality of photonic crystal supercells, and the plurality of photonic crystal supercells surround the two-dimensional topological photonic crystal cavity There is a vortex structure change in the center of the cavity, and the energy bands of the plurality of photonic crystal supercells have a Dirac point at the equilibrium position of the vortex structure change.
  • the cavity center of the plurality of photonic crystal supercells surrounding the two-dimensional topological photonic crystal cavity has a vortex structure change, including: a type of sublattice in the plurality of photonic crystal supercells Or multiple types of sub-lattices have coordinated movement and rotation relative to their respective equilibrium positions.
  • the continuous phase rotation of the moved sub-lattices from 0 to 2 ⁇ can open the Dirac in the energy band of the photonic crystal supercell when the photonic crystal is in the equilibrium position. point.
  • one type of sub-lattice or multiple types of sub-lattices in the plurality of photonic crystal supercells have coordinated movement and rotation relative to their respective equilibrium positions, specifically including: two-dimensional topological photons
  • the cavity center of the crystal cavity is an arbitrary point in space.
  • the multiple photonic crystal supercells have vortex structure changes according to their distance and angle relative to the cavity center.
  • the form of change is one or more types of subcrystals in the photonic crystal supercell.
  • the lattice moves the displacement vector relative to their respective equilibrium positions.
  • the amplitude and phase of the displacement vector are functions of the sub-lattice relative to the cavity center position.
  • each sub-lattice displacement vector has a fixed phase difference; the amplitude of the displacement vector is along the radial direction of the cavity.
  • the range of variation is from 0 to a maximum amplitude.
  • the phase of the displacement vector changes continuously or discretely along the cavity angle, but the increment after one circle around the cavity center is an integer multiple of 2 ⁇ , and this arbitrary positive or negative integer is the winding number.
  • the parameters of the vortex structure change include the spatial distribution function of the displacement vector, the number of windings, the maximum amplitude, the size and shape of the cavity, the position of the cavity center, the refractive index of the material, the material duty ratio, The size of the supercell and the primitive cell, the working wavelength and frequency of the cavity, the shape of the supercell, the number of Dirac points in the energy band of the supercell and the position in the Brillouin zone when the supercell is in the equilibrium position, the position of the primitive cell in the supercell One or more of the group consisting of the number and shape, the number and shape of the sub-lattice in the unit cell, and the truncated form of the photonic crystal at the edge of the cavity.
  • the polygonal supercell is a hexagonal supercell
  • the hexagonal supercell is composed of three quadrilateral primitive cells, and each quadrilateral primitive cell includes two sub-lattices; a honeycomb is formed at an equilibrium position In the lattice, the two Dirac points at the edge of the Brillouin zone in the primitive cell band are folded to the center of the Brillouin zone of the supercell, forming a double Dirac point; the vortex structure changes include three in the supercell.
  • a sub-lattice of the same kind has a phase difference of 120 degrees when rotating, and the number of windings is plus or minus one.
  • a method for designing a two-dimensional topological photonic crystal cavity is provided.
  • the method is to perform vortex-type spatial position modulation around the cavity center of a two-dimensional topological photonic crystal cavity with a plurality of photonic crystal supercells.
  • the energy bands of the plurality of photonic crystal supercells have a Dirac point at an equilibrium position modulated by the vortex-shaped spatial position.
  • the coordinated movement and rotation of one type of sub-lattice or multiple types of sub-lattices in the plurality of photonic crystal supercells with respect to their respective equilibrium positions specifically includes: selecting any point as a two-dimensional In the cavity center of the topological photonic crystal cavity, the photonic crystal supercell is modulated in vortex type space according to its distance and angle relative to the cavity center. The form of modulation is to make one or more types of sublattices in the photonic crystal supercell The respective equilibrium positions move the displacement vector.
  • the amplitude and phase of the displacement vector are functions of the sub-lattice relative to the cavity center position.
  • each sub-lattice displacement vector has a fixed phase difference; the amplitude of the displacement vector varies along the radial direction of the cavity. From 0 to a maximum amplitude, the phase of the displacement vector changes continuously or discretely along the cavity angle, but the increment after one circle around the cavity center is an integer multiple of 2 ⁇ , and this arbitrary positive or negative integer is the winding number.
  • a two-dimensional topological photonic crystal cavity in another aspect of the present disclosure, includes multiple layers of materials with different refractive indexes, and any one or more layers of the multiple layers of materials with different refractive indexes are provided.
  • the above-mentioned two-dimensional topological photonic crystal cavity is adopted, or any one or more layers of the materials with different refractive indexes are the two-dimensional topological photonic crystal cavity obtained by the above-mentioned design method.
  • the materials with different refractive indexes are semiconductor materials, organic light-emitting materials, air, gases, metals, or insulators, and the semiconductor materials are in the III-V, II-VI, or IV groups Any elementary material or any compound material; any elementary material or any compound material in the III-V, II-VI or IV group is Si, Ge, GaN, GaP, GaAs, One or more of the group consisting of InGaP, InGaAs, AlGaAs, AlGaN, GaAsP, InAs, InAlGaN, InSb, InP or InGaAsP.
  • a laser having the above-mentioned two-dimensional topological photonic crystal cavity, or having a two-dimensional topological photonic crystal cavity obtained by adopting the above-mentioned design method.
  • the two-dimensional topological photonic crystal cavity provided by the present disclosure is a new integrable optical cavity with independently controllable mode number, mode field area, radiation coupling and far-field radiation. Better than other cavities.
  • This two-dimensional topological photonic crystal cavity is a two-dimensional upgrade of phase shift distributed feedback and vertical cavity surface emitting lasers in the feedback structure. It provides a single interband mode with a large mode field diameter, which can range from a few microns to a millimeter in size. Continuously adjustable.
  • the two-dimensional topological photonic crystal cavity provided by the present disclosure can be compatible with the current photonic crystal surface emitting laser semiconductor material platform.
  • the surface emitting laser prepared by using this cavity will have the following advantages: 1. It can provide unique single-mode laser emission; 2. Larger free spectral range; 3.
  • the hexagonal lattice produces more coherent in-plane feedback than the square lattice.
  • people choose square lattices more than hexagonal lattices but this will no longer be a problem for two-dimensional topological photonic crystal cavities; 4.
  • the cavity design and the above advantages are topologically robust to processing errors; 5.
  • the application of two-dimensional topological photonic crystal cavity in photonic crystal surface emitting laser products can enhance working stability, improve repeatability and laser brightness, and can achieve laser output with high power, narrow line width and wide tuning range.
  • the two-dimensional topological photonic crystal cavity provided by the present disclosure has the characteristics of large mode field area, large free spectral range, narrow beam divergence angle, arbitrary mode degeneracy, compatibility with multiple substrate materials, etc., and can be applied to surface emitting lasers , To ensure that the laser can work stably in single transverse mode and single longitudinal mode in large area and high energy output.
  • the two-dimensional topological photonic crystal cavity provided by the present disclosure can work at any wavelength and frequency, including radio, microwave, terahertz, infrared, visible, and ultraviolet bands, through changes in structural dimensions.
  • Fig. 1 schematically shows the symmetry analysis of the four-band two-dimensional boson Dirac Hamiltonian according to an embodiment of the present disclosure, where chirality is protection symmetry.
  • Figures 2a to 2d schematically show a two-dimensional topology photonic crystal cavity structure design according to an embodiment of the present disclosure.
  • 3a to 3c schematically show three-dimensional calculation results of a silicon air bridge structure of a two-dimensional topological photonic crystal cavity according to an embodiment of the present disclosure.
  • Fig. 4 schematically shows a schematic diagram of three choices of cavity centers of a two-dimensional topological photonic crystal cavity according to an embodiment of the present disclosure.
  • Fig. 5a is a schematic structural diagram of a two-dimensional topological photonic crystal cavity according to an embodiment of the present disclosure.
  • Fig. 5b is a cross-sectional view of a two-dimensional topological photonic crystal cavity according to an embodiment of the present disclosure.
  • Fig. 5c is a schematic diagram of a planar structure of a two-dimensional topological photonic crystal cavity according to an embodiment of the present disclosure.
  • Fig. 5d is a schematic diagram of the hexagonal supercell structure in the two-dimensional topological photonic crystal cavity shown in Fig. 5c.
  • Fig. 6 is a two-dimensional simulation calculation analysis of a two-dimensional topological photonic crystal cavity characteristic according to an embodiment of the present disclosure as a function of the vortex size, where a is the cavity spectrum and mode field distribution characteristics; b is the mode field diameter and the vortex The ratio of spin diameter, free spectral range (FSR), and far-field half-angle; c is the near-field and far-field characteristics at different ⁇ .
  • a is the cavity spectrum and mode field distribution characteristics
  • b is the mode field diameter and the vortex The ratio of spin diameter, free spectral range (FSR), and far-field half-angle
  • c is the near-field and far-field characteristics at different ⁇ .
  • FIG. 7 is a schematic diagram of the invariance of cavity mode frequency according to an embodiment of the present disclosure.
  • FIG. 8 is detailed information of the mode field of all cavity modes according to an embodiment of the present disclosure.
  • FIG. 9 is a schematic diagram of the variation rule of the cavity quality factor Q with the refractive index of the substrate according to an embodiment of the present disclosure.
  • SEM scanning electron microscope
  • Fig. 11a is a schematic structural diagram of a laser with a two-dimensional topological photonic crystal cavity according to an embodiment of the present disclosure.
  • Fig. 11b is a cross-sectional view of the laser shown in Fig. 11a.
  • the embodiments of the present disclosure provide a two-dimensional topological photonic crystal cavity and its design method and application in a laser.
  • the following first introduces the realization principle of the two-dimensional topological photonic crystal cavity.
  • DFB Distributed feedback
  • VCSEL vertical cavity surface emitting lasers
  • Both optical cavities have a single inter-band mode (mid-band gap mode, mid-band gap mode) with one-dimensional lattice topology defects. gap mode)
  • the present disclosure uses a honeycomb photonic crystal with Dirac vortex quality-similar to the Jackiw-Rossi zero mode, to extend the design of the topological cavity to two dimensions, and obtain a two-dimensional topological photonic crystal cavity.
  • This two-dimensional topological photonic crystal cavity also called Dirac vortex cavity, has the characteristics of large mode field area, large free spectral range, narrow beam divergence angle, arbitrary mode degeneracy, and compatibility with multiple substrate materials.
  • this two-dimensional topological photonic crystal cavity has several orders of magnitude tunable mode field area, arbitrary mode degeneracy, robust large free spectral range, and low Divergent vector beam output and compatibility with high refractive index substrates.
  • This kind of topological cavity can make the photonic crystal surface emitting laser (PCSEL) stable in single transverse mode and single longitudinal mode in large area and high energy output. jobs.
  • the present disclosure first recognizes that the interband modes of phase-shift distributed feedback and vertical cavity surface emitting lasers are actually topological, which is mathematically equivalent to the one-dimensional Jackiw Rebbi Kink state and Su-Schrieffer -Heeger boundary mode.
  • This topological concept leads us to the two-dimensional Jackiw-Rossi zero-mode, and designs a two-dimensional topological photonic crystal cavity.
  • the cavity design adopts a continuous supercell library with a mass band gap ⁇ 0 covering the entire 2 ⁇ range, and realizes a vortex
  • the spin-mass Dirac photonic crystal using silicon on an insulating substrate (SOI) in the experiment, fabricated a two-dimensional topological photonic crystal cavity, also known as the Dirac vortex cavity.
  • Massless Dirac fermions in condensed matter are a class of quasi-particles whose energy and momentum have a linear relationship, and their conduction and valence bands are degenerate in energy at a certain point in the momentum space.
  • the Dirac point of a massless Dirac fermion in a solid that is, the energy degeneracy point of the conduction band and the valence band, is usually protected by symmetry.
  • the inter-band mode (mid-gap mode) of the Dirac vortex cavity is the zero-mode solution of the two-dimensional Dirac formula with vortex mass in the photon domain.
  • the Dirac Hamiltonian in the following formula 1 contains anticommutation five items, where T i of the ⁇ i are the Pauli matrices. In two dimensions, the first two are the 4 times 4 quality-independent Dirac Hamiltonian, and the last three are the quality terms.
  • the Hamiltonian is a time-reversal invariant. For a detailed symmetry analysis, please refer to Figure 1.
  • ⁇ is the number of Dirac mass windings, and the magnitude and sign of ⁇ determine the number and chirality of the inter-band modes.
  • a two-dimensional photonic crystal Jackiw-Rossi interband mode is designed on a silicon thin film with a wavelength of 1.55 ⁇ m and a thickness of 220 nm (0.46a).
  • the air bridge structure is first designed, and then the characteristics of the case with a dielectric substrate are evaluated.
  • all models are up and down symmetric (Z-mirror), so the mode field can be classified according to the mirror image feature value.
  • Figures 2a to 2d schematically show a two-dimensional topology photonic crystal cavity structure design according to an embodiment of the present disclosure.
  • Figure 2b shows the double Dirac point band structure of an undisturbed supercell.
  • Figure 2c shows the band opening of ⁇ 0 within an angle of 2 ⁇ .
  • Fig. 2a is a hexagonal super cell constituting a two-dimensional topological photonic crystal cavity according to an embodiment of the present disclosure.
  • the super cell is composed of three quadrilateral primitive cells, and the black and gray filled parts are the sub-lattices of the primitive cells.
  • silicon thin film materials are preferred, and the sub-lattice is preferably a triangular air hole structure.
  • the Dirac point originally located at the boundary of the Brillouin zone ⁇ K point under the light cone
  • the Dirac point at the center of the Brillouin zone the ⁇ point on the light cone
  • the black and gray sublattices represent the air pore structure of the silicon thin film. Compared with the circular structure, the triangular structure air pores can improve the frequency independence of the Dirac point.
  • the present disclosure applies the generalized Kekule modulation in the supercell to generate a 2 ⁇ vortex mass and open the double Dirac point energy band.
  • 2d is the variation of the band gap size with m 0 according to an embodiment of the present disclosure.
  • the maximum value of this 2 ⁇ mass band gap is 6%.
  • Figure 3a shows an illustration of a two-dimensional topological photonic crystal cavity and mass potential well function.
  • the enlarged image is the electric field distribution.
  • Figure 3c shows the Fourier component of the electric field E x.
  • Figure 3a is a schematic diagram of a two-dimensional topological photonic crystal cavity structure design according to an embodiment of the present disclosure.
  • the cavity design of the present disclosure uses a continuous supercell library with a mass band gap ⁇ 0 covering the entire 2 ⁇ range, and an arbitrary point is selected as the two-dimensional topology
  • multiple photonic crystal supercells have vortex structure changes according to their distance and angle relative to the cavity center.
  • the form of change is that one or more types of sublattices in the photonic crystal supercell are relative to each other.
  • the equilibrium position moves the displacement vector m.
  • each sub-lattice displacement vector has a fixed phase difference;
  • the amplitude varies from 0 to a maximum amplitude m 0 along the radial direction of the cavity.
  • the phase of the displacement vector changes continuously or discretely along the cavity angle, but the increment after one circle around the cavity center is an integer multiple of 2 ⁇ , which is arbitrary Positive and negative integers are the number of windings to form a two-dimensional topological photonic crystal cavity, also known as a Dirac vortex cavity.
  • the in-plane electric field is space vortex.
  • the calculation result of Fig. 3b proves this point well, and the Fourier component of the electric field (E x) of Fig. 3c reveals Its momentum distribution relative to the light cone.
  • the design of the cavity vortex mass m(rr 0 ) has a great degree of freedom.
  • the present disclosure applies formula 2 to express it, which can be determined by four parameters ( ⁇ , m 0 , R, ⁇ ).
  • x ⁇ + ⁇ +1 and tanh(x ⁇ )
  • m(r r 0 )
  • 0 to the boundary Maximum mass
  • m 0 .
  • the first parameter ⁇ is the number of vortex windings, which is a positive or negative integer.
  • determines the number of inter-band modes, and the mode field area generally increases with the increase of
  • the sign of ⁇ represents the chirality of the mode field, which determines the distribution of the mode field in the sublattice.
  • the topological mode of the two-dimensional topological photonic crystal cavity is only concentrated in one sub-lattice of the cavity cell. When the sign of ⁇ changes, it is concentrated in the other sub-lattice.
  • the magnetic field (H z ) and electric field (E x , Y ) peaks are in the triangle pointing to the left, which provides a lot of freedom for the design and preparation of the cavity.
  • the second parameter m 0 is the maximum Dirac mass, which represents the depth of the mass potential well in Figure 3a.
  • m 0 represents the maximum moving amplitude of the sub-lattice in the cavity (corresponding to the phase ⁇ 0 ), and it is also the radiation coupling strength of the double Dirac cone coupling into the light cone, so the quality factor Q of the cavity increases with m 0 increases and decreases.
  • (rr 0 ) is the position vector of each sub-lattice relative to the coordinate r 0 in the two-dimensional topological photonic crystal cavity supercell, and the maximum Dirac mass m 0 is obtained when (r>>r 0 ).
  • the third parameter R is the vortex radius of the two-dimensional topological photonic crystal cavity.
  • the value can be R ⁇ 0.
  • the mode field size is not zero.
  • the vortex There is an envelope layer on the periphery, and an envelope layer of 50 cycles is preferred in the present disclosure.
  • the fourth parameter ⁇ is the shape factor-a positive exponent that controls the shape of the potential well, which can be from 0 to + ⁇ . ⁇ also controls the envelope and radiation pattern of the cavity mode near field.
  • the cavity mode field size may not be like a vortex. As the size grows rapidly, it also depends on the value of ⁇ .
  • FSR free spectral range
  • the cavity center of the two-dimensional topological photonic crystal cavity of the present disclosure can be any point in space. In the present disclosure, three different cavity center situations are shown. The cavity center is at any sub-lattice and the apex of the original cell. , Corresponding to a, b, and c in Fig. 4, respectively, a, b, and c in Fig. 4 schematically show a schematic diagram of three choices of the cavity center of a two-dimensional topological photonic crystal cavity according to an embodiment of the present disclosure. All three options maintain the cavity with C 3 ⁇ symmetry.
  • an embodiment of the present disclosure provides a two-dimensional topological photonic crystal cavity.
  • the two-dimensional topological photonic crystal cavity includes a plurality of photonic crystal super cells, and the plurality of photonic crystal super cells surround the two-dimensional topological photonic crystal cavity.
  • the cavity center of the photonic crystal cavity has a vortex structure change, and the energy bands of the plurality of photonic crystal supercells have a Dirac point at the equilibrium position of the vortex structure change.
  • the cavity center of the multiple photonic crystal supercells surrounding the two-dimensional topological photonic crystal cavity has a vortex structure change, including: one or more types of sublattices in the multiple photonic crystal supercells are relative to each other
  • the equilibrium position of is coordinated movement and rotation, and the continuous phase rotation of the moved sublattice from 0 to 2 ⁇ can open the Dirac point in the energy band of the photonic crystal supercell when it is in the equilibrium position.
  • the coordinated movement and rotation of one type of sub-lattice or multiple types of sub-lattices in the plurality of photonic crystal supercells relative to their respective equilibrium positions specifically includes: the cavity center of the two-dimensional topological photonic crystal cavity is in space At any point, multiple photonic crystal supercells have vortex structure changes according to their distance and angle relative to the cavity center.
  • the form of change is that one or more types of sublattices in the photonic crystal supercell move and shift relative to their respective equilibrium positions.
  • Vector, the amplitude and phase of the displacement vector are functions of the position of the sub-lattice relative to the center of the cavity.
  • each sub-lattice displacement vector has a fixed phase difference; the amplitude of the displacement vector along the radial direction of the cavity varies from 0 to a maximum
  • the amplitude and the phase of the displacement vector change continuously or discretely along the cavity angle, but the increment after a circle around the cavity center is an integer multiple of 2 ⁇ .
  • This arbitrary positive or negative integer is the winding number, thus forming a two-dimensional topological photonic crystal cavity. Also called the Dirac vortex chamber.
  • the photonic crystal supercell has a double Dirac point
  • the generalized Kekule modulation is applied to the photonic crystal supercell.
  • the generalized Kekule modulation includes coordinated rotation and movement of a type of sublattice or all sublattices, resulting in a 2 ⁇ Dirac mass , Open the double Dirac point band.
  • the parameters modulated by this generalized Kekule modulation include the spatial distribution function of the displacement vector, the number of windings, the maximum amplitude, the size and shape of the cavity, the position of the cavity center, the refractive index of the material, the material duty cycle, the size of the supercell and the primitive cell, The working wavelength and frequency of the cavity, the shape of the super cell, the number of Dirac points in the energy band of the super cell and the position in the Brillouin zone when the super cell is in the equilibrium position, the number and shape of the primitive cell in the super cell, and the primitive cell One or more of the group consisting of the number and shape of the sub-lattice, and the truncated form of the photonic crystal at the edge of the cavity.
  • the photonic crystal supercell is a polygonal supercell with a planar close-packed structure, and the shape of the polygonal supercell is a triangle, a quadrilateral, a pentagon, a hexagon, a heptagon, or an octagon.
  • the polygonal super cell is a hexagonal super cell
  • the hexagonal super cell is composed of three quadrilateral primitive cells, and each quadrilateral primitive cell includes two sub-lattices; a honeycomb lattice is formed at the equilibrium position, and the primitive cell energy band is The two Dirac points at the edge of the Brillouin zone are folded into the center of the supercell Brillouin zone, forming a double Dirac point.
  • the vortex structure changes include a sub-lattice in the original package rotating around its equilibrium position, while the three similar sub-lattices in the supercell have a phase difference of 120 degrees when rotating, and the continuous phase rotation is 0 to 2 ⁇ . It can open the double Dirac point in the energy band when the supercell is in the equilibrium position.
  • the cavity center of the two-dimensional topological photonic crystal cavity can be any point, and the sub-lattice can have a circle, a triangle, or any other regular or irregular shapes and patterns.
  • Another embodiment of the present disclosure also provides a method for designing a two-dimensional topological photonic crystal cavity.
  • the method is to perform vortex-type spatial position modulation around the cavity center of the two-dimensional topological photonic crystal cavity with a plurality of photonic crystal supercells.
  • the energy bands of the plurality of photonic crystal supercells have a Dirac point at an equilibrium position modulated by the vortex-shaped spatial position.
  • the plurality of photonic crystal supercells perform vortex-type spatial position modulation around the cavity center of the two-dimensional topological photonic crystal cavity.
  • One type of sub-lattice or multiple types of sub-lattices move and rotate in coordination with respect to their respective equilibrium positions. Rotating the moved sub-lattice from 0 to 2 ⁇ in a continuous phase can open the photonic crystal supercell when it is at the equilibrium position. Dirac points in the band.
  • the coordinated movement and rotation of one type of sub-lattice or multiple types of sub-lattices in a plurality of photonic crystal supercells relative to their respective equilibrium positions specifically includes: selecting Any point is used as the cavity center of the two-dimensional topological photonic crystal cavity, and the photonic crystal supercell is modulated according to its distance and angle relative to the cavity center. The form of modulation is to modulate one or more types of photonic crystal supercells.
  • the sub-lattices move the displacement vector from their respective equilibrium positions.
  • the amplitude and phase of the displacement vector are functions of the sub-lattice relative to the center of the cavity.
  • each sub-lattice displacement vector has a fixed phase difference; the amplitude of the displacement vector is along the cavity
  • the radial variation range is from 0 to a maximum amplitude.
  • the phase of the displacement vector changes continuously or discretely along the cavity angle, but the increment after one circle around the cavity center is an integer multiple of 2 ⁇ . This arbitrary positive or negative integer is the number of windings. , Thus forming a two-dimensional topological photonic crystal cavity, also called Dirac vortex cavity.
  • Another embodiment of the present disclosure also provides a two-dimensional topological photonic crystal cavity prepared by using the above-mentioned design method of the two-dimensional topological photonic crystal cavity.
  • the two-dimensional topological photonic crystal cavity includes multiple layers of materials with different refractive indexes, and any one or more layers of the multiple layers of materials with different refractive indexes use the above-mentioned two-dimensional topological photonic crystal cavity, or the multiple layers have different refractive indexes. Any one or more layers of the material is a two-dimensional topological photonic crystal cavity obtained by the above-mentioned design method.
  • FIG. 5a is a schematic structural diagram of a two-dimensional topological photonic crystal cavity according to an embodiment of the present disclosure.
  • the two-dimensional topological photonic crystal cavity includes multiple layers of materials with different refractive indexes. Any one or more layers in the material are prepared using the above-mentioned two-dimensional topological photonic crystal cavity design method.
  • the two-dimensional topological photonic crystal cavity is a sandwich structure composed of a first material 1, a second material 2, a third material 3, and a fourth material 4, wherein the second material 2 and the second material 2 The three materials 3 are nested in the middle layer, and the first material 1 and the fourth material 4 are respectively located on the upper and lower sides of the middle layer.
  • the first material 1, the second material 2, the third material 3, and the fourth material 4 are made of materials with different refractive indexes, such as semiconductor materials, organic materials, air, gas, metals or insulators, which are used for two-dimensional topological photonic crystals The composition and support of the cavity.
  • the semiconductor material can be any elementary material or any compound material in the III-V, II-VI or IV group, such as Si, Ge, GaN, GaP, GaAs, InGaP, InGaAs, AlGaAs, AlGaN, One or more of the group consisting of GaAsP, InAs, InAlGaN, InSb, InP or InGaAsP.
  • the second material 2 and the third material 3 are located in the same layer, that is, the middle layer of the sandwich structure, the second material 2 can be a semiconductor material, and the third material 3 can be air, which means that The gap formed by etching the second material 2 is shown in Figure 5b; when the second material 2 is a semiconductor material, the third material 3 can also be a dielectric material with a different refractive index than the second material 2, as shown in Figure 5b The gap shown is filled with a semiconductor material having a refractive index different from that of the second material 2.
  • the second material 2 is a semiconductor material and the third material 3 is air, or the second material 2 and the third material 3 are semiconductor materials with different refractive indexes, and the first material is located on the upper and lower sides of the intermediate layer.
  • 1 and the fourth material 4 may also use semiconductor materials at the same time, or air at the same time, or one of the first material 1 and the fourth material 4 may use a semiconductor material, and the other of them may use air.
  • the depth of the void does not exceed the thickness of the second material 2. In practical applications, the depth of the void may exceed the thickness of the second material 2. Extend into the first material 1 or the fourth material 4.
  • the second material 2 can be air
  • the third material 3 can be semiconductor materials.
  • the first material 1 and the fourth material 4 located on the upper and lower sides of the intermediate layer can also be used at the same time.
  • the semiconductor material one of the first material 1 and the fourth material 4 may be a semiconductor material, and the other may be air.
  • the two-dimensional topological photonic crystal cavity provided by the present disclosure has the characteristics of large mode field area, large free spectral range (FSR), narrow beam divergence angle, degeneracy of any mode, and compatibility with multiple substrate materials. These features are These advantages are necessary for high-power single-mode lasers. These advantages can be well applied to surface-emitting lasers, ensuring that the laser can work stably in single-transverse mode and single-longitudinal mode even when the laser has a large area and high energy output.
  • FSR free spectral range
  • Fig. 5c is a schematic diagram of a planar structure of a two-dimensional topological photonic crystal cavity according to an embodiment of the present disclosure.
  • the planar structure of the two-dimensional topological photonic crystal cavity is composed of a plurality of hexagonal supercells. An arbitrary point is selected as the cavity center of the two-dimensional topological photonic crystal cavity, and the photonic crystal supercell is performed according to its distance and angle relative to the cavity center.
  • Vortex type spatial position modulation the form of modulation is to move one or more types of sub-lattices in the photonic crystal supercell from their respective equilibrium positions by the displacement vector m, the amplitude of the displacement vector
  • and the phase ⁇ Arg(m) are both It is a function of the position of the sub-lattice relative to the cavity center.
  • the phase of each sub-lattice displacement vector has a fixed phase difference; the amplitude of the displacement vector along the radial direction of the cavity varies from 0 to a maximum amplitude m 0 , and the phase of the displacement vector
  • the cavity angle changes continuously or discretely, but the increment after a circle around the cavity center is an integer multiple of 2 ⁇ . This arbitrary positive or negative integer is the winding number, thus forming a two-dimensional topological photonic crystal cavity, also called Dirac vortex Cavity.
  • Figure 5d is a schematic diagram of the hexagonal supercell structure.
  • the hexagonal supercell is composed of 3 quadrilateral primitive cells.
  • Each quadrilateral primitive cell contains 2 sub-lattices.
  • One of the sub-lattices (filled in light gray in the figure) is balanced The position is shifted by the amplitude
  • the sub-lattice is formed by filling different dielectric materials (including air) in the second material 2.
  • the shape of the sub-lattice can be a circle, a triangle, or any other regular or irregular shapes and patterns, but is not limited to these structure.
  • the two-dimensional topological photonic crystal cavity structure of the present disclosure has great design freedom.
  • the cavity can have a constant frequency by adjusting the size of the air hole in the center of the cavity.
  • the calculation result in Figure 7 is a good proof Up to this point.
  • the topological mode due to the lack of chiral symmetry in a small-sized cavity, the topological mode generally does not appear in the middle of the band gap; for a larger-sized cavity, the frequency of the topological mode always converges to the Dirac point frequency, because at this time The central region of the cavity is close to the unmodulated Dirac lattice, which corresponds to the original Dirac spectrum.
  • the small-sized cavity topology mode can also be adjusted to the center of the band gap.
  • Figure 7b by increasing the size of the sub-lattice in the center region, the frequency of the cavity topological mode converges to Dirac point frequency. As R increases, these higher-order non-topological cavity modes will come from phantoms above or below the band gap. Due to the C 3 ⁇ symmetry of the structure, high-order molds have dual-mode and single-mode.
  • Figure 6a shows the near-field and far-field diagrams of a single-mode two-dimensional topological photonic crystal cavity.
  • the diameter (L) of the cavity mode field of the two-dimensional topological photonic crystal of the present disclosure increases with the increase of the vortex diameter (2R).
  • the diameter (L) is proportional to The calculation result in Fig. 6b proves this point.
  • the wave function ⁇ 0 (r) of the zero mode depends on the radial integral of the mass function: This is consistent with the quality definition in Equation 2.
  • ⁇ ⁇ , it is an ideal linear growth ratio.
  • the two-dimensional topological photonic crystal cavity of the present disclosure has a robust large free spectral range (FSR), as shown in FIG. 6a, which is essential for single-mode operation.
  • the free spectral range of the linear Dirac band edge ( ⁇ L -1 ) is much larger than the free spectral range of the quadratic band edge ( ⁇ L -2 ).
  • this advantage is very large.
  • the two-dimensional topological photonic crystal cavity of the present disclosure has the same L -1 advantage for a large free spectral range (FSR), and this scaling ratio is topologically robust to any system parameter disturbance.
  • the calculation result of Figure 6b is very good.
  • the far field of the single-mode two-dimensional topological photonic crystal cavity of the present disclosure is a vector beam, and the far field is obtained by integrating the near field by using the Rayleigh-Sommerfeld diffraction theory.
  • the beam angle is inversely proportional to the mode field diameter.
  • the far field half angle will be less than 1°, which can be well applied to the preparation of narrow beam lasers.
  • the two-dimensional topological photonic crystal cavity of the present disclosure can work on various substrates such as heat dissipation, conduction, and mechanical support.
  • the two-dimensional topological photonic crystal cavity is placed on a uniform substrate.
  • Si-Air silicon-air
  • PCSEL photonic crystal surface emitting laser
  • the silicon film cavity is placed on the substrate, and the quality factor Q of the cavity gradually decreases with the increase of n sub (according to the power law) until the critical refractive index
  • this Values have covered common substrate materials such as silicon dioxide, sapphire, and gallium nitride.
  • PCSEL photonic crystal surface emitting lasers
  • Fig. 10a is a scanning electron microscope (SEM) image of a two-dimensional topological photonic crystal cavity, including a top view and a cross-sectional oblique view.
  • the radiation pattern is a horizontally polarized field distribution, and the number of zero-intensity radial lines is equal to the topological charge (size) of these vector beams.
  • Figure 10c is the relationship between the quality factor Q and the wavelength ( ⁇ ) corresponding to the maximum Dirac mass (m 0 ) and the vortex diameter (2R).
  • the quality factor Q increases with the increase of the mode field area.
  • Increase the area of the mode field increases with the decrease of the Dirac mass band gap and the increase of the vortex diameter.
  • Fig. 10d shows the variation of the spectrum of the two-dimensional topological photonic crystal cavity with the diameter of the vortex, and the experimental results are consistent with the simulation calculation results of Fig. 6a.
  • the wavelength of the topological mode converges to the Dirac wavelength.
  • We also analyzed the high-order modes, and plotted the full spectrum of 2R 50 ⁇ m, and measured the polarized far field in the single mode. The experimental results are in good agreement with the simulation calculation results.
  • the laser may be a surface emitting laser with the above-mentioned two-dimensional topological photonic crystal cavity, or with The two-dimensional topological photonic crystal cavity obtained by the above-mentioned design method.
  • FIG. 11a is a schematic diagram of a laser structure with a two-dimensional topological photonic crystal cavity according to an embodiment of the present disclosure
  • FIG. 11b is a cross-sectional view of the laser structure shown in FIG. 11a.
  • the laser structure includes, from bottom to top, a lower electrode 1, a lower substrate layer 2, an active layer 3, a photonic crystal layer 4, an upper substrate layer 5, and an upper electrode 6, wherein the photonic crystal layer 4 may be above the active layer 3, Below or in the active layer 3.
  • the upper and lower electrodes are mainly used for charge injection in the active layer, and the lower electrode 1 can also reflect the laser energy upward so that the laser is output in one direction.
  • the upper and lower substrate layers include substrate materials, buffer materials, distributed Bragg reflector (DBR) materials and so on.
  • DBR distributed Bragg reflector
  • the structure provided in the present disclosure is suitable for the current common material systems of lasers, such as GaAs, InP, GaN and other material systems.
  • the active layer 3 selects multiple quantum wells or quantum dots to generate optical gain and form laser output.
  • a spatial arrangement of refractive index changes photonic crystal layer 4 is formed.
  • the photonic crystal structure shown in Figures 11a and 11b is just one arrangement of the present disclosure. .
  • the photonic crystal cavity confines the photons in the cavity with optical gain, and the cavity selectively amplifies the optical signal to form laser oscillation, thereby achieving high-performance laser output.
  • the two-dimensional topological photonic crystal cavity of the present disclosure has the characteristics of large mode field area, large free spectral range (FSR), narrow beam divergence angle, arbitrary mode degeneracy, and compatibility with multiple substrate materials. These features are high power These advantages are necessary for single-mode lasers. These advantages can be well applied to surface-emitting lasers to ensure that the laser can work stably in single-transverse mode and single-longitudinal mode even when the laser has a large area and high energy output. The calculation results in Fig. 6 It is confirmed that the two-dimensional topological photonic crystal cavity of the present disclosure has these characteristics.

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Abstract

一种二维拓扑光子晶体腔及其设计方法和在激光器中的应用。二维拓扑光子晶体腔包括多个光子晶体超胞，多个光子晶体超胞围绕着二维拓扑光子晶体腔的腔中心有涡旋型结构变化，并且多个光子晶体超胞的能带在涡旋型结构变化的平衡位置具有狄拉克点。二维拓扑光子晶体腔，也称作狄拉克涡旋腔，具有大模场面积、大自由光谱范围、窄光束发散角、任意模式简并度、和多种衬底材料兼容等特点，可应用于面发射半导体激光器中，保证激光器在大面积、高能量输出时依然可以稳定地以单横模且单纵模工作。

Description

二维拓扑光子晶体腔及其设计方法和在激光器中的应用 技术领域
本公开涉及二维拓扑光子晶体腔技术领域，更具体地，涉及一种二维拓扑光子晶体腔及其设计方法和在激光器中的应用。
背景技术
半导体激光器具有效率高、寿命长、体积小、波长范围广、易于集成和调制等优点，广泛应用于光通信、光加工、医疗和军事等领域。但是传统半导体激光器增益谱较宽，存在很多个模式，并且存在发散角大、单个器件功率低等现象。
单模半导体激光器是光通讯、光谱学、计量和传感领域的标准光源。均匀一维布拉格光栅分布反馈激光器(DFB)以窄线宽、波长稳定等优势广泛应用于长距离光纤网络中，但是它具有两个竞争的带边模(band-edge modes)，为了实现稳定带间单模(mid-gap mode)运转在布拉格波长，需要在腔的设计中引入四分之一波长的相移。垂直腔面发射激光器(VCSEL)也采用了相同的一维缺陷模来选择单一纵向模输出，广泛使用于在近距离通讯、鼠标、激光打印机和人脸识别的应用。
近年来开发的二维光子晶体面发射激光器相比一维设计具有大面积、大功率、低发散角的多方面优势。但是周期结构的二维光子晶体面发射激光器也至少具有两个高品质因子(Q)的带边模竞争输出。因此迫切需求设计出单模二维光子晶体腔，尤其是具有鲁棒的带间单模的二维腔，这一点也是二维分布反馈激光器自提出以来一直所缺乏的，一个单一稳定的激光模通常意味着激光器拥有更高的产量，更宽的调谐范围、更窄的线宽和高的功率。
发明内容
为满足上述需求的至少一个方面，本公开提供了一种二维拓扑光子晶体腔及其设计方法和在激光器中的应用。
本公开的第一方面，提供了一种二维拓扑光子晶体腔，该二维拓扑光子晶体腔包括多个光子晶体超胞，所述多个光子晶体超胞围绕着该二维拓扑光子晶体腔的腔中心有涡旋型结构变化，并且所述多个光子晶体超胞的能带在涡旋型结构变化的平衡位置具有狄拉克点。
根据本公开的实施例，其中所述多个光子晶体超胞围绕着该二维拓扑光子晶体腔的腔中心有涡旋型结构变化，包括：多个光子晶体超胞中的一类子晶格或多类子晶格相对于各自的平衡位置有协同的移动和旋转，其中移动后的子晶格从0到2π连续相位旋转都能打开光子晶体超胞在平衡位置时能带中的狄拉克点。
根据本公开的实施例，其中所述对多个光子晶体超胞中的一类子晶格或多类子晶格相对于各自的平衡位置有协同的移动和旋转，具体包括：二维拓扑光子晶体腔的腔中心为空间中任意点，多个光子晶体超胞按照其相对于腔中心的距离和角度有涡旋型结构变化，变化的形式是光子晶体超胞内一类或多类子晶格相对于各自平衡位置移动位移矢量，位移矢量的振幅和相位都是子晶格相对腔中心位置的函数，每个子晶格位移矢量的相位有固定相位差；位移矢量的振幅沿着腔径向的变化范围从0到一个最大振幅，位移矢量的相位沿着腔角向连续或离散变化，但绕腔中心一圈后的增量为2π的整数倍，这个任意正负整数为缠绕数。
根据本公开的实施例，其中所述涡旋型结构变化的参量包括位移矢量的空间分布函数、缠绕数、最大振幅、腔的尺寸和形状、腔中心位置、材料折射率、材料占空比、超胞和原胞的尺寸、腔的工作波长和频率、超胞的形状、超胞在平衡位置时能带中狄拉克点的个数和所在布里渊区中的位置、超胞中原胞的个数和形状、原胞中子晶格的个数和形状、腔边缘光子晶体的截断形式所组成的群组中的一个或多个。
根据本公开的实施例，其中所述多边形超胞为六边形超胞，该六边形超胞由三个四边形原胞构成，每个四边形原胞包括两个子晶格；在平 衡位置形成蜂窝晶格，原胞能带中位于布里渊区边缘的两个狄拉克点被折叠到了超胞布里渊区的中心，形成一个双重狄拉克点；涡旋型结构变化包括超胞中的三个同类子晶格在旋转时有120度的相位差，并且缠绕数为正负一。
本公开的再一方面，提供了一种二维拓扑光子晶体腔的设计方法，该方法是将多个光子晶体超胞围绕着二维拓扑光子晶体腔的腔中心进行涡旋型空间位置调制，所述多个光子晶体超胞的能带在涡旋型空间位置调制的平衡位置具有狄拉克点。
根据本公开的实施例，其中所述多个光子晶体超胞围绕着该二维拓扑光子晶体腔的腔中心被涡旋型空间位置调制包括：对多个光子晶体超胞中一类子晶格或多类子晶格相对于各自的平衡位置进行协同移动和旋转，其中对移动后的子晶格从0到2π连续相位进行旋转都能打开光子晶体超胞在平衡位置时能带中的狄拉克点。
根据本公开的实施例，其中所述对多个光子晶体超胞中一类子晶格或多类子晶格相对于各自的平衡位置进行协同移动和旋转，具体包括：选取任意点作为二维拓扑光子晶体腔的腔中心，将光子晶体超胞按照其相对于腔中心的距离和角度进行涡旋型空间位置调制，调制的形式是将光子晶体超胞内一类或多类子晶格由各自平衡位置移动位移矢量，位移矢量的振幅和相位都是子晶格相对腔中心位置的函数，每个子晶格位移矢量的相位有固定相位差；位移矢量的振幅沿着腔径向的变化范围从0到一个最大振幅，位移矢量的相位沿着腔角向连续或离散变化，但绕腔中心一圈后的增量为2π的整数倍，这个任意正负整数为缠绕数。
本公开的再一方面，提供了一种二维拓扑光子晶体腔，该二维拓扑光子晶体腔包括多层折射率不同的材料，该多层折射率不同的材料中的任意一层或多层是采用上述的二维拓扑光子晶体腔，或者该多层折射率不同的材料中的任意一层或多层是采用上述的设计方法得到的二维拓扑光子晶体腔。
根据本公开的实施例，其中所述折射率不同的材料是半导体材料、有机发光材料、空气、气体、金属或绝缘体，所述半导体材料是III-V 族、II-VI族或IV族中的任一种单质材料或者任一种化合物材料；所述III-V族、II-VI族或IV族中的任一种单质材料或者任一种化合物材料是Si、Ge、GaN、GaP、GaAs、InGaP、InGaAs、AlGaAs、AlGaN、GaAsP、InAs、InAlGaN、InSb、InP或InGaAsP组成的群组中的一种或多种。
本公开的再一方面，还提供了一种激光器，具有上述的二维拓扑光子晶体腔，或者具有采用上述的设计方法得到的二维拓扑光子晶体腔。
根据本公开的实施例，本公开提供的二维拓扑光子晶体腔，是一种新的可集成的光学腔，具有独立可控的模式数量，模场面积，辐射耦合和远场辐射，这些都优于其它腔。该二维拓扑光子晶体腔是相移分布反馈和垂直腔面发射激光器在反馈结构上的二维升级，提供了具有大模场直径的单一带间模，模场直径可以从几微米到毫米尺寸连续可调。
本公开提供的二维拓扑光子晶体腔，可以兼容当前光子晶体面发射激光器半导体材料平台，利用此腔制备的面发射激光器将具有以下优势：1、可以提供独特的单模激光发射；2、具有更大的自由光谱范围；3、在目前的光子晶体面发射激光器中，六边形晶格比正方形晶格产生更多的相干平面内反馈，实际上为了减少带边模的数量，抑制多模激光，人们选择正方形晶格要超过选择六边形晶格，然而这对于二维拓扑光子晶体腔来说将不再是问题；4、腔设计和上述优点对于加工误差具有拓扑鲁棒性；5、在光子晶体面发射激光器产品中应用二维拓扑光子晶体腔，可以增强工作稳定性、提高重复性和激光亮度，可以实现高功率、窄线宽、宽调谐范围的激光输出。
本公开提供的二维拓扑光子晶体腔，具有大模场面积、大自由光谱范围、窄光束发散角、任意模式简并度、和多种衬底材料兼容等特点，可以应用于面发射激光器中，保证激光器在大面积、高能量输出时依然可以稳定地以单横模且单纵模工作。
本公开提供的二维拓扑光子晶体腔，通过结构尺寸的变化，可以在任意波长和频率工作，包括无线电、微波、太赫兹、红外、可见、和紫外波段。
附图说明
通过以下参照附图对本公开实施例的描述，本公开的上述以及其他目的、特征和优点将更为清楚，在附图中：
图1示意性示出了根据本公开实施例的四能带二维玻色子狄拉克哈密顿量的对称性分析，其中手性是保护对称性。
图2a至图2d示意性示出了依照本公开实施例的二维拓扑光子晶体腔结构设计。
图3a至图3c示意性示出了依照本公开实施例的二维拓扑光子晶体腔硅空气桥结构三维计算结果。
图4示意性示出了依据本公开实施例的二维拓扑光子晶体腔的腔中心三种选择的示意图。
图5a是依照本公开实施例的二维拓扑光子晶体腔的结构示意图。
图5b是依照本公开实施例的二维拓扑光子晶体腔的剖视图。
图5c是依照本公开实施例的二维拓扑光子晶体腔的平面结构示意图。
图5d是图5c所示的二维拓扑光子晶体腔中六边形超胞结构的示意图。
图6是依照本公开实施例的二维的仿真计算分析二维拓扑光子晶体腔特性随着涡旋尺寸的变化规律，其中a是腔的光谱和模场分布特性；b是模场直径与涡旋直径、自由光谱范围(FSR)、远场半角度的比例关系特性；c是不同α时的近场和远场特性。
图7是依照本公开实施例的腔模频率的不变性的示意图。
图8是依照本公开实施例的所有腔模的模场详细信息。
图9是依照本公开实施例的腔品质因子Q随着基底折射率的变化规律示意图。
图10是依照本公开实施例的α＝4时二维拓扑光子晶体腔的实验分析结果，其中a是R＝0μm，m 0＝50nm，ω＝+1时腔的电子扫描显微镜(SEM)图像；b是当2R＝50μm，m 0＝50nm时，对应于不同缠绕数的腔光谱和远场分布，六个模式的品质因子均介于5×10 3和 1×10 4之间；c是单一涡旋腔(ω＝+1)的品质因子Q和共振波长(λ)对应于狄拉克质量m 0和涡旋尺寸R的变化关系；d是ω＝+1，m 0＝50nm时腔光谱随涡旋尺寸的变化情况。
图11a是依据本公开实施例的具有二维拓扑光子晶体腔的激光器的结构示意图。
图11b是图11a所示激光器的剖视图。
具体实施方式
以下，将参照附图来描述本公开的实施例。但是应该理解，这些描述只是示例性的，而并非要限制本公开的范围。在下面的详细描述中，为便于解释，阐述了许多具体的细节以提供对本公开实施例的全面理解。然而，明显地，一个或多个实施例在没有这些具体细节的情况下也可以被实施。此外，在以下说明中，省略了对公知结构和技术的描述，以避免不必要地混淆本公开的概念。
在此使用的术语仅仅是为了描述具体实施例，而并非意在限制本公开。在此使用的术语“包括”、“包含”等表明了所述特征、步骤、操作和/或部件的存在，但是并不排除存在或添加一个或多个其他特征、步骤、操作或部件。
在此使用的所有术语(包括技术和科学术语)具有本领域技术人员通常所理解的含义，除非另外定义。应注意，这里使用的术语应解释为具有与本说明书的上下文相一致的含义，而不应以理想化或过于刻板的方式来解释。
本公开的实施例提供了一种二维拓扑光子晶体腔及其设计方法和在激光器中的应用，下面首先对二维拓扑光子晶体腔的实现原理进行介绍。
分布反馈(DFB)和垂直腔面发射激光器(VCSEL)是在应用领域占主导的半导体激光器，这两个光学腔都具有一维晶格拓扑缺陷的单一带间模(中间带隙模，mid-gap mode)，本公开利用具有狄拉克涡旋质 量的蜂窝光子晶体-类似于Jackiw-Rossi零模，将拓扑腔的设计推广到了二维，得到二维拓扑光子晶体腔。该二维拓扑光子晶体腔，也称作狄拉克涡旋腔，具有大模场面积、大自由光谱范围、窄光束发散角、任意模式简并度、和多种衬底材料兼容等特点，可应用于面发射半导体激光器中，保证激光器在大面积、高能量输出时依然可以稳定地以绝对单模(单横模且单纵模)工作。本公开从理论上预测并在实验上证明了，这种二维拓扑光子晶体腔具有几个数量级上可调谐的模场面积、任意的模式简并度、鲁棒的大的自由光谱范围、低发散的矢量光束输出、以及于高折射率基底兼容等特性，这种拓扑腔可以使光子晶体面发射激光器(PCSEL)在大面积、高能量输出时依然可以稳定地以单横模且单纵模工作。
为了设计二维带间缺陷腔，本公开首先认识到相移分布反馈和垂直腔面发射激光器的带间模实际上是拓扑的，在数学上等价于一维Jackiw Rebbi Kink态和Su-Schrieffer-Heeger边界模。这一拓扑概念将我们引向了二维Jackiw-Rossi零模，设计了二维拓扑光子晶体腔，腔的设计采用具有质量带隙φ 0覆盖整个2π范围的连续超胞库，实现了具有涡旋质量的狄拉克光子晶体，在实验中采用绝缘基底上的硅(SOI)，制备了二维拓扑光子晶体腔，也称作狄拉克涡旋腔。
凝聚态物质中的无质量狄拉克(Dirac)费米子是一类能量与动量呈线性关系，且其导带和价带在动量空间某点能量简并的准粒子。固体中无质量狄拉克费米子的狄拉克点，即导带和价带的能量简并点，通常受到对称性的保护。
狄拉克涡旋腔的带间模(中间带隙模，mid-gap mode)是具有涡旋质量的二维狄拉克公式光子领域的零模解，下述公式1中的狄拉克哈密顿量包含五个反对易项，其中σ i和T i是泡利矩阵。在二维中，前两项是4乘4的质量无关的狄拉克哈密顿量，后三个是质量项，该哈密顿量为时间反演不变量，详细的对称性分析请参见图1。
H(k)＝(σ xk x+σ zk y)T z+m 1T x+m 2T y+m′σ yT z   公式1
当m′项为0时，这个对称性保护为手性对称S＝σ yT z(SHS -1＝ -H)，剩下的两个质量项构成一个复数[m＝m 1+jm 2]，可以在平面内缠绕ω次，即m(r)∝exp[jωarg(r)]，其中r是空间坐标、j 2＝-1。ω是狄拉克质量缠绕数，ω的幅值和符号决定了带间模的数量和手性。
在一个有限频率的真实光子系统中，S有轻微的对称性破缺，而m′也不完全为零，从而导致狄拉克谱并不完全是上下对称的，ω拓扑模在频率上也不是严格简并的。
在本公开中，在1.55μm波长在220nm(0.46a)厚的硅薄膜上设计了二维光子晶体Jackiw-Rossi带间模，首先设计了空气桥结构，然后评估了具有介质基底情况的特性。为了提高计算效率，所有的模型都是上下对称的(Z-mirror)，于是可以根据镜像特征值对模场进行分类。
图2a至图2d示意性地示出了依照本公开实施例的二维拓扑光子晶体腔结构设计。其中，图2a示出了广义Kekule微扰的六边形蜂窝超胞，r＝0.32a，a二维拓扑光子晶体腔的晶格常数，r是超胞中原胞三角形的外接圆半径。图2b示出了无扰动超胞的双重狄拉克点能带结构。图2c示出了φ 0在2π角度内能带打开情况。图2d示出了带隙大小随m 0的变化情况，插图是φ 0＝π/3时双重狄拉克点能带打开情况。
图2a是依照本公开实施例的组成二维拓扑光子晶体腔的六边形超胞，超胞由三个四边形原胞构成，黑色和灰色填充部分为原胞的子晶格。本公开中优选硅薄膜材料，子晶格优选三角形空气孔结构。在超胞中原本位于布里渊区边界(光锥下±K点)的狄拉克点，折叠到了布里渊区中心(光锥上Γ点)的狄拉克点，从而形成了一个双重狄拉克点，图2b是依照本公开实施例的双重狄拉克点能带图。黑色和灰色子晶格代表硅薄膜的空气孔结构，与圆形结构相比，三角形结构空气孔可以提高狄拉克点的频率独立性。本公开在超胞中应用广义的Kekule调制，产生2π涡旋质量，打开双重狄拉克点能带。
图2a中超胞的三个灰色子晶格，从平衡位置移动了相同的振幅m 0，以及对应的相位φ 0。本公开设计的腔结构，对于非零的m 0，2π角度内任意的相位φ 0值，带隙始终是打开的，当m 0＝0时带隙在涡旋中心闭合， 图2c是依照本公开实施例的质量带隙计算结果。由于超胞的对称性，图2c中质量带隙具有π/3的角周期，当φ 0＝π/3时带隙最小。图2d是依照本公开实施例的带隙大小随着m 0的变化情况，这个2π质量带隙的最大值是6％，随着m 0的增加带隙最终将闭合，其中插图部分是φ 0＝π/3时，双重狄拉克点能带打开情况。在公式1中，调制矢量
Figure PCTCN2019113621-appb-000001
与混合狄拉克质量m＝m 1+jm 2具有相同的物理意义，于是在本公开中使用相同的符号。
图3a示出了二维拓扑光子晶体腔和质量势阱函数的说明。图3b示出了m 0＝0.1a时拓扑模的近场(H z)，品质因子Q＝317，模式体积V＝4.0(λ 0/n) 3，远场半角度为4.3°，中心区域放大图是电场分布。图3c示出了电场E x的傅里叶分量。
图3a是依照本公开实施例的二维拓扑光子晶体腔结构设计示意图，本公开的腔设计是采用有一个质量带隙φ 0覆盖整个2π范围的连续超胞库，选取任意点作为二维拓扑光子晶体腔的腔中心，多个光子晶体超胞按照其相对于腔中心的距离和角度有涡旋型结构变化，变化的形式是光子晶体超胞内一类或多类子晶格相对于各自平衡位置移动位移矢量m，位移矢量的振幅|m|和相位φ＝Arg(m)都是子晶格相对腔中心位置的函数，每个子晶格位移矢量的相位有固定相位差；位移矢量的振幅沿着腔径向的变化范围从0到一个最大振幅m 0，位移矢量的相位沿着腔角向连续或离散变化，但绕腔中心一圈后的增量为2π的整数倍，这个任意正负整数为缠绕数，从而形成二维拓扑光子晶体腔，也称作狄拉克涡旋腔。
本公开的二维拓扑光子晶体腔带间模，其平面内电场是空间涡旋的，图3b的计算结果很好的证明了这一点，图3c电场(E x)的傅里叶分量揭示了其相对于光锥的动量分布。
腔涡旋质量m(r-r 0)的设计具有很大的自由度，本公开应用公式2的形式表示，可由四个参数(ω，m 0，R，α)决定。这个质量势阱函数tanh(x)| x→+∞＝+1和tanh(x α)| x→0＝x α，解释了从中心零质量|m(r＝r 0)|＝0到边界最大质量|m(r＞＞r 0)|＝m 0。
Figure PCTCN2019113621-appb-000002
在公式2中，第一个参数ω是涡旋的缠绕数，为正负整数，|ω|的大小决定了带间模的数量，模场面积一般随着|ω|的增加而增大。ω的正负代表模场的手性，决定了模场在子晶格中的分布情况。二维拓扑光子晶体腔拓扑模仅聚集于腔原胞的一个子晶格中，当ω改变符号时，则聚集于另一个子晶格中，图3b中磁场(H z)和电场(E x，y)的峰值均在指向左边的三角形中，这对于腔的设计和制备提供了很大自由度。
第二个参数m 0是最大狄拉克质量，代表图3a中质量势阱的深度。在图2a中，m 0代表腔中子晶格的最大移动振幅量(对应相位为φ 0)，也是双狄拉克锥耦合进入光锥的辐射耦合强度，因此腔的品质因子Q值随着m 0的增大而减小。(r-r 0)是二维拓扑光子晶体腔超胞中每个子晶格相对于坐标r 0的位置矢量，(r＞＞r 0)时得到最大狄拉克质量m 0。
第三个参数R为二维拓扑光子晶体腔的涡旋半径，取值可以是R≥0，涡旋尺寸R＝0时，模场尺寸不为零，为确保足够的模场束缚，涡旋外围有一层包络层，本公开中优选50个周期的包络层。
第四个参数α是形状因子-一个控制势阱形状的正指数，可以从0到+∞，α还控制着腔模近场的包络和辐射图形，腔模场尺寸不一定会像涡旋尺寸一样快速增长，它还取决于α值。
形状因子α控制了二维拓扑光子晶体腔尺寸特性，为了平衡这些特性本公开案例中优选了α＝4；腔参数ω设置为+1或者-1时，可以实现单一拓扑模，本公开中可选ω＝+1；为了获得大的自由光谱范围(FSR)，本公开中可选大的质量带隙m 0＝0.1a。
本公开的二维拓扑光子晶体腔的腔中心可以为空间中的任意一点，在本公开中展示了三种不同的腔中心情况，分别为腔中心在原胞中任意一个子晶格和原胞顶点，分别对应于图4中的a、b和c，图4中的a、b和c示意性示出了依据本公开实施例的二维拓扑光子晶体腔的腔中心三种选择的示意图，这三种选择都保持腔具有C 3υ对称性。由于子晶格在平衡位置时(m 0＝0)腔具有C 6υ对称性，因此如果选择了一个ω相关的对称涡旋中心，本公开的腔(m 0≠0)可以始终保持C 3υ对称性。
基于上述内容，本公开的一个实施例提供了一种二维拓扑光子晶体腔，该二维拓扑光子晶体腔包括多个光子晶体超胞，所述多个光子晶体超胞围绕着该二维拓扑光子晶体腔的腔中心有涡旋型结构变化，并且所述多个光子晶体超胞的能带在涡旋型结构变化的平衡位置具有狄拉克点。
其中，所述多个光子晶体超胞围绕着该二维拓扑光子晶体腔的腔中心有涡旋型结构变化，包括：多个光子晶体超胞中的一类或多类子晶格相对于各自的平衡位置有协同的移动和旋转，其中移动后的子晶格从0到2π连续相位旋转都能打开光子晶体超胞在平衡位置时能带中的狄拉克点。
所述对多个光子晶体超胞中的一类子晶格或多类子晶格相对于各自的平衡位置有协同的移动和旋转，具体包括：二维拓扑光子晶体腔的腔中心为空间中任意点，多个光子晶体超胞按照其相对于腔中心的距离和角度有涡旋型结构变化，变化的形式是光子晶体超胞内一类或多类子晶格相对于各自平衡位置移动位移矢量，位移矢量的振幅和相位都是子晶格相对腔中心位置的函数，每个子晶格位移矢量的相位有固定相位差；位移矢量的振幅沿着腔径向的变化范围从0到一个最大振幅，位移矢量的相位沿着腔角向连续或离散变化，但绕腔中心一圈后的增量为2π的整数倍，这个任意正负整数为缠绕数，从而形成二维拓扑光子晶体腔，也称作狄拉克涡旋腔。
其中，光子晶体超胞具有双重狄拉克点，对该光子晶体超胞应用广义的Kekule调制，该广义的Kekule调制包括协同旋转并移动一类子晶格或全部子晶格，产生2π狄拉克质量，打开双重狄拉克点能带。该广义的Kekule调制所调制的参量包括位移矢量的空间分布函数、缠绕数、最大振幅、腔的尺寸和形状、腔中心位置、材料折射率、材料占空比、超胞和原胞的尺寸、腔的工作波长和频率、超胞的形状、超胞在平衡位置时能带中狄拉克点的个数和所在布里渊区中的位置、超胞中原胞的个数和形状、原胞中子晶格的个数和形状、腔边缘光子晶体的截断形式所组成的群组中的一个或多个。
光子晶体超胞是具有平面密堆积结构的多边形超胞，该多边形超胞的形状为三边形、四边形、五边形、六边形、七边形或八边形等形状。当多边形超胞为六边形超胞时，该六边形超胞由三个四边形原胞构成，每个四边形原胞包括两个子晶格；在平衡位置形成蜂窝晶格，原胞能带中位于布里渊区边缘的两个狄拉克点被折叠到了超胞布里渊区的中心，形成一个双重狄拉克点。涡旋型结构变化包括原包中一个子晶格绕着其平衡位置旋转，而超胞中的三个同类子晶格在旋转时有120度的相位差，并且对0到2π连续相位旋转都能打开超胞在平衡位置时能带中的双重狄拉克点。二维拓扑光子晶体腔的腔中心可以是任意一点，所述子晶格可以具有圆形、三角形、或者其它任意规则或非规则形状及图案。
本公开的另一个实施例还提供一种二维拓扑光子晶体腔的设计方法，该方法是将多个光子晶体超胞围绕着二维拓扑光子晶体腔的腔中心进行涡旋型空间位置调制，所述多个光子晶体超胞的能带在涡旋型空间位置调制的平衡位置具有狄拉克点。
在该二维拓扑光子晶体腔的设计方法中，所述多个光子晶体超胞围绕着该二维拓扑光子晶体腔的腔中心进行涡旋型空间位置调制，是对多个光子晶体超胞中一类子晶格或多类子晶格相对于各自的平衡位置进行协同移动和旋转，其中对移动后的子晶格从0到2π连续相位进行旋转都能打开光子晶体超胞在平衡位置时能带中的狄拉克点。
在该二维拓扑光子晶体腔的设计方法中，所述对多个光子晶体超胞中一类子晶格或多类子晶格相对于各自的平衡位置进行协同移动和旋转，具体包括：选取任意点作为二维拓扑光子晶体腔的腔中心，将光子晶体超胞按照其相对于腔中心的距离和角度进行涡旋型空间位置调制，调制的形式是将光子晶体超胞内一类或多类子晶格由各自平衡位置移动位移矢量，位移矢量的振幅和相位都是子晶格相对腔中心位置的函数，每个子晶格位移矢量的相位有固定相位差；位移矢量的振幅沿着腔径向的变化范围从0到一个最大振幅，位移矢量的相位沿着腔角向连续或离散变化，但绕腔中心一圈后的增量为2π的整数倍，这个任意正负整数为缠绕数，从而形成二维拓扑光子晶体腔，也称作狄拉克涡旋腔。
本公开的另一个实施例还提供的采用上述二维拓扑光子晶体腔的设计方法所制备的二维拓扑光子晶体腔。该二维拓扑光子晶体腔包括多层折射率不同的材料，该多层折射率不同的材料中的任意一层或多层是采用上述的二维拓扑光子晶体腔，或者该多层折射率不同的材料中的任意一层或多层是采用上述的设计方法得到的二维拓扑光子晶体腔。
如图5a所示，图5a是依照本公开实施例的二维拓扑光子晶体腔的结构示意图，该二维拓扑光子晶体腔包括多层折射率不同的材料，其中，该多层折射率不同的材料中的任意一层或多层是采用上述的二维拓扑光子晶体腔的设计方法制备而成。在图5a所示的实施例中，该二维拓扑光子晶体腔是由第一材料1、第二材料2、第三材料3和第四材料4构成的三明治结构，其中第二材料2和第三材料3相互嵌套位于中间层，第一材料1和第四材料4分别位于中间层的上下两侧。第一材料1、第二材料2、第三材料3和第四材料4采用的是折射率不同的材料，例如半导体材料、有机材料、空气、气体、金属或绝缘体，用于二维拓扑光子晶体腔的构成和支撑。该半导体材料可以是III-V族、II-VI族或IV族中的任一种单质材料或者任一种化合物材料，例如Si、Ge、GaN、GaP、GaAs、InGaP、InGaAs、AlGaAs、AlGaN、GaAsP、InAs、InAlGaN、InSb、InP或InGaAsP组成的群组中的一种或多种。
在本公开的一个实施例中，第二材料2和第三材料3位于同一层，即三明治结构的中间层，第二材料2可采用半导体材料，第三材料3可采用空气，即通过对第二材料2进行刻蚀而形成的空隙，如图5b所示；在第二材料2采用半导体材料时，第三材料3也可采用折射率不同于第二材料2的介质材料，即在图5b所示的空隙中填充折射率不同于第二材料2的半导体材料。
在上述实施例中，第二材料2采用半导体材料和第三材料3采用空气，或者第二材料2和第三材料3采用折射率不同的半导体材料，位于中间层的上下两侧的第一材料1和第四材料4也可以同时采用半导体材料，也可以同时采用空气，或者第一材料1和第四材料4的其中之一采用半导体材料，其中之另一采用空气。
在上述实施例中，对第二材料2进行刻蚀而形成的空隙时，空隙的深度并未超过第二材料2的厚度，在实际应用中，空隙的深度可以超过第二材料2的厚度而延伸至第一材料1或第四材料4中。
在本公开的另一个实施例中，第二材料2可采用空气，第三材料3可采用半导体材料，此时位于中间层的上下两侧的第一材料1和第四材料4也可以同时采用半导体材料，也可以第一材料1和第四材料4的其中之一采用半导体材料，其中之另一采用空气。
本公开提供的二维拓扑光子晶体腔，具有大模场面积、大自由光谱范围(FSR)、窄光束发散角，任意模式简并度、和多种衬底材料兼容等特点，这些特点都是大功率单模激光器所必须的，这些优点可以很好的应用于面发射激光器中，保证了激光器在大面积、高能量输出时依然可以稳定地以单横模且单纵模工作。
图5c是依照本公开实施例的二维拓扑光子晶体腔的平面结构示意图。该二维拓扑光子晶体腔的平面结构由多个六边形超胞构成，选取任意点作为二维拓扑光子晶体腔的腔中心，将光子晶体超胞按照其相对于腔中心的距离和角度进行涡旋型空间位置调制，调制的形式是将光子晶体超胞内一类或多类子晶格由各自平衡位置移动位移矢量m，位移矢量的振幅|m|和相位φ＝Arg(m)都是子晶格相对腔中心位置的函数，每个子晶格位移矢量的相位有固定相位差；位移矢量的振幅沿着腔径向的变化范围从0到一个最大振幅m 0，位移矢量的相位沿着腔角向连续或离散变化，但绕腔中心一圈后的增量为2π的整数倍，这个任意正负整数为缠绕数，从而形成二维拓扑光子晶体腔，也称作狄拉克涡旋腔。
图5d是六边形超胞结构的示意图，六边形超胞由3个四边形原胞组成，每个四边形原胞包含2个子晶格，其中一个子晶格(图中浅灰色填充)从平衡位置移动了振幅|m|和对应相位φ。子晶格通过在第二材料2中填充不同介质材料(包括空气)而形成，子晶格的形状可以是圆形、三角形、或者其它任意规则或非规则形状及图案，但并不限定于这些结构。
本公开的二维拓扑光子晶体腔结构具有很大的设计自由度，对于所 有涡旋尺寸，通过调整腔中心空气孔的尺寸，可以使腔具有恒定的频率，图7的计算结果很好的证明了这一点。如图7a所示，小尺寸的腔，由于缺乏手性对称性，拓扑模一般不出现在带隙中间；较大尺寸的腔，拓扑模的频率总是收敛于狄拉克点频率，因为此时腔中心区域接近未调制的狄拉克晶格，于是对应于原始的狄拉克光谱。通过调整腔中子晶格的尺寸，也可以将小尺寸的腔拓扑模调整到带隙中心，如图7b所示，通过增大中心区域子晶格的尺寸，腔拓扑模的频率均收敛于狄拉克点频率。随着R增大，这些高阶的非拓扑腔模将来源于带隙之上或者之下的体模。由于结构具有C 3υ对称性，高阶模具有双重模和单模，图6a是二维拓扑光子晶体腔单模的近场和远场图，所有模场的详细信息列在图8中，其中右插图是2R＝100a时拓扑模式的偏振态，这些拓扑模具有最大最均匀的模场区域和最小的远场发散，这些特性也正是目前激光器腔所需要的。
本公开二维拓扑光子晶体腔模场的直径(L)随着涡旋直径(2R)的增加而增大，对于大的模场直径L正比于
Figure PCTCN2019113621-appb-000003
图6b计算结果证明了这一点，零模的波函数Ψ 0(r)取决于质量函数的径向积分：
Figure PCTCN2019113621-appb-000004
这与公式2中的质量定义相符合。对于有限的α，拓扑模场尺寸随着R的增大次线性的增长，α＝∞时是理想的线性增长比例。
本公开的二维拓扑光子晶体腔具有鲁棒的大的自由光谱范围(FSR)，如图6a所示，这一点对于单模运行是必不可少的。线性狄拉克带边(∝L -1)的自由光谱范围远远大于二次方带边(∝L -2)的自由光谱范围，在大的模式下，这种优势是非常大的。本公开的二维拓扑光子晶体腔对于大的自由光谱范围(FSR)具有相同的L -1优势，并且这种缩放比例对于任何系统参数的扰动是拓扑鲁棒的，图6b计算结果很好的证明了本公开二维拓扑光子晶体腔的这些特点，在大的模式下，模场直径(L)正比于
Figure PCTCN2019113621-appb-000005
自由光谱范围大小正比于L -1，远场角度大小正比于L -1。
本公开的二维拓扑光子晶体腔单模的远场是矢量光束，远场是利用 Rayleigh-Sommerfeld衍射理论对近场的积分而得到。在大模场下，光束角度与模场直径成反比，本公开中当涡旋直径超过200a时远场半角将小于1°，可以很好的应用于窄光束激光器的制备中。
作为一个实用的器件，本公开的二维拓扑光子晶体腔可以在散热、导电和机械支撑等各种基底上工作。图9中，将二维拓扑光子晶体腔置于均匀的基底上，对于两种不同的芯波导结构：“硅-空气(Si-Air)”和“光子晶体面发射激光器(PCSEL)”，计算了品质因子Q与基底折射率(n sub)的关系，腔的品质因子Q值仍然可以随着涡旋尺寸的增加而增大。
在“硅-空气(Si-Air)”结构中，将硅薄膜腔置于基底上，腔的品质因子Q值随着n sub的增大逐渐减小(按幂律)，直到临界折射率
Figure PCTCN2019113621-appb-000006
时，品质因子Q值将呈指数下降(图9中的圆圈点线)，这个
Figure PCTCN2019113621-appb-000007
值已经覆盖了常见的基底材料，比如二氧化硅、蓝宝石和氮化镓等。对于
Figure PCTCN2019113621-appb-000008
正与目前用于光子晶体面发射激光器(PCSEL)的GaAs/AlGaAs材料体系兼容(图9中的方格点线)，这也充分证明了本公开的二维拓扑光子晶体腔在面发射激光器中的应用潜力。
为了验证本公开二维拓扑光子晶体腔的光谱和模场等特性，我们采用电子束光刻和干法刻蚀的方法，在绝缘基底上的硅(SOI)薄膜上进行光子晶体腔的制备，光子晶体腔底层的二氧化硅用于提供机械稳定性，本案例实验中我们优选了α＝4，晶格常数为490nm。
图10a为二维拓扑光子晶体腔的电子扫描显微镜图(SEM)，包括俯视图和截面斜视图。图10b是腔具有不同缠绕数ω＝+1，2，3的测量结果，这些光谱图证实了拓扑模的数目等于缠绕数数值，拓扑模的远场实验结果都与仿真计算结果吻合很好，实验测量利用我们的交叉偏振装置进行，辐射图形为水平偏振的场分布，零强度径向线的数目等于这些矢量光束的拓扑荷数(大小)。
在图10c是品质因子Q和波长(λ)对应于最大狄拉克质量(m 0)和涡旋直径(2R)的变化关系，在两种情况下，品质因子Q随着模场面积的增加而增大，模场面积随着狄拉克质量带隙的减小和涡旋直径的增 加而增大。
图10d是二维拓扑光子晶体腔光谱随着涡旋直径的变化情况，实验结果与图6a的仿真计算结果一致。在本公开案例中，当涡旋直径增加到大约30μm时，拓扑模的波长收敛于狄拉克波长。我们也分析了高阶模，并且绘制了2R＝50μm的全光谱，测量了单模情况下的偏振远场，实验结果与仿真计算结果吻合的很好。
基于上述本公开提供的二维拓扑光子晶体腔，下面进一步阐述该二维拓扑光子晶体腔在激光器中的应用，该激光器可以为面发射激光器，具有上述的二维拓扑光子晶体腔，或者具有采用上述的设计方法得到的二维拓扑光子晶体腔。
图11a是依据本公开实施例的具有二维拓扑光子晶体腔的激光器结构示意图，图11b是图11a所示激光器结构的剖视图。该激光器结构由下至上依次包括：下电极1、下衬底层2、有源层3、光子晶体层4、上衬底层5和上电极6，其中光子晶体层4可以在有源层3上方、下方、或者处于有源层3中。上下两电极主要用于有源层中的电荷注入，其中下电极1还可将激光能量向上反射，使激光沿一个方向输出。其中上下两衬底层包括衬底材料、缓冲材料、分布布拉格反射(DBR)材料等。本公开提供的结构适用于目前激光器常用材料体系如GaAs、InP、GaN等材料体系，有源层3选用多重量子阱或量子点，用于产生光增益，形成激光输出。通过在有源层3中填充不同介质材料(包括空气)，形成折射率变化的空间排布(光子晶体层4)，图11a和图11b所示光子晶体结构只是本公开的一种排布方式。光子晶体腔将光子限制在具有光增益的腔中，腔对光信号进行选择放大，形成激光振荡，从而实现高性能激光输出。
本公开的二维拓扑光子晶体腔具有大模场面积、大自由光谱范围(FSR)、窄光束发散角、任意模式简并度、和多种衬底材料兼容等特点，这些特点都是大功率单模激光器所必须的，这些优点可以很好的应用于面发射激光器中，保证了激光器在大面积、高能量输出时依然可以稳定地以单横模且单纵模工作，图6的计算结果证实了本公开的二维拓扑光 子晶体腔具有这些特性。
本领域技术人员可以理解，本公开的各个实施例和/或权利要求中记载的特征可以进行多种组合或/或结合，即使这样的组合或结合没有明确记载于本公开中。特别地，在不脱离本公开精神和教导的情况下，本公开的各个实施例和/或权利要求中记载的特征可以进行多种组合和/或结合。所有这些组合和/或结合均落入本公开的范围。
以上对本公开的实施例进行了描述。但是，这些实施例仅仅是为了说明的目的，而并非为了限制本公开的范围。尽管在以上分别描述了各实施例，但是这并不意味着各个实施例中的措施不能有利地结合使用。本公开的范围由所附权利要求及其等同物限定。不脱离本公开的范围，本领域技术人员可以做出多种替代和修改，这些替代和修改都应落在本公开的范围之内。
以上所述的具体实施例，对本公开的目的、技术方案和有益效果进行了进一步详细说明，所应理解的是，以上所述仅为本公开的具体实施例而已，并不用于限制本公开，凡在本公开的精神和原则之内，所做的任何修改、等同替换、改进等，均应包含在本公开的保护范围之内。

Claims (11)

  1. 一种二维拓扑光子晶体腔，该二维拓扑光子晶体腔包括多个光子晶体超胞，所述多个光子晶体超胞围绕着该二维拓扑光子晶体腔的腔中心有涡旋型结构变化，并且所述多个光子晶体超胞的能带在涡旋型结构变化的平衡位置具有狄拉克点。
  2. 根据权利要求1所述的二维拓扑光子晶体腔，其中所述多个光子晶体超胞围绕着该二维拓扑光子晶体腔的腔中心有涡旋型结构变化，包括：
    多个光子晶体超胞中的一类或多类子晶格相对于各自的平衡位置有协同的移动和旋转，其中移动后的子晶格从0到2π连续相位旋转都能打开光子晶体超胞在平衡位置时能带中的狄拉克点。
  3. 根据权利要求2所述的二维拓扑光子晶体腔，其中所述多个光子晶体超胞中的一类或多类子晶格相对于各自的平衡位置有协同的移动和旋转，具体包括：
    二维拓扑光子晶体腔的腔中心为空间中任意点，多个光子晶体超胞按照其相对于腔中心的距离和角度有涡旋型结构变化，变化的形式是光子晶体超胞内一类或多类子晶格相对于各自平衡位置移动位移矢量，位移矢量的振幅和相位都是子晶格相对腔中心位置的函数，每个子晶格位移矢量的相位有固定相位差；位移矢量的振幅沿着腔径向的变化范围从0到一个最大振幅，位移矢量的相位沿着腔角向连续或离散变化，但绕腔中心一圈后的增量为2π的整数倍，这个任意正负整数为缠绕数。
  4. 根据权利要求3所述的二维拓扑光子晶体腔，其中所述涡旋型结构变化的参量包括位移矢量的空间分布函数、缠绕数、最大振幅、腔的尺寸和形状、腔中心位置、材料折射率、材料占空比、超胞和原胞的尺寸、腔的工作波长和频率、超胞的形状、超胞在平衡位置时能带中狄拉克点的个数和所在布里渊区中的位置、超胞中原胞的个数和形状、原胞中子晶格的个数和形状、腔边缘光子晶体的截断形式所组成的群组中的一个或多个。
  5. 根据权利要求4所述的二维拓扑光子晶体腔，其中所述多边形超胞为六边形超胞，该六边形超胞由三个四边形原胞构成，每个四边形原胞包括两个子晶格；在平衡位置形成蜂窝晶格，原胞能带中位于布里渊区边缘的两个狄拉克点被折叠到了超胞布里渊区的中心，形成一个双重狄拉克点；涡旋型结构变化包括超胞中的三个同类子晶格在旋转时有120度的相位差，并且缠绕数为正负一。
  6. 一种二维拓扑光子晶体腔的设计方法，该方法是将多个光子晶体超胞围绕着二维拓扑光子晶体腔的腔中心进行涡旋型空间位置调制，所述多个光子晶体超胞的能带在涡旋型空间位置调制的平衡位置具有狄拉克点。
  7. 根据权利要求6所述的二维拓扑光子晶体腔的设计方法，其中所述多个光子晶体超胞围绕着该二维拓扑光子晶体腔的腔中心进行涡旋型空间位置调制包括：
    对多个光子晶体超胞中一类或多类子晶格相对于各自的平衡位置进行协同移动和旋转，其中对移动后的子晶格从0到2π连续相位进行旋转都能打开光子晶体超胞在平衡位置时能带中的狄拉克点。
  8. 根据权利要求7所述的二维拓扑光子晶体腔的设计方法，其中所述对多个光子晶体超胞中一类子晶格或多类子晶格相对于各自的平衡位置进行协同移动和旋转，具体包括：
    选取任意点作为二维拓扑光子晶体腔的腔中心，将光子晶体超胞按照其相对于腔中心的距离和角度进行涡旋型空间位置调制，调制的形式是将光子晶体超胞内一类或多类子晶格由各自平衡位置移动位移矢量，位移矢量的振幅和相位都是子晶格相对腔中心位置的函数，每个子晶格位移矢量的相位有固定相位差；位移矢量的振幅沿着腔径向的变化范围从0到一个最大振幅，位移矢量的相位沿着腔角向连续或离散变化，但绕腔中心一圈后的增量为2π的整数倍，这个任意正负整数为缠绕数。
  9. 一种二维拓扑光子晶体腔，其中，该二维拓扑光子晶体腔包括多层折射率不同的材料，该多层折射率不同的材料中的任意一层或多层是采用权利要求1至5中任一项所述的二维拓扑光子晶体腔，或者该多 层折射率不同的材料中的任意一层或多层是采用权利要求6至8中任一项所述的设计方法得到的二维拓扑光子晶体腔。
  10. 根据权利要求9所述的二维拓扑光子晶体腔，其中所述折射率不同的材料是半导体材料、有机材料、空气、气体、金属或绝缘体，所述半导体材料是III-V族、II-VI族或IV族中的任一种单质材料或者任一种化合物材料；所述III-V族、II-VI族或IV族中的任一种单质材料或者任一种化合物材料是Si、Ge、GaN、GaP、GaAs、InGaP、InGaAs、AlGaAs、AlGaN、GaAsP、InAs、InAlGaN、InSb、InP或InGaAsP组成的群组中的一种或多种。
  11. 一种激光器，具有权利要求1至5或9至10中任一项所述的二维拓扑光子晶体腔，或者具有采用权利要求6至8中任一项所述的设计方法得到的二维拓扑光子晶体腔。
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