Dual-band multimode multiplexing two-dimensional photonic crystal cavity, design method and optical device

Abstract

The invention discloses a dual-band multimode multiplexing two-dimensional photonic crystal cavity, a design method and an optical device. The dual-band multimode multiplexing two-dimensional photonic crystal cavity comprises at least one photonic crystal layer, the photonic crystal layer comprises a plurality of photonic crystal supercells, and the plurality of photonic crystal supercells form a two-dimensional topological structure; the energy band of the photonic crystal supercell has band gaps at two Dirac points, and the structural phase of the two-dimensional photonic crystal cavity is a non-zero integer multiple of 2 pi, so that the two-dimensional photonic crystal cavity has a plurality of light field modes.

Description

Technical Field

[0001] The present invention relates to the field of photonic crystal cavities, and in particular to a dual-band multi-mode multiplexing two-dimensional photonic crystal cavity and a design method and an optical device. Background Art

[0002] The demand for greater information capacity in semiconductor devices is driving the development of multi-channel technology. To enhance the multiplexing communication capabilities of these devices, various methods have been proposed to improve information transmission efficiency. These technologies include wavelength division multiplexing (WDM), polarization division multiplexing (PDM), spatial division multiplexing (SDM), mode division multiplexing (MDM), orbital angular momentum multiplexing (OAMM), and hybrid multiplexing, which combines multiple of these multiplexing methods into shared channels for transmission. Furthermore, achieving stable multi-channel light source output within the same semiconductor micro-nano device is a hot topic for researchers.

[0003] In recent years, topological photonics, due to its robust stability and tunability, has been widely introduced into a wide range of photonic systems, including photonic crystals, plasmonic systems, metamaterials, and coupled resonant waveguides. Due to their exceptional light field modulation capabilities, high integration capabilities, and multi-degree-of-freedom adjustability, photonic crystals have become a key component of photonic systems and play a crucial role in the development of topological photonic applications, such as the realization of unidirectional optical waveguides, topological photonic crystal fibers, and topological photonic crystal cavities.

[0004] Topological photonic crystal cavities are a key research area. Their topological modes can be designed using a variety of models, including one-dimensional optical waveguides designed using the SSH model and the Jackiw-Rebbi model, two-dimensional Dirac vortex topological cavities designed using the Jackiw-Rossi model, and higher-order topological modes based on the BBH model. In particular, Dirac vortex cavities based on honeycomb lattices on SOI platforms, realized through generalized Kekulé modulation, offer advantages such as mode scalability and mode degeneracy, providing new insights into surface-emitting lasers.

[0005] However, existing technologies have a significant limitation: they can only controllably open a single Dirac point. This limitation makes the Dirac vortex cavity, despite its excellent single-frequency characteristics, difficult to meet the requirements of multi-channel multiplexing communications. Summary of the Invention

[0006] In view of this, the present invention provides a two-dimensional photonic crystal cavity and a design method and an optical device for dual-band multi-mode multiplexing.

[0007] As a first aspect of the present invention, a two-dimensional photonic crystal cavity with dual-band multimode multiplexing is provided, comprising:

[0008] at least one photonic crystal layer, wherein the photonic crystal layer comprises a plurality of photonic crystal supercells, the plurality of photonic crystal supercells forming a two-dimensional topological structure;

[0009] The energy band of the photonic crystal supercell exists a band gap at two Dirac points, and the structure phase of the two-dimensional photonic crystal cavity is a non-zero integer multiple of 2π, so that the two-dimensional photonic crystal cavity has a plurality of optical field modes.

[0010] According to an embodiment of the present application, the photonic crystal supercell comprises a plurality of unit cells, the energy band of each unit cell exists a Dirac point at two frequencies, and the size of each unit cell in the photonic crystal supercell is configured to make the energy band of the photonic crystal supercell exist a band gap at two Dirac points.

[0011] According to an embodiment of the present application, the size of the unit cell is determined by the inverse lattice vector of the photonic crystal supercell in which the unit cell is located and the position of the unit cell in the two-dimensional photonic crystal cavity.

[0012] According to an embodiment of the present application, the unit cell has a two-dimensional structure.

[0013] According to an embodiment of the present application, the photonic crystal layer comprises:

[0014] A first material layer formed of a first material, a regular array of holes being formed on the first material layer;

[0015] A second material layer formed of a second material, the second material being filled into the holes, the holes and the first material located in the holes forming unit cells, and a plurality of unit cells forming the photonic crystal supercell.

[0016] As a second aspect of the present application, an optical device is also provided, comprising:

[0017] A first electrode;

[0018] A first substrate layer disposed on the first electrode;

[0019] An active layer disposed on the first substrate layer;

[0020] A second substrate layer disposed on the active layer;

[0021] A second electrode disposed on the second substrate layer;

[0022] A two-dimensional photonic crystal cavity as described above disposed between the active layer and the first substrate layer or disposed between the active layer and the second substrate layer;

[0023] When the optical device operates as a laser: a forward bias voltage is applied to the first electrode and the second electrode; a population inversion is achieved in the active layer under carrier injection, forming an optical gain medium; spontaneous emission photons generated by the optical gain medium are input into the two-dimensional photonic crystal cavity, and the two-dimensional photonic crystal cavity selectively enhances the spontaneous emission photons that match the frequency of one of the Dirac points to form laser light;

[0024] When the optical device operates as a photodetector: a reverse bias voltage is applied to the first electrode and the second electrode or zero bias is maintained; the light component of the incident light signal that matches the frequency of any Dirac point in the two-dimensional photonic crystal cavity is locally enhanced, and the enhanced incident light signal is absorbed in the active layer and generates photogenerated carriers; under the applied reverse bias voltage or zero bias conditions, the photogenerated carriers are collected by the electrodes to form a detectable photocurrent signal.

[0025] As a third aspect of the present invention, a method for designing a two-dimensional photonic crystal cavity for dual-band multimode multiplexing is also provided, for obtaining the two-dimensional photonic crystal cavity as described above, wherein the two-dimensional photonic crystal cavity includes at least one photonic crystal layer, and the at least one photonic crystal layer includes a plurality of photonic crystal supercells, wherein the design method includes:

[0026] Adjusting the photonic crystal supercell so that the energy band of the photonic crystal supercell has band gaps at two Dirac points;

[0027] The multiple photonic crystal supercells are formed into a two-dimensional topological structure, and the structural phase of the two-dimensional photonic crystal cavity is a non-zero integer multiple of 2π.

[0028] According to an embodiment of the present invention, the photonic crystal supercell includes a plurality of primitive cells.

[0029] Adjusting the photonic crystal supercell so that the energy band of the photonic crystal supercell has band gaps at two Dirac points includes:

[0030] The sizes of all the primitive cells in the photonic crystal supercell are adjusted so that the energy band of the photonic crystal supercell has band gaps at two Dirac points.

[0031] According to an embodiment of the present invention, adjusting the sizes of all primitive cells in the photonic crystal supercell includes:

[0032] The size of the primitive cell is adjusted according to the position of the primitive cell in the two-dimensional photonic crystal cavity, the structural phase of the two-dimensional photonic crystal cavity, the azimuth angle of the primitive cell, and the reciprocal lattice vector of the supercell in which the primitive cell is located.

[0033] According to an embodiment of the present invention, determining the phase of the two-dimensional photonic crystal cavity includes:

[0034] Obtaining the maximum topological charge number and light field mode number in the far field of the two-dimensional photonic crystal cavity;

[0035] The structural phase of the two-dimensional photonic crystal cavity is determined according to the maximum topological charge number.

[0036] According to embodiments of the present invention, a photonic crystal layer utilizes a specially designed supercell structure, with its energy bands opening simultaneously at two different frequency Dirac points. This overcomes the limitation of conventional topological cavities that only operate at a single frequency. By forming a two-dimensional topological structure with multiple photonic crystal supercells, and ensuring that the structural phase of the two-dimensional photonic crystal cavity is a non-zero integer multiple of 2π (the winding number), each winding number w generates w light field modes at each Dirac point. Therefore, embodiments of the present invention can generate 2w light field modes. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The above and other objects, features and advantages of the present invention will become more apparent through the following description of the embodiments of the present invention with reference to the accompanying drawings, in which:

[0038] Figure 1 A schematic diagram of a two-dimensional photonic crystal cavity provided according to an embodiment of the present invention is shown.

[0039] Figure 2 A perspective view of an optical device provided according to an embodiment of the present invention is shown.

[0040] Figure 3A FIG. 1 shows a primitive cell before size change according to an embodiment of the present invention.

[0041] Figure 3B Shown Figure 3A The band structure of the unit cell in .

[0042] Figure 3C FIG. 4 shows a primitive cell after size change according to an embodiment of the present invention.

[0043] Figure 3D The band structure of the photonic crystal supercell in which the primitive cell is located is shown before and after the band gap of the Dirac point P1 of the primitive cell is opened.

[0044] Figure 3E The band structure of the photonic crystal supercell in which the primitive cell is located is shown before and after the band gap of the Dirac point P2 of the primitive cell is opened.

[0045] Figure 4A Shown are the normalized frequencies of the cavity modes near the Dirac point P1 after the band gap is opened.

[0046] Figure 4B Shown are the normalized frequencies of the cavity modes near the Dirac point P2 after the band gap opens.

[0047] Figure 4C The distribution of the Z component of the cavity mode electric field and the polarization direction of the magnetic field near different Dirac points after the band gap is opened are shown.

[0048] Figure 5A The effective mode diameter, cavity diameter, free spectral range, and far-field divergence angle at the Dirac point P1 after the band gap is opened are shown.

[0049] Figure 5B The effective mode diameter, cavity diameter, free spectral range, and far-field divergence angle at the Dirac point P2 after the band gap is opened are shown.

[0050] Figure 5C Shown Figure 3A Mode spectrum near the Dirac point P1 and modal distribution of topological modes in a two-dimensional photonic crystal cavity.

[0051] Figure 5D Shown Figure 3A Mode spectrum near the Dirac point P2 and modal distribution of topological modes in a two-dimensional photonic crystal cavity.

[0052] Figure 6A The near-field, far-field and mode frequency of the cavity topology mode of the two-dimensional photonic crystal cavity with winding numbers of 1 to 3 at low frequency provided by the embodiment of the present invention are shown.

[0053] Figure 6B The near field, far field and mode frequency of the cavity topology mode of the two-dimensional photonic crystal cavity with winding numbers of 1 to 3 at high frequencies provided by the embodiments of the present invention are shown.

[0054] Figure 7A The near field, far field and mode frequency of the topological modes of the two-dimensional photonic crystal cavity with winding numbers of 4 and 8 at low frequency provided by an embodiment of the present invention are shown.

[0055] Figure 7B The near field, far field and mode frequency of the topological mode of the two-dimensional photonic crystal cavity with winding numbers of 4 and 8 at high frequencies provided by an embodiment of the present invention are shown.

[0056] Figure 7C The far-field topological numbers of different topological modes of the high winding number phase gradient and two-dimensional photonic crystal cavity provided by the embodiments of the present invention are shown.

[0057] Figure 8A The frequency distribution of the modes of the two-dimensional photonic crystal cavity with different winding numbers provided by the embodiment of the present invention is shown.

[0058] Figure 8B The quality factors of the modes of the two-dimensional photonic crystal cavity with different winding numbers provided by the embodiment of the present invention are shown.

[0059] Figure 9A The three-dimensional model and energy band structure of the dual-wavelength emission two-dimensional photonic crystal cavity provided by an embodiment of the present invention are shown.

[0060] Figure 9B Shown Figure 9A Mode field spectrum and quality factor of the three-dimensional model in .

[0061] Figure 9C Shown Figure 9A The high-frequency mode far-field intensity and linear polarization intensity of the three-dimensional model of the single mode.

[0062] Figure 9D Shown Figure 9A The far-field intensity and linear polarization intensity of the low-frequency mode in the single-mode 3D model.

[0063] Description of the accompanying drawings.

[0064] 1. Two-dimensional photonic crystal cavity;

[0065] 11 photonic crystal layers;

[0066] 111 photonic crystal supercell;

[0067] 1111 protocell;

[0068] 1111-1 first material layer;

[0069] 1111-2 second material layer;

[0070] 2 first electrode;

[0071] 3 first substrate layer;

[0072] 4 active layer;

[0073] 5 second substrate layer;

[0074] 6. Second electrode. DETAILED DESCRIPTION

[0075] To make the objectives, technical solutions, and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to specific embodiments and the accompanying drawings. However, the present invention can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to make the present invention thorough and complete and to fully convey the scope of the present invention to those skilled in the art. In the drawings, the dimensions and relative dimensions of layers and regions may be exaggerated for clarity, and like reference numerals denote like elements throughout.

[0076] The terms used herein are only for describing specific embodiments and are not intended to limit the present invention. The terms "comprise", "include", etc. used herein indicate the presence of the features, steps, operations and / or components, but do not exclude the presence or addition of one or more other features, steps, operations or components.

[0077] Figure 1 A schematic diagram of a two-dimensional photonic crystal cavity provided according to an embodiment of the present invention is shown.

[0078] like Figure 1 As shown, the two-dimensional photonic crystal cavity 1 includes at least one photonic crystal layer 11, wherein the photonic crystal layer 11 includes multiple photonic crystal supercells 111, and the multiple photonic crystal supercells 111 form a two-dimensional topological structure. The energy bands of the photonic crystal supercells 111 have band gaps at both Dirac points, and the structural phase of the two-dimensional photonic crystal cavity 1 is a non-zero integer multiple of 2π, so that the two-dimensional photonic crystal cavity 1 has multiple light field modes.

[0079] According to an embodiment of the present invention, the photonic crystal layer 11 utilizes a specially designed supercell structure, with its energy bands opening simultaneously at two different frequency Dirac points. This overcomes the limitation of conventional topological cavities that they can only operate at a single frequency. By forming a two-dimensional topological structure with multiple photonic crystal supercells, and by ensuring that the structural phase of the two-dimensional photonic crystal cavity is a non-zero integer multiple of 2π (the winding number), each winding number w corresponds to w light field modes at each Dirac point. Therefore, the present embodiment can generate 2w light field modes.

[0080] According to an embodiment of the present invention, the photonic crystal supercell 111 includes a plurality of unit cells 1111, the energy band of each unit cell 1111 has Dirac points at two frequencies, and the respective sizes of all unit cells in the photonic crystal supercell are configured so that the energy band of the photonic crystal supercell has band gaps at both Dirac points.

[0081] The two-dimensional optical crystal cavity comprises a plurality of photonic crystal supercells, and each photonic crystal supercell has a different phase. The structural phase of the two-dimensional photonic crystal cavity 11 is related to the phase of each photonic crystal supercell 111 . Figure 1 , the phases of the photonic crystal supercell at six positions are shown in FIG. , and the phases of the photonic crystal supercell 111 at the six positions are 0°, 60°, 120°, 180°, 240°, and 300°, respectively.

[0082] According to an embodiment of the present invention, the size of the primitive cell 1111 is determined by the reciprocal lattice vector of the supercell of the photonic crystal 111 in which it is located and its position in the two-dimensional photonic crystal cavity 1 .

[0083] According to an embodiment of the present invention, the primitive cell has a two-dimensional structure, which may include a polygonal structure such as a triangle, a square, a hexagon, or a circle.

[0084] According to an embodiment of the present invention, the photonic crystal layer includes: a first material layer formed of a first material, on which a regularly distributed array of holes is formed; a second material layer formed of a second material, which is filled into the holes, and the holes and the first material located in the holes form a primitive cell, and multiple primitive cells form a photonic crystal supercell.

[0085] As a second aspect of the present invention, an optical device is also provided.

[0086] Figure 2 A perspective view of an optical device provided according to an embodiment of the present invention is shown.

[0087] The optical device includes: a first electrode 2 , a first substrate layer 3 , an active layer 4 , a second substrate layer 5 , and a second electrode 6 .

[0088] The first substrate layer 3 is disposed on the first electrode 2. The active layer 4 is disposed on the first substrate layer 3. The second substrate layer 5 is disposed on the active layer 4. The second electrode 6 is disposed on the second substrate layer 5. The second electrode 6 is disposed between the active layer 4 and the first substrate layer 3 or between the active layer 4 and the second substrate layer 5.

[0089] When the optical device operates as a laser: a forward bias voltage is applied to the first electrode 2 and the second electrode 6; a population inversion is achieved in the active layer 4 under carrier injection, forming an optical gain medium; the spontaneously emitted photons generated by the optical gain medium are input into the two-dimensional photonic crystal cavity 1, and the two-dimensional photonic crystal cavity 1 selectively enhances the spontaneously emitted photons whose frequency matches one of the Dirac points to form a laser.

[0090] When the optical device works as a photodetector: a reverse bias voltage is applied to the first electrode 2 and the second electrode 6 or zero bias is maintained; the light component of the incident light signal that matches the frequency of any Dirac point in the two-dimensional photonic crystal cavity is locally enhanced, and the enhanced incident light signal is absorbed in the active layer 4 and generates photogenerated carriers; under the applied reverse bias voltage or zero bias conditions, the photogenerated carriers are collected by the electrodes to form a detectable photocurrent signal.

[0091] As a third aspect of the present invention, a design method for a dual-band multimode multiplexed two-dimensional photonic crystal cavity is also provided, which is used to obtain the two-dimensional photonic crystal cavity as described above, wherein the two-dimensional photonic crystal cavity includes at least one photonic crystal layer, and the at least one photonic crystal layer includes multiple photonic crystal supercells, wherein the above-mentioned design method includes operations S1 to S2.

[0092] In operation S1 , the photonic crystal supercell is adjusted so that the energy band of the photonic crystal supercell has band gaps at both Dirac points.

[0093] In operation S2 , a plurality of photonic crystal supercells are formed into a two-dimensional topological structure, and a structural phase of the two-dimensional photonic crystal cavity is made to be a non-zero integer multiple of 2π.

[0094] According to an embodiment of the present invention, a photonic crystal supercell includes a plurality of primitive cells, and adjusting the photonic crystal supercell so that the energy band of the photonic crystal supercell has band gaps at both Dirac points includes: adjusting the respective sizes of all primitive cells in the photonic crystal supercell so that the energy band of the photonic crystal supercell has band gaps at both Dirac points.

[0095] According to an embodiment of the present invention, the primitive cell is in an equilibrium state before adjustment, and is in a non-equilibrium state after the size of the primitive cell is adjusted. Adjusting the sizes of all primitive cells in a photonic crystal supercell includes adjusting the size of the primitive cell based on the position of the primitive cell in a two-dimensional photonic crystal cavity, the structural phase of the two-dimensional photonic crystal cavity, the azimuth angle of the primitive cell, and the reciprocal lattice vector of the lattice of the supercell in which the primitive cell is located.

[0096] Determining the phase of the two-dimensional photonic crystal cavity includes: obtaining the maximum topological charge number and the number of light field modes in the far field of the two-dimensional photonic crystal cavity; and determining the structural phase of the two-dimensional photonic crystal cavity according to the maximum topological charge number.

[0097] The following is a detailed introduction to the primitive cell regulation method.

[0098] First, calculate the energy bands of the unit cell.

[0099] Figure 3A FIG. 1 shows a primitive cell before size change according to an embodiment of the present invention.

[0100] The photonic crystal supercell of the embodiment of the present invention is composed of multiple hexagonal lattice primitive cells. The energy bands of atoms can be calculated by the finite element method to find two Dirac points. Figure 3A As shown, in the embodiment of the present invention, the first material 1111-1 forming the hexagonal lattice is silicon, and the second material 1111-2 is air. Figure 3A In the figure, orange is silicon and white is air. The lattice constant of the photonic crystal is a, and the side length of the unit cell before adjustment (i.e., the side length of the unit cell in equilibrium or the initial side length of the unit cell) is .

[0101] Figure 3B Shown Figure 3A The band structure of the unit cell in .

[0102] like Figure 3B As shown in the transverse magnetic mode (TM) band diagram of the unit cell, there are two Dirac points (P1 and P2) with different frequencies at point K. P1 ​​represents a low-frequency Dirac point with a normalized frequency of approximately 0.257, and P2 represents a high-frequency Dirac point with a normalized frequency of approximately 0.537. The frequency of P1 is smaller than that of P2.

[0103] Next, the unit cell structure is extended to a supercell structure, and the band gaps of two Dirac points are simultaneously opened using the generalized Kekulé modulation method.

[0104] Figure 3C FIG. 4 shows a primitive cell after size change according to an embodiment of the present invention.

[0105] like Figure 3C As shown, the size change displacement dr = dr0 × cos (G (x + y)) is applied to the primitive cell with the center position (x, y) to control the expansion or contraction of the primitive cell. The coordinates (x, y) represent the center position of any primitive cell, dr0 = 0.05a, and the lattice reciprocal vector of the photonic crystal supercell where the primitive cell at (x, y) is located is , Dirac's position is , G represents the coupling degree between the two Dirac points in the photonic crystal supercell. After adjusting the size of the original cell, a 2π phase band gap was successfully opened at the two Dirac points P1 and P2.

[0106] Figure 3D The band structure of the photonic crystal supercell in which the primitive cell is located is shown before and after the band gap of the Dirac point P1 of the primitive cell is opened.

[0107] Figure 3E The band structure of the photonic crystal supercell in which the primitive cell is located is shown before and after the band gap of the Dirac point P2 of the primitive cell is opened.

[0108] like Figure 3D~Figure 3E As shown in the figure, a 6.8% band gap is opened at low frequency P1 and a 1.3% band gap is opened at high frequency P2. The gray line represents the energy band before the size change. The gray quadruple degenerate Γ point is caused by the folding of the Dirac point after expanding the primitive cell into a photonic crystal supercell. The black line in the figure represents the energy band of the photonic crystal supercell after the size change. The structure with a double band gap is the basis for the design of a dual-path topological Dirac vortex cavity.

[0109] In order to construct a dual-channel two-dimensional topological Dirac vortex cavity (two-dimensional photonic crystal cavity), the primitive cells can be arranged according to the spatial function formula of vortex modulation. The primitive cell at position , the modulated side length is , Satisfies formula (1).

[0110] (1)

[0111] It is at the coordinates The side length of the unit cell (lattice). , where dr0 is the maximum amplitude of cavity modulation, is the spatial position coordinate of the primitive cell, R is the potential well radius of the local mode of the cavity, w is the winding number of the entire two-dimensional photonic crystal cavity, When the primitive cell (lattice) arrangement satisfies the modulation function of formula (1), a topological Dirac vortex cavity (two-dimensional topological structure) can be constructed.

[0112] The formation of a two-dimensional photonic crystal cavity is to arrange photonic crystal supercells at a certain angle around the center coordinate (0,0) of the cavity. In actual practice, the phase distribution of the photonic crystal supercell is continuous. The composition of a two-dimensional photonic crystal cavity is as follows: Figure 1 shown.

[0113] The embodiment of the present invention uses a two-dimensional finite element simulation method to obtain the normalized spectrum and electromagnetic field distribution of the eigenmode of a two-dimensional photonic crystal cavity (a dual-channel two-dimensional Dirac vortex topological cavity).

[0114] Figure 4A Shown are the normalized frequencies of the cavity modes near the Dirac point P1 after the band gap is opened.

[0115] Figure 4B Shown are the normalized frequencies of the cavity modes near the Dirac point P2 after the band gap opens.

[0116] exist Figure 4A In the figure, the red solid circle is the topological single mode near P1, and the black hollow circle is the body model. Figure 4B In the figure, the red solid circle is the topological single mode near P2, and the black hollow circle is the bulk mode.

[0117] Figure 4C The distribution of the Z component of the cavity mode electric field and the polarization direction of the magnetic field near different Dirac points after the band gap is opened are shown.

[0118] like Figure 4C As shown, part (a) shows the Z component distribution of the cavity mode electric field and the magnetic field polarization direction near the Dirac point P1 after the band gap is opened, and part (b) shows the Z component distribution of the cavity mode electric field and the magnetic field polarization direction near the Dirac point P2 after the band gap is opened.

[0119] because Figure 4A and Figure 4B The two topology modes in are TM modes, so they are not Figure 4C The Z component distribution (Ez distribution) of the topological mode electric field is shown. The entire electric field is not symmetrical around the center of the two-dimensional photonic crystal cavity. The electromagnetic field distribution at the P1 point frequency is basically distributed in the medium, and the light spot is larger. The P2 point frequency is relatively high, so the field mode distribution near the P2 point is more concentrated. Figure 4A and Figure 4B The polarization distributions of the two topological modes in the magnetic field are both vortex, such as Figure 4C Indicated by black arrows.

[0120] The present invention provides the relationship between the topological mode diameter, free spectral range (FSR) and far-field divergence half angle and the Dirac vortex cavity diameter 2R. The scaling law and modal distribution of different cavity diameters at high and low frequencies are as follows: Figure 5A to Figure 5D shown.

[0121] Figure 5A The effective mode diameter, cavity diameter, free spectral range, and far-field divergence angle at the Dirac point P1 after the band gap is opened are shown.

[0122] Figure 5B The effective mode diameter, cavity diameter, free spectral range, and far-field divergence angle at the Dirac point P2 after the band gap is opened are shown.

[0123] like Figure 5A~Figure 5B The figures show the scaling laws of the effective mode diameters at low frequencies (frequency at P1) and high frequencies (frequency at P2) with respect to the cavity diameter, FSR, and far-field divergence half-angle. The effective mode diameter, L, is derived from the mode area. The results show that the scaling laws for high-frequency and low-frequency modes are consistent, with the effective mode diameter and cavity diameter showing a linear relationship. The FSR and far-field divergence half-angle are inversely proportional to the effective mode diameter, and the far-field divergence half-angle at low frequencies is larger than that at high frequencies. This is because the larger the band gap at low frequencies, the smaller the intra-cavity mode area.

[0124] Figure 5C Shown Figure 3A Mode spectrum near the Dirac point P1 and modal distribution of topological modes in a two-dimensional photonic crystal cavity.

[0125] Figure 5D Shown Figure 3A Mode spectrum near the Dirac point P2 and modal distribution of topological modes in a two-dimensional photonic crystal cavity.

[0126] Figure 5C to Figure 5D The modal spectra and near-field and far-field distributions for the two frequency bands are shown. It can be seen that as the cavity diameter increases, the topological mode gradually approaches the center of the band gap, while the bulk mode gradually enters the inner part of the band gap. Comparing the spectral distributions within the two band gaps, we find that as the cavity diameter of the high-frequency mode increases, the number of bulk modes entering the band gap decreases compared to the low-frequency mode. This indicates that with larger cavity diameters, the high-frequency mode has better single-mode properties and is less susceptible to interference from other modes.

[0127] Next, we further studied the relationship between the Dirac vortex topological cavity mode and the winding number in the band gap at different frequencies. The results are as follows Figure 6A-6B shown.

[0128] Figure 6AThe near-field, far-field and mode frequency of the cavity topology mode of the two-dimensional photonic crystal cavity with winding numbers of 1 to 3 at low frequency provided by the embodiment of the present invention are shown.

[0129] Figure 6B The near field, far field and mode frequency of the cavity topology mode of the two-dimensional photonic crystal cavity with winding numbers of 1 to 3 at high frequencies provided by the embodiments of the present invention are shown.

[0130] Figure 6A In the figure, parts (a) to (c) are the near-field, far-field and mode frequencies of the cavity topology modes of the two-dimensional photonic crystal cavity with winding numbers of 1, 2 and 3 at low frequency (193.55THz). Figure 6B In the figure, parts (a) to (c) are the near-field, far-field and mode frequencies of the cavity topology modes of the two-dimensional photonic crystal cavity with winding numbers of 1, 2 and 3 at high frequency (400 THz).

[0131] like Figure 6A-6B The upper half shows the modal electric field distribution, and the lower half shows the far-field and far-field X-linear polarization (XLP) components. The red line indicates the mode frequency. It can be seen that in both band gaps, the topological mode numbers at both frequencies are consistent with |w|. This is determined by the number of solutions to the Dirac equation. When w = 1, the two near-field distributions are relatively uniform. As w increases, the near-field distribution diverges. When w = 2, the x-polarized near-field and far-field complement each other. When w = 3, the first two near-fields complement the x-polarized far-field, and the third mode forms near-field mode coupling. The difference is that the local density of the high-frequency mode field is greater than that of the low-frequency mode field. The far-field spot properties are essentially the same at both frequencies, and the multimode far-field also exhibits vectorial characteristics. The difference is that for the same number of turns, the high-frequency far-field divergence half-angle is much smaller than that of the low-frequency mode. This is because the effective mode area of ​​the high-frequency mode is larger than that of the low-frequency mode. Furthermore, it is noted that when w = 3, the far-field XLP components of the three modes are divided into 6, 6, and 8 parts, respectively, indicating that the far-field topological numbers of the three modes are 3, 3, and 4, respectively.

[0132] In order to further study the potential mechanism of high winding number topological modes, Dirac vortex cavities with 4 and 8 winding numbers were further calculated in the embodiments of the present invention.

[0133] Figure 7A The near field, far field and mode frequency of the topological modes of the two-dimensional photonic crystal cavity with winding numbers of 4 and 8 at low frequency provided by an embodiment of the present invention are shown.

[0134] Figure 7B The near field, far field and mode frequency of the topological mode of the two-dimensional photonic crystal cavity with winding numbers of 4 and 8 at high frequencies provided by an embodiment of the present invention are shown.

[0135] It can be seen that when the cavity diameter is the same, whether at low frequency (193.55 THz) or high frequency (400 THz), the mode area of ​​w = 8 is usually larger than that of w = 4, and the far-field divergence half-angle is larger when w = 8. The reason for the increase in the far-field divergence angle is that the increase in the winding number increases the orbital angular momentum of the far-field mode, which does not contradict the above conclusion.

[0136] Figure 7C The far-field topological numbers of different topological modes of the high winding number phase gradient and two-dimensional photonic crystal cavity provided by the embodiments of the present invention are shown.

[0137] By observing the linear polarization component of the far-field mode, it is found that the far-field topological core numbers of the four topological modes with w = 4 are 4, 4, 5, and 5, respectively, and the far-field topological charge numbers of w = 8 are 8, 8, 9, 9, 10, 10, and 11, respectively, and the topological charge number gradually increases.

[0138] After calculation, the far-field topological charge with winding number w is as follows Figure 7C As shown in Figure 3 . By summarizing the far-fields of high-winding-number modes, we find that the topological number of the far-field modes is not completely consistent with the topological number of the cavity structure. The minimum far-field topological number coincides with the cavity winding number and begins to increase in pairs. When w is an odd number, the maximum topological charge is |w|+(|w|-1) / 2, and when w is an even number, the maximum topological charge is |w|+(|w|-2) / 2. This is mainly due to the cavity structure not strictly satisfying chiral symmetry, resulting in near-field coupling.

[0139] Next, we further analyze the characteristics of the multimode cavity mode and select the cavity radius R as 0 and the wavelength as 1550nm for calculation.

[0140] Figure 8A The frequency distribution of the modes of the two-dimensional photonic crystal cavity with different winding numbers provided by the embodiment of the present invention is shown.

[0141] Figure 8A The following are the cavity mode spectra for different winding numbers. It can be seen that the mode number and winding number remain consistent. As the winding number increases, the bulk state outside the bandgap gradually approaches the topological mode. This is because an increase in the winding number is accompanied by a greater orbital angular momentum, which weakens the cavity binding ability and increases the effective mode area of ​​the cavity mode. When w = 32, it becomes difficult to distinguish between the topological mode and the bulk mode.

[0142] Figure 8B The quality factors of the modes of the two-dimensional photonic crystal cavity with different winding numbers provided by the embodiment of the present invention are shown.

[0143] Figure 8BThe quality factors of the modes at different winding numbers are shown. Before w = 8, the quality factors of the topological modes are high. When w = 16, the quality factors of the topological modes are comparable to those of the nearby bulk modes. However, due to the low localization of the mode field, the quality factors of several bulk modes are higher than those of the topological modes.

[0144] In order to further verify the experimental feasibility of the dual-path two-dimensional photonic crystal cavity, the plane wave expansion method and the finite time difference method were used in the embodiment of the present invention to simulate the dual-wavelength emission of the three-dimensional model of the two-dimensional photonic crystal cavity. Gallium arsenide with a refractive index of 3.52 was selected as the photonic crystal layer material, and silicon dioxide with a refractive index of 1.45 was selected as the substrate. First, the band structure of the hexagonal lattice three-dimensional model was calculated using MPB. Hexagonal holes in the lattice structure , dr=0.05a, a is the unit cell size, and the thickness of the photonic crystal cavity is 630nm.

[0145] Figure 9A The three-dimensional model and energy band structure of the dual-wavelength emission two-dimensional photonic crystal cavity provided by an embodiment of the present invention are shown.

[0146] Figure 9A The calculation results for the band structure show the presence of two Dirac points in the 3D model, enabling dual-wavelength emission. A 3D model of a dual-wavelength emission Dirac cavity was then constructed using the finite-difference time-domain method. An electric dipole was placed within the cavity as a light source to simulate the TM mode light field, covering both the low-frequency (1550 nm) and high-frequency (980 nm) bands.

[0147] Figure 9B Shown Figure 9A Mode field spectrum and quality factor of the three-dimensional model in .

[0148] like Figure 9B As shown in the figure, the quality factor of the cavity mode is 233 at low frequency and 275 at high frequency.

[0149] Figure 9C Shown Figure 9A The high-frequency mode far-field intensity and linear polarization intensity of the three-dimensional model of the single mode.

[0150] Figure 9D Shown Figure 9A The far-field intensity and linear polarization intensity of the low-frequency mode in the three-dimensional model of the single mode.

[0151] Figure 9C to Figure 9D The far-field morphology of the high-frequency (400 THz) and low-frequency (193.55 THz) modes of the 3D model is shown. Because the band gap near the Dirac point at high frequencies is very small, the mode field requires a relatively large photonic crystal structure to enclose it. Therefore, the far-field at high frequencies is not as obvious as the vector characteristics at low frequencies.

[0152] The embodiment of the present invention uses a unit cell of a hexagonal lattice to realize a dual-path emission model of a two-dimensional photonic crystal cavity. First, the generalized Kekulé modulation in the hexagonal lattice is used to simultaneously open the band gaps of the two Dirac points of the photonic crystal supercell, and the potential well function is used to construct a Dirac vortex cavity at low / high frequencies; secondly, the proportionality between the cavity diameter, free spectral range, and far-field divergence half-angle and the mode diameter at low / high frequencies is studied. Then, by changing the winding number of the Dirac vortex cavity, multiple topological modes are generated in the band gap, and the number of modes is consistent with the winding number. The properties of the multiple topological modes of the Dirac vortex cavity are obtained, and the general law of far-field orbital angular momentum and winding number is discovered. In addition, the topological mode integrated emission of any number of dual-path two-dimensional photonic crystal cavities and any angular momentum can be realized. Therefore, this work increases the number of channels of the two-dimensional photonic crystal cavity and explores the communication multiplexing capability of the two-dimensional photonic crystal cavity.

[0153] The above describes embodiments of the present invention. However, these embodiments are for illustrative purposes only and are not intended to limit the scope of the present invention. Although each embodiment has been described separately above, this does not mean that the measures in each embodiment cannot be advantageously used in combination. The scope of the present invention is defined by the appended claims and their equivalents. Without departing from the scope of the present invention, those skilled in the art may make various substitutions and modifications, which are intended to fall within the scope of the present invention.

Claims

1. A two-dimensional photonic crystal cavity for dual-band multimode multiplexing, comprising: At least one photonic crystal layer, wherein the photonic crystal layer includes a plurality of photonic crystal supercells, and the plurality of photonic crystal supercells form a two-dimensional topological structure; The energy band of the photonic crystal supercell has band gaps at two Dirac points, and the structural phase of the two-dimensional photonic crystal cavity is a non-zero integer multiple of 2π, so that the two-dimensional photonic crystal cavity has multiple light field modes.

2. The two-dimensional photonic crystal cavity according to claim 1, wherein: The photonic crystal supercell includes multiple primitive cells, the energy band of each primitive cell has Dirac points at two frequencies, and the respective sizes of all primitive cells in the photonic crystal supercell are configured so that the energy band of the photonic crystal supercell has band gaps at both Dirac points.

3. The two-dimensional photonic crystal cavity according to claim 2, wherein: The size of the primitive cell is determined by the reciprocal lattice vector of the photonic crystal supercell in which it is located and its position in the two-dimensional photonic crystal cavity.

4. The two-dimensional photonic crystal cavity according to claim 2, wherein: The unit cell has a two-dimensional structure.

5. The two-dimensional photonic crystal cavity according to claim 1, wherein: The photonic crystal layer comprises: A first material layer is formed of a first material, and a regularly distributed hole array is formed on the first material layer; The second material layer is formed of a second material. The second material is filled into the hole. The hole and the first material in the hole form a primitive cell. A plurality of primitive cells form the photonic crystal super cell.

6. An optical device comprising: a first electrode; a first substrate layer, disposed on the first electrode; an active layer, disposed on the first substrate layer; a second substrate layer, disposed on the active layer; a second electrode, disposed on the second substrate layer; The two-dimensional photonic crystal cavity according to any one of claims 1 to 5, arranged between the active layer and the first substrate layer or between the active layer and the second substrate layer; When the optical device operates as a laser: a forward bias voltage is applied to the first electrode and the second electrode; The active layer achieves population inversion under carrier injection to form an optical gain medium; spontaneous emission photons generated by the optical gain medium are input into the two-dimensional photonic crystal cavity, and the two-dimensional photonic crystal cavity selectively enhances the spontaneous emission photons that match the frequency of one of the Dirac points to form a laser; When the optical device operates as a photodetector: a reverse bias voltage is applied to the first electrode and the second electrode or zero bias is maintained; a light component of an incident light signal whose frequency matches that of any Dirac point in the two-dimensional photonic crystal cavity is locally enhanced, and the enhanced incident light signal is absorbed in the active layer and generates photogenerated carriers; Under an applied reverse bias voltage or zero bias condition, the photogenerated carriers are collected by the electrodes to form a detectable photocurrent signal.

7. A method for designing a dual-band multimode multiplexed two-dimensional photonic crystal cavity, for obtaining the two-dimensional photonic crystal cavity according to any one of claims 1 to 5, wherein the two-dimensional photonic crystal cavity comprises at least one photonic crystal layer, wherein the at least one photonic crystal layer comprises a plurality of photonic crystal supercells, wherein: The design method includes: Adjusting the photonic crystal supercell so that the energy band of the photonic crystal supercell has band gaps at two Dirac points; The multiple photonic crystal supercells are formed into a two-dimensional topological structure, and the structural phase of the two-dimensional photonic crystal cavity is a non-zero integer multiple of 2π.

8. The method for designing a two-dimensional photonic crystal cavity according to claim 7, wherein: The photonic crystal supercell includes a plurality of primitive cells. Adjusting the photonic crystal supercell so that the energy band of the photonic crystal supercell has band gaps at two Dirac points includes: The sizes of all the primitive cells in the photonic crystal supercell are adjusted so that the energy band of the photonic crystal supercell has band gaps at two Dirac points.

9. The method for designing a two-dimensional photonic crystal cavity according to claim 7, wherein: Adjusting the sizes of all primitive cells in the photonic crystal supercell comprises: The size of the primitive cell is adjusted according to the position of the primitive cell in the two-dimensional photonic crystal cavity, the structural phase of the two-dimensional photonic crystal cavity, the azimuth angle of the primitive cell, and the reciprocal lattice vector of the supercell in which the primitive cell is located.

10. The method for designing a two-dimensional photonic crystal cavity according to claim 7, wherein: Determining the phase of the two-dimensional photonic crystal cavity includes: Obtaining the maximum topological charge number and light field mode number in the far field of the two-dimensional photonic crystal cavity; The structural phase of the two-dimensional photonic crystal cavity is determined according to the maximum topological charge number.

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