Topological laser resonant cavity, design method thereof and topological valley photonic crystal laser

Abstract

The invention belongs to the technical field of topological photonic crystals, and discloses a topological laser resonant cavity, a design method thereof and a topological valley photonic crystal laser. According to the invention, three different photonic crystal areas are utilized to form a three-layer heterostructure, and the three different photonic crystal areas are divided into A, B and A'areas according to the same lattice period array arrangement; the area A and the area A'are the innermost layer and the outermost layer of the topological laser resonant cavity respectively, the closed topological laser resonant cavity is formed at the interface of the area A and the area A ', and the area B is embedded in the middle of the interface; the three different photonic crystal regions have different primitive cell energy band characteristics, and the energy band structure of the photonic crystal primitive cell in the region B has a linear dispersion curve and can be described by a Dirac equation; and the photonic crystal primitive cells in the A'and the A region are energy band structures with different topological valley numbers obtained by breaking the symmetry of the photonic crystal primitive cells in the B region. According to the invention, the performance of the topological valley photonic crystal laser can be enhanced.

Description

Technical Field

[0001] The present invention belongs to the technical field of topological photonic crystals, and more specifically, relates to a topological laser resonator and its design method, and a topological valley photonic crystal laser. Background Art

[0002] Topological nanophotonic systems have developed rapidly and shown great potential in the design and application of multifunctional photonic and optoelectronic devices. Valley-Hall photonic crystals (PhCs) have attracted extensive attention due to their topologically protected edge states, whose momenta are locked in the K / K' valleys, thus being beneficial for planar integrated applications. However, the large out-of-plane scattering losses of these edge states pose significant challenges to replacing traditional ridge waveguides and PhC (photonic crystal) defect waveguides and carrying out practical applications. For example, the performance of topological semiconductor lasers based on valley-Hall photonic crystals is greatly limited. Currently, topological valley semiconductor lasers still face the following problems: high lasing thresholds, limited robustness in mode selection, and easy emission of defect states in the high-frequency band. In addition, limited by the mode selection mechanism of the topological resonator loop, topological valley semiconductor lasers also generate multiple topological edge state modes, prone to mode competition. Summary of the Invention

[0003] The present invention provides a topological laser resonator and its design method, and a topological valley photonic crystal laser to solve the problem that the performance of topological valley photonic crystal lasers in the prior art needs to be enhanced.

[0004] In a first aspect, the present invention provides a design method of a topological laser resonator, including:

[0005] Using three different photonic crystal regions to form a three-layer heterostructure, and the three different photonic crystal regions are arranged in the same lattice period array and divided into region A, region B, and region A';

[0006] Region A and region A' are respectively the innermost layer and the outermost layer of the topological laser resonator, and the interface between region A and region A' forms a closed topological laser resonator, and region B is embedded in the middle of the interface;

[0007] The three different photonic crystal regions have different primitive cell band characteristics. The band structure of the photonic crystal primitive cell in region B has a linear dispersion relationship and can be described by the Dirac equation; the photonic crystal primitive cells in region A' and region A are obtained by breaking the symmetry of the photonic crystal primitive cell in region B to obtain band structures with different topological valley Chern numbers.

[0008] Preferably, the primitive cell of the photonic crystal in the B region has a linear dispersion curve, and the intersection point of the two linear dispersions is called the Dirac point, corresponding to the effective mass term of the Dirac equation being zero.

[0009] Preferably, a suspended photonic crystal slab is used as the gain material, and air holes or dielectric columns are formed in the photonic crystal slab to form a photonic crystal.

[0010] Preferably, the lattice arrangement type of the photonic crystal is a triangular lattice, a square lattice, a hexagonal lattice, or a honeycomb lattice.

[0011] Preferably, the shape of the air hole or the dielectric column is circular, triangular, rectangular, or hexagonal.

[0012] Preferably, the material of the photonic crystal is GaAs, InP, GaN, InGaAsP, or InGaAlAs.

[0013] Preferably, the symmetry is mirror symmetry, space inversion symmetry, rotational symmetry, or time-reversal symmetry.

[0014] Preferably, the symmetry is broken by deforming the primitive cell of the photonic crystal in the B region to obtain the primitive cells of the A' region and the A region; the deformation method is: compressing and stretching the air hole or the dielectric column in the primitive cell of the photonic crystal, or expanding and shrinking the area of the air hole or the dielectric column in the primitive cell of the photonic crystal, or rotating the air hole or the dielectric column in the primitive cell of the photonic crystal by different angles.

[0015] In a second aspect, the present invention provides a topological laser resonator obtained by using the design method of the above topological laser resonator.

[0016] In a third aspect, the present invention provides a topological valley photonic crystal laser, and the topological valley photonic crystal laser has the above topological laser resonator.

[0017] One or more technical solutions provided in the present invention have at least the following technical effects or advantages:

[0018] The present invention utilizes three different photonic crystal regions to form a three-layer heterostructure. The three different photonic crystal regions are arranged in the same lattice period array and divided into region A, region B, and region A'. Region A and region A' are respectively the innermost layer and the outermost layer of the topological laser resonator. The interface between region A and region A' forms a closed topological laser resonator, and region B is embedded in the middle of the interface. The three different photonic crystal regions have different primitive cell energy band characteristics. The energy band structure of the photonic crystal primitive cell in region B has a linear dispersion relationship and can be described by the Dirac equation. The photonic crystal primitive cells in region A' and region A are obtained by breaking the symmetry of the photonic crystal primitive cell in region B to have energy band structures with different topological valley Chern numbers, thus possessing different topological characteristics. The three-layer heterostructure formed by the above topological structure design shows a projected energy band diagram similar to the traditional valley-locked boundary state mode because a layer of photonic crystal with Dirac cone dispersion at the valley K and K' points is embedded in the middle of the boundary state. Moreover, its valley-locked boundary state mode also shows a similar electric field and phase distribution and a similar Poynting vector. Therefore, the valley-locked boundary state mode extends into region B and does not change the valley-momentum locking characteristic, thus retaining the topological robustness. When light travels in the three-layer heterojunction topological laser resonator, the light radiated out of the plane will interfere destructively along the transmission path, especially at the sharp corners, and there is almost no backscattering. Therefore, the out-of-plane scattering loss is significantly reduced, and thus the quality factor of the valley-locked boundary state mode is significantly improved. At the same time, the loss during the transmission process is also reduced. Based on the above topological laser resonator, a topological valley photonic crystal laser with better robustness, low threshold, and high power can be realized. In summary, the present invention can enhance the performance of the topological valley photonic crystal laser and provides a new topological laser resonator and laser different from the traditional structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 is the overall design flow chart of the present invention;

[0020] Figure 2 In (a) is a schematic diagram of the structure of the traditional topological photonic crystal laser resonator AA' and the photonic crystal primitive cells in regions A and A';

[0021] Figure 2 In (b) is a schematic diagram of the structure of the topological photonic crystal laser resonator ABA' designed by the present invention and the photonic crystal primitive cell in region B;

[0022] Figure 2 In (c) is Figure 2 a schematic diagram of the topological boundary state laser formed by the topological waveguides shown in (a) and (b) in [FIGURE NUMBER] forming an annular triangular cavity;

[0023] Figure 2 In (d) isFigure 2 Band diagrams of the primitive cells of the photonic crystal in regions A, B, and A' shown in (a) and (b) thereof;

[0024] Figure 2 In (e) thereof is the projected band diagram of the valley-locked edge states of the AA' and ABA' supercells;

[0025] Figure 2 In (f) thereof is Figure 2 At the K valley in (e) thereof, the electric field and phase distributions of the valley-locked edge states of the AA' and ABA' supercells;

[0026] Figure 3 In (a) thereof is the quality factor of the eigenmode of the valley-locked edge state calculated in the AA' and ABA' cavities;

[0027] Figure 3 In (b) thereof is the effective mode volume of the eigenmode of the valley-locked edge state calculated in the AA' and ABA' cavities;

[0028] Figure 3 In (c) thereof is the overlap factor of the eigenmode of the valley-locked edge state calculated in the AA' and ABA' cavities;

[0029] Figure 3 In (d) thereof is the normalized electric field distribution diagram at the center of the photonic crystal slab for the edge state mode with the highest quality factor in the AA' cavity;

[0030] Figure 3 In (e) thereof is the normalized electric field distribution diagram at 1.5 μm above the photonic crystal slab for the edge state mode with the highest quality factor in the AA' cavity;

[0031] Figure 3 In (f) thereof is the Fourier transform analysis diagram of the near-field electric field distribution of the AA' cavity;

[0032] Figure 3 In (g) thereof is the normalized electric field distribution diagram at the center of the photonic crystal slab for the edge state mode with the highest quality factor in the ABA' cavity;

[0033] Figure 3 In (h) thereof is the normalized electric field distribution diagram at 1.5 μm above the photonic crystal slab for the edge state mode with the highest quality factor in the ABA' cavity;

[0034] Figure 3 In (i) thereof is the Fourier transform analysis diagram of the near-field electric field distribution of the ABA' cavity;

[0035] Figure 4 In (a) thereof is the in-plane transmittance and out-of-plane scattering spectrum of the Z-shaped waveguide formed by the AA' and ABA' structures;

[0036] Figure 4 In (b) is Figure 4 The out-of-plane scattering loss coefficient calculated from the out-of-plane scattering spectrum in (a) of

[0037] Figure 4 In (c) is the electric field intensity distribution diagram of the valley-locked edge state propagating in the Z-shaped waveguides of AA' and ABA' in the photonic crystal slab;

[0038] Figure 4 In (d) is the electric field intensity distribution diagram of the valley-locked edge state propagating in the Z-shaped waveguides of AA' and ABA' in air;

[0039] Figure 4 In (e) is the magnetic field distribution diagram of the valley-locked edge state propagating in the Z-shaped waveguides of AA' and ABA' in the photonic crystal slab;

[0040] Figure 4 In (f) is the electric field distribution diagram of the valley-locked edge state propagating in the Z-shaped waveguides of AA' and ABA' in air;

[0041] Figure 5 In (a) is the scanning electron microscope image of the AA' topological laser resonator fabricated on a 120-nm MQW multi-quantum well wafer;

[0042] Figure 5 In (b) is the scanning electron microscope image of the ABA' topological laser resonator fabricated on a 120-nm MQW multi-quantum well wafer;

[0043] Figure 5 In (c) is the laser input and output curve diagram of the AA' and ABA' topological lasers, and the inset is the corresponding logarithmic diagram;

[0044] Figure 5 In (d) is the emission light image of the AA' topological laser taken under an infrared CCD camera at different pump power densities;

[0045] Figure 5 In (e) is the emission light image of the ABA' topological laser taken under an infrared CCD camera at different pump power densities;

[0046] Figure 5 In (f) is the photoluminescence spectrum of the AA' topological laser in the entire dynamic range;

[0047] Figure 5 In (g) is the photoluminescence spectrum of the ABA' topological laser in the entire dynamic range. Detailed implementation mode

[0048] To better understand the above technical solution, the above technical solution will be described in detail below in conjunction with the accompanying drawings of the specification and specific implementation manners.

[0049] Example 1:

[0050] Example 1 provides a design method for a topological laser resonator. Refer to Figure 1 , which includes: using three different photonic crystal regions to form a three-layer heterostructure. The three different photonic crystal regions are arranged in an array according to the same lattice period (the photonic crystal lattice periods of the three regions are all set to a) and divided into region A, region B, and region A'. Region A and region A' are the innermost and outermost layers of the topological laser resonator respectively. The interface between region A and region A' forms a closed topological laser resonator, and region B is embedded in the middle of the interface. The three different photonic crystal regions have different primitive cell energy band characteristics. The energy band structure of the photonic crystal primitive cell in region B has a linear dispersion relationship and can be described by the Dirac equation. The photonic crystal primitive cells in region A' and region A are obtained by breaking the symmetry of the photonic crystal primitive cell in region B to obtain energy band structures with different topological valley Chern numbers.

[0051] Among them, the photonic crystal primitive cell in region B has a linear dispersion curve. The intersection point of the two linear dispersions is called the Dirac point, and the effective mass term corresponding to the Dirac equation is zero.

[0052] The photonic crystal primitive cells in region A' and region A are obtained by breaking the symmetry of the photonic crystal primitive cell in region B (for example, mirror symmetry, space inversion symmetry, rotational symmetry, or time-reversal symmetry). When the symmetry is broken, the Dirac points will disappear and energy band gaps will be opened. These two types of photonic crystals can obtain energy band structures with different topological valley Chern numbers and have different topological properties.

[0053] Due to different lattice designs, different types of interfaces can be constructed at the splicing of region A' and region A. Such interfaces with different configurations are the topological laser resonator, which has topological protection and can regulate the propagation direction, localization degree, and optical properties of light waves.

[0054] Insert the photonic crystal in region B into the interface between the photonic crystals in region A' and region A to form a three-layer heterostructure. The interface formed by the photonic crystals in region A', region B, and region A also has topological protection, can better suppress backscattering, and has stronger immunity to sharp corners, defects, etc.

[0055] Specifically, a suspended photonic crystal flat plate can be used as a gain material, and air holes or dielectric columns are formed in the photonic crystal flat plate to form a photonic crystal. That is, the present invention forms a three-layer heterostructure by opening three different photonic crystal regions on the photonic crystal flat plate.

[0056] The present invention embeds the Dirac photonic crystal in the B region into the interface between the A' region and the A region to form a novel topological photonic crystal laser resonator with an arbitrary closed geometric shape. The topological laser resonator can have any geometric shape, such as an annular triangle, an annular hexagon, etc.

[0057] Among them, the lattice arrangement type of the photonic crystal is a triangular lattice, a square lattice, a hexagonal lattice, a honeycomb lattice, etc. The shape of the air hole or the dielectric column is circular, triangular, rectangular or hexagonal. The material of the photonic crystal can be a semiconductor quantum well laser gain material such as GaAs, InP, GaN, InGaAsP or InGaAlAs.

[0058] Specifically, the symmetry is broken by deforming the primitive cell of the photonic crystal in the B region to obtain the primitive cells of the photonic crystals in the A' region and the A region; the deformation method can be to compress and stretch the air holes or the dielectric columns in the primitive cell of the photonic crystal; or, expand and shrink the area of the air holes or the dielectric columns in the primitive cell of the photonic crystal; or, rotate the air holes or the dielectric columns in the primitive cell of the photonic crystal by different angles.

[0059] Embodiment 2:

[0060] Embodiment 2 provides a topological laser resonator obtained by using the design method of the topological laser resonator described in Embodiment 1.

[0061] Embodiment 3:

[0062] Embodiment 3 provides a topological valley photonic crystal laser, and the topological valley photonic crystal laser has the topological laser resonator described in Embodiment 2.

[0063] In the present invention, a three - layer heterojunction topological laser resonator is formed by embedding a PhC layer with Dirac - cone dispersion in the interface of a traditional topological laser resonator. When light propagates in the three - layer heterojunction topological laser resonator, the light radiated out - of - plane undergoes destructive interference along the propagation path. Therefore, the out - of - plane scattering loss can be significantly reduced, resulting in a higher quality factor for its valley - locked edge mode. Among them, the highest quality factor reaches approximately 11,000, which is about 4 times higher than that of the traditional topological laser resonator. The increase in the quality factor of the valley - locked edge state mode helps to reduce mode - gain competition. Therefore, compared with traditional topological lasers, this new type of topological valley photonic crystal laser is more likely to exhibit single - mode emission. At the same time, with the reduction of out - of - plane scattering loss, the laser is easier to emit laser light. Therefore, the three - layer heterojunction topological laser has a lower pump - threshold and a higher output power.

[0064] That is, the topological valley photonic crystal laser provided in Embodiment 3 has better robustness, lower threshold, and higher power than traditional topological lasers.

[0065] The following further describes the present invention.

[0066] See Figure 2 , based on the valley - Hall effect, a traditional triangular topological laser resonator is constructed using the topological interface of the A and A' photonic crystal regions, as shown in (a) of Figure 2 .

[0067] In the topological interface of this traditional triangular topological laser resonator, a photonic crystal in the B region (i.e., Dirac photonic crystal) is inserted to construct a three - layer heterostructure. The widened topological interface is the new topological laser resonator, as shown in (b) of Figure 2 .

[0068] For example, in the present invention, air holes are opened in a suspended two - dimensional - structure photonic crystal slab, as shown in (b) of Figure 2 . The shapes of the air holes in the three photonic crystal regions A, B, and A' are all triangular, arranged in a honeycomb lattice, and the polarization mode of the photonic crystal is the Transverse - Electric (TE) mode.

[0069] As Figure 2 The inset in (b) of 6 shows that the primitive cell of the photonic crystal in the B region is a C 0 - symmetric structure. The side lengths of the two triangular air holes in the primitive cell are both L Figure 2 . The lattice period is a. Its primitive - cell energy - band structure is shown in (d) of

[0070] There are Dirac points in the Brillouin zone. 6Symmetry breaking becomes C 3 Symmetrical structures. This is achieved by maintaining the same filling fraction in the dielectric material and changing the relative sizes of the two triangular air holes in the primitive cell, as shown in the inset of (a) in Figure 2 In the primitive cell of the photonic crystal in regions A and A', the sizes of the two equilateral triangular air holes are L 1 and L 2 respectively, and the two primitive cells of the photonic crystal are rotationally symmetric by 180°. The band structures of these two primitive cells of the photonic crystal are also as shown in Figure 2 (d) in. A band gap is opened near the Dirac point. Since the lattices of the photonic crystals in regions A and A' are opposite, the upper and lower bands shown in the figure are also exchanged.

[0071] The following is a specific example in combination with parameters.

[0072] The present invention provides a three-layer heterostructure of a two-dimensional honeycomb lattice, in which air holes (refractive index of air is 1) are periodically arranged on a substrate of a multi-quantum well material (refractive index of the multi-quantum well material is 3.2), and the thickness h of the photonic crystal is 120 nm.

[0073] Figure 2 (a) in is a schematic structural diagram of a conventional topological photonic crystal laser resonator, mainly composed of regions A and A', called the AA' topological cavity. The local enlarged view shows that the topological interface is in the Bearded configuration (two primitive cells of the photonic crystal with flip symmetry are spliced into a shape similar to a "beard"). The lattice constant a of the primitive cells in regions A and A' is 635 nm, and the air holes are two equilateral triangular holes with different sizes, and the side lengths are L 1 = 214 nm and L 2 = 434 nm.

[0074] Figure 2 (b) in is a schematic structural diagram of the novel topological photonic crystal laser resonator provided by the present invention. By embedding region B into the conventional topological photonic crystal laser resonator, a three-layer heterostructure is formed, called the ABA' topological cavity. The local enlarged view shows the broadened topological interface, and the primitive cell of region B is a Dirac photonic crystal primitive cell. Similarly, its lattice constant a is 635 nm, and the air holes are two equilateral triangular holes with the same size, and the side length is L 0 = 344 nm.

[0075] Figure 2 (c) in shows a schematic diagram of the topological cavity drawn on a multi-quantum well flat plate with a refractive index of 3.2 and a thickness h = 120 nm. The red triangular ring represents the topological interface of the AA' and ABA' laser resonators.

[0076] Figure 2 In (d), it is the band structure distribution diagram of these three photonic crystal unit cells. There is a Dirac point at the K(K’) point in the Brillouin zone of the Dirac photonic crystal unit cell, with a frequency of 193.5 THz, while a band gap is opened near the Dirac point in the unit cells of regions A and A’.

[0077] Figure 2 In (e), it shows the projected bands of the AA’ and ABA’ supercells, where the gray dashed line represents the light cone. Figure 2 In (f), it shows the electric field intensity and phase distribution diagrams at the K valley of the AA’ and ABA’ supercells. The black arrows are the Poynting vectors, which show a unidirectional energy flow, that is, the black arrows represent the direction of the energy flux density in the electromagnetic field. Combining Figure 2 In (e) and (f), it can be seen that in the AA’ supercell, the edge states are locked at the K and K' valleys and show a localized electric field profile. Adding a layer of Dirac photonic crystal in the AA’ supercell results in almost the same topological edge states within the band gap, with only a slight redshift in frequency, and also shows a similar electric field and phase distribution as well as the Poynting vector. This indicates that introducing Dirac photonic crystal at the interface does not change the characteristics of the momentum-valley locked edge states.

[0078] Figure 3 In (a), it shows multiple pairs of valley-locked edge state eigenmodes of the AA’ and ABA’ topological cavities within the photonic crystal band gap. The eigenmodes in these two cavities correspond one by one, with only a slight frequency shift. It can be seen that the quality factor of the ABA’ topological cavity is significantly higher than that of the valley-locked edge states of the AA’ topological cavity, with a maximum value of about 11000, while the quality factor of the AA’ topological cavity is less than 2700. It is worth mentioning that no troublesome defect state modes are observed within the band gap, which is different from the coexistence of edge state modes and high-quality factor defect states in other configuration topological interfaces. And the quality factor of the valley-locked edge state modes in the ABA’ topological cavity is also significantly higher than that of the bulk modes.

[0079] Figure 3 In (b) and Figure 3 In (c), they are the effective mode volumes and overlap factors of the valley-locked edge states of the AA’ and ABA’ topological cavities. As mentioned before, the valley-locked edge states of ABA’ extend to region B, thus resulting in a larger mode volume and overlap factor. The electric field distributions of the valley-locked edge state modes with the corresponding highest quality factors are respectively as Figure 3As shown in (d) of [reference] and (g) of [reference 3], it exhibits a uniform field strength along the topological triangular cavity loop, which is a typical feature of topological robustness. Since these two topological cavities have almost the same cavity length and the same number of lattice periods in the A’ region to ensure in-plane mode confinement, the four-fold increase in the maximum quality factor in the ABA’ topological cavity can be attributed to the suppression of out-of-plane scattering loss.

[0080] Figure 3 In (e) and (f) of [reference] and Figure 3 In (h) and (i) of [reference] respectively show the electric field distribution map and Fourier transform mode map of the maximum quality factor mode in the AA’ and ABA’ topological cavities in air. The dashed line represents the first Brillouin zone, and the circle represents the boundary of the light cone. It can be seen that the degenerate state superposition electric field scattered in free space (1.5 μm above the photonic crystal plate) presents the same bright spot at the sharp corners of the AA’ topological cavity. The free space electric field of the ABA’ topological cavity also presents a 3 C-symmetric profile, but the bright spot is divided into two lobes, indicating the presence of destructive interference around the sharp corners. For the maximum quality factor mode in the ABA’ topological cavity, the Fourier transform intensity distribution obtained from the real space electric field profile shows prominent wave vector components under light, accounting for 98.55%. In contrast, in the AA’ topological cavity, for the maximum quality factor eigenmode, only 97.52% of the wave vector components are outside the light cone. These results indicate that the loss in the vertical direction of the ABA’ topological cavity is reduced, which is consistent with the high quality factor of the valley-locked boundary state mode in the ABA’ topological cavity.

[0081] Figure 4 In (a) of [reference] is the transmittance simulation spectrum of the Z-type topological waveguide of the AA’ and ABA’ structures, where the shaded area is the spectral range of the valley-locked boundary state. At the same incident wave amplitude, the in-plane transmission and out-of-plane scattering transmission spectra in the waveguide plane are shown. It can be seen that the valley-locked boundary state intervals of these two configurations show high transmittance in in-plane transmission. However, the in-plane transmittance of the Z-type topological waveguide of the AA’ structure is significantly lower than that of the ABA’ structure, mainly because a large amount of light is scattered into free space.

[0082] Figure 4 In (b) of [reference] is the curve of the change in the loss coefficient calculated from the out-of-plane scattered light. The scattering loss coefficient (α) of the Z-type topological waveguide of the ABA’ structure is 10 to 30 cm -1 in the high transmittance range, which is about 4 to 5 times less than that of the AA’ structure.

[0083] Figure 4 In (c) of [reference] and Figure 4In (d), it is the distribution diagram of the electric field intensity when a plane wave propagates through a Z-shaped waveguide at the center of a photonic crystal slab and in air. At the center of the photonic crystal slab, the plane wave mainly transmits along the topological interface of the bearded configuration. In contrast, the scattered light wave in air presents an obvious contour, and the Z-shaped waveguide of the AA’ structure shows a more obvious electric field intensity along the propagation trajectory, indicating that the AA’ structure has greater out-of-plane scattering loss, especially at the sharp corners. While the ABA’ structure shows a weaker scattered light intensity.

[0084] Figure 4 In (e) Figure 4 and (f) in it respectively show the magnetic field (H z ) distribution of the Z-shaped waveguide of the AA’ and ABA’ structures at the center of the photonic crystal slab and the electric field (E y ) distribution in air. Similarly, for the two topological waveguide configurations, no difference in the magnetic field distribution is observed inside the slab, while the electric field (E y ) distribution in free space is different. For the ABA’ topological waveguide, electric fields (E y ) with a π phase difference can be observed on both sides of the straight waveguide and around the waveguide corner, which is a characteristic of destructive interference, resulting in the double-lobe far field as shown in (f) in Figure 4 . Therefore, when a plane wave propagates along a valley-Hall topological waveguide, including an additional Dirac photonic crystal layer will produce destructive interference in the out-of-plane direction scattering. This can reduce the transmission loss and further significantly improve the quality factor of the characteristic modes in the topological cavity.

[0085] To verify the high-quality factor characteristics of the valley-locked boundary state mode of the ABA’ structure and its influence on laser emission, we fabricated AA’ and ABA’ topological laser resonators on a multi-quantum well wafer with a total thickness of 120 nm.

[0086] Figure 5 In (a) Figure 5 and (b) in it show the scanning electron microscope (SEM) images of the AA’ and ABA’ structures with the topological interface decorated with different colors, where the highlighted colors prominently show the topological interfaces that support the valley-locked boundary states. The side lengths of the triangular topological laser resonators of the AA’ and ABA’ types are both about 6 μm. Subsequently, we used a laser with an emission wavelength of about 1064 nm, a pulse width of 9 ns, and a repetition frequency of 400 kHz to pump the laser. The spot size of the pump laser is equivalent to the size of the topological cavity.

[0087] Figure 5 In (c) in it is the laser input and output (LL) curves of the AA’ and ABA’ topological laser resonators, respectively showing obvious values of about 44 kW / cm 2 and about 29 kW / cm2 Emission threshold. The two black arrows in the figure indicate the threshold pump power density. The corresponding logarithmic plot in the inset shows an S-shaped LL curve, indicating typical laser emission characteristics. The ABA’ topological laser has a higher output power due to its better emission performance.

[0088] Figure 5 (d) in Figure 5 and (e) in Figure 5 depict the radiation patterns of AA’ and ABA’ topological lasers captured by a CCD camera at different pump power densities. As shown in 2 (d), when the pump power density is about 40 kW / cm Figure 5 , a weak emission spot appears at the sharp corner of the AA' topological laser, which is the enhanced spontaneous emission phenomenon of the momentum-valley locked edge state. Then, at higher pump power densities, these spots become brighter. In 2 (e), emission spots also appear around the sharp corners of the laser cavity of the ABA’ topological laser. When the pump power density is higher than 25 kW / cm 2 , the intensity of the emission spots suddenly increases. There are high-intensity spots at the three sharp corners between 29 kW / cm 2 and 222 kW / cm

[0089] Figure 5 (f) in Figure 5 and (g) in

[0090] show the photoluminescence (PL) spectra of AA’ and ABA’ topological lasers at different pump power densities. The AA’ topological laser has two emission peaks above the threshold power density, with wavelengths of 1577 nm and 1610 nm respectively. These two emission peaks correspond to the valley-locked edge state modes with the two highest quality factors. In contrast, the ABA’ topological laser has only one emission peak with a wavelength of 1603 nm in the entire dynamic range, corresponding to the valley-locked edge state mode with the highest quality factor. The emission linewidths of both lasers are less than 1.5 nm. It can be seen that the ABA’ topological laser has a significantly lower laser threshold and shows good single-mode emission characteristics in a large dynamic range.

[0090] In summary, the present invention provides a new structural design of a topological laser resonator and can enhance the performance of a topological valley photonic crystal laser.

[0091] Finally, it should be noted that the above specific embodiments are only used to illustrate the technical solutions of the present invention rather than to limit them. Although the present invention has been described in detail with reference to the examples, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the spirit and scope of the technical solutions of the present invention, and they should all be covered within the scope of the claims of the present invention.

Claims

1. A method for designing a topological laser resonant cavity, characterized in that: include: A three-layer heterostructure is formed by using three different photonic crystal regions, and the three different photonic crystal regions are divided into region A, region B and region A' according to the same lattice periodic array arrangement; The A region and the A' region are the innermost layer and the outermost layer of the topological laser resonant cavity respectively, the interface between the A region and the A' region forms a closed topological laser resonant cavity, and the B region is embedded in the middle of the interface; The three different photonic crystal regions have different unit cell energy band characteristics. The band structure of the photonic crystal unit cell in the B region has a linear dispersion curve and can be described by the Dirac equation; the photonic crystal unit cell in the A' region and the A region has a band structure with different topological valley Chern numbers obtained by breaking the symmetry of the photonic crystal unit cell in the B region.

2. The design method of a topological laser resonant cavity according to claim 1, characterized in that: The photonic crystal unit cell in the B region has a linear dispersion curve, and the intersection of two linear dispersions is called a Dirac point, and the effective mass term of the corresponding Dirac equation is zero.

3. The design method of a topological laser resonant cavity according to claim 1, characterized in that: A suspended photonic crystal slab is used as a gain material, and air holes or dielectric columns are opened in the photonic crystal slab to form a photonic crystal.

4. The design method of a topological laser resonant cavity according to claim 3, characterized in that: The lattice arrangement type of the photonic crystal is a triangular lattice, a tetragonal lattice, a hexagonal lattice or a honeycomb lattice.

5. The method for designing a topological laser resonant cavity according to claim 3, characterized in that: The air holes or the dielectric columns are in a circular, triangular, rectangular or hexagonal shape.

6. The method for designing a topological laser resonant cavity according to claim 3, characterized in that: The photonic crystal is made of GaAs, InP, GaN, InGaAsP or InGaAlAs.

7. The design method of a topological laser resonant cavity according to claim 3, characterized in that: The symmetry is mirror symmetry, space inversion symmetry, rotational symmetry or time reversal symmetry.

8. The method for designing a topological laser resonant cavity according to claim 7, characterized in that: The photonic crystal primitive cells in the B region are deformed to break the symmetry, thereby obtaining the photonic crystal primitive cells in the A' region and the A region; the deformation method is: compressing and stretching the air holes or the dielectric columns in the photonic crystal primitive cells, or expanding and reducing the areas of the air holes or the dielectric columns in the photonic crystal primitive cells, or rotating the air holes or the dielectric columns in the photonic crystal primitive cells at different angles.

9. A topological laser resonant cavity, characterized in that: The topological laser resonant cavity is obtained by adopting the design method of any one of claims 1 to 8.

10. A topological valley photonic crystal laser, characterized in that: The topological valley photonic crystal laser has the topological laser resonant cavity as claimed in claim 9.

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