Combined photonic crystal structure and method for generating tunable vector laser

Abstract

Embodiments of the present disclosure describe a combined photonic crystal structure for generating an adjustable vector laser and a method of designing the combined photonic crystal structure. The combined photonic crystal structure comprises one or more periodic units, each periodic unit comprises a plurality of photonic crystal splicing units which are orderly arranged around a central point in the angular direction, and each photonic crystal splicing unit in each periodic unit supports a linear polarization characteristic. The first number of periodic units are orderly arranged around the central point in the angular direction to form a first combined photonic crystal structure, and the second number of periodic units are orderly arranged around the central point in the angular direction to form a second combined photonic crystal structure. The topological charge of the vector laser formed by the first combined photonic crystal structure is different from the topological charge of the vector laser formed by the second combined photonic crystal structure, so that the vector laser with controllable topological charge is realized.

Description

Technical Field

[0001] The present disclosure relates to a method for generating tunable vector lasers and a combined photonic crystal structure, in particular to a method for generating vector lasers with controllable topological charges and a combined photonic crystal structure, such as generating a vector laser with a flexible and tunable topological polarization structure of the lasing light field. Background Art

[0002] Optical fields with non-trivial topological structures can carry more information dimensions, such as vector optical fields, and have important application values. The complex polarization distribution enables vector beams to exhibit unique advantages in applications such as optical communication, microscopy imaging, optical trapping and micro-manipulation. Implementing vector optical fields with different topological charges can provide more adjustable degrees of freedom for these applications, which is of great significance. Therefore, there is a need for a miniature vector laser that can realize vector optical fields with different topological charges, has free design, stable performance and can be integrated. Summary of the Invention

[0003] In one aspect of the present disclosure, there is provided a combined photonic crystal structure for generating tunable vector lasers, the structure comprising: one or more periodic units, each periodic unit comprising a plurality of photonic crystal splicing units arranged in an orderly manner along the angular direction around a central point, wherein each photonic crystal splicing unit in each periodic unit supports a linear polarization characteristic, wherein the orderly arrangement of the first number of periodic units along the angular direction around the central point forms a first combined photonic crystal structure; the orderly arrangement of the second number of periodic units along the angular direction around the central point forms a second combined photonic crystal structure; and the topological charge of the vector laser formed by the first combined photonic crystal structure is different from the topological charge of the vector laser formed by the second combined photonic crystal structure, so as to realize a vector laser with controllable topological charge.

[0004] In some embodiments, the linear polarization characteristic includes the linear polarization characteristic of the bound state in the quasi-continuous spectrum (q-BIC); all crystal unit cells of the first photonic crystal splicing unit in the periodic unit have a first structural parameter; all crystal unit cells of the second photonic crystal splicing unit in the periodic unit have a second structural parameter; and the linear polarization characteristic of the q-BIC supported by the first structural parameter is different from the linear polarization characteristic of the q-BIC supported by the second structural parameter.

[0005] In some embodiments, the inner contour shape of the crystal unit cell has a specific rotational symmetry, the structural parameter is related to the orientation of the inner contour shape with the specific rotational symmetry, the orientation of the inner contour shape in the first structural parameter of the first photonic crystal splicing unit is different from the orientation of the inner contour shape in the second structural parameter of the second photonic crystal splicing unit, and the first photonic crystal splicing unit and the second photonic crystal splicing unit have the same outer contour of the crystal unit cell.

[0006] In some embodiments, the inner contour shape includes the shape of the internal holes of the primitive cell of the crystal or the shape of the dielectric pillars of the primitive cell of the crystal.

[0007] In some embodiments, the orientation of the inner contour shape of the primitive cell of the crystal is related to the direction of the major axis of the shape of the internal holes or the dielectric pillars.

[0008] In some embodiments, the center of the momentum space of a partial photonic band of the primitive cell of the crystal with the designed structural parameters corresponds to the q-BIC of the linearly polarized state.

[0009] In some embodiments, the ordered arrangement of a plurality of periodic units in the angular direction is related to the polarization vortex configuration of the target vector laser.

[0010] In some embodiments, the wavelength of the vector laser is in the range of 400 nm to 5000 nm.

[0011] In a second aspect of the present disclosure, there is provided a method for designing a combined photonic crystal structure for generating an adjustable vector laser, the method comprising: designing a periodic unit of the combined photonic crystal structure such that the periodic unit includes a plurality of photonic crystal splicing units arranged in an orderly manner in the angular direction, each photonic crystal splicing unit supporting a linearly polarized characteristic; and arranging one or more periodic units in an orderly manner in the angular direction around a central point based on the polarization configuration of the target vector laser and the required topological charge to form a combined photonic crystal structure, wherein the orderly arrangement of a first number of periodic units in the angular direction around the central point forms a first combined photonic crystal structure; the orderly arrangement of a second number of periodic units in the angular direction around the central point forms a second combined photonic crystal structure; and wherein the topological charge of the vector laser formed by the first combined photonic crystal structure is different from the topological charge of the vector laser formed by the second combined photonic crystal structure to achieve a vector laser with controllable topological charge.

[0012] In some embodiments, designing the periodic unit of the combined photonic crystal structure includes: determining the correspondence between the structural parameters of the primitive cell of each photonic crystal splicing unit and the linearly polarized characteristic of the bound state in the quasi-continuous spectrum (q-BIC) supported by it; and determining a plurality of photonic crystal splicing units in the periodic unit based on the correspondence.

[0013] In some embodiments, determining the correspondence between the structural parameters of a crystal primitive cell and the linear polarization characteristics of bound states (q-BICs) in the quasi-continuous spectrum supported thereby includes: selecting materials for fabricating a combined photonic crystal structure based on the target wavelength band of a vector laser; determining the structural parameters of the crystal primitive cell of the combined photonic crystal structure based on the selected materials, where the structural parameters can achieve bound states (q-BICs) in the quasi-continuous spectrum with an adjustable linear polarization state that conforms to the target wavelength band; fabricating a series of photonic crystal slabs with different structural parameters and testing the corresponding polarization states of the lasers generated by the corresponding photonic crystal slabs; based on the test results, verifying whether each photonic crystal slab in the series of photonic crystal slabs can achieve linearly polarized photonic crystal lasers; and in response to being able to achieve linearly polarized photonic crystal lasers, determining that specific structural parameters correspond to the linear polarization characteristics of specific bound states (q-BICs) in the quasi-continuous spectrum to obtain the correspondence.

[0014] In the combined photonic crystal structure for generating tunable vector lasers and the method for designing the combined photonic crystal structure according to the present disclosure, a combined photonic crystal is realized by periodically splicing a periodic photonic crystal (i.e., a periodic unit) as a structural unit around a center in real space to generate vector lasers. For example, photonic crystal structures with different structural parameters are arranged periodically in the angular direction around a geometric center to construct a combined photonic crystal structure that generates vector lasers carrying different topological charges. The number of angular periods and the arrangement order determine the topological charge of the vector beam. Starting from the polarization distribution of the target light field, the rotational arrangement mode of the photonic crystal structure is designed reversely, which greatly broadens the degree of freedom in vector laser design and enables the construction of vector lasers with arbitrary-order topological charges, such that the polarization configuration of the excited vector beam is not restricted by the symmetry of a single photonic crystal.

[0015] It should be understood that the content described in the Summary of the Invention section is not intended to limit the key or important features of the embodiments of the present disclosure, nor is it used to limit the scope of the present disclosure. Other features of the present disclosure will become easily understandable through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In conjunction with the accompanying drawings and with reference to the following detailed description, the above and other features, advantages, and aspects of the embodiments of the present disclosure will become more apparent. In the drawings, the same or similar reference numerals denote the same or similar elements, where:

[0017] Figure 1 shows a method for generating vector lasers carrying arbitrary topological charges according to some embodiments of the present disclosure;

[0018] Figure 2 shows an exemplary schematic diagram of the spatial periodic dimension of a photonic crystal according to some embodiments of the present disclosure;

[0019] Figure 3A and Figure 3B shows a schematic diagram of a two-dimensional photonic crystal slab according to some embodiments of the present disclosure;

[0020] Figures 4A to 4C shows a schematic diagram of a photonic crystal slab for polarization-tunable quasi-BIC design and hole array according to some embodiments of the present disclosure;

[0021] Figures 5A to 5C shows some exemplary ways of changing the shape and orientation of holes or cylinders according to some embodiments of the present disclosure;

[0022] Figures 6A to 6D shows a photonic crystal slab with C 2 symmetry and a schematic diagram of experimental verification characterization of linearly polarized laser implemented based on this structure;

[0023] Figure 7 shows a schematic diagram of the correspondence between hole orientation and laser linear polarization state orientation under given structural parameters according to some embodiments of the present disclosure;

[0024] Figures 8A to 8C shows a schematic diagram of a vector laser construction scheme carrying -2 topological charge according to some embodiments of the present disclosure;

[0025] Figures 8D to 8E shows a schematic diagram of a first combined photonic crystal structure and a schematic diagram of a second combined photonic crystal structure according to some embodiments of the present disclosure;

[0026] Figure 9 shows a picture of the momentum space of a vector laser carrying -2 topological charge according to some embodiments of the present disclosure; and

[0027] Figure 10 shows a method for designing a combined photonic crystal structure used to generate tunable vector lasers according to some embodiments of the present disclosure. Detailed Description of the Invention

[0028] Reference is now made to the accompanying drawings, in which like reference numerals are used throughout to refer to like elements. In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of one or more embodiments. However, in some or all instances, it may be apparent that any of the embodiments described below may be practiced without the use of the specific design details described below. In other instances, well-known structures and devices are shown in block diagram form in order to facilitate the description of one or more embodiments. A simplified overview of one or more embodiments is given below in order to provide a basic understanding of the embodiments. This overview is not an exhaustive overview of all contemplated embodiments, is not intended to identify key or critical elements of any or all embodiments, nor is it intended to define the scope of any or all embodiments.

[0029] References to "an embodiment" or "one embodiment" in the context of this description are intended to indicate that a particular configuration, structure, or characteristic described in connection with the embodiment is included in at least one embodiment. Thus, phrases such as "in an embodiment" or "in one embodiment" that may occur in one or more places in this description are not necessarily all referring to the same embodiment. Moreover, in one or more embodiments, the particular configurations, structures, or characteristics may be combined in any suitable manner.

[0030] In the following disclosure, unless otherwise indicated, when referring to absolute position modifiers (such as the terms "front", "rear", "top", "bottom", "left", "right", etc.) or relative position modifiers (such as the terms "above", "below", "higher", "lower", etc.), or when referring to directional modifiers (such as "horizontal", "vertical", etc.), it refers to the orientation shown in the figures. Unless otherwise specified, the terms "about", "approximately", "substantially", and "around" mean within 10%, preferably within 5%.

[0031] In the following description, one or more specific details are illustrated in order to provide an in-depth understanding of examples of embodiments of this description. The embodiments may be obtained without one or more specific details, or by using other methods, components, materials, etc. In other cases, well-known structures, materials, or operations are not shown or described in detail so that certain aspects of the embodiments will not be obscured.

[0032] Throughout the accompanying drawings, the same components or elements are indicated by the same reference numerals, and the corresponding descriptions will not be repeated for the sake of brevity. The reference numerals used herein are provided for convenience only and thus do not define the scope of protection or the scope of the embodiments.

[0033] A vector optical field describes an optical field whose polarization distribution varies continuously with spatial position. A representative vector optical field is one with a vortex configuration in its polarization distribution. The topological properties of such vector optical fields can be quantitatively described based on the angular accumulation of the polarization direction in the polarization vortex in space, from which the topological charge of the vector optical field is obtained. Optical fields with non-trivial topological structures can carry more information dimensions, such as vector optical fields, which have important application values. The complex polarization distribution enables vector beams to exhibit unique advantages in applications such as optical communication, microscopy imaging, optical trapping and micro-manipulation. Realizing vector optical fields with different topological charge configurations can provide more adjustable degrees of freedom for these applications, which is of great significance.

[0034] Currently, micro-nano photonics and integrated photonics are in a stage of rapid development. Developing active photonic devices based on micro-nano photon structures is an important development direction, and micro-lasers realized using micro-nano photon structures are the key research and development objects. Laser directly carrying a vector optical field distribution with topological charge based on micro-nano photon structures can endow such active photonic devices with significant advantages. Developing such micro-lasers requires the realized optical field to have a topological structure of polarization vector vortex, and realizing vector lasers with different topological charges is an important content that needs to be promoted for such micro-lasers.

[0035] Currently, active vector lasers can be realized through various technical solutions.

[0036] For example, in one technical solution, a vector laser involving intracavity integration of a metasurface and related polarization elements mainly precisely manipulates the phase, amplitude, and polarization state of light at the sub-wavelength scale through the metasurface to generate and control the vector optical field, and then integrates it with a gain medium in a Fabry-Perot cavity with a high quality factor to generate vector laser. Although this technology integrates the cutting-edge micro-nano structure of the metasurface, which can control the polarization distribution of the optical field, the laser with intracavity integrated metasurface, although able to flexibly control the optical field, must rely on an external resonant cavity to generate laser. The components required for laser generation are numerous and large in volume, making the integration difficult and the integration degree very limited.

[0037] In the second technical solution, specific micro-nano structures such as microring resonators and nanocolumns can also enhance the optical field and control the polarization state, thereby realizing the output of a micro vector laser. However, these structures face certain limitations in manufacturing accuracy and output efficiency. Achieving a vector beam requires precise design of structural parameters to control the spatial distribution of the polarization state, which poses extremely high requirements for micro-nano manufacturing. In addition, when designing vector optical fields with different topological charge values, there is a lack of effective design freedom to regulate the topological polarization configuration of the vector optical field, and it is also a great challenge to achieve higher-order vector optical fields. In addition, the limitations of loss and output efficiency also affect the practical application of the micro vector laser.

[0038] In the second solution, the above problems are related to the working principle of the micro vector laser implemented by using specific micro-nano structures such as microring resonators and nanocolumns. In this micro vector laser, the generation of the vector beam depends on the coupling of multiple optical modes supported by the structure. Any subtle structural error may cause deviations in the frequency and phase of the optical modes, thereby affecting the polarization state distribution and beam purity of the coupled optical field. Therefore, such micro-nano structures have extremely high requirements for preparation accuracy and are very sensitive to the external environment. Changes in temperature and vibration may cause instability in the output frequency and mode. In addition, the inherent limitations of these structures make it difficult to obtain high-quality factor modes, and it is thus difficult to meet the requirements of highly directional radiation while achieving low-threshold and high-efficiency laser output.

[0039] In the third technical solution, micro-laser generation is achieved through photonic crystals in micro-nano structures. This technology has a long development history. In recent years, the development of topological photonics has revealed the existence of bound states in the continuum in this periodic structure of photonic crystal slabs. These special modes with extremely high quality factors can be used to generate micro-lasers. At the same time, these special modes also appear as the center of the polarization vortex configuration in momentum space, that is, polarization singularities, which also regulate the polarization state and distribution of the emitted beam during the laser generation process, realizing the emission of a vector beam. Protected by the structural symmetry, the polarization singularities have a certain tolerance for processing errors. Coupled with their highly compact structure, micro-nano processing is relatively simple, especially with the support of processes such as nanoimprinting, showing outstanding application prospects.

[0040] However, the traditional photonic crystal laser technology in the third solution is based on the special momentum-space polarization singularities therein. By utilizing the high-quality factor characteristics of the modes corresponding to the polarization singularities, vector lasers are generated. The polarization distribution of the laser is directly related to the momentum-space polarization vortex configuration where the high-quality factor modes are located. However, due to the symmetry constraints of a single photonic crystal slab, the topological charge of the momentum-space polarization vortex is highly correlated with the structural parameters, and these polarization vortex configurations are in the momentum space and cannot be directly edited and designed through the regulation of the real-space structure. Moreover, in actual situations, it is difficult to find higher-order polarization vortices with an absolute value of the topological charge greater than two. Therefore, it is difficult to directly apply it to the realization of vector lasers with higher-order topological charges. For example, most of the current polarization configurations only carry topological charges of -1, -2, and +1.

[0041] Therefore, the micro-lasers realized through photonic crystals in such micro-nano structures have limitations in the flexibility of polarization regulation. The polarization distribution of the excitation beam is directly related to the momentum-space polarization field of the photonic crystal, and the configuration of the momentum-space polarization field of the photonic crystal is simultaneously protected and constrained by symmetry. The polarization configurations supported by a photonic crystal slab with a certain symmetry are incomplete, and most of the currently realized polarization configurations only carry very low-order topological charges (for example, topological charges of -1, -2, and +1). All these greatly limit the topological charges of the vector lasers that can be arbitrarily adjusted and designed, significantly restricting their wide application in vector laser applications.

[0042] Therefore, the current micro-laser technologies all have their own shortcomings in the generation and regulation flexibility of vector lasers, significantly restricting the application of micro-vector lasers.

[0043] Considering the above problems, embodiments of the present disclosure provide a combined photonic crystal structure for generating tunable vector lasers. The combined photonic crystal structure includes one or more periodic units, and each periodic unit includes a plurality of photonic crystal splicing units arranged in an orderly manner along the angular direction around a central point. Each photonic crystal splicing unit in each periodic unit supports a linear polarization characteristic. Among them, the orderly arrangement of the first number of periodic units along the angular direction around the central point forms a first combined photonic crystal structure, and the orderly arrangement of the second number of periodic units along the angular direction around the central point forms a second combined photonic crystal structure. The topological charge of the vector laser formed by the first combined photonic crystal structure is different from the topological charge of the vector laser formed by the second combined photonic crystal structure, so as to realize a vector laser with controllable topological charge.

[0044] In a combined photonic crystal structure, by providing different numbers of periodic units (where each periodic unit includes one or more photonic crystal splicing units and each photonic crystal splicing unit supports a linear polarization characteristic) arranged in an angular direction around a central point (for example, the above-mentioned first number is different from the above-mentioned second number), multiple vector lasers carrying different topological charges can be realized. In this way, vector lasers with adjustable topological charges can be obtained by arranging and combining different numbers of periodic units, and thus any desired topological charge can be achieved.

[0045] Method 100 for stably generating vector lasers carrying arbitrary topological charges within a broad spectrum range will be specifically described below, as Figure 1 shown.

[0046] In step 101, the photonic crystal and the gain material system are determined. When designing a laser, according to the wavelength band of the target laser, the gain medium material to be used is determined to generate laser in the target wavelength band. Then, considering the characteristics such as the refractive index of the material in the target wavelength band, the material for preparing the photonic crystal laser system is determined.

[0047] In step 102, a polarization-tunable high-quality factor optical mode is designed, which includes the design of polarization-tunable quasi-BIC and the analysis of the relationship between the quasi-BIC polarization state and the structural parameters. After selecting the materials for each part required for the micro-laser generation system, based on the band theory of photonic crystals and the concept of the polarization field in momentum space, combined with simulation methods such as the finite element method, the structure of the photonic crystal thin film is designed, and parameters such as the lattice shape, symmetry, period, thickness, and hole shape of the structure are determined to obtain a high-quality factor optical mode that matches the wavelength band.

[0048] From the perspective of the topology of the polarization field in momentum space, the bound states in the continuum, that is, Bound states in the continuum (BICs), which are special modes with extremely high quality factors, are vortex singularities in the polarization field of momentum space, and most of them are protected by the rotational symmetry of the structure. Therefore, in a structure with a certain rotational symmetry, BICs can be found at the center of the momentum space corresponding to the photonic band (that is, the Γ point, corresponding to the direction perpendicular to the plane). For a photonic crystal with a specific in-plane rotational symmetry, there are BICs (as the center of the polarization vortex, the polarization state cannot be defined) at the origin of the momentum space corresponding to some of its energy bands (usually called the Γ point), which are protected by the in-plane rotational symmetry. These BICs are the key to generating vector lasers in the photonic crystal system. The polarization states of the optical modes around the BIC in momentum space together form a polarization vortex, and affected by the BIC, these modes all have very high quality factors.

[0049] During the generation of photonic crystal lasers, BICs themselves do not radiate outward, but the high-quality factor modes around these BICs (corresponding to the centers of polarization vortices) will all radiate outward and have corresponding polarization states, thus constituting a vector laser carrying polarization vortices.

[0050] In the case of breaking the rotational symmetry of the photonic crystal slab, for example, by changing the shape of the holes inside the structural unit cell or changing the shape of the dielectric pillars to break the original rotational symmetry, the BICs and the polarization vortices where they are located will also be affected accordingly. When the original BICs are destroyed, there will still be some quasi-BICs (q-BICs) with high-quality factor characteristics in the momentum space. They can radiate outward and exhibit specific polarization states, and can also be used for photonic crystal lasers. That is to say, after changing the structural shape to break the symmetry, the quasi-BICs will be evolved from this BIC, with a specific linear polarization state, and the method of breaking the symmetry is diverse.

[0051] In some embodiments, by changing the shape of the structure (holes or pillars) inside the photonic crystal unit cell and adjusting the spatial orientation of this shape, the linear polarization state can be adjusted. The present disclosure will also be based on these high-quality factor optical modes (for example, quasi-BICs). After the structural symmetry is broken, the evolved polarization field in the momentum space will further evolve accordingly with the change of the structural parameters, and the polarization state of the quasi-BICs among them will also evolve, thereby enabling a photonic crystal laser with an adjustable linear polarization state to be realized.

[0052] Photonic crystals can be divided into one-dimensional, two-dimensional, and three-dimensional photonic crystals according to the spatial periodicity dimension of their structures. As Figure 2 shown, 1D photonic crystals, 2D photonic crystals, and 3D photonic crystals. As Figure 2 shown, for a two-dimensional photonic crystal, it has periodicity in two dimensions and is infinitely extended in the remaining one dimension, such as the z direction in the above figure. If a truncation is applied in this extended direction to make it a photonic crystal slab with a finite thickness, that is, a two-dimensional photonic crystal slab, they can control the light field in free space. In some embodiments, the photonic crystal structure designed according to the present disclosure can be a two-dimensional photonic crystal slab, but the present disclosure does not limit the dimension of the photonic crystal.

[0053] There are two typical two-dimensional photonic crystal slabs. One type is the periodic array of dielectrics prepared by micro-nano processing methods as Figure 3A shown, and the other type is the hole photonic crystal slab as Figure 3B shown, where a periodic array of holes is prepared on the dielectric thin film by micro-nano processing methods. Both have corresponding polarization fields, BICs, and quasi-BIC phenomena in the momentum space, and vector lasers with controllable topological charges can be realized through appropriate design.

[0054] In the following, taking Figures 4A to 4C the design of a photonic crystal slab structure including a hole array shown as an example, the linear polarization characteristics of the crystal primitive cell will be explained. Figures 4A to 4C shows a polarization-tunable quasi-BIC design process, starting from Figures 4A to 4B is a photonic crystal slab with C 6 symmetry changing from a hole shape to C 2 symmetry process.

[0055] The photonic crystal splicing unit may include multiple photonic crystals as shown in the upper half of Figure 4A and Figure 4B . As Figure 4A stated, the photonic crystal in the photonic crystal slab structure has a hexagonal lattice, and the center of the primitive cell is a circular hole, so it has six-fold rotational symmetry, that is, C 6 symmetry. The polarization field in momentum space corresponding to one of its energy bands is shown below the structural schematic diagram. There is a BIC carrying a -2 charge at the center of momentum space. The BIC carrying a -2 charge is marked with a black dot in Figure 4A .

[0056] Next, as Figure 4B shown, the circular hole is changed into an elliptical hole, and the symmetry of the structure also becomes C 2 . At this time, the BIC with a -2 charge at the center of momentum space can no longer exist and is transformed into a quasi-BIC in a linearly polarized state (q-BIC, represented by double arrows in Figure 4B and Figure 4C ), and this quasi-BIC can be used to generate linearly polarized laser. In addition, the polarization orientation of this linearly polarized laser (the orientation of the arrows in Figure 4B and Figure 4C ) will also change with the orientation of the elliptical hole. For example, when the hole orientation angle θ changes from 0° to 30°, the eigenpolarization orientation corresponding to the intermediate quasi-BIC will also rotate accordingly, for example, from the vertical direction in Figure 4B to the inclined direction shown in Figure 4C .

[0057] The quasi-BIC at the Γ point not only has the characteristic of a high quality factor, but also has a high photon state density near its energy. Therefore, it is very advantageous to use the quasi-BIC to realize laser. Different from the non-radiating BIC, the laser generated based on the regulation of these quasi-BICs mainly shows a single linearly polarized state, which is consistent with the polarization state of the quasi-BIC. Therefore, all linearly polarized vertical emission lasers can be realized using these modes.

[0058] Although Figures 4A to 4CThe description is made with reference to the design of a photonic crystal slab structure including an array of holes, but the present disclosure does not limit the implementation manner of the photonic crystal slab. A photonic crystal slab structure composed of a columnar periodic array (such as Figure 3A shown) can also be used to generate a linearly polarized state. By changing the structural shape to break the symmetry, this BIC evolution can obtain a quasi-BIC, which has a specific linearly polarized state. The methods of breaking symmetry are diverse. For example, by changing the shape of the structure (holes or cylinders) within the primitive cell of the photonic crystal and adjusting the spatial orientation of this shape, the linearly polarized state can be adjusted.

[0059] The following will refer to Figures 5A to 5C to illustrate some exemplary ways of changing the shape and orientation of holes or cylinders according to some embodiments of the present disclosure.

[0060] As Figure 5A shown, starting from a circular hole or dielectric column, the circle can be changed into a structure such as a circular segment or a sector. The corresponding BIC will evolve into a quasi-BIC with a linearly polarized state, and its linearly polarized state can also change with the rotation of the structure. As Figure 5B shown, starting from a square hole or dielectric column, the square can be changed into a triangle, a trapezoid, or other shapes, and a quasi-BIC with adjustable linear polarization can also be realized.

[0061] As Figure 5C shown, for some special shapes (for example, an I-shaped hole or dielectric column), there are also corresponding symmetry-breaking methods. By using electromagnetic simulation methods such as finite element method to find the corresponding quasi-BIC with a linearly polarized state and verifying experimentally that it can achieve adjustable linearly polarized laser emission, it can be used as a structural unit for constructing a composite photonic crystal slab.

[0062] The outer contour of the primitive cell of the crystal can be in the shape of a square or an equilateral hexagon, etc. According to the symmetry-breaking method, multiple spliced photonic crystal units can be obtained, but the outer contour shape of the primitive cell shape of each spliced structure is the same, and the shape of the inner contour (holes or dielectric columns) is also the same. Only the orientation or orientation of the inner contour has an angular distribution in space.

[0063] Returning to the reference Figure 1 , in step 103, the laser verification of the photonic crystal with adjustable linearly polarized state is performed, specifically including the preparation of a quasi-BIC sample with adjustable polarization, the characterization of the quasi-BIC with a linearly polarized state, and the characterization of the adjustable linearly polarized laser based on the quasi-BIC.

[0064] Figures 6A to 6D shows a schematic diagram of the experimental verification characterization of a photonic crystal slab with C 2 symmetry and the linearly polarized laser realized based on this structure.

[0065] Specifically, after designing the polarization-tunable quasi-BIC, a corresponding photonic crystal slab system is fabricated using semiconductor processes and micro-nano processing technologies to prepare a series of photonic crystal slabs with different hole orientations (such as Figure 6A shown), which is the preparation of the above-mentioned polarization-tunable quasi-BIC sample. The band structure and other momentum space information of the photonic crystal slab are characterized by momentum space spectral imaging technology, that is, the above-mentioned linearly polarized state quasi-BIC characterization, to verify the quasi-BIC mode with tunable linearly polarized state.

[0066] Figure 6A Shows a scanning electron microscope photograph of the photonic crystal slab. As Figure 6A shown, the photonic crystal slab has multiple crystal unit cells, each crystal unit cell includes elliptical holes, and the orientation of the elliptical holes is in the horizontal direction.

[0067] Figure 6B Shows the angle-resolved transmission spectrum of the sample in the kx direction (the horizontal axis represents the angle, and the vertical axis represents the wavelength). The corresponding polarization singularities are marked on the energy band. Especially for the middle quasi-BIC, linearly polarized laser generation can be achieved with this sample. Figure 6B The result of Figure 6B is the first step, which is used to verify that a linearly polarized quasi-BIC is obtained. Using the angle-resolved transmission spectrum, the energy band and its polarization information of the photonic crystal can be directly characterized. As Figure 6B shown, the BIC (the BIC as Figure 6B shown) does not couple with the outside world, so it appears as a quenching point on the energy band (as Figure 6B shown, the color at the point indicated by the arrow of the BIC is white). However, the quasi-BIC (the q-BIC as Figure 6B shown) is located at the center (the lowest point of the energy band) and appears as a linearly polarized state (as

[0068] shown, the color at the point indicated by the arrow at the q-BIC is not white). Figure 6C and Figure 6D The results of Figure 6C are the results of the laser experiment, that is, the second step, which is used to verify that linearly polarized laser can be realized based on the linearly polarized state quasi-BIC. Figure 6B is the angle-resolved fluorescence spectrum. By comparing with Figure 6C shown, it can be seen that the quasi-BIC mode becomes the mode of the final laser emission, and its polarization state can be measured. As Figure 6DIt is the experimental result of analyzing the polarization of the emitted laser, which indicates that linearly polarized laser has been achieved.

[0069] Furthermore, pump excitation is also required to verify that the fabricated photonic crystal structure can achieve linearly polarized tunable laser based on quasi-BIC, and simultaneously measure the corresponding relationship between the linearly polarized state and the hole orientation. As Figures 6A to 6D described, the linearly polarized state corresponds to the hole orientation of 0° (i.e., the long axis of the hole is along the horizontal direction, and if the hole orientation changes, the corresponding linearly polarized state will also change). That is to say, the characterization of tunable linearly polarized laser based on quasi-BIC is required here. If the above experimental results do not meet the design expectations (i.e., laser with linearly polarized state cannot be obtained), then go back to step 101 of selecting the material system and step 102 of optimizing the structural parameters, etc., until a photonic crystal laser with tunable linearly polarized state is achieved.

[0070] Therefore, based on the design and simulation in step 102 and the experimental verification in step 103, the corresponding relationship between the orientation of the holes in the unit cell and the quasi-BIC linearly polarized state can be determined, which can be used as a guide for the subsequent arrangement of the photonic crystal structure.

[0071] Figure 7 FIG. shows a schematic diagram of the corresponding relationship between the hole orientation and the laser linearly polarized state orientation under given structural parameters according to some embodiments of the present disclosure, where the horizontal axis represents the hole orientation and the vertical axis represents the laser linearly polarized orientation. Figure 7 is the linearly polarized laser achieved by using photonic crystals with a series of different hole orientations according to the design mentioned above. The linearly polarized orientation of the laser is measured, which corresponds well to the simulation results, indicating that the linearly polarized state of the laser can be changed by rotating the holes. The dots represent the actual experimental results, and the dashed lines represent the simulation results.

[0072] Return to reference Figure 1 , in step 104, the design of the photonic crystal composite structure is carried out. That is to say, it is necessary to design and determine the specific angular arrangement of the photonic crystal structure according to the polarization configuration of the target vector laser.

[0073] Different from the single linearly polarized laser, the beam cross-section of the vector laser has a polarization distribution configuration, which can be decomposed into various linearly polarized state lasers and arranged in a specific distribution manner in space. Therefore, using the polarization-tunable quasi-BIC laser as the basic structural unit (i.e., the photonic crystal splicing unit) and combining it according to a specific polarization configuration can construct a laser beam with vector characteristics. The photonic crystals designed in step 102 can generate lasers covering all linearly polarized states, and their unit cell shapes are the same, ensuring the compatibility of the combination of linearly polarized state lasers in space.

[0074] To construct a vector laser, it is necessary to decompose the polarization state distribution of the cross-section of the target beam. At each azimuth of the beam cross-section, there should be a corresponding polarized laser. The required structural parameters of the photonic crystal are determined by the corresponding relationship between the obtained structure and polarization. Combining these photonic crystals with the same primitive cells but different hole orientations can design a composite structure for realizing the vector laser.

[0075] Specifically, for a polarization vortex, its topological charge characterizes the change in the polarization distribution therein. For example, for a polarization vortex with a topological charge of q, select a counterclockwise closed path around the vortex center. The polarization state, more specifically, the polarization principal axis, on this path will have a rotational change. The polarization principal axis will rotate counterclockwise q circles around the path for one full circle.

[0076] Therefore, in order to make the polarization state of the laser beam have such a distribution in space, it is necessary to rotate the holes inside each primitive cell in the photonic crystal composite structure along the angular direction to form a periodic arrangement in the angular upward direction. In this way, the photonic crystals at each angle can excite lasers with different polarization states, jointly forming a vector beam with a polarization vortex. And the rotation of the holes does not need to be continuously variable. Selecting the structures corresponding to several representative angles and arranging them periodically around the angular direction can also achieve continuous evolution of polarization and form a polarization vortex. The number of periods of the circular arrangement is equal to the absolute value of the topological charge.

[0077] Figures 8A to 8C The schematic diagram of the construction scheme of the vector laser carrying a -2 topological charge according to some embodiments of the present disclosure is shown. Figure 8A The polarization vortex on the cross-section of the -2 charge vector laser beam is shown, where the arrow represents the representative of the partial polarization state. In fact, the polarization state should be continuously variable within the ring. Figure 8B The actual photonic crystal composite structure drawing for realizing the -2 charge vector laser is shown. The outer ring is the polarization distribution corresponding to the structure distribution, and the gray dashed arrow is used to help analyze the configuration of the vortex. Figure 8C The schematic diagram of the composite photonic crystal structure for realizing the -2 charge vector laser is shown. As Figure 8C shown, in order to generate such a polarization distribution, it is necessary to make the holes inside the composite structure have such a change in the angular direction. It can be seen that this structure is composed of hexagonal primitive cells spliced together, and the holes rotate periodically around the center of the structure. As Figure 8B shown, I represents the first photonic crystal splicing unit, II represents the second photonic crystal splicing unit, and III represents the third photonic crystal splicing unit. Among them, the first, second, and third photonic crystal splicing units form a periodic unit. A -2 charge only requires 2 periodic units (for example, I, II, and III form a periodic unit). Arranging n periodic units counterclockwise / clockwise can obtain a vortex with -n / +n charges.

[0078] Therefore, in the embodiments of the present disclosure, in order to form a combined photonic crystal structure of tunable vector lasers or to generate tunable vector lasers, one or more periodic units are required. Each periodic unit includes a plurality of spliced photonic crystal units arranged in an orderly manner along the angular direction around a central point (such as the central point shown, the black dot shown). Figure 8B As shown, each of the spliced photonic crystal units in each periodic unit supports a linear polarization characteristic. For example, the first spliced photonic crystal unit represented by I supports the first linear polarization characteristic (as shown by the corresponding double arrow), the second spliced photonic crystal unit represented by II supports the second linear polarization characteristic (as shown by the corresponding double arrow), and the third spliced photonic crystal unit represented by III supports the third linear polarization characteristic (as shown by the corresponding double arrow).

[0079] The orderly arrangement of the first number of periodic units along the angular direction around the central point forms a first combined photonic crystal structure. The orderly arrangement of the second number of periodic units along the angular direction around the central point forms a second combined photonic crystal structure, where the first number is different from the second number. Since each spliced photonic crystal unit supports a linear polarization characteristic, and the number and arrangement of the spliced photonic crystal units in the combined photonic crystal structure are different, the topological charge of the vector laser formed by the first combined photonic crystal structure is different from the topological charge of the vector laser formed by the second combined photonic crystal structure. Therefore, a vector laser with controllable topological charge can be realized.

[0080] As Figure 8D shown, six spliced units together form a first combined photonic crystal structure, which can generate a vector laser with a topological charge of -2. The primitive cells of the photonic crystals inside each spliced unit (the six triangular regions that make up the hexagon) are all hexagons, and the inner contour (here it is an elliptical hole) changes periodically in the angular direction (in groups of three, cycling twice).

[0081] As Figure 8E shown, twelve spliced units together form a second combined photonic crystal structure, which can generate a vector laser with a topological charge of -4. The primitive cells of the photonic crystals inside each spliced unit (the six triangular regions that make up the dodecagon) are all hexagons, and the inner contour (here it is an elliptical hole) changes periodically in the angular direction (in groups of three, cycling four times).

[0082] Therefore, it can be seen that in the method of obtaining tunable vector lasers by breaking symmetry as shown in Figure 8D and Figure 8E shown, the outer contours of the primitive cells of all the photonic crystals are consistent hexagons, and the shapes of the inner contours of the primitive cells are also the same, only the orientation of the inner contour shape has changed. However, the outer contours of the two combined photonic crystal structures are different. Figure 8DWhat is shown is a hexagon. Figure 8E What is shown is a dodecagon. However, the external contour of the overall structure is not important as long as the angular arrangement around the center of the structure is correct. The boundary of the external contour of the large structure does not affect the topological charge of the generated laser.

[0083] Therefore, embodiments of the present disclosure propose a design and implementation method for generating lasers with different topological charge vectors. By orderly rotating and combining a photonic crystal array (for example, the orderly arrangement of multiple periodic units along the angular direction around the center point), a composite real-space structure is constructed to edit and realize the polarization distribution configuration of the optical mode of the laser in momentum space. In an active device constructed using a gain medium, a vector laser carrying a topological charge can be directly realized. The topological charge of the vector laser can vary according to different polarization distribution configurations. As Figure 8B and Figure 8C shown, the orderly arrangement of two periodic units in the clockwise or counterclockwise direction constitutes a vector laser with a topological charge of -2. However, if the number of periodic units is different or the arrangement direction is different, a vector laser carrying another topological charge can be formed.

[0084] Some embodiments of the present disclosure are based on the advantages of photonic crystal lasers and the construction principle of the polarization field in momentum space, and establish the correspondence between high-quality factor polarization singularities and photonic crystal structures (that is, each photonic crystal splicing unit in each periodic unit supports a linear polarization characteristic), thereby initially realizing polarization-tunable vertical emission linearly polarized lasers (for example, such as Figure 6C the laser emission shown).

[0085] Next, using the periodic photonic crystal array as a basic unit, different basic units of photonic crystals are orderly arranged around a center to form an overall composite structure (for example, such as Figure 8B , Figure 8D and Figure 8E shown). Such a composite structure will also have a polarization distribution corresponding to the orderly arrangement in real space in the laser light field in momentum space when generating a laser, generating a vector laser carrying a specific topological charge.

[0086] Furthermore, by selecting parameters such as the structural material, period, and thickness of the photonic crystal, based on a suitable gain medium, the wavelength band of laser radiation can be controlled, and a vector laser with a topologically charge that can be designed and controlled can be realized in a wide spectral range. For example, the combined photonic crystal structure can be widely applied to laser emissions in different wavelength bands. By adjusting the basic structural parameters (period, etching duty cycle) and the material selection (dielectric, gain medium), vector lasers in the visible to mid-infrared wavelength bands (for example, the wavelength band is between 400 nm and 5000 nm) can be realized.

[0087] In some embodiments, the linear polarization characteristic represents the linear polarization characteristic of the quasi-bound state (q-BIC) in the quasi-continuous spectrum, as Figure 4B and Figure 4C shown. In some embodiments, all the crystal unit cells of the first photonic crystal splicing unit in the periodic unit have a first structural parameter; all the crystal unit cells of the second photonic crystal splicing unit in the periodic unit have a second structural parameter; and the linear polarization characteristic of the q-BIC supported by the first structural parameter is different from the linear polarization characteristic of the q-BIC supported by the second structural parameter. For example, as Figure 8B shown, the first periodic unit includes three photonic crystal splicing units represented by I, II, and III, and the second periodic unit also includes three photonic crystal splicing units represented by I, II, and III. The three photonic crystal splicing units represented by I, II, and III have different structural parameters respectively, and the linear polarization characteristics of the q-BICs supported by the different structural parameters are also different. For example, Figure 8B the corresponding double arrows. In some embodiments, the inner contour shape of the crystal unit cell (e.g., the internal hole or the dielectric column) has a specific rotational symmetry, and the orientations of the inner contour shapes in the structural parameters of different photonic crystal splicing units are different, but different photonic crystal splicing units have the same outer contour of the crystal unit cell, so as to ensure the compatibility of the combination of linearly polarized lasers in space (i.e., different splicing units can be closely arranged into a whole in real space. Since the cell shape (outer contour) is the same, then to break the symmetry and turn the BIC into a tunable linearly polarized quasi-BIC mode, it is necessary to change the shape of the inner contour of the cell. Further, by changing the orientation of the inner contour (hole or column) of the cell, the linear polarization state of the quasi-BIC mode can be continuously regulated.

[0088] As Figure 8B and 8C shown, the structural parameter of each photonic crystal splicing unit is related to the orientation of the internal hole with a specific rotational symmetry of the included crystal unit cell. The orientations of the internal holes in the same photonic crystal splicing unit are the same, and the orientations of the internal holes in different photonic crystal splicing units are different.

[0089] In some embodiments, the center of the momentum space of a part of the photonic energy bands of the crystal unit cell with the designed structural parameter corresponds to the q-BIC of the linear polarization state. For example, as Figure 4B shown, changing the circular hole into an elliptical hole, the symmetry of the structure also becomes C 2 , and at this time, the BIC with a -2 charge at the center of the momentum space can no longer exist and turns into a quasi-BIC (q-BIC, represented by a double arrow in Figure 4B ) of the linear polarization state. This quasi-BIC can be used to generate linearly polarized laser, and the polarization orientation of this linearly polarized laser (inFigure 4B and Figure 4C the orientation of the arrow) will also change as the orientation of the elliptical hole changes.

[0090] In some embodiments, the ordered arrangement of multiple periodic units in the angular direction is related to the polarization vortex configuration of the target vector laser. For example, by rotating the holes inside each primitive cell in the photonic crystal composite structure along the angular direction to form a periodic arrangement in the angle, the photonic crystals at each angle can excite lasers with different polarization states, jointly forming a vector beam with a polarization vortex.

[0091] Therefore, by designing and adjusting the structural parameters of the photonic crystal through the evolution relationship of the bound states in the continuum under the broken structural symmetry of the photonic crystal, a quasi-bound state in the continuum mode (q-BIC) with a high-quality factor of the linear polarization state can be generated, which is excited to obtain a vertically emitted laser with a linear polarization state in the presence of a gain medium.

[0092] By only changing the orientation of some characteristic structures in the primitive cell of the photonic crystal, such as the orientation of the internal holes or the shape of the dielectric pillars in the primitive cell of the photonic crystal, the orientation of the high-quality factor linear polarization state can be further adjusted, thereby realizing a laser with an adjustable linear polarization state.

[0093] Taking such a periodically photonic crystal structure with adjusted structural parameters as a splicing unit, by orderly rotating and splicing the photonic crystals, the high-quality factor quasi-bound state optical modes of the formed photonic crystal composite structure also present a specific polarization distribution in the momentum space. Therefore, when stimulated by a gain medium, a laser with a corresponding polarization distribution is generated. By considering the laser light field with a specific polarization distribution, it can be mapped to a specific photonic crystal splicing composite structure according to the corresponding relationship between the photonic crystal structure and its quasi-bound state in the continuum, and thus a vector laser carrying any topological charge can be realized.

[0094] Therefore, the present disclosure can make up for various deficiencies in the traditional technology. For example, by utilizing the quasi-bound state optical modes generated by the photonic crystal slab after the broken structural symmetry, such optical modes have the characteristics of high-quality factors, and these quasi-bound states in the continuum are at the bottom or top of the energy band, with a high photon state density, and both can well meet the basic conditions for laser emission, and the realized laser has good directivity.

[0095] For the topological charge control of the laser radiation light field, the present disclosure utilizes the hidden topological correspondence relationship between the photonic crystal structure and the linear polarization characteristics of the quasi-bound state in the continuum. The linear polarization characteristics of the bound state in the continuum can continuously change with the change of the orientation of the internal structure of the primitive cell of the photonic crystal structure, and this continuity enables the realization of the expected continuous polarization change through a finite number of photonic crystals.

[0096] Based on this correspondence, the present disclosure proposes to splice photonic crystals with the orientations of the internal structures of different unit cells to form a combined photonic crystal. The topological charge required by the vector laser can be matched by adjusting the number of blocks and the arrangement of the combined photonic crystal. This arrangement is based on the hidden topological correspondence between the photonic crystal structure and the linearly polarized characteristics of the bound states in the quasi-continuous spectrum. Starting from the polarization distribution of the target light field, the rotational arrangement of the photonic crystal structure is inversely designed, greatly broadening the degree of freedom in the design of vector lasers. Therefore, the construction of vector lasers with arbitrary-order topological charges can be realized, such that the polarization configuration of the excited vector beam is not restricted by the symmetry of a single photonic crystal.

[0097] Return to reference Figure 1 , in step 105, a micro vector laser is realized. Specifically, according to the method in step 104, the arrangement of the photonic crystal composite structure is designed. A thin film of the required structure is grown using semiconductor processes and micro-nano processing technologies, and then the designed photonic crystal structure is fabricated through patterning processes such as electron beam lithography and reactive ion etching. After the sample preparation is completed, vector laser emission is realized by optical pumping or electrical pumping. Figure 9 Shows a picture of the momentum space of a vector laser carrying a -2 topological charge according to some embodiments of the present disclosure. Polarization vortex configurations of the target can be verified by polarization measurement in the momentum space. In other words, Figure 9 For the vector laser realized according to the designed photonic crystal composite structure, the polarization state distribution of the beam cross-section is verified by measuring its momentum space imaging. The leftmost figure is the momentum space imaging without polarization analysis, and the beam shows a hollow circular ring shape, conforming to the characteristics of a polarization vortex beam. Figure 9 The four rightmost figures are the momentum space imaging after linear polarization analysis, and the analysis directions are indicated by the double arrows below the pictures, conforming to the designed polarization vortex distribution.

[0098] Figure 10 Illustrates a method for designing a combined photonic crystal structure used to generate tunable vector lasers according to some embodiments of the present disclosure.

[0099] In block 1001, a periodic unit of the combined photonic crystal structure is designed. The periodic unit includes a plurality of photonic crystal splicing units arranged in an orderly manner along the angular direction, and each of the photonic crystal splicing units supports a linearly polarized characteristic. In some embodiments, the combined photonic crystal structure utilizes the bound states in the quasi-continuous spectrum after the symmetry of the photonic crystal is broken.

[0100] In block 1002, based on the polarization configuration of the target vector laser and the required topological charge, one or more periodic units are arranged in an angular direction around the center point to form a combined photonic crystal structure. Since each of the photonic crystal splicing units supports a linear polarization characteristic, there is a hidden topological correspondence between the structural parameters (e.g., internal orientation) of the primitive cell of the photonic crystal structure of the photonic crystal splicing unit and the linear polarization characteristic of the bound state in the quasi-continuous spectrum. Given the polarization configuration and topological charge of the target vector laser, this topological correspondence can be used to arrange multiple periodic units in an orderly manner to obtain the target polarization configuration. In other words, this combined photonic crystal structure utilizes the hidden topological correspondence between the structural parameters (e.g., internal orientation) of the primitive cell of the photonic crystal structure and the linear polarization characteristic of the bound state in the quasi-continuous spectrum, and thus, using this correspondence, periodic photonic crystals are used as splicing units to be arranged around a center in an orderly manner to design a combined photonic crystal structure, realizing the regulation of the polarization distribution of the light field of the laser.

[0101] In some embodiments, designing the periodic unit of the combined photonic crystal structure includes: determining the correspondence between the structural parameters of the crystal primitive cell of each photonic crystal splicing unit and the linear polarization characteristic of the bound state (q-BIC) in the quasi-continuous spectrum it supports; and determining multiple photonic crystal splicing units in the periodic unit based on the correspondence.

[0102] In some embodiments, to determine the correspondence between the structural parameters of the crystal primitive cell and the linear polarization characteristic of the bound state (q-BIC) in the quasi-continuous spectrum it supports, the following operations need to be performed: Based on the target wavelength band of the vector laser, select the material for preparing the combined photonic crystal structure (e.g., step 101 as shown Figure 1 ). This operation also includes: Based on the selected material, determine the structural parameters of the crystal primitive cell of the combined photonic crystal structure, which can achieve the bound state (q-BIC) in the quasi-continuous spectrum with an adjustable linear polarization state that conforms to the target wavelength band (e.g., step 102 as shown Figure 1 ). This operation further includes: Prepare a series of photonic crystal slabs with different structural parameters, and test the polarization states corresponding to the q-BIC modes of the corresponding photonic crystal slabs; Based on the test results, verify whether each photonic crystal slab in the series of photonic crystal slabs can achieve a linearly polarized photonic crystal laser; and in response to being able to achieve a linearly polarized photonic crystal laser, determine that a specific structural parameter corresponds to the linear polarization characteristic of a specific bound state (q-BIC) in the quasi-continuous spectrum to obtain the correspondence, e.g., Figure 1 step 103 as shown.

[0103] A method of designing a combined photonic crystal structure for generating an adjustable vector laser according to some embodiments of the present disclosure is based on the hidden topological correspondence between the orientation of the internal structure of the primitive cell of the photonic crystal structure and the linearly polarized characteristics of the bound states in the quasi-continuous spectrum to design the combined photonic crystal. In addition, a periodic photonic crystal is used as a structural unit to orderly splice around a center in real space to construct a combined photonic crystal to achieve vector laser. For example, photonic crystal structures with different structural parameters (such as the orientation of holes in a slab) are arranged angularly around a geometric center periodically to construct a combined photonic crystal structure that generates vector lasers carrying different topological charges. The number of angular periods and the arrangement order determine the topological charge of the vector beam.

[0104] Without prejudice to the basic principles, details and embodiments may vary, even significantly, from what is described by way of example only, without departing from the scope of protection.

[0105] The various embodiments described above may be combined to provide additional embodiments. Aspects of the embodiments may be modified if concepts from various patents, applications and publications are needed to provide further embodiments.

[0106] These and other changes may be made to the embodiments in light of the above detailed description. Generally, in the following claims, the terms used should not be construed as limiting the claims to the specific embodiments disclosed in the specification and claims, but should be construed to include all possible embodiments and the full scope of equivalents to such claims. Thus, the claims are not limited by the disclosure.

Claims

1. A combined photonic crystal structure for generating adjustable vector lasers, comprising: One or more periodic units, each periodic unit includes a plurality of photonic crystal splicing units arranged in an orderly manner along an angular direction around a center point, wherein each photonic crystal splicing unit in each periodic unit supports a linear polarization characteristic, wherein a first number of the periodic units are arranged in an orderly manner around the center point along the angular direction to form a first combined photonic crystal structure; A second number of the periodic units are arranged in an orderly manner around the center point along the angular direction to form a second composite photonic crystal structure; and The topological charge of the vector laser formed by the first combined photonic crystal structure is different from the topological charge of the vector laser formed by the second combined photonic crystal structure, so as to realize vector laser with controllable topological charge.

2. The combined photonic crystal structure according to claim 1, wherein: The linear polarization characteristics include linear polarization characteristics of bound states (q-BIC) in a quasi-continuum spectrum; All crystal primitives of the first photonic crystal splicing unit in the periodic unit have first structural parameters; All crystal primitives of the second photonic crystal tiling unit in the periodic unit have second structural parameters; and The linear polarization characteristics of the q-BIC supported by the first structural parameters are different from the linear polarization characteristics of the q-BIC supported by the second structural parameters.

3. The combined photonic crystal structure according to claim 2, wherein The structural parameters are related to the orientation of the inner contour shape with a certain rotational symmetry, The orientation of the inner contour shape in the first structural parameter of the first photonic crystal splicing unit is different from the orientation of the inner contour shape in the second structural parameter of the second photonic crystal splicing unit, and The first photonic crystal splicing unit and the second photonic crystal splicing unit have the same outer contour of the crystal primitive cell. 4 . The composite photonic crystal structure according to claim 3 , wherein the inner contour shape comprises a shape of an internal hole of the crystal unit cell or a shape of a dielectric column of the crystal unit cell.

5. The combined photonic crystal structure according to claim 4, wherein The orientation of the inner contour shape of the crystal unit cell is related to the direction of the long axis of the shape of the internal hole or the dielectric column.

6. The combined photonic crystal structure according to any one of claims 2 to 5, wherein the center of the momentum space of the partial photonic band of the crystal unit cell having the designed structural parameters corresponds to the q-BIC of the linear polarization state.

7. The combined photonic crystal structure according to any one of claims 1 to 6, wherein the orderly arrangement of the plurality of periodic units along the angular direction is associated with a polarization vortex configuration of a target vector laser.

8. The combined photonic crystal structure according to any one of claims 1 to 7, wherein the wavelength of the vector laser light is in the range of 400 nm to 5000 nm.

9. A method for designing a combined photonic crystal structure used to generate tunable vector laser light, comprising: Designing a periodic unit of the combined photonic crystal structure so that the periodic unit includes a plurality of photonic crystal splicing units arranged in an orderly manner along an angular direction, each of the photonic crystal splicing units supports a linear polarization characteristic; and Based on the polarization configuration of the target vector laser and the required topological charge, one or more of the periodic units are orderly arranged in an angular direction around the center point to form the combined photonic crystal structure. Among them, the ordered arrangement of the first number of periodic units around the center point along the angular direction can form a first combined photonic crystal structure, the ordered arrangement of the second number of periodic units around the center point along the angular direction can form a second combined photonic crystal structure, and the topological charge of the vector laser formed by the first combined photonic crystal structure is different from the topological charge of the vector laser formed by the second combined photonic crystal structure, so as to realize a vector laser with controllable topological charge.

10. The method according to claim 9, wherein designing the periodic unit of the combined photonic crystal structure comprises: Determine the correspondence between the structural parameters of the crystal unit cell of each photonic crystal tiling unit and the linear polarization characteristics of the bound state (q-BIC) in the quasi-continuum spectrum it supports; and Based on the corresponding relationship, a plurality of photonic crystal splicing units in the periodic unit are determined.

11. The method according to claim 10, wherein determining the correspondence between the structural parameters of the crystal unit cell and the linear polarization characteristics of the bound state (q-BIC) in the quasi-continuum spectrum it supports comprises: Based on the target wavelength band of the vector laser, selecting a material for preparing the combined photonic crystal structure; Based on the selected materials, determining the structural parameters of the crystal unit cell of the combined photonic crystal structure, wherein the structural parameters can realize a quasi-continuous spectrum bound state (q-BIC) with an adjustable linear polarization state conforming to the target band; Prepare a series of photonic crystal slabs with different structural parameters, and test the corresponding polarization states of lasers generated by the corresponding photonic crystal slabs; Based on the test results, verify whether each photonic crystal slab in the series of photonic crystal slabs can realize linearly polarized photonic crystal laser; and In response to being able to realize linearly polarized photonic crystal laser, it is determined that a specific structural parameter corresponds to a specific linear polarization characteristic of a bound state (q-BIC) in the quasi-continuous spectrum to obtain the corresponding relationship.

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