Construction method of multimode topological slow light waveguide

Abstract

The present invention belongs to the field of integrated optical technology, and in particular, relates to a method for constructing a multimode topological slow light waveguide. The method includes: S1: constructing a topological photonic crystal; S2: setting a resonant cavity array at the boundary of a first magneto-optical photonic crystal and a second magneto-optical photonic crystal; S3: adjusting the size of each resonant cavity contained in the resonant cavity array based on the preset slow light bandwidth of the multimode topological slow light waveguide; S4: constructing a mode matching mechanism, and based on the mode matching mechanism, performing mode matching on the topological boundary mode between the first magneto-optical photonic crystal and the second magneto-optical photonic crystal and the resonant cavity mode of each resonant cavity; S5: detecting whether there is an asymmetric obstacle in the transmission path of the multimode topological slow light waveguide, if so, performing a broken mirror symmetry perturbation design on the topological photonic crystal to complete the construction of the multimode topological slow light waveguide, otherwise completing the construction of the multimode topological slow light waveguide. The present invention can achieve group velocity selective regulation.

Description

Technical Field

[0001] The invention belongs to the technical field of integrated optics, and in particular relates to a method for constructing a multi-mode topological slow light waveguide. Background Art

[0002] Slow light technology is to enhance the interaction between light and matter by reducing the transmission speed of light. In recent years, on-chip devices based on slow light waveguides have been widely used in biochemical sensing, optical modulation, optical storage, optical communication and nonlinear optics. Periodic optical resonant cavity arrays and photonic crystal waveguides are the two most commonly used integrated slow light waveguide structures, which have the advantages of flexible design, high group refractive index and compatibility with silicon-based integration processes. However, due to the limitations of micro-nano optical preparation processes, when the group refractive index of the slow light device exceeds 30, the transmission loss is as high as 100 dB / cm, which makes the slow light device unable to be used in practice.

[0003] The non-trivial band structure of topological photonic crystals can effectively suppress the backscattering loss caused by processing defects. Therefore, topological photonic crystal waveguides can break through the bottleneck of the transmission length of slow light integrated devices. In addition, the topological photonic crystal waveguide based on magneto-optical media can not only obtain an average group refractive index of more than 40 through the Brillouin zone winding mechanism of the band structure, but also has achieved a continuous wide spectrum of more than 1.5 GHz in the microwave spectrum. In addition, the above-mentioned topological slow light mechanism also has extremely small group velocity dispersion properties, which can effectively suppress pulse broadening. In summary, this technology is currently the most promising broadband slow light solution.

[0004] However, due to the restrictions on the number of modes and the control mechanism in topological photonics, topological slow light waveguides are currently unable to achieve important functions such as slow light mode mode division multiplexing and group velocity fidelity. Specifically, they include: 1. Limitation on the number of modes: Most existing topological slow light waveguides only support a single mode. Although this reduces the complexity of control, they have three main disadvantages: a. The transmission capacity of a single mode is limited, and the mode division multiplexing function cannot be achieved; b. The mode is confined to the topological boundary, and the mode area is small, resulting in low coupling efficiency of the topological slow light waveguide; c. Key on-chip functions such as mode conversion, group velocity switching, and multi-mode interference cannot be achieved. 2. For multi-mode waveguides, their slow light control mechanism has the following limitations: a. There is a lack of group velocity selectivity control function. Usually, the group velocities of multiple modes increase or decrease synchronously, making it difficult to achieve a large group velocity contrast; b. For slow light waveguides that support odd and even modes, when there are non-mirror-symmetric defects or obstacles, mode conversion is inevitable, resulting in group velocity fidelity. In response to the above problems, it is urgent to break through the mode control mechanism of slow topology slow light waveguide and realize the group velocity control and fidelity of multi-mode broadband slow light waveguide. Summary of the invention

[0005] The present invention aims to solve the problem of lack of group velocity selection control mechanism in topological optical waveguides, and adopts two topological photonic crystals with opposite magnetization directions to construct a multimode topological optical waveguide. The mirror symmetry of the photonic crystals ensures the existence of multiple orthogonal topological boundary modes of odd and even field distribution. At the same time, a resonant cavity array is designed at the topological boundary to control the symmetry matching coupling between the topological boundary mode and the resonant cavity mode, so as to realize the selective control of the group velocity of different modes. However, the existing multimode topological optical waveguide lacks the mode selective matching coupling mechanism and cannot realize the selective control of the group velocity. Secondly, in view of the problem of lack of slow light mode mode division multiplexing function in topological optical waveguides, the quasi-degenerate orthogonal resonant mode (coexistence of resonant cavity odd mode and resonant cavity even mode) is used to realize the precise control of the slow light frequency and group velocity of the multimode optical waveguide mode. However, the existing technology is limited by the dispersion engineering control mechanism, lacks the ability to accurately and selectively control the multi-mode resonant frequency, and cannot realize the function of broadband slow light mode division multiplexing. Finally, in order to address the shortcoming that the group velocity in slow multimode optical waveguides is sensitive to defects, a topological photonic crystal with symmetry perturbation design is used to break the orthogonality of the waveguide mode, thereby achieving the topological waveguide mode's defect immunity and group velocity fidelity preservation functions.

[0006] In view of this, the present invention aims to provide a method for constructing a multimode topological slow light waveguide to solve the problems in the prior art, such as the lack of group velocity selection control mechanism in the topological optical waveguide, the lack of mode selective matching coupling mechanism in the multimode topological optical waveguide, the lack of slow light mode mode division multiplexing function in the topological optical waveguide, and the lack of ability to accurately and selectively control the multimode resonant frequency due to the limitation of the dispersion engineering control mechanism. The present invention solves the problems of the lack of group velocity selective control, slow light mode mode division multiplexing and group velocity fidelity in the topological photonic crystal waveguide.

[0007] To achieve the above object, the technical solution created by the present invention is implemented as follows:

[0008] A method for constructing a multimode topological slow light waveguide, wherein the multimode topological slow light waveguide is used to realize group velocity regulation, specifically comprising the following steps:

[0009] S1: construct a topological photonic crystal, the topological photonic crystal comprising a first magneto-optical photonic crystal and a second magneto-optical photonic crystal with opposite magnetization directions;

[0010] S2: setting a resonant cavity array at the boundary between the first magneto-optical photonic crystal and the second magneto-optical photonic crystal;

[0011] S3: adjusting the size of each resonant cavity included in the resonant cavity array based on the preset slow light bandwidth of the multi-mode topological slow light waveguide, so that the resonant frequency of each resonant cavity enters the topological band gap of the topological photonic crystal;

[0012] S4: Construct a mode matching mechanism, and based on the mode matching mechanism, perform mode matching on the topological boundary mode between the first magneto-optical photonic crystal and the second magneto-optical photonic crystal and the resonant cavity mode of each resonant cavity, so that the group velocity of the multi-mode topological slow light waveguide is less than c / 100, c is the speed of light in a vacuum;

[0013] S5: Detect whether there are asymmetric obstacles in the transmission path of the multi-mode topological slow light waveguide. If so, perform mirror symmetry breaking perturbation design on the topological photonic crystal to complete the construction of the multi-mode topological slow light waveguide. Otherwise, complete the construction of the multi-mode topological slow light waveguide.

[0014] Further, in step S1, the first magneto-optical photonic crystal and the second magneto-optical photonic crystal are both composed of magneto-optical medium pillars arranged periodically;

[0015] The material of the magneto-optical medium column is yttrium iron garnet, and the radius of the magneto-optical medium column is 0.0975 a , the dielectric constant of yttrium iron garnet is 14.63;

[0016] The background medium of the first magneto-optical photonic crystal and the second magneto-optical photonic crystal is air;

[0017] The lattices of the first magneto-optical photonic crystal and the second magneto-optical photonic crystal are both square lattices. a is the lattice constant of the square lattice, and each lattice has a magneto-optical medium column built in it.

[0018] Furthermore, the magnetic permeability tensor of yttrium iron garnet for:

[0019] ;

[0020] in, , , is the off-diagonal magnetic permeability, the off-diagonal magnetic permeability of the first magneto-optical photonic crystal is 12.4, the off-diagonal magnetic permeability of the second magneto-optical photonic crystal is -12.4, and i is an imaginary unit.

[0021] Furthermore, in step S2, the resonant cavity array includes periodically arranged resonant cavities, all of which are filled with a dielectric having a refractive index of 3, and both side surfaces of each resonant cavity are narrow strips of perfect conductors.

[0022] Furthermore, step S3 specifically includes the following steps:

[0023] S31: Based on the preset slow light bandwidth of the multimode topological slow light waveguide and the topological band gap of the topological photonic crystal, determining the resonant frequency adjustment range of the resonant cavity array within a single cycle;

[0024] S32: based on the group velocity adjustment value set by the user, the resonant frequency in the resonant frequency adjustment interval is divided into h equal parts to obtain h resonant frequency values ​​to be calculated, and the size of each resonant cavity is calculated based on each resonant frequency value to be calculated to obtain the size of each resonant cavity in a single period;

[0025] S33: adjusting the size of each resonant cavity included in the resonant cavity array according to the arrangement rule of each resonant cavity of different sizes within a single period, so that the resonant frequencies of all the resonant cavities enter the topological band gap of the topological photonic crystal.

[0026] Further, in step S31, the difference between the upper adjustment limit and the lower adjustment limit of the resonance frequency adjustment interval is equal to the preset slow light bandwidth value, and the resonance frequency adjustment interval of the resonant cavity array is located in the center area of ​​the topological band gap of the topological photonic crystal.

[0027] Furthermore, the specific steps of step S32 include:

[0028] S321: Calculate the initial group velocity of the current multimode topology slow light waveguide:

[0029] Initial group velocity = preset slow light bandwidth / wave vector change;

[0030] S322: Determine the number h of resonant frequencies to be calculated within the resonant frequency adjustment interval according to the group velocity adjustment value set by the user:

[0031] h=(initial group velocity / group velocity adjustment value)-1;

[0032] Wherein, the initial group velocity / group velocity adjustment value is rounded off;

[0033] S323: dividing the resonant frequency within the resonant frequency adjustment interval into h equal parts and performing normalization processing thereon to obtain h normalized resonant frequency values ​​to be calculated;

[0034] S324: Substitute the values ​​of the resonant frequencies to be calculated into the following formula in turn to calculate the corresponding dimensions of the resonant cavity:

[0035]

[0036] in, f 0 is the current resonant frequency value to be calculated, p , q =1, 2…are the mode orders in the width and height directions of the resonant cavity respectively, n eff is the equivalent refractive index of the resonant cavity mode, is the width of the resonant cavity, is the height of the resonant cavity, a is the lattice constant.

[0037] Further, in step S4, the topological boundary mode of the transverse magnetic polarization with mirror symmetry is taken as the topological boundary even mode, the topological boundary mode of the transverse magnetic polarization with mirror antisymmetry is taken as the topological boundary odd mode, the resonant cavity mode of the transverse magnetic polarization with mirror symmetry is taken as the resonant cavity even mode, and the resonant cavity mode of the transverse magnetic polarization with mirror antisymmetry is taken as the resonant cavity odd mode.

[0038] Further, in step S4, the mode matching mechanism is: the resonant cavity even mode is mode-coupled with the topological boundary even mode, and the resonant cavity odd mode is mode-coupled with the topological boundary odd mode;

[0039] If there is only a resonant cavity odd mode in the topological band gap of the topological photonic crystal, the resonant cavity odd mode is coupled with the topological boundary odd mode according to the mode matching mechanism, so as to realize the group velocity control of the multimode topological slow light waveguide, generate an odd mode of topological slow light, and keep the group velocity of the topological boundary even mode unchanged;

[0040] If there is only a resonant cavity even mode in the topological band gap of the topological photonic crystal, according to the mode matching mechanism, the resonant cavity even mode is mode-coupled with the topological boundary even mode, so as to achieve group velocity control of the multimode topological slow light waveguide, generate even-mode topological slow light, and keep the group velocity of the topological boundary odd mode unchanged;

[0041] If both the resonant cavity odd mode and the resonant cavity even mode exist in the topological band gap of the topological photonic crystal, that is, the resonant cavity odd mode and the resonant cavity even mode are in a quasi-degenerate state, the resonant cavity odd mode is matched with the topological boundary odd mode, and the resonant cavity even mode is matched with the topological boundary even mode, thereby realizing the wavelength division multiplexing function of the slow light mode of the multi-mode topological slow light waveguide.

[0042] Furthermore, in step S5, the specific process of performing broken mirror symmetry perturbation design on the topological photonic crystal is: reducing the cylindrical radius of the magneto-optical medium column adjacent to the topological boundary in the first magneto-optical photonic crystal to 70% of the original cylindrical radius.

[0043] Compared with the prior art, the invention can achieve the following beneficial effects:

[0044] The invention creates a construction method for the multimode topological slow light waveguide, which solves the problem of selective regulation of group velocity in the topological optical waveguide. The invention realizes the multimode topological optical waveguide by adopting two magneto-optical photonic crystals with opposite magnetization directions, and then selectively reduces the group velocity of the symmetry matching mode by designing a periodic array of resonant cavities, thereby realizing mode selective regulation and a great group velocity contrast between odd and even modes, and increasing the mode area, thereby improving the coupling efficiency of light input and output of the multimode topological slow light waveguide; the invention realizes topological slow light mode division multiplexing based on the coupling of multiple quasi-degenerate resonant cavity modes (coexistence of resonant cavity odd modes and resonant cavity even modes) and topological boundary modes; the invention adopts symmetry perturbation photonic crystals to solve the problem of defect-induced mode conversion, thereby realizing the group velocity fidelity function. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] The drawings constituting part of the present invention are used to provide a further understanding of the present invention. The exemplary embodiments and descriptions of the present invention are used to explain the present invention and do not constitute an improper limitation on the present invention. In the drawings:

[0046] Figure 1 A schematic diagram of a process for constructing a multimode topological slow light waveguide according to an embodiment of the present invention;

[0047] Figure 2 A schematic diagram of the structure of a multi-mode topological slow light waveguide according to an embodiment of the present invention;

[0048] Figure 3 A schematic diagram of the structure of the resonant cavity described in the embodiment of the present invention;

[0049] Figure 4 A schematic diagram of the out-of-plane electric field distribution of the odd and even modes described in the embodiments of the present invention;

[0050] Figure 5 A schematic diagram of the energy band structure of the topological boundary mode described in the embodiment of the present invention;

[0051] Figure 6 A schematic diagram showing a comparison of the maximum group velocities of the odd and even modes described in an embodiment of the present invention;

[0052] Figure 7 A schematic diagram of the structure of the multimode topological slow light waveguide and the electric field distribution of the eigenmode described in the embodiment of the present invention;

[0053] Figure 8 A schematic diagram of slow light control based on two resonant cavities in even modes according to an embodiment of the present invention;

[0054] Fig. 9 A schematic diagram of slow light control based on three types of resonant cavities in even modes according to an embodiment of the present invention;

[0055] Fig.10 A schematic diagram of slow light control of a resonant cavity based on an odd mode according to an embodiment of the present invention;

[0056] Fig.11 A schematic diagram of slow light control based on two odd-mode resonant cavities according to an embodiment of the present invention;

[0057] Fig.12 A schematic diagram of slow light control based on three odd-mode resonant cavities according to an embodiment of the present invention;

[0058] Fig.13 A trend diagram showing the resonant frequency of the resonant cavity mode according to the embodiment of the present invention changing with the height and width of the resonant cavity;

[0059] Fig.14 A schematic diagram of the electric field distribution of the resonant cavity mode described in the embodiment of the present invention;

[0060] Fig.15 A schematic diagram of slow light mode division multiplexing of odd and even modes of a resonant cavity according to an embodiment of the present invention;

[0061] Fig.16 A schematic diagram of the symmetry perturbation design of the topological photonic crystal described in the embodiment of the present invention;

[0062] Fig.17 A schematic diagram of the energy band structure of the quasi-odd-even mode described in an embodiment of the present invention;

[0063] Fig.18 The calculation results of the group velocity fidelity of the quasi-odd and quasi-even modes described in the embodiments of the present invention are created;

[0064] Fig.19 A schematic diagram of the quasi-odd mode group velocity fidelity function described in an embodiment of the present invention;

[0065] Fig. 20 A schematic diagram of the quasi-even mode group velocity fidelity function described in an embodiment of the present invention.

[0066] Description of reference numerals:

[0067] 1. A first magneto-optical photonic crystal; 2. A second magneto-optical photonic crystal; 3. A resonant cavity array. DETAILED DESCRIPTION

[0068] In order to make the purpose, technical solution and advantages of the invention more clear, the invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described here are only used to explain the invention and do not constitute a limitation of the invention.

[0069] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0070] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention. In addition, the terms "first", "second", etc. are only used for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, features defined as "first", "second", etc. may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0071] In the description of the invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installation", "connection" and "connection" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the invention can be understood according to specific circumstances.

[0072] The present invention will be described in detail below with reference to the accompanying drawings and in combination with embodiments.

[0073] like Figure 1 As shown, the present invention proposes a method for constructing a multimode topological slow light waveguide, which is used to achieve group velocity control, and specifically includes the following steps:

[0074] S1: construct a topological photonic crystal, which includes a first magneto-optical photonic crystal 1 and a second magneto-optical photonic crystal 2 with opposite magnetization directions.

[0075] S2: Arranging a resonant cavity array 3 at the boundary between the first magneto-optical photonic crystal 1 and the second magneto-optical photonic crystal 2;

[0076] In step S2, the resonant cavity array 3 includes periodically arranged resonant cavities, all of which are filled with a dielectric having a refractive index of 3, and both side surfaces of each resonant cavity are narrow strips of perfect conductors.

[0077] S3: adjusting the size of each resonant cavity included in the resonant cavity array 3 based on the preset slow light bandwidth of the multi-mode topological slow light waveguide, so that the resonant frequency of each resonant cavity enters the topological band gap of the topological photonic crystal;

[0078] S31: Based on the preset slow-light bandwidth of the multi-mode topological slow-light waveguide and the topological band gap of the topological photonic crystal, determining the resonant frequency adjustment range of the resonant cavity array 3 within a single cycle.

[0079] S32: based on the group velocity adjustment value set by the user, the resonant frequency in the resonant frequency adjustment interval is divided into h equal parts to obtain h resonant frequency values ​​to be calculated, and the size of each resonant cavity is calculated based on each resonant frequency value to be calculated to obtain the size of each resonant cavity in a single period;

[0080] S321: Calculate the initial group velocity of the current multimode topology slow light waveguide:

[0081] Initial group velocity = preset slow light bandwidth / wave vector change;

[0082] S322: Determine the number h of resonant frequencies to be calculated within the resonant frequency adjustment interval according to the group velocity adjustment value set by the user:

[0083] h=(initial group velocity / group velocity adjustment value)-1;

[0084] The initial group velocity / group velocity adjustment value is rounded off; the number of resonant frequency values ​​to be calculated is the same as the number of resonant cavities in a single period.

[0085] S323: dividing the resonant frequency within the resonant frequency adjustment interval into h equal parts and performing normalization processing thereon to obtain h normalized resonant frequency values ​​to be calculated;

[0086] S324: Substitute the values ​​of the resonant frequencies to be calculated into the following formula in turn to calculate the corresponding dimensions of the resonant cavity:

[0087]

[0088] in, f 0 is the current resonant frequency value to be calculated, p , q =1, 2…are the mode orders in the width and height directions of the resonant cavity respectively, n eff is the equivalent refractive index of the resonant cavity mode, is the width of the resonant cavity, is the height of the resonant cavity, a is the lattice constant.

[0089] During the calculation process, the width (or height) of the resonant cavity is preset first, and then the height (or width) of the resonant cavity is adjusted accordingly according to the formula.

[0090] S33: adjusting the size of each resonant cavity included in the resonant cavity array 3 according to the arrangement rule of each resonant cavity of different sizes within a single period, so that the resonant frequency of all the resonant cavities enters the topological band gap of the topological photonic crystal.

[0091] Since the resonant cavities included in the resonant cavity array 3 are arranged periodically, if the arrangement rule of the width values ​​of the resonant cavities in a single period is known, the width of each resonant cavity included in the resonant cavity array 3 can be adjusted according to the arrangement rule.

[0092] S4: Construct a mode matching mechanism, and based on the mode matching mechanism, perform mode matching on the topological boundary mode between the first magneto-optical photonic crystal 1 and the second magneto-optical photonic crystal 2 and the resonant cavity mode of each resonant cavity, so that the group velocity of the multi-mode topological slow light waveguide is less than c / 100, c is the speed of light in a vacuum;

[0093] The topological boundary mode of transverse magnetic polarization with mirror symmetry is regarded as the topological boundary even mode, the topological boundary mode of transverse magnetic polarization with mirror antisymmetry is regarded as the topological boundary odd mode, the resonant cavity mode of transverse magnetic polarization with mirror symmetry is regarded as the resonant cavity even mode, and the resonant cavity mode of transverse magnetic polarization with mirror antisymmetry is regarded as the resonant cavity odd mode.

[0094] Due to the orthogonality of the modes, the mode matching mechanism is: the resonant cavity even mode is mode-coupled with the topological boundary even mode, and the resonant cavity odd mode is mode-coupled with the topological boundary odd mode;

[0095] If there is only a resonant cavity odd mode in the topological band gap of a topological photonic crystal, the resonant cavity odd mode is mode-coupled with the topological boundary odd mode according to the mode matching mechanism, thereby realizing group velocity control of the multimode topological slow light waveguide, generating odd-mode topological slow light, and keeping the group velocity of the topological boundary even mode unchanged. This is because for the topological boundary even mode, since there is no resonant cavity even mode at the topological band gap frequency, mode coupling does not occur, that is, the group velocity remains unchanged.

[0096] If there is only a resonant cavity even mode in the topological band gap of the topological photonic crystal, according to the mode matching mechanism, the resonant cavity even mode is mode-coupled with the topological boundary even mode, so as to achieve group velocity control of the multimode topological slow light waveguide, generate even-mode topological slow light, and keep the group velocity of the topological boundary odd mode unchanged;

[0097] If both the resonant cavity odd mode and the resonant cavity even mode exist in the topological band gap of the topological photonic crystal, that is, the resonant cavity odd mode and the resonant cavity even mode are in a quasi-degenerate state, the resonant cavity odd mode is matched with the topological boundary odd mode, and the resonant cavity even mode is matched with the topological boundary even mode, thereby realizing the wavelength division multiplexing function of the slow light mode of the multi-mode topological slow light waveguide.

[0098] S5: Detect whether there are asymmetric obstacles in the transmission path of the multi-mode topological slow light waveguide. If so, perform mirror symmetry breaking perturbation design on the topological photonic crystal to complete the construction of the multi-mode topological slow light waveguide with group velocity fidelity function. Otherwise, complete the construction of the multi-mode topological slow light waveguide with group velocity fidelity function.

[0099] The specific process of breaking mirror symmetry perturbation design for topological photonic crystals is: reducing the cylindrical radius of the magneto-optical medium column adjacent to the topological boundary in the first magneto-optical photonic crystal 1 to 70% of the original cylindrical radius. The topological optical waveguide mode is transformed from an orthogonal odd-even mode to a non-orthogonal quasi-odd-even mode, and the ratio of the group velocity of the even mode to the odd mode is greater than 100. When there is an asymmetric obstacle with a width of a and a length of 3.4a, it is proved by mode analysis that the odd mode group velocity fidelity exceeds 98% and the even mode fidelity exceeds 99.8%. The present invention exhibits excellent mode conversion suppression capability.

[0100] Topological optical waveguide modes are very sensitive to defects that break mirror symmetry (asymmetric obstacles). During transmission, odd and even modes convert to each other, which will cause group velocity distortion. Therefore, by designing a preset symmetry perturbation for topological photonic crystals, the topological optical waveguide modes that break mirror symmetry still have similar characteristics of odd and even modes. Even if the topological boundary mode and the resonant cavity mode change from an orthogonal state to a weakly coupled state, the perturbation mode can ensure near-perfect suppression of mode conversion and achieve group velocity fidelity.

[0101] like Figure 2 As shown, the topological photonic crystal includes a first magneto-optical photonic crystal 1 and a second magneto-optical photonic crystal 2 with opposite magnetization directions and a resonant cavity array 3 as an intermediate sandwich structure. The first magneto-optical photonic crystal 1 and the second magneto-optical photonic crystal 2 are both composed of periodically arranged magneto-optical medium columns. By constructing a photonic band structure with a Dirac cone shape and combining magneto-optical materials to break the time reversal symmetry, a topological photonic crystal with a complete topological band gap is realized. According to the body-edge correspondence in topological theory, two magneto-optical photonic crystals with opposite magnetization directions generate an even number of topological chiral boundary modes at the junction, which can show excellent anti-scattering robustness far exceeding that of traditional optical waveguides.

[0102] The material of the magneto-optical medium column is yttrium iron garnet, and the radius of the magneto-optical medium column is 0.0975 a, the dielectric constant of yttrium iron garnet is 14.63;

[0103] The background medium of the first magneto-optical photonic crystal 1 and the second magneto-optical photonic crystal 2 is air;

[0104] The lattices of the first magneto-optical photonic crystal 1 and the second magneto-optical photonic crystal 2 are both square lattices. a is the lattice constant of the square lattice, and each lattice has a magneto-optical medium column built in it.

[0105] Magnetic permeability tensor of yttrium iron garnet for:

[0106] ;

[0107] in, , , The off-diagonal magnetic permeability is 12.4 for the first magneto-optical photonic crystal 1 and -12.4 for the second magneto-optical photonic crystal 2, both of which are typical parameters in the microwave band.

[0108] like Figure 3 As shown, the slow light mode is realized by introducing a resonant cavity array 3 at the topological boundary. The resonant cavity array 3 includes periodically arranged resonant cavities. All resonant cavities are filled with a high refractive index dielectric with a refractive index of 3, and the cavity surfaces on both sides of each resonant cavity are perfect conductor narrow strips. The precise control of the frequency of different order modes is achieved by controlling the size of the resonant cavity. The height of the resonant cavity is h 2, width is w , the height of the perfect conductor strip is h 1.

[0109] like Figure 4-Figure 5 As shown, a broadband slow-light topological optical waveguide mode is realized through the dispersion engineering of Brillouin zone winding, that is, a resonant cavity array 3 with continuously changing frequency is used to effectively reduce the group velocity of the slow-light waveguide mode. The resonant cavity uses two narrow strips of perfect conductors. The size of the narrow strips is designed according to the required resonant frequency, and the resonant frequency is adjusted to enter the topological band gap to achieve coupling based on the resonant cavity mode and the topological boundary mode, thereby realizing topological slow light. Since the resonant cavity mode also has an even-odd spatial distribution, only modes that satisfy symmetry matching can be coupled, that is, the resonant cavity even (odd) mode and the topological boundary even (odd) mode are coupled, and there is no coupling between the odd and even modes. As shown Figure 6 As shown, the group velocity selection mechanism of the topological slow light waveguide is constructed by utilizing the above-mentioned mode coupling principle. By designing the resonant cavity, odd-mode and even-mode slow light are obtained respectively, and there is a great contrast in the group velocities of the two modes.

[0110] For ease of understanding, Figure 7As shown in the figure, an example is given of using the periodic continuous change of the resonant cavity to achieve the slow light bandwidth expansion of the mode: Assuming that the width of the resonant cavity is w 1, w 2, w 3. Fine-tune the width using the above method: w 2=0.98 w 1, w 3=0.96 w 1. The height of the perfect conductor strips is consistent, and three strips are repeated periodically in groups, forming a new Brillouin zone of 1 / 3 of the original, i.e. 2 / 3 a For the resonant cavity even mode, the resonant frequency of the resonant cavity is adjusted to match the topological band gap, and the resonant cavity even mode is wound in the folded Brillouin zone. The number of windings is equal to the number of resonant cavities in the period. The group refractive index of the slow light mode is increased by 2~3 orders of magnitude, and the bandwidth is extended to about three times that of the unfolded structure. Figure 8-Figure 9 Similarly, for the odd mode of the resonant cavity, the resonant frequency of the odd mode of the resonant cavity is optimized and adjusted to match the topological band gap, so as to realize the winding of the odd mode of the resonant cavity in the folded Brillouin zone, as shown in Figure 10-12 It should be noted that the number of resonant cavities in a period can continue to increase until the slow light bandwidth covers the entire topological band gap.

[0111] In order to realize the slow light mode division multiplexing function of odd mode and even mode, it is necessary to control the resonant cavity odd mode and the resonant cavity even mode to enter the topological band gap at the same time, that is, to form a quasi-degenerate mode. By adjusting the width and height of the resonant cavity, the overlapping frequency range of multiple resonant cavity modes can be determined. Mode 1, mode 2 and mode 3 are all resonant cavity modes, such as Fig.13 The parity of the resonant cavity mode is determined by the distribution of the electromagnetic field, as shown in Fig.14 As shown, mode 1 and mode 2 are the even modes of the resonant cavity, and mode 3 is the odd mode of the resonant cavity. According to the mode matching principle, the slow light mode multiplexing function of the topological optical waveguide is realized. The light in the odd mode and even mode in the topological band gap has a low group velocity, such as Fig.15 shown.

[0112] When there are large mirror symmetry-breaking obstacles in the topological optical waveguide structure, the odd and even modes will be converted to each other, that is, the modes cannot be transmitted with fidelity, and the group velocity fidelity function cannot be achieved. To solve the above problem, the photonic crystal is designed with a preset symmetry perturbation, such as Fig.16 As shown in Figure 2, the radius of the upper YIG cylinder (magneto-optical medium cylinder) adjacent to the topological boundary is reduced by 30%, and the optical waveguide mode is transformed from the orthogonal odd-even mode to the non-orthogonal quasi-odd-even mode, and the group velocity ratio of the topological boundary quasi-even mode to the topological boundary quasi-odd mode is greater than 100, as shown in Figure 2. Fig.17 As shown. When there is a width of a, with a length of 3.4 a When there is an asymmetric perfect conductor obstacle, the mode analysis proves that the odd mode group velocity fidelity exceeds 98% and the even mode fidelity exceeds 99.8%. Fig.18 By analyzing the electromagnetic field distribution, the fidelity transmission of quasi-odd and quasi-even topological boundary modes can be determined, as shown in Figure 19~Figure 20 shown.

[0113] It should be understood that the various forms of processes shown above can be used to reorder, add or delete steps. For example, the steps described in the disclosure of the present invention can be performed in parallel, sequentially or in different orders, as long as the desired results of the technical solution disclosed in the present invention can be achieved, and this document does not limit this.

[0114] The above specific implementations do not constitute a limitation on the protection scope of the present invention. It should be understood by those skilled in the art that various modifications, combinations, sub-combinations and substitutions can be made according to design requirements and other factors. Any modification, equivalent substitution and improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for constructing a multimode topological slow light waveguide, wherein the multimode topological slow light waveguide is used to achieve group velocity control, characterized in that: The specific steps include: S1: constructing a topological photonic crystal, wherein the topological photonic crystal comprises a first magneto-optical photonic crystal and a second magneto-optical photonic crystal having opposite magnetization directions; S2: setting a resonant cavity array at the boundary between the first magneto-optical photonic crystal and the second magneto-optical photonic crystal; S3: adjusting the size of each resonant cavity included in the resonant cavity array based on the preset slow light bandwidth of the multi-mode topological slow light waveguide, so that the resonant frequency of each resonant cavity enters the topological band gap of the topological photonic crystal; S31: determining a resonance frequency adjustment interval of the resonant cavity array within a single cycle based on a preset slow light bandwidth of the multimode topological slow light waveguide and a topological band gap of the topological photonic crystal; S32: based on the group velocity adjustment value set by the user, the resonant frequency in the resonant frequency adjustment interval is divided into h equal parts to obtain h resonant frequency values ​​to be calculated, and the size of each resonant cavity is calculated based on each resonant frequency value to be calculated to obtain the size of each resonant cavity in a single period; S33: adjusting the size of each resonant cavity included in the resonant cavity array according to the arrangement rule of each resonant cavity of different sizes in a single period, so that the resonant frequency of all the resonant cavities enters the topological band gap of the topological photonic crystal; S4: Construct a mode matching mechanism, and based on the mode matching mechanism, perform mode matching on the topological boundary mode between the first magneto-optical photonic crystal and the second magneto-optical photonic crystal and the resonant cavity mode of each resonant cavity, so that the group velocity of the multi-mode topological slow light waveguide is less than c / 100, c is the speed of light in a vacuum; S5: Detect whether there are asymmetric obstacles in the transmission path of the multi-mode topological slow-light waveguide. If there are asymmetric obstacles, the topological photonic crystal is designed to break the mirror symmetry perturbation to complete the construction of the multi-mode topological slow-light waveguide. If there are no asymmetric obstacles, the construction of the multi-mode topological slow-light waveguide is directly completed.

2. The method for constructing a multimode topological slow light waveguide according to claim 1, characterized in that: In step S1, the first magneto-optical photonic crystal and the second magneto-optical photonic crystal are both composed of magneto-optical medium columns arranged periodically; The material of the magneto-optical medium column is yttrium iron garnet, and the cylindrical radius of the magneto-optical medium column is 0.0975 a , the dielectric constant of yttrium iron garnet is 14.63; The background medium of the first magneto-optical photonic crystal and the second magneto-optical photonic crystal is air; The lattices of the first magneto-optical photonic crystal and the second magneto-optical photonic crystal are both square lattices, a is the lattice constant of the square lattice, and each lattice has a magneto-optical medium column built in it.

3. The method for constructing a multimode topological slow light waveguide according to claim 2, characterized in that: The magnetic permeability tensor of the yttrium iron garnet for: ； in, , , is the off-diagonal magnetic permeability, the off-diagonal magnetic permeability of the first magneto-optical photonic crystal is 12.4, the off-diagonal magnetic permeability of the second magneto-optical photonic crystal is -12.4, and i is an imaginary unit.

4. The method for constructing a multimode topological slow light waveguide according to claim 1, characterized in that: In step S2, the resonant cavity array includes periodically arranged resonant cavities, all of which are filled with a dielectric having a refractive index of 3, and both side surfaces of each resonant cavity are narrow strips of perfect conductors.

5. The method for constructing a multimode topological slow light waveguide according to claim 1, characterized in that: In step S31, the difference between the upper adjustment limit and the lower adjustment limit of the resonance frequency adjustment interval is equal to the value of the preset slow light bandwidth, and the resonance frequency adjustment interval of the resonant cavity array is located in the center area of ​​the topological band gap of the topological photonic crystal.

6. The method for constructing a multimode topological slow light waveguide according to claim 1, characterized in that: The specific steps of step S32 include: S321: Calculate the initial group velocity of the current multimode topology slow light waveguide: Initial group velocity = preset slow light bandwidth / wave vector change; S322: Determine the number h of resonant frequencies to be calculated within the resonant frequency adjustment interval according to the group velocity adjustment value set by the user: h=(initial group velocity / group velocity adjustment value)-1; Wherein, the initial group velocity / group velocity adjustment value is rounded off; S323: dividing the resonant frequency within the resonant frequency adjustment interval into h equal parts and performing normalization processing thereon to obtain h normalized resonant frequency values ​​to be calculated; S324: Substitute the values ​​of the resonant frequencies to be calculated into the following formula in turn to calculate the corresponding dimensions of the resonant cavity: ； in, f 0 is the current resonant frequency value to be calculated, p is the mode order in the width direction of the resonant cavity, q is the mode order in the height direction of the resonant cavity, n eff is the equivalent refractive index of the resonant cavity mode, is the width of the resonant cavity, is the height of the resonant cavity, a is the lattice constant.

7. The method for constructing a multimode topological slow light waveguide according to claim 1, characterized in that: In step S4, the topological boundary mode of the transverse magnetic polarization with mirror symmetry is taken as the topological boundary even mode, the topological boundary mode of the transverse magnetic polarization with mirror antisymmetry is taken as the topological boundary odd mode, the resonant cavity mode of the transverse magnetic polarization with mirror symmetry is taken as the resonant cavity even mode, and the resonant cavity mode of the transverse magnetic polarization with mirror antisymmetry is taken as the resonant cavity odd mode.

8. The method for constructing a multimode topological slow light waveguide according to claim 7, characterized in that: In step S4, the mode matching mechanism is: the resonant cavity even mode is mode-coupled with the topological boundary even mode, and the resonant cavity odd mode is mode-coupled with the topological boundary odd mode; If there is only a resonant cavity odd mode in the topological band gap of the topological photonic crystal, the resonant cavity odd mode is coupled with the topological boundary odd mode according to the mode matching mechanism, so as to realize the group velocity control of the multimode topological slow light waveguide, generate an odd mode of topological slow light, and keep the group velocity of the topological boundary even mode unchanged; If there is only a resonant cavity even mode in the topological band gap of the topological photonic crystal, according to the mode matching mechanism, the resonant cavity even mode is mode-coupled with the topological boundary even mode, so as to achieve group velocity control of the multimode topological slow light waveguide, generate even-mode topological slow light, and keep the group velocity of the topological boundary odd mode unchanged; If both the resonant cavity odd mode and the resonant cavity even mode exist in the topological band gap of the topological photonic crystal, that is, the resonant cavity odd mode and the resonant cavity even mode are in a quasi-degenerate state, the resonant cavity odd mode is matched with the topological boundary odd mode, and the resonant cavity even mode is matched with the topological boundary even mode, thereby realizing the wavelength division multiplexing function of the slow light mode of the multi-mode topological slow light waveguide.

9. The method for constructing a multimode topological slow light waveguide according to claim 6, characterized in that: In step S5, the specific process of performing broken mirror symmetry perturbation design on the topological photonic crystal is: reducing the cylindrical radius of the magneto-optical medium column adjacent to the topological boundary in the first magneto-optical photonic crystal to 70% of the original cylindrical radius.

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