Construction of magneto-optical photonic crystal waveguide and non-trivialness unidirectional posture robust transmission method

Abstract

The invention discloses a magneto-optical photonic crystal waveguide construction and non-trivialness unidirectional posture robust transmission method, and the method comprises the steps: carrying out the parameter design of a square magneto-optical photonic crystal waveguide, and enabling the waveguide to be able to excite an anti-chirality unidirectional boundary state and a reverse transmission unidirectional posture at the same time, the reverse chirality one-way boundary state is absorbed by upper and lower boundaries with scattering boundary conditions; and under the strong light transmission limiting effect of the square magneto-optical photonic crystal, the unidirectional state is limited in a strip to be transmitted along the unidirectional direction and is prevented from being absorbed, so that the waveguide forms a non-trivialness unidirectional state, and the structure is protected by topology, so that non-trivialness unidirectional state robust transmission with complete unidirectional conduction of a waveguide channel is realized. Furthermore, by adjusting the magnetic field intensity, the controllability of the non-trivialness one-way posture transmission frequency can be realized. The method has a wide application prospect in the fields of robust energy transmission, optical communication technologies, integrated photonic circuits and the like.

Description

Technical Field

[0001] The present invention belongs to the fields of microwave optics, topological photonics and robust energy transmission, and particularly relates to the construction of a magneto-optical photonic crystal waveguide and a non-trivial unidirectional body robust transmission method. Background Art

[0002] Microwave technology refers to the technology of using electromagnetic waves in the microwave frequency band (frequency range is generally 300MHz to 300GHz, corresponding to wavelength of 1 meter to 1 mm) for information transmission, signal processing, energy transmission and other related applications. The research and application of microwave technology are constantly expanding, such as millimeter wave communication, quantum communication and other cutting-edge fields, with broad development potential. The present invention proposes a method for realizing non-trivial unidirectional robust transmission in the microwave frequency band.

[0003] Robust energy transfer refers to a technology that can ensure that signals are transmitted in a specific direction, and can maintain a stable and efficient transmission process in the face of interference, noise or external disturbances. Compared with traditional bidirectional or multidirectional transmission methods, robust energy transfer emphasizes the stability and anti-interference ability of unidirectional transmission. The original inspiration for robust energy transfer came from the study of topological states, especially the discovery of phenomena such as topological insulators and quantum Hall effect. Topological insulators are a class of materials that are insulating inside but can support the conductive behavior of electrons on the surface or boundary. These surface states form topologically protected states on the edge of the material, which have the characteristics of unidirectional propagation and are robust to interference such as defects and impurities. The quantum Hall effect is a topological phenomenon caused by the strong magnetic field when electrons move in two-dimensional materials. The quantum Hall effect shows that at the boundary of the material, electrons can be transmitted in a single direction without reflection and are robust to impurities and defects.

[0004] In addition, in the classical Haldane model, the time reversal symmetry of the system is broken by making the electrons of the next-nearest-neighbor transitions in the two sets of sublattices obtain opposite phases, thereby realizing chiral topological boundary states similar to the quantum Hall effect without the need for an external magnetic field. Therefore, the Haldane model proves that the quantum Hall effect does not need to rely on strong magnetic fields or Landau levels, as long as the time reversal symmetry of the system can be broken. The modified Haldane model makes the electrons of the next-nearest-neighbor transitions in the two sets of sublattices obtain the same phase, so that the chiral boundary states originally transmitted in opposite directions obtain the same dispersion, and then transform into anti-chiral boundary states transmitted in the same direction. However, the anti-chiral state energy band is covered by the mediocre bulk state. The heterogeneous Haldane model is composed of stacking two opposite modified Haldane models. This model not only moves the unidirectional anti-chiral boundary state into the band gap, but also generates a new unidirectional bulk state in the frequency range of the anti-chiral state, which is transmitted inside the model and in the opposite direction of the anti-chiral state transmission. However, these two states usually coexist in the band gap as a mediocre energy band composed of the two.

[0005] With the in-depth study of topological insulators and quantum Hall effect, topological photonics has gradually emerged as an emerging field. Researchers began to explore the transmission characteristics of light waves in materials and structures with topological properties, and photonic crystals have become a structure worthy of attention. Photonic crystals refer to structures with periodic arrangement of dielectrics on the wavelength scale, which can produce photon passbands and photon band gaps, and have the function of effectively manipulating electromagnetic wave transmission. Similar to the transmission behavior of electrons in crystal materials in solid physics being modulated by periodic potential energy, the transmission behavior of photons in photonic crystal materials is also regulated by periodic media, and its global characteristics can be described by the photon band structure. Therefore, the concept of topological structure can naturally be extended to photonic crystals. Secondly, inspired by topological phases and topological phase transitions in condensed matter physics, people realized that topological phases are ubiquitous phenomena in periodic structures, and thus predicted that topologically protected chiral unidirectional boundary states can be generated in photonic crystals with broken time reversal symmetry.

[0006] Subsequently, people used the magnetically responsive yttrium iron garnet (YIG) material to construct a two-dimensional microwave honeycomb magneto-optical photonic crystal by analogy with the Haldane model; and by applying the same-direction external magnetic field on each YIG to break the time reversal symmetry of the structure, they successfully made the two-dimensional microwave honeycomb magneto-optical photonic crystal produce topological chiral unidirectional boundary states with opposite transmission directions on the upper and lower boundaries.

[0007] Secondly, by analogy with the modified Haldane model, people applied external magnetic fields of opposite directions to the two sets of sublattices embedded in the two-dimensional microwave honeycomb magneto-optical photonic crystal. This not only breaks the time reversal symmetry of the structure, but also realizes the concept of equal next-nearest neighbor transition coefficients in the modified Haldane model, thus successfully observing the reverse-handed unidirectional boundary state that transmits in the same direction on the upper and lower boundaries in this structure.

[0008] In addition, people have constructed a two-dimensional microwave honeycomb magneto-optical photonic crystal waveguide by analogy with the heterogeneous Haldane model and periodically stacking two opposite magneto-optical photonic crystals analogous to the modified Haldane model, so that the anti-chiral one-way boundary state and the one-way bulk state that transmits in the opposite direction are generated in the band gap, and successfully observed the one-way bulk state that can be robustly transmitted in the strip. However, based on the law of conservation of energy, at the same frequency, the anti-chiral one-way boundary state needs to achieve transmission balance with the one-way bulk state that transmits in the opposite direction. Therefore, the waveguide supports the transmission of anti-chiral one-way boundary states and the transmission of reverse one-way bulk states on the boundary and in the strip, respectively. (J.Chen and ZYLi, "Prediction and Observation of Robust One-Way Bulk States in aGyromagnetic Photonic Crystal," Physical Review Letters 128 (25), 257401 (2022)). The waveguide designed by the latest results cannot achieve a completely unidirectional conduction characteristic that only supports one-way bulk state transmission. Even if the anti-chiral unidirectional boundary state and the unidirectional bulk state have little interference in space, the robust transmission performance of the unidirectional bulk state will still be weakened. In addition, existing results usually use honeycomb magneto-optical photonic crystal waveguides to achieve unidirectional bulk state transmission, and the structure and magnetic field configuration of the waveguide are relatively complex; at the same time, the adjustability of the unidirectional bulk state transmission frequency is also ignored. These are all problems that need to be solved urgently.

[0009] The main reason for the problem that the existing honeycomb magneto-optical photonic crystal waveguide cannot achieve the completely unidirectional conduction characteristics of the unidirectional state is that the high-frequency energy band of the honeycomb magneto-optical photonic crystal with a sawtooth boundary is located below the light cone, thereby limiting the leakage of the anti-chiral boundary state to the outside of the sawtooth boundary. The present invention provides a square magneto-optical photonic crystal waveguide composed of a square magneto-optical photonic crystal with a straight boundary. The waveguide can also generate a unidirectional anti-chiral boundary state and a unidirectional state of reverse transmission. However, since the high-frequency energy band of the square magneto-optical photonic crystal with a straight boundary is located above the light cone, the anti-chiral boundary state can leak out of the straight boundary. At the same time, the leaked anti-chiral boundary state is absorbed by utilizing the upper and lower boundaries of the waveguide with scattering boundary conditions, thereby blocking the transmission channel supporting the anti-chiral boundary state, thereby effectively reducing the transmission influence on the unidirectional state inside the structure and improving its transmission efficiency. On this basis, the square magneto-optical photonic crystal's powerful light transmission limiting ability is used to make it difficult for the unidirectional state in the strip to be transmitted to the upper and lower boundaries, thereby avoiding absorption, thereby achieving a non-trivial unidirectional robust transmission of the state with complete unidirectional conductivity in the transmission channel. In addition, compared with the honeycomb magneto-optical photonic crystal waveguide, the square magneto-optical photonic crystal waveguide used in the present invention has a simpler structure and magnetic field configuration; and based on the influence of magnetic field changes on the frequency of non-trivial unidirectional state generation, the present invention achieves the adjustability of the non-trivial unidirectional state transmission frequency. Summary of the invention

[0010] In order to overcome the shortcomings and deficiencies of the above-mentioned existing unidirectional bulk transmission technology, one of the purposes of the present invention is to provide a method for constructing and robustly transmitting a non-trivial unidirectional bulk state based on a square magneto-optical photonic crystal waveguide, which not only makes the waveguide for transmitting the unidirectional bulk state completely unidirectional, but also makes the unidirectional bulk state have strong transmission robustness against obstacles, defects and interference; and by adjusting the magnetic field, the transmission frequency of the non-trivial unidirectional bulk state supported by the square magneto-optical photonic crystal waveguide can be flexibly controlled. The square magneto-optical photonic crystal waveguide provides a new platform for studying robust non-trivial unidirectional bulk transmission, and its rich characteristics will play a role in application fields such as robust energy transmission, optical communication technology and integrated photonic circuits.

[0011] The purpose of the present invention is achieved by at least one of the following technical solutions.

[0012] A method for constructing a magneto-optical photonic crystal waveguide comprises the following steps:

[0013] S1. Construct a square magneto-optical photonic crystal with yttrium iron garnet (YIG) columns as dielectric columns;

[0014] S2, taking the plane where the YIG columns in the square magneto-optical photonic crystal are periodically arranged as the xoy plane of the coordinate, applying a magnetic field to the square magneto-optical photonic crystal in the z direction;

[0015] S3. Set boundaries and boundary conditions around the square magneto-optical photonic crystal to construct a square magneto-optical photonic crystal waveguide.

[0016] Furthermore, in step S1, a YIG medium column with a radius of r is used as the magneto-optical material of a square magneto-optical photonic crystal, and multiple YIG columns are arranged in a square lattice to construct a square magneto-optical photonic crystal with a lattice constant of a, wherein the square magneto-optical photonic crystal contains m rows and n columns of YIG columns.

[0017] Furthermore, in step S2, external magnetic fields of equal magnitude and opposite direction are applied to the odd-numbered rows and even-numbered rows of dielectric pillars of the square magneto-optical photonic crystal, respectively, wherein the magnetic field H of the odd-numbered rows has a magnitude of k and a direction along +z.

[0018] Furthermore, in step S3, a boundary with a scattering boundary condition is set at 1.7a in the +y direction of the first row of dielectric columns of the square magneto-optical photonic crystal, which serves as the upper boundary of the square magneto-optical photonic crystal waveguide; a boundary with a scattering boundary condition is set at 1.7a in the -y direction of the last row of dielectric columns of the square magneto-optical photonic crystal, which serves as the lower boundary of the waveguide; a is the lattice constant.

[0019] Furthermore, a boundary with incident and exiting functions is set at 3.5a in the -x direction of the leftmost column of dielectric columns of the square magneto-optical photonic crystal, which serves as the left boundary of the waveguide; a boundary with incident and exiting functions is set at 3.5a in the +x direction of the rightmost column of dielectric columns of the square magneto-optical photonic crystal, which serves as the right boundary of the waveguide, wherein the left boundary and the right boundary are each other's incident end and exit end.

[0020] Furthermore, the background medium within the boundary is air.

[0021] Furthermore, in step S3, the frequency range of the constructed square magneto-optical photonic crystal waveguide projected band gap is within the microwave frequency band.

[0022] The non-trivial unidirectional body robust transmission method implemented based on the construction method of the magneto-optical photonic crystal waveguide comprises the following steps:

[0023] S1. Use the finite element method to calculate and analyze the projected band structure and intrinsic mode field of the square magneto-optical photonic crystal waveguide under the current conditions, and determine the group velocity direction of the non-trivial unidirectional state by calculating the slope of the non-trivial unidirectional state energy band, and then determine the completely unidirectional conduction direction of the non-trivial unidirectional state in the square magneto-optical photonic crystal waveguide;

[0024] S2. A plane electromagnetic wave within the frequency range of the non-trivial unidirectional bulk energy band is sequentially incident from the conducting end and the non-conducting end of the square magneto-optical photonic crystal waveguide, and the electromagnetic wave intensity at the corresponding emitting end of the square magneto-optical photonic crystal waveguide and the electric field distribution in the corresponding waveguide are detected to verify the unidirectional bulk transmission and the complete unidirectional conductivity of the waveguide;

[0025] S3, after inserting an obstacle in the center of the square magneto-optical photonic crystal waveguide or creating a defect by removing the dielectric column in the center of the square magneto-optical photonic crystal waveguide, the same plane electromagnetic wave as in step S2 is incident from the conducting end of the waveguide to detect the electromagnetic wave intensity at the output end and the electric field distribution in the waveguide;

[0026] S4. Compare the electromagnetic wave intensity at the output end and the electric field distribution in the waveguide when the plane electromagnetic wave is incident from the conducting end of the waveguide in step S3 and step S2, and analyze whether the non-trivial unidirectional state can be transmitted robustly in the face of obstacles and defects.

[0027] Furthermore, the finite element method is used to calculate and analyze in the radio frequency-frequency domain module in COMSOL MULTIPHYSICS software.

[0028] Furthermore, by continuously changing the magnetic field intensity applied to the square magneto-optical photonic crystal waveguide and adjusting the magnetic field size, the transmission frequency of the non-trivial unidirectional state is changed, and the adjustability of the transmission frequency of the non-trivial unidirectional state is achieved, as follows:

[0029] While keeping the other parameters of the square magneto-optical photonic crystal waveguide unchanged, the magnetic field intensity applied to the square magneto-optical photonic crystal waveguide is continuously changed. By calculating the corresponding energy band structure, it can be obtained that: since the non-trivial unidirectional state energy band in the square magneto-optical photonic crystal waveguide has a certain tolerance to the change of magnetic field, as the magnetic field intensity increases, the non-trivial unidirectional state energy band gradually shifts to the high energy zone, and its structure changes slowly; within the magnetic field range of 2500Gs-11000Gs, the energy band always exists, and the central frequency of the energy band moves in a wide range of 9GHz-13GHz. Therefore, the transmission frequency of the non-trivial unidirectional state supported by the square magneto-optical photonic crystal waveguide can be adjusted by simply adjusting the magnetic field, thereby realizing the adjustability of the transmission frequency of the non-trivial unidirectional state.

[0030] The principle of the present invention is as follows: The present invention uses a square magneto-optical photonic crystal waveguide to realize non-trivial unidirectional bulk robust transmission, and the waveguide is composed of a square lattice magneto-optical photonic crystal. First, by applying a same-direction external magnetic field to the dielectric pillars of the square magneto-optical photonic crystal to break the time reversal symmetry of the structure, the square magneto-optical photonic crystal can generate a topologically protected chiral boundary state in the band gap. However, since the high-frequency energy band of the square magneto-optical photonic crystal with a straight boundary is located above the light cone, the unidirectional chiral boundary state will leak out of the straight boundary. Therefore, it is necessary to set a metal cladding at the upper and lower boundaries of the square magneto-optical photonic crystal waveguide to prevent the leakage of the chiral boundary state, thereby realizing stable chiral unidirectional boundary state robust transmission at the upper and lower boundaries. Further, when the odd-numbered and even-numbered rows of dielectric pillars of the square magneto-optical photonic crystal are respectively applied with opposite external magnetic fields and the parameters are adjusted, due to the reversal of the direction of part of the magnetic field, the original chiral unidirectional boundary state will obtain the same dispersion, thereby transforming into an anti-chiral unidirectional boundary state of the same-direction transmission. Based on the law of conservation of energy, the anti-chiral unidirectional boundary state needs to achieve transmission balance with the corresponding reverse-transmitting body state. Therefore, the waveguide will generate anti-chiral unidirectional boundary states and unidirectional body states in the same band gap. These two states are transmitted in opposite directions at the upper and lower boundaries of the square magneto-optical photonic crystal waveguide with metal cladding and inside the structure of the waveguide. Therefore, the waveguide supporting the transmission of these two states is not completely unidirectional. Then, when the metal cladding is removed and the upper and lower boundaries of the square magneto-optical photonic crystal waveguide are made to present scattering boundary conditions, the anti-chiral unidirectional boundary state will leak outward and be absorbed by the upper and lower boundaries with scattering boundary conditions. This blocks the transmission channel supporting the anti-chiral unidirectional boundary state. At the same time, due to the powerful light transmission restriction ability of the square magneto-optical photonic crystal, the body state is effectively restricted to unidirectional transmission within the strip, making it difficult to diffuse to the upper and lower boundaries, avoiding absorption, thereby ensuring the integrity of the unidirectional body state. This mechanism enables the square magneto-optical photonic crystal waveguide to produce non-trivial unidirectional states in the band gap, thereby realizing non-trivial unidirectional state transmission with completely unidirectional conductivity in the waveguide channel. In addition, due to the topological protection of the structure, the non-trivial unidirectional state is resistant to backscattering and has strong transmission robustness in the face of obstacles, defects and interference. Finally, since the non-trivial unidirectional state energy band has a high tolerance to magnetic field changes, as the external magnetic field changes within a certain range, the non-trivial unidirectional state energy band shifts to the high energy zone or low energy zone, and its structure has a certain stability. Therefore, by adjusting the size of the external magnetic field, the transmission frequency of the non-trivial unidirectional state supported by the square magneto-optical photonic crystal waveguide can be flexibly controlled.

[0031] Compared with the prior art, the present invention has the following advantages and excellent effects:

[0032] (1) The mechanism of the present invention to achieve unidirectional robust transmission: the existing unidirectional robust transmission technology is usually achieved by using a unidirectional state located below the light cone generated by a honeycomb magneto-optical photonic crystal with a sawtooth boundary, while the present invention uses a non-trivial unidirectional state located above the light cone generated by a square magneto-optical photonic crystal with a straight boundary.

[0033] (2) Complete unidirectional conductivity: The existing honeycomb magneto-optical photonic crystal waveguide that supports unidirectional bulk robust transmission often supports reverse-handed unidirectional boundary state transmission in the opposite direction of bulk transmission at the boundary, so the waveguide does not have complete unidirectional conductivity. The square magneto-optical photonic crystal waveguide of the present invention only supports non-trivial unidirectional bulk robust transmission, and the channel accompanying the reverse transmission of the bulk is prohibited, so it has complete unidirectional conductivity.

[0034] (3) Robust transmission: The existing honeycomb magneto-optical photonic crystal waveguide transmits the reverse-handed unidirectional boundary state and the reverse-transmitting unidirectional bulk state in the boundary and strip, respectively. Although the interference between these two states in space is small, it still weakens the robust transmission performance of the unidirectional bulk state. However, the square magneto-optical photonic crystal waveguide of the present invention does not have a transmission channel in the opposite direction of the unidirectional bulk state transmission, so the unidirectional bulk state has better transmission robustness.

[0035] (4) Adjustability of transmission frequency: No existing waveguide that supports adjustable transmission frequency of unidirectional bulk states has been reported. In the present invention, as the external magnetic field increases, the non-trivial unidirectional bulk state energy band will shift to the high energy region, but its structure will change slightly. Therefore, the transmission frequency of the non-trivial unidirectional bulk state supported by the square magneto-optical photonic crystal waveguide can be flexibly adjusted by simply changing the magnetic field size, and the adjustable frequency range is relatively wide.

[0036] (5) Simple structure and magnetic field configuration: Most of the existing magneto-optical photonic crystals that support unidirectional bulk robust transmission adopt a honeycomb lattice structure, and it is necessary to apply external magnetic fields in opposite directions to the two sets of sub-lattices in the honeycomb lattice. The present invention adopts a square lattice magneto-optical photonic crystal, and only needs to apply external magnetic fields in opposite directions to the odd-numbered rows and even-numbered rows of dielectric columns in the square lattice, respectively, so that its structure and magnetic field configuration become simpler. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is a schematic structural diagram of a waveguide based on a square magneto-optical photonic crystal of the present invention;

[0038] Figure 2 The projected energy band diagram along the x direction and the eigenmode field diagram of the corresponding frequency of the waveguide of Example 1 of the present invention;

[0039] Figure 3 The electric field intensity distribution and electric field intensity curve diagram of Example 1 and Example 2 of the present invention;

[0040] Figure 4 This is a graph showing how the width and center frequency of the non-trivial unidirectional bulk energy band of Example 3 of the present invention change with increasing magnetic field intensity. DETAILED DESCRIPTION

[0041] The present invention will be further described in detail below in conjunction with examples, but the embodiments of the present invention are not limited thereto.

[0042] Example 1

[0043] The method for constructing the magneto-optical photonic crystal waveguide of this embodiment comprises the following steps:

[0044] S1. Constructing a square magneto-optical photonic crystal with yttrium iron garnet (YIG) columns as dielectric columns; the square in the present invention means that the lattice type of the photonic crystal is a square lattice;

[0045] A YIG medium column with a radius of r=1.83 mm is used as the magneto-optical material of a square magneto-optical photonic crystal. Multiple YIG columns are arranged in a square lattice to construct a square magneto-optical photonic crystal with a lattice constant of a=1.16 cm, wherein the square magneto-optical photonic crystal contains 14 rows and 30 columns of YIG columns.

[0046] S2, the xoy plane with the plane of periodic arrangement of YIG columns in the square magneto-optical photonic crystal as the coordinate, such as Figure 1 As shown in the middle coordinate axis, a magnetic field is applied to the square magneto-optical photonic crystal in the z direction;

[0047] External magnetic fields of equal magnitude and opposite direction are applied to the odd-numbered and even-numbered rows of dielectric pillars of the square magneto-optical photonic crystal, respectively, where the magnetic field H of the odd-numbered rows is 4800 Gs and is directed along +z.

[0048] S3. Set boundaries and boundary conditions around the square magneto-optical photonic crystal to construct a square magneto-optical photonic crystal waveguide, such as Figure 1 As shown;

[0049] A boundary with a scattering boundary condition is set at 1.7a in the +y direction of the first row of dielectric columns of the square magneto-optical photonic crystal, which serves as the upper boundary of the square magneto-optical photonic crystal waveguide; a boundary with a scattering boundary condition is set at 1.7a in the -y direction of the last row of dielectric columns of the square magneto-optical photonic crystal, which serves as the lower boundary of the waveguide;

[0050] A boundary with incident and exiting functions is set at 3.5a in the -x direction of the leftmost column of dielectric columns of the square magneto-optical photonic crystal, which serves as the left boundary of the waveguide; a boundary with incident and exiting functions is set at 3.5a in the +x direction of the rightmost column of dielectric columns of the square magneto-optical photonic crystal, which serves as the right boundary of the waveguide, wherein the left boundary and the right boundary are each other's incident end and exit end.

[0051] The background medium within the boundary is air.

[0052] The frequency range of the projected band gap of the constructed square magneto-optical photonic crystal waveguide is within the microwave frequency band.

[0053] Since the upper and lower boundaries of the square magneto-optical photonic crystal waveguide with scattering boundary conditions absorb the anti-chiral one-way boundary state, the anti-chiral one-way boundary state cannot be transmitted in the waveguide;

[0054] Due to the strong light transmission limitation ability of the square magneto-optical photonic crystal, the unidirectional state located in the waveguide, which is opposite to the transmission direction of the boundary state, is difficult to be transmitted to the upper and lower boundaries, thus avoiding absorption, so that the state can maintain unidirectional transmission in the waveguide.

[0055] In this embodiment, the method for implementing non-trivial unidirectional body transmission includes the following steps:

[0056] The first step is to take Figure 1 The supercell unit of the square magneto-optical photonic crystal waveguide shown in the figure uses the finite element method to calculate the projected band structure and the intrinsic mode field along the x direction. It can be found that only non-trivial unidirectional body energy bands exist in the band gap. The group velocity direction of the non-trivial unidirectional body is determined by calculating the slope of the non-trivial unidirectional body energy band, and then the completely unidirectional conduction direction of the non-trivial unidirectional body in the square magneto-optical photonic crystal waveguide is determined. The design and simulation calculations of the present invention are completed with the support of the RF-frequency domain module in the COMSOLMULTIPHYSICS software.

[0057] like Figure 2 As shown, in the photonic band gap with a frequency f of 11.34 GHz-11.62 GHz, there are two dispersion curves connecting the upper and lower trivial bulk state energy bands. The slope of the dispersion curve represents the group velocity of the electromagnetic wave, and the slopes of the two curves are both negative; and the eigenmode fields of the dispersion curves at points M1 and M2 are distributed in the supercell unit in the form of bulk states, which means that the waveguide only supports non-trivial unidirectional bulk states transmitted along the -x direction.

[0058] Step 2: Build Figure 1 The normal waveguide structure model shown in Figure 1 is shown in Figure 2. Figure 2The frequency 11.55 GHz marked by the dotted line is used as the excitation frequency to verify the non-trivial unidirectional bulk transmission characteristics of the square magneto-optical photonic crystal waveguide. When a plane wave of 11.55 GHz is incident from the left end of the waveguide, the electric field intensity distribution in the waveguide is as follows Figure 3 As shown in (a), it can be seen from the figure that the plane wave will decay rapidly when it is transmitted along the +x direction, and the waveguide transmission channel in the +x direction is completely prohibited; when a plane wave with the same frequency is incident from the right end of the waveguide, the electric field intensity distribution in the waveguide is as follows Figure 3 As shown in (b), it can be seen that the plane wave is transmitted along the -x direction in the form of a bulk state, and the unidirectional bulk waveguide transmission channel in the -x direction is conductive. These results are consistent with the conclusions drawn from the energy band analysis in the first step.

[0059] Step 3: Collection Figure 3 (a) shows the electric field strength along the line 1 near the right edge of the waveguide, and the Figure 3 (b) shows the electric field intensity along the marked line 2 near the left boundary of the waveguide. The results are as follows Figure 3 As shown in curves 1 and 2 in (e), it can be seen that the electric field strength near the right boundary is almost 0, basically lower than 10 -5 The electric field strength near the left boundary is basically greater than 10 -2 This shows that the waveguide has a strong non-reciprocal transmission characteristic, supports only a non-trivial unidirectional state along the -x direction, and has complete unidirectional conductivity.

[0060] Example 2

[0061] In this embodiment, the method for realizing non-trivial unidirectional body robust transmission has the same features as those of Embodiment 1 except for the following features.

[0062] The first step is to construct an obstacle waveguide and a defect waveguide. Since a perfect conductor has perfect reflection and scattering functions for electromagnetic waves, this embodiment uses a perfect conductor as an obstacle to the transmission of electromagnetic waves. By inserting a perfect conductor with a length and width of 2a and 0.1a in the center of the waveguide, a defect waveguide can be constructed as follows: Figure 3 In addition, by removing the two YIG dielectric columns in the center of the waveguide, a Figure 3 The defect waveguide shown in (d).

[0063] The second step is to use the same frequency of 11.55 GHz as the excitation frequency to verify the robust transmission characteristics of the non-trivial unidirectional state. Figure 3 As shown, Figure 31 is an electric field intensity distribution diagram when the plane wave of Example 1 and Example 2 is incident on the left end of the normal waveguide, and on the right end of the normal waveguide, the obstacle waveguide and the defect waveguide, and an electric field intensity curve diagram along the dotted line near the corresponding output end; when the plane wave with a frequency of 11.55 GHz is incident from the right end of the obstacle waveguide and the defect waveguide, the electric field intensity distribution is respectively as follows: Figure 3 As shown in (c) and (d). Figure 3 (c) shows that the plane wave can return to the same state after bypassing the obstacle. Figure 3 The electric field distribution is similar to the normal transmission condition shown in (b), and continues to transmit unidirectionally along the -x direction; Figure 3 It can be seen from (d) that the plane wave can also recover to the same level as Figure 3 The electric field distribution form is similar to the normal transmission situation shown in (b), and continues to transmit unidirectionally along the -x direction.

[0064] Step 3: Collection Figure 3 (c) shows the electric field strength along the marked line 3 near the left boundary of the obstacle waveguide, and the Figure 3 (d) shows the electric field intensity along the marked line 4 near the left boundary of the defective waveguide. The results are as follows: Figure 3 As shown in curve 3 and curve 4 in (e). It can be seen from the figure that curve 3 and curve 4 are Figure 3 Compared with the electric field intensity curve 2 along the marked line 2 near the left boundary under normal transmission shown in (b), they are almost completely consistent due to the topological protection of the structure. That is, the non-trivial unidirectional state transmitted in the waveguide can be robustly transmitted in the face of obstacles and defects. Thus, robust transmission of non-trivial unidirectional state is achieved.

[0065] Example 3

[0066] In this embodiment, the method for achieving the adjustability of the non-trivial unidirectional body transmission frequency is the same as that of Embodiment 2 except for the following features.

[0067] By continuously changing the magnetic field intensity applied to the square magneto-optical photonic crystal waveguide and adjusting the magnetic field size, the transmission frequency of the non-trivial unidirectional state is changed, and the adjustability of the transmission frequency of the non-trivial unidirectional state is achieved, as follows:

[0068] The first step is to take Figure 1 The supercell unit of the square magneto-optical photonic crystal waveguide is shown, and the energy band structure under different magnetic field strengths is calculated by keeping other structural parameters unchanged. By analyzing the calculation results, the magnetic field strength range in which the square magneto-optical photonic crystal waveguide produces non-trivial unidirectional bulk energy bands in the band gap is obtained.

[0069] The second step is to calculate the frequency range and central frequency variation of the non-trivial unidirectional energy band when the magnetic field intensity increases continuously within the above-mentioned magnetic field intensity range; draw a relationship diagram between the magnetic field intensity and the width of the non-trivial unidirectional energy band ( Figure 4 (a)) and plotting the relationship between magnetic field intensity and the center frequency of the non-trivial unidirectional body energy band ( Figure 4 (b)). Figure 4 (a) shows that as the magnetic field strength increases from 2500Gs to 11000Gs, the non-trivial unidirectional body energy band always exists; its frequency range increases first and then decreases, reaching a maximum of 0.281GHz at 5000Gs. Figure 4 (b) shows that: as the magnetic field strength increases from 2500Gs to 11000Gs, the center frequency of the non-trivial unidirectional state energy band moves from 9GHz to around 13GHz, and the moving range is close to 4GHz, of which the center frequency at 5000Gs is 11.59GHz. It can be obtained that: by adjusting the intensity of the external magnetic field, the transmission frequency of the non-trivial unidirectional state supported by the square magneto-optical photonic crystal waveguide can be flexibly controlled, and the controllable frequency range is relatively wide. Thus, the adjustability of the non-trivial unidirectional state transmission frequency is achieved. This feature significantly improves the availability and practicality of the square magneto-optical photonic crystal waveguide of the present invention.

[0070] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.

Claims

1. A method for constructing a magneto-optical photonic crystal waveguide, characterized in that: The following steps are involved: S1. Construct a square magneto-optical photonic crystal with yttrium iron garnet (YIG) columns as dielectric columns; S2, taking the plane where the YIG columns in the square magneto-optical photonic crystal are periodically arranged as the xoy plane of the coordinate, applying a magnetic field to the square magneto-optical photonic crystal in the z direction; S3. Set boundaries and boundary conditions around the square magneto-optical photonic crystal to construct a square magneto-optical photonic crystal waveguide.

2. The method for constructing a magneto-optical photonic crystal waveguide according to claim 1, characterized in that: In step S1, a YIG medium column with a radius of r is used as the magneto-optical material of a square magneto-optical photonic crystal, and multiple YIG columns are arranged in a square lattice to construct a square magneto-optical photonic crystal with a lattice constant of a, wherein the square magneto-optical photonic crystal contains m rows and n columns of YIG columns.

3. The method for constructing a magneto-optical photonic crystal waveguide according to claim 1, characterized in that: In step S2, external magnetic fields of equal magnitude and opposite direction are applied to the odd-numbered rows and even-numbered rows of dielectric pillars of the square magneto-optical photonic crystal, respectively, wherein the magnetic field H of the odd-numbered rows has a magnitude of k and a direction along +z.

4. The method for constructing a magneto-optical photonic crystal waveguide according to claim 1, characterized in that: In step S3, a boundary with a scattering boundary condition is set at 1.7a in the +y direction of the first row of dielectric columns of the square magneto-optical photonic crystal, which serves as the upper boundary of the square magneto-optical photonic crystal waveguide; a boundary with a scattering boundary condition is set at 1.7a in the -y direction of the last row of dielectric columns of the square magneto-optical photonic crystal, which serves as the lower boundary of the waveguide; a is the lattice constant.

5. The method for constructing a magneto-optical photonic crystal waveguide according to claim 4, characterized in that: A boundary with incident and exiting functions is set at 3.5a in the -x direction of the leftmost column of dielectric columns of the square magneto-optical photonic crystal, which serves as the left boundary of the waveguide; a boundary with incident and exiting functions is set at 3.5a in the +x direction of the rightmost column of dielectric columns of the square magneto-optical photonic crystal, which serves as the right boundary of the waveguide, wherein the left boundary and the right boundary are each other's incident end and exit end.

6. The method for constructing a magneto-optical photonic crystal waveguide according to claim 5, characterized in that: The background medium within the boundary is air.

7. The method for constructing a magneto-optical photonic crystal waveguide according to claim 1, characterized in that: In step S3, the frequency range of the projected band gap of the constructed square magneto-optical photonic crystal waveguide is within the microwave frequency band.

8. A non-trivial unidirectional bulk robust transmission method implemented based on the construction method of the magneto-optical photonic crystal waveguide according to any one of claims 1 to 7, characterized in that: The following steps are involved: S1. Use the finite element method to calculate and analyze the projected band structure and intrinsic mode field of the square magneto-optical photonic crystal waveguide under the current conditions, and determine the group velocity direction of the non-trivial unidirectional state by calculating the slope of the non-trivial unidirectional state energy band, and then determine the completely unidirectional conduction direction of the non-trivial unidirectional state in the square magneto-optical photonic crystal waveguide; S2. A plane electromagnetic wave within the frequency range of the non-trivial unidirectional bulk energy band is sequentially incident from the conducting end and the non-conducting end of the square magneto-optical photonic crystal waveguide, and the electromagnetic wave intensity at the corresponding emitting end of the square magneto-optical photonic crystal waveguide and the electric field distribution in the corresponding waveguide are detected to verify the unidirectional bulk transmission and the complete unidirectional conductivity of the waveguide; S3, after inserting an obstacle in the center of the square magneto-optical photonic crystal waveguide or creating a defect by removing the dielectric column in the center of the square magneto-optical photonic crystal waveguide, the same plane electromagnetic wave as in step S2 is incident from the conducting end of the waveguide to detect the electromagnetic wave intensity at the output end and the electric field distribution in the waveguide; S4. Compare the electromagnetic wave intensity at the output end and the electric field distribution in the waveguide when the plane electromagnetic wave is incident from the conducting end of the waveguide in step S3 and step S2, and analyze whether the non-trivial unidirectional state can be transmitted robustly in the face of obstacles and defects.

9. The non-trivial unidirectional bulk robust transmission method based on square magneto-optical photonic crystal waveguide according to claim 8, characterized in that: The finite element method is used to calculate and analyze in the RF-frequency domain module of COMSOL MULTIPHYSICS software.

10. The non-trivial unidirectional bulk robust transmission method based on square magneto-optical photonic crystal waveguide according to claim 8, characterized in that: By continuously changing the intensity of the magnetic field applied to the square magneto-optical photonic crystal waveguide and adjusting the size of the magnetic field, the transmission frequency of the non-trivial unidirectional state is changed, thereby achieving the adjustability of the transmission frequency of the non-trivial unidirectional state.

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