A Topological Unidirectional Waveguide with a Square-Hexagonal Composite Lattice

Abstract

The present invention discloses a topological unidirectional boundary waveguide of a square-hexagonal composite lattice. The square-hexagonal composite lattice includes dielectric columns and a metal boundary. All dielectric columns are placed under an air background, and a square-hexagonal composite lattice structure with a square-hexagonal staggered arrangement is formed by periodically arranging rotated square lattices along the x and y directions respectively. There are five types of boundaries in total, namely the first boundary, the second boundary, the third boundary, the fourth boundary, and the fifth boundary. Each boundary can form a unidirectional waveguide with the metal boundary. The metal boundary and the dielectric column closest to the metal boundary form an optical waveguide transmission channel, and the waveguides formed by these five boundaries all have the topological property of anti-backscattering transmission. The present invention designs topological unidirectional waveguides based on five different boundary types of the square-hexagonal composite lattice structure, enriching the geometric and physical means for constructing unidirectional transport photonic topological states, and having great significance for efficient transmission in the field of optical communication.

Description

Technical Field

[0001] The present invention belongs to the fields of microwave optics, topological photonics, and magneto-optical photonic crystals, and particularly relates to a topological one-way waveguide with a square-hexagonal composite lattice. Background Art

[0002] In recent years, waveguides based on photonic crystals have been favored by a wide range of researchers. Photonic crystal waveguides utilize the property of line defects to guide light to achieve optical waveguide devices. However, waveguides formed by ordinary photonic crystals do not have topological protection and essentially suffer from significant backscattering losses. On the contrary, topological edge states have strong robustness against backscattering caused by defects on the transport path, and the development of related technologies has become one of the leading fronts in physics and optics. A typical example is the construction of a topological one-way waveguide using chiral one-way edge states existing in magnetized gyrotropic photonic crystals (GPCs). In this case, the one-way edge waveguide has topological protection properties, allowing electromagnetic waves to propagate only in one direction and prohibiting backscattering under any type of defect, greatly improving the transmission efficiency.

[0003] Recently, the use of magneto-optical photonic crystals to generate topological photonic states with excellent properties such as one-way transmission, anti-backscattering, and immune-defect transmission has attracted extensive attention from researchers. However, so far, the vast majority of well-studied magneto-optical photonic crystals are based on basic square lattices [S.N. Zhuang, J.F. Chen, W.Y. Liang, and Z.Y. Li, Zero GVD slow-light originating from a strong coupling of one-way modes in double-channel magneto-optical photonic crystal waveguide, Opt. Express 29(2), 2478-2487(2021); S.A. Mann and A. Alu, Broadband topological slow light through Brillouin zone winding, Phys. Rev. Lett. 127(12), 123601(2021); A.C. Tasolamprou, M. Kafesaki, C.M. Soukoulis, E.N. Economou, and T. Koschny, Chiral topological surface on a finite square photonic crystal bounded by air, Phys. Rev. A 16(4), 044011(2021)], honeycomb lattices [X.Y. Ao, Z.F. Lin, and C.T. Chan, One-way edge mode in a magneto-optical honeycomb photonic crystal, Phys. Rev. B 80(3), 033105(2009); J.F. Chen, W.Y. Liang, and Z.Y. Li, Antichiral one-way edge states in a gyromagnetic photonic crystal, Phys. Rev. B 101(21), 214102(2020); P.H. Zhou, G.G. Liu, Y.H. Yang, Y.H. Hu, S.L. Ma, H.R. Xue, Q. Wang, L.J. Deng, and B.L. Zhang, Observation of photonic antichiral edge states, Phys. Rev. Lett.[[ID=125(26),263603(2020)]] and triangular lattice [[Y.F.Gao,L.He,X.F.Xu,J.P.Sun,Z.Jiang,and W.F.Bai,Achievement of unidirectional air waveguide with extra-broad operation bandwidth in magneto-optical photonic crystals with a triangle lattice,J.Magn.Magn.Mater.496,165921(2020);M.D.Wang,R.Y.Zhang,L.Zhang,D.Y.Wang,Q.H.Guo,Z.Q.Zhang,and C.T.Chan, “Topological One-Way Large-Area Waveguide States in Magnetic Photonic Crystals,” Phys.Rev.Lett.126(6),067401(2021)]]. However, the above materials are restricted by the simple geometric shape of the lattice, and these magneto-optical photonic crystal structures have only relatively few edge types, which is not conducive to establishing a transmission line with multiple edge types and studying the waveguide transmission of actual complex boundaries. Summary of the Invention

[0004] In order to overcome the disadvantages and deficiencies of existing waveguides, the object of the present invention is to propose a topological unidirectional waveguide based on a square-hexagonal composite lattice. This structure has five different types of unidirectional boundary waveguides, enriching the geometric and physical means for constructing unidirectional transport photonic topological states.

[0005] The object of the present invention is achieved by at least one of the following technical solutions.

[0006] A topological unidirectional waveguide of a square-hexagonal composite lattice, wherein the square-hexagonal composite lattice structure includes dielectric columns and a metal boundary. All dielectric columns are placed under an air background, and a square-hexagonal composite lattice structure with a square-hexagonal staggered pattern is formed by periodically arranging rotated square lattices along the x and y directions respectively.

[0007] Furthermore, the square-hexagonal composite lattice structure has five boundary types, namely the first boundary, the second boundary, the third boundary, the fourth boundary, and the fifth boundary. Among them, there are three zigzag boundaries along the x direction: the first boundary, the second boundary, and the third boundary; and there are two armchair boundaries along the y direction: the fourth boundary and the fifth boundary.

[0008] Among them, the first boundary removes a row of dielectric columns closest to the metal boundary to form the second boundary, and the second boundary continues to remove a row of dielectric columns closest to the metal boundary to form the third boundary; the fourth boundary removes a row of dielectric columns closest to the metal boundary to form the fifth boundary.

[0009] Further, a DC magnetic field is applied along the +z or -z direction of the dielectric column. Under the action of the applied magnetic field, the first boundary, the second boundary, the third boundary, the fourth boundary, and the fifth boundary composed of dielectric columns and the metal boundary can all generate topologically protected one-way waveguides.

[0010] Further, the magnitude of the magnetic field applied to the dielectric column along the +z or -z direction is H0 = 0.05 - 0.1 T, where T is the magnetic field unit tesla.

[0011] Further, the working frequencies of the topological one-way waveguides formed by the first boundary, the second boundary, the third boundary, the fourth boundary, and the fifth boundary are the same.

[0012] Further, the period constant of the rotated square lattice along the x direction is a; the period constant along the y direction is a is the lattice constant.

[0013] Further, the dielectric column is a circular dielectric column. The magneto-optical material used for the dielectric column includes yttrium iron garnet ferrite. The radius r of the dielectric column is 0.09a - 0.11a, where a is the lattice constant. (When the radius r of the dielectric column is 0.09a - 0.11a, a relatively wide working frequency range can be obtained. This is the result obtained through simulation, and the boundary states generated under this data are strong and have good topology. The specific values can be adjusted.) If the lattice constant a and the radius r of the dielectric column are changed, the working frequency corresponding to the topological one-way boundary waveguide will also change.

[0014] Further, the distance from the metal boundary to the center of the row of dielectric columns closest to it is called the waveguide width, and the waveguide width is 0.5a.

[0015] The present invention designs topological one-way waveguides of five different boundary types based on a square-hexagonal composite lattice structure. Each boundary and the metal boundary can form a one-way waveguide, and the waveguides formed by these five boundaries all have the topological property of anti-backscattering transmission, enriching the geometric and physical means for constructing one-way transport photonic topological states, and having great significance for efficient transmission in the field of optical communication.

[0016] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0017] (1) Topological protection: Compared with ordinary photonic crystals, the topological one-way waveguide of the present invention uses a magneto-optical photonic crystal. An externally applied magnetic field makes its operating frequency fall within the bandgap, thereby realizing topological properties such as anti-backscattering of the waveguide and immune defect transmission.

[0018] (2) High transmission efficiency: The topological one-way waveguide based on the one-way boundary state of the square-hexagonal composite lattice structure magneto-optical photonic crystal can better achieve high-efficiency transmission due to the anti-backscattering effect of waveguide transmission.

[0019] (3) Strong locality: The topological boundary state generated by the square-hexagonal composite lattice magneto-optical photonic crystal of the present invention has strong locality, making most of the energy concentrated at the boundary and preventing energy leakage into the dielectric column.

[0020] (4) Multiple boundary types: The topological one-way waveguide of the square-hexagonal composite lattice of the present invention has topological one-way waveguides with five different boundary types.

[0021] (5) Adjustable working bandwidth: The working frequency range of the square-hexagonal composite lattice topological one-way waveguide of the present invention is 17.45 - 17.95 (GHz). Brief Description of the Drawings

[0022] Figure 1 It is a schematic structural diagram of the topological one-way waveguide of the square-hexagonal composite lattice described in the present invention.

[0023] Figure 2 It is a one-way waveguide composed of the first boundary formed by circular dielectric columns and a metal boundary in Example 1, where Figure 2 (a) in it is the projected energy band diagram of the first boundary; Figure 2 (b) in it is the schematic diagram of the eigenfield corresponding to 2 points falling within the energy band gap in (a); Figure 2 (c) in it is the schematic diagram of the field transmission of the first boundary waveguide; Figure 2 (d) in it is the schematic diagram of the corresponding experimental measurement transmission spectrum.

[0024] Figure 3 It is a one-way waveguide composed of the second boundary formed by circular dielectric columns and a metal boundary in Example 2, where Figure 3 (a) in it is the projected energy band diagram of the second boundary; Figure 3 (b) in it is the schematic diagram of the eigenfield corresponding to 2 points falling within the energy band gap in (a); Figure 3 (c) in it is the schematic diagram of the field transmission of the second boundary waveguide; Figure 3 (d) in it is the schematic diagram of the corresponding experimental measurement transmission spectrum.

[0025] Figure 4The unidirectional waveguide formed by the third boundary composed of circular dielectric columns and the metal boundary in Embodiment 3, where Figure 4 Figure (a) in Figure 4 is the projected energy band diagram of the third boundary; Figure 4 Figure (b) in Figure 4 is the schematic diagram of the eigenfield corresponding to two points falling within the energy band gap in (a);

[0026] Figure 5 The unidirectional waveguide formed by the fourth boundary composed of circular dielectric columns and the metal boundary in Embodiment 4, where Figure 5 Figure (a) in Figure 5 is the projected energy band diagram of the fourth boundary; Figure 5 Figure (b) in Figure 5 is the schematic diagram of the eigenfield corresponding to two points falling within the energy band gap in (a);

[0027] Figure 6 The unidirectional waveguide formed by the fifth boundary composed of circular dielectric columns and the metal boundary in Embodiment 5, where Figure 6 Figure (a) in Figure 6 is the projected energy band diagram of the fifth boundary; Figure 6 Figure (b) in Figure 6 is the schematic diagram of the eigenfield corresponding to two points falling within the energy band gap in (a);

[0028] Figure 7 is the structural data diagram of the topological unidirectional waveguide with a square - hexagonal composite lattice of the present invention to verify its transmission robustness.

[0029] Figure 8 The unidirectional waveguide formed by the first boundary composed of circular dielectric columns and the metal boundary in Embodiment 6, where Figure 6 Figure (a) in Figure 6 is the projected energy band diagram of the first boundary; Figure (b) in

[0030] The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments, but the scope of implementation of the present invention is not limited thereto.

[0031] A topological unidirectional waveguide with a square - hexagonal composite lattice, the structural schematic diagram is as shown in Figure 1As shown, it consists of circular dielectric columns 7 with a square - hexagonal composite lattice structure and a metal boundary 8. All dielectric columns are placed in an air background. The square - hexagonal composite lattice structure is formed by the periodic arrangement of rotated square lattices 6 along the x and y directions respectively, where the periodic constant along the x - direction is a; the periodic constant along the y - direction is a is the lattice constant.

[0032] As Figure 1 shown, there are five types of boundaries in this square - hexagonal composite lattice structure, namely the first boundary 1, the second boundary 2, the third boundary 3, the fourth boundary 4, and the fifth boundary 5. Among them, there are three zigzag boundaries along the x - direction: the first boundary 1, the second boundary 2, and the third boundary 3; there are two armchair - shaped boundaries along the y - direction: the fourth boundary 4 and the fifth boundary 5.

[0033] Among them, removing the row of dielectric columns closest to the metal boundary from the first boundary 1 forms the second boundary 2, and continuing to remove the row of dielectric columns closest to the metal boundary from the second boundary 2 forms the third boundary 3. Removing the row of dielectric columns closest to the metal boundary from the fourth boundary 4 forms the fifth boundary 5.

[0034] Example 1

[0035] Place YIG cylindrical dielectric columns (the radius r of the dielectric column is taken as 0.11a, the lattice constant a is 14 mm, and the radius r of the dielectric column is 1.5 mm) between parallel metal plates with a height of 5 mm. The thickness of the metal plate is 1 mm; two other metal plates of the same height are embedded with cylindrical permanent magnets with a radius of 2 mm and a height of 2 mm at the bottom layer and the top layer. The cylindrical permanent magnets are vertically aligned with the YIG cylinder to apply a magnetic field, and the magnetic field magnitude is 0.08 T. Under the action of the external magnetic field, a topologically protected one - way waveguide is generated between the first boundary composed of circular dielectric columns and the metal boundary. The width of the waveguide is 0.5a, the lattice constant a is 14 mm, and the waveguide width is 7 mm. The operating frequency of the topological one - way waveguide formed by the first boundary is 17.45 - 17.95 GHz.

[0036] Figure 2 This is the one - way waveguide formed by the first boundary and the metal boundary in this example. Among them, Figure 2 (a) is the projected energy - band diagram corresponding to the first boundary. Two dispersion curves appear in the frequency range of 17.45 - 17.95 GHz. According to the slope of the dispersion curve being the direction of the group velocity, it is obtained that the directions of the group velocities of these two dispersion curves are opposite in this frequency range, and the electromagnetic field is transmitted in opposite directions along the two parallel boundaries, that is, the boundary state supported by the first boundary exhibits chiral transmission characteristics. Figure 2 (b) of Figure 2In (a), for the two points (1, 2) falling within the bandgap, the corresponding eigenfields can be seen. Their electric fields are both localized at the boundaries, so they are both boundary states. And since the slopes of the dispersion curves of eigenstate 1 and eigenstate 2 are positive and negative respectively, eigenstate 1 will propagate to the right along the lower boundary, while eigenstate 2 will propagate to the left along the upper boundary. Figure 2 (c) is a schematic diagram of field propagation. The lower boundary is set as an ideal electric conductor to form a waveguide channel, and other boundaries are set with scattering boundary conditions. A point excitation source is set at the lower boundary. The simulation results intuitively show that the first boundary of the square-hexagonal composite lattice structure can excite boundary states that propagate unidirectionally to the right. Using a network analyzer for transmission measurement, the transmitting and receiving probes are placed Figure 2 at the two marked points (Port1, Port2) in (c) for measurement. Figure 2 (d) is an experimental transmission spectrum diagram of the boundary state propagation at the first boundary. The transmission coefficients S21 and S12 show a strong contrast. The waveguide transmission only propagates to the right while suppressing the leftward propagation. The signal non-reciprocity between the leftward and rightward propagated signals reaches 30 - 35 dB, demonstrating good unidirectional propagation characteristics. Among them, the transmission coefficient Sab refers to the transmission coefficient from point b to point a. The experimental results are Figure 2 consistent with the theoretical prediction results in (a).

[0037] Example 2

[0038] A YIG cylindrical dielectric column (the radius r of the dielectric column is taken as 0.11a, the lattice constant a is 14 mm, and the radius r of the dielectric column is 1.5 mm) is placed between parallel metal plates with a height of 5 mm, and the thickness of the metal plates is 1 mm; another two metal plates of the same height are embedded with cylindrical permanent magnets with a radius of 2 mm and a height of 2 mm at the bottom layer and the top layer. The cylindrical permanent magnets are vertically aligned with the YIG cylinder to apply a magnetic field, and the magnetic field magnitude is 0.08 T. Under the action of the externally applied magnetic field, a topologically protected unidirectional waveguide is generated between the second boundary composed of circular dielectric columns and the metal boundary. The waveguide width is 0.5a, the lattice constant a is 14 mm, and the waveguide width is 7 mm. The operating frequency of the topologically unidirectional waveguide formed by the second boundary is 17.45 - 17.95 GHz.

[0039] Figure 3 is the unidirectional waveguide formed by the second boundary and the metal boundary of this example. Among them, Figure 3 (a) is the projected band diagram corresponding to the second boundary. Two dispersion curves appear in the frequency range of 17.45 - 17.95 GHz. According to the slope of the dispersion curve being the direction of the group velocity, it is obtained that the directions of the group velocities of these two dispersion curves are opposite in this frequency range, and the electromagnetic field propagates in opposite directions along the two parallel boundaries, that is, the boundary states supported by the second boundary exhibit chiral transmission characteristics.Figure 3 In (b) of Figure 3 For the two points (1, 2) in (a) of that fall within the bandgap, the corresponding eigenfields can be seen. Their electric fields are both localized at the boundary, so they are both boundary states. And since the slopes of the dispersion curves of eigenstate 1 and eigenstate 2 are positive and negative respectively, eigenstate 1 will propagate to the right along the lower boundary, while eigenstate 2 will propagate to the left along the upper boundary. Figure 3 In (c) of is a schematic diagram of field propagation. The lower boundary is set as an ideal electric conductor to form a waveguide channel, and other boundaries are set with scattering boundary conditions. A point excitation source is set at the lower boundary, and the simulation results intuitively show that the lower second boundary of the square - hexagonal composite lattice structure can excite boundary states that propagate unidirectionally to the right. Figure 3 In (d) of is the experimental transmission spectrum of the boundary state propagation at the second boundary. The transmission coefficients S21 and S12 show a strong contrast. The waveguide transmission only propagates to the right and suppresses the left - hand propagation. The signal non - reciprocity between the left - and right - hand propagating signals reaches 30 - 35 dB, indicating good unidirectional propagation characteristics. The experimental results are Figure 3 consistent with the theoretical prediction results in (a) of .

[0040] Example 3

[0041] A YIG cylindrical dielectric column (with the radius r of the dielectric column taken as 0.11a, the lattice constant a being 14 mm, and the radius r of the dielectric column being 1.5 mm) is placed between parallel metal plates with a height of 5 mm and a thickness of 1 mm for the metal plates. Additionally, two other metal plates of the same height are embedded with cylindrical permanent magnets with a radius of 2 mm and a height of 2 mm at the bottom layer and the top layer. The cylindrical permanent magnets are vertically aligned with the YIG cylinder to apply a magnetic field, and the magnetic field magnitude is 0.08 T. Under the action of the externally applied magnetic field, a topologically protected unidirectional waveguide is generated between the third boundary composed of circular dielectric columns and the metal boundary. The waveguide width is 0.5a, the lattice constant a is 14 mm, and the waveguide width is 7 mm. The operating frequency of the topologically unidirectional waveguide formed by the third boundary is 17.45 - 17.95 GHz.

[0042] Figure 4 This is the unidirectional waveguide formed by the third boundary and the metal boundary of this example. Among them, Figure 4 In (a) of is the projected band diagram corresponding to the third boundary. Two dispersion curves appear in the frequency range of 17.45 - 17.95 GHz. According to the slope of the dispersion curve being the direction of the group velocity, it is obtained that the directions of the group velocities of these two dispersion curves are opposite in this frequency range, and the electromagnetic fields propagate in opposite directions along the two parallel boundaries, that is, the boundary states supported by the third boundary exhibit chiral propagation characteristics. Figure 4 In (b) of is Figure 4In (a), the eigenfields corresponding to the two points (1, 2) falling within the bandgap can be seen. Their electric fields are both localized at the boundaries, so they are both boundary states. And since the slopes of the dispersion curves of eigenstate 1 and eigenstate 2 are positive and negative respectively, eigenstate 1 will propagate to the right along the lower boundary, while eigenstate 2 will propagate to the left along the upper boundary. Figure 4 (c) is a schematic diagram of field propagation. The lower boundary is set as an ideal electric conductor to form a waveguide channel, and other boundaries are set with scattering boundary conditions. A point excitation source is set on the lower boundary. The simulation results intuitively show that the lower third boundary of the square-hexagonal composite lattice structure can excite boundary states that propagate unidirectionally to the right. Figure 4 (d) is an experimental transmission spectrum diagram of the boundary state propagation on the third boundary. The transmission coefficients S21 and S12 show a strong contrast. The waveguide transmission only propagates to the right and suppresses the leftward propagation. The signal non-reciprocity between the leftward and rightward propagating signals reaches 26 - 32 dB, indicating good unidirectional propagation characteristics. The experimental results are consistent with Figure 4 the theoretical prediction results in (a).

[0043] Example 4

[0044] Place YIG cylindrical dielectric columns (the radius r of the dielectric column is taken as 0.11a, the lattice constant a is 14 mm, and the radius r of the dielectric column is 1.5 mm) between parallel metal plates with a height of 5 mm. The thickness of the metal plates is 1 mm; two other metal plates of the same height are embedded with cylindrical permanent magnets with a radius of 2 mm and a height of 2 mm at the bottom layer and the top layer. The cylindrical permanent magnets are vertically aligned with the YIG cylinders to apply a magnetic field, and the magnetic field magnitude is 0.08 T. Under the action of the applied magnetic field, a topologically protected unidirectional waveguide is generated between the fourth boundary composed of circular dielectric columns and the metal boundary. The waveguide width is 0.5a, the lattice constant a is 14 mm, and the waveguide width is 7 mm. The operating frequency of the topologically unidirectional waveguide formed by the fourth boundary is 17.45 - 17.95 GHz.

[0045] Figure 5 This is the unidirectional waveguide formed by the fourth boundary and the metal boundary in this example. Figure 5 (a) is the projected band diagram corresponding to the fourth boundary. Two dispersion curves appear in the frequency range of 17.45 - 17.95 GHz. According to the slope of the dispersion curve being the direction of the group velocity, it is obtained that the directions of the group velocities of these two dispersion curves are opposite in this frequency range, and the electromagnetic field propagates in opposite directions along the two parallel boundaries, that is, the boundary states supported by the fourth boundary exhibit chiral transmission characteristics. Figure 5 (b) is Figure 5In the (a) figure, for the two points (1, 2) in the bandgap, the corresponding eigenfields can be seen. Their electric fields are both localized on the boundary, so they are both boundary states. And since the slopes of the dispersion curves of eigenstate 1 and eigenstate 2 are positive and negative respectively, eigenstate 1 will propagate to the right along the lower boundary, while eigenstate 2 will propagate to the left along the upper boundary. Figure 5 Figure (c) is a schematic diagram of field propagation. The lower boundary is set as an ideal electric conductor to form a waveguide channel, and other boundaries are set with scattering boundary conditions. A point excitation source is set on the lower boundary. The simulation results intuitively show that the lower fourth boundary of the square-hexagonal composite lattice structure can excite boundary states that propagate unidirectionally to the right. Figure 5 Figure (d) is an experimental transmission spectrum diagram of the boundary state propagation on the fourth boundary. The transmission coefficients S21 and S12 show a strong contrast. The waveguide transmission only propagates to the right and suppresses the leftward propagation. The signal non-reciprocity between the leftward and rightward propagated signals reaches 30 - 35 dB, indicating good unidirectional propagation characteristics. The experimental results are Figure 5 consistent with the theoretical prediction results in (a) of

[0046] Example 5

[0047] Place a YIG cylindrical dielectric column (the radius r of the dielectric column is taken as 0.11a, the lattice constant a is 14 mm, and the radius r of the dielectric column is 1.5 mm) between parallel metal plates with a height of 5 mm, and the thickness of the metal plates is 1 mm; another two metal plates of the same height are embedded with cylindrical permanent magnets with a radius of 2 mm and a height of 2 mm at the bottom layer and the top layer. The cylindrical permanent magnets are vertically aligned with the YIG cylinder to apply a magnetic field, and the magnetic field magnitude is 0.08 T. Under the action of the applied magnetic field, a topologically protected unidirectional waveguide is generated between the fifth boundary composed of circular dielectric columns and the metal boundary. The waveguide width is 0.5a, the lattice constant a is 14 mm, and the waveguide width is 7 mm. The operating frequency of the topological unidirectional waveguide formed by the fifth boundary is 17.45 - 17.95 GHz.

[0048] Figure 6 is the unidirectional waveguide formed by the fifth boundary and the metal boundary of this example. Figure 6 Figure (a) is the projected band diagram corresponding to the fifth boundary. Two dispersion curves appear in the frequency range of 17.45 - 17.95 GHz. According to the slope of the dispersion curve being the direction of the group velocity, it is obtained that the directions of the group velocities of these two dispersion curves are opposite in this frequency range, and the electromagnetic fields propagate in opposite directions along the two parallel boundaries, that is, the boundary states supported by the fifth boundary exhibit chiral transmission characteristics. Figure 6 Figure (b) is Figure 6In (a), for the two points (1, 2) in the bandgap, the corresponding eigenfields can be seen. Their electric fields are both localized on the boundary, so they are both boundary states. And since the slopes of the dispersion curves of eigenstate 1 and eigenstate 2 are positive and negative respectively, eigenstate 1 will propagate to the right along the lower boundary, while eigenstate 2 will propagate to the left along the upper boundary. Figure 6 (c) is a schematic diagram of field propagation. The lower boundary is set as an ideal electric conductor to form a waveguide channel, and other boundaries are set with scattering boundary conditions. An excitation source is set at a point on the lower boundary. The simulation results intuitively show that the fifth lower boundary of the square - hexagonal composite lattice structure can excite boundary states that propagate unidirectionally to the right. Figure 6 (d) is the experimental transmission spectrum diagram of the boundary state propagation on the fifth boundary. The transmission coefficients S21 and S12 show a strong contrast. The waveguide transmission only propagates to the right and suppresses the left - hand propagation. The signal non - reciprocity between the left - hand and right - hand propagating signals reaches 20 - 25 dB, indicating good unidirectional propagation characteristics. The experimental results are Figure 6 consistent with the theoretical prediction results in (a).

[0049] To further verify that the unidirectional waveguides generated by the five boundaries have topological protection functions, in the above - mentioned Examples 1 - 5, Figure 1 (c), Figure 2 (c), Figure 3 (c), Figure 4 (c), Figure 5 (c), Figure 6 On each channel in (c), a metal rod (width 0.3a, height 2a) is inserted, as shown in (a1) of Figure 7 , (b1) of Figure 7 , (c1) of Figure 7 , (d1) of Figure 7 , (e1) of Figure 7 respectively, and the remaining features are the same. It is observed that the electromagnetic waves in each channel can bypass the metal rod and continue to propagate, and the transmitted energy is hardly affected. It is verified that the unidirectional waveguides generated by the five boundaries all have the topological property of anti - defect transmission. Figure 7 (a2) - (e2) respectively correspond to Figure 7 (a1) - (e1) of the experimental transmission spectrum diagrams. The forward transmission and the reverse transmission also show a large contrast, proving that the metal obstacles have no impact on the transmission of the unidirectional boundary states, indicating that the topological unidirectional waveguide of a square - hexagonal composite lattice of the present invention has transmission robustness.

[0050] Example 6

[0051] The radius r of the dielectric column is taken as 0.09a, the lattice constant a is 35.5 mm, and the radius r of the dielectric column is 3.2 mm. Under the action of an external magnetic field, the magnetic field magnitude is 0.05 T. The first boundary and the metal boundary generate a topologically protected one-way waveguide. The waveguide width is 0.5a, the lattice constant a is 35.5 mm, and the waveguide width is 17.75 mm. The operating frequency of the topological one-way waveguide formed by the first boundary is 5.7 - 5.9 GHz, and the corresponding normalized frequency is 0.67 - 0.70(2πc / a), where (2πc / a) is the unit, π is the pi, c is the speed of light, and a is the lattice constant.

[0052] Figure 8 This is the one-way waveguide formed by the first boundary and the metal boundary of this embodiment. Figure 8 (a) is the projected energy band diagram corresponding to the first boundary. Two dispersion curves appear in the frequency range of 0.67 - 0.70(2πc / a). According to the slope of the dispersion curve being the direction of the group velocity, it is obtained that the directions of the group velocities of these two dispersion curves are opposite in this frequency range, and the electromagnetic field is transmitted in opposite directions along two parallel boundaries, that is, the boundary state supported by the first boundary exhibits chiral transmission characteristics. Figure 8 (b) is the schematic diagram of field transmission. The lower boundary is set as an ideal electric conductor to form a waveguide channel, and other boundaries are set as scattering boundary conditions. A point excitation source is set at the lower boundary, and the simulation results intuitively show that the lower first boundary of the square - hexagonal composite lattice structure can excite a boundary state that transmits unidirectionally to the right.

[0053] The above embodiments are the preferred embodiments of the present invention, but the embodiments of the present invention are not limited by the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications made without departing from the spirit and principle of the present invention shall be equivalent replacement methods and are all included in the protection scope of the present invention.

Claims

1. A topological unidirectional waveguide with a square - hexagonal composite lattice, characterized in that, The topological one-way waveguide of the square-hexagonal composite lattice includes dielectric columns (7) and a metal boundary (8); the magneto-optical material used for the dielectric columns (7) includes yttrium iron garnet ferrite. The topological one-way waveguide of the square-hexagonal composite lattice is a topological one-way waveguide based on the one-way edge state of a magneto-optical photonic crystal of the square-hexagonal composite lattice. All the dielectric columns are placed in an air background. A rotating square lattice (6) is formed by four dielectric columns (7), and the rotating square lattice (6) is periodically arranged along the x , y directions to form a square-hexagonal composite lattice with a square-hexagonal staggered structure.

2. The topological unidirectional waveguide of a square-hexagonal composite lattice according to claim 1, wherein There are five boundary types for the topological one-way waveguide of the square-hexagonal composite lattice, namely the first boundary (1), the second boundary (2), the third boundary (3), the fourth boundary (4), and the fifth boundary (5), among which there are three zigzag boundaries along the x direction: the first boundary (1), the second boundary (2), and the third boundary (3); and there are two armchair boundaries along the y direction: the fourth boundary (4) and the fifth boundary (5).

3. The topological unidirectional waveguide of a square-hexagonal composite lattice according to claim 2, characterized in that, Removing the row of dielectric pillars closest to the metal boundary from the first boundary (1) forms the second boundary (2), and continuously removing the row of dielectric pillars closest to the metal boundary from the second boundary (2) forms the third boundary (3); removing the row of dielectric pillars closest to the metal boundary from the fourth boundary (4) forms the fifth boundary (5).

4. A topological unidirectional waveguide of a square-hexagonal composite lattice according to claim 1, characterized in that, Applying a DC magnetic field along the +z or -z direction of the dielectric pillar (7), under the action of the applied magnetic field, the first boundary (1), the second boundary (2), the third boundary (3), the fourth boundary (4), and the fifth boundary (5) composed of dielectric pillars generate a topologically protected one-way waveguide with the metal boundary.

5. A topological unidirectional waveguide of a square-hexagonal composite lattice according to claim 4, characterized in that, The magnitude of the magnetic field applied to the dielectric column (7) in the +z or -z direction is H 0 = 0.05 T to 0.1 T, where T is the magnetic field unit tesla.

6. The topological unidirectional waveguide of a square-hexagonal composite lattice according to claim 4, characterized in that, The working frequencies of the topological one-way waveguides formed by the first boundary (1), the second boundary (2), the third boundary (3), the fourth boundary (4), and the fifth boundary (5) are the same.

7. A topological unidirectional waveguide of a square-hexagonal composite lattice according to claim 1, characterized in that The periodic constant of the rotating square lattice (6) in the x direction is a ; the periodic constant in the y direction is a .

8. A topological unidirectional waveguide of a square-hexagonal composite lattice according to claim 1, characterized in that The dielectric pillar (7) is a circular dielectric pillar, and the radius of the dielectric pillar (7) r is 0.09 a ~0.11 a , a being the periodic constant of the rotated square lattice (6) in the x direction.

9. A topological unidirectional waveguide of a square-hexagonal composite lattice according to claim 8, characterized in that Changing the periodic constant of the rotating square lattice (6) along the x-direction a and the radius of the dielectric pillar r , the operating frequency corresponding to the topological unidirectional waveguide of the square-hexagonal composite lattice will also change.

10. A topological unidirectional waveguide of a square-hexagonal composite lattice according to any one of claims 7-9, characterized in that, The center distance from the metal boundary (8) to the center of the nearest row of dielectric columns (7) is called the waveguide width, and the waveguide width is 0.5 a .

Images