Terahertz valley topology photonic crystal and broadband topology optical waveguide based on rotating elliptical medium column

Abstract

The application provides a terahertz valley topology photonic crystal based on a rotating elliptical medium column and a wideband topology optical waveguide, the valley topology photonic crystal is arranged by rotating elliptical medium columns in a medium with a background refractive index of 1.39, the deflection angle of the rotating elliptical medium column rotating counterclockwise around the axis can be adjusted between 0° and 60°, the VPC of two topological properties is realized, and two photonic band gaps can be obtained, wherein the low-frequency band gap width can reach 0.21 (2pi c / a), and the high-frequency band gap width can reach 0.38 (2pi c / a), which is significantly increased compared with the previous structure, and thus is suitable for the design of wideband, frequency selection and devices. The optical waveguide constructed by the crystal structure has unidirectional robust transmission, high transmission rate, enhanced optical localization, and immunity to defects such as disorder, cavity and sharp bend. The optical waveguide structure can realize unidirectional transmission of different paths such as "U", "Y" and "Z" through rotating medium columns.

Description

Technical Field

[0001] This invention relates to the field of valley topological photonic crystals, and more particularly to a terahertz valley topological photonic crystal and a broadband topological waveguide based on a rotating elliptical dielectric pillar. Background Technology

[0002] Valley topological photonics, a subfield of topological photonics, requires breaking time-reversal symmetry using gyromagnetic materials to realize the photonic quantum Hall effect. Because the chiral boundary states of the photonic quantum Hall effect are topologically protected, they are robust to any perturbations at the boundaries, especially photonic topological insulators based on the photonic quantum Hall effect. Photonic topological insulators based on the photonic quantum spin Hall effect are achieved by constructing pseudospins, which provide the possibility of optical manipulation. Although the robustness of the photonic quantum spin Hall effect is not as robust as that of the photonic quantum Hall effect, its implementation is relatively easy, making it highly attractive. Valley topological photonic crystals have applications in many fields, such as topological lasers, robust optical delay lines, and optical waveguide devices.

[0003] The quantum valley Hall effect does not require breaking time reversal symmetry or constructing pseudospin; it only requires that the quantum valley Hall effect has the following properties: In a symmetric lattice, the Dirac point is positioned on inequivalent valleys (K and K′ valleys), and the valley Hall effect is achieved through a phase transition mechanism. Similar to the quantum spin Hall effect, realizing the quantum valley Hall effect also requires the introduction of a degree of freedom, namely the valley degree of freedom. Currently, there are two main ways to introduce the valley degree of freedom: using electromagnetically dual valley photonic crystals or using all-dielectric valley photonic crystals. Summary of the Invention

[0004] This invention designs a terahertz valley topological photonic crystal based on a rotating elliptical dielectric pillar. By rotating the dielectric pillar, two topological properties and double Dirac cone degeneracy can be achieved. The structure is simple, with high transmission efficiency and enhanced photon localization, making it easier to apply in practice. Based on the proposed valley topological photonic crystal, a flexible optical waveguide structure capable of multi-path transmission is designed. Electromagnetic waves within the operating bandwidth can robustly propagate unidirectionally along the interface of the two valley photonic crystals.

[0005] The present invention achieves the above-mentioned technical objectives through the following technical means:

[0006] A terahertz valley topological photonic crystal based on rotating elliptical dielectric pillars is characterized by being composed of rotating elliptical dielectric pillars arranged in a medium with a background refractive index of 1.39. The cross-sectional shape of each rotating elliptical dielectric pillar is a C3 symmetrical structure formed by three elliptical arcs joined end-to-end. The refractive index of the rotating elliptical dielectric pillars is... The ellipse has a major semi-axis of a and a minor semi-axis of b. Each rotating elliptical dielectric pillar constitutes a regular hexagonal unit cell, and the distance between the centers of adjacent regular hexagonal unit cells is a lattice constant. The deflection angle of the rotating elliptical medium column rotating counterclockwise about its axis is . ,and Define the deflection angle when the minor axis of the elliptical arc of the rotating elliptical dielectric cylinder lies on the line connecting the axis of the rotating elliptical dielectric cylinder and the vertex of the regular hexagonal unit cell. .

[0007] Furthermore, the deflection angle of the rotating elliptical medium column rotating counterclockwise about its axis is... The valley topological photonic crystal has two photonic band gaps, referred to as VPC1.

[0008] Furthermore, the deflection angle of the rotating elliptical medium column rotating counterclockwise about its axis The valley topological photonic crystal has two photonic band gaps, referred to as VPC2.

[0009] Furthermore, the deflection angle of the rotating elliptical medium column rotating counterclockwise about its axis = At that time, the valley topological photonic crystal has a degenerate Dirac cone, referred to as VPC3.

[0010] Furthermore, the major semi-axis of the rotating elliptical medium cylinder short half-shaft , where r is .

[0011] Furthermore, the lattice constant .

[0012] A broadband topological optical waveguide based on the valley topological photonic crystal described above, characterized in that the optical waveguide structure is composed of components with a deflection angle of... Photonic crystal VPC2 and deflection angle of The photonic crystals VPC1 and VPC2 are spliced ​​together adjacent to each other, and there is a splicing boundary between the photonic crystals VPC1 and VPC2 that is parallel to the axis of the rotating elliptical dielectric cylinder. The optical waveguide structure has two common band gaps, one for low frequency and one for high frequency.

[0013] Furthermore, the splicing boundary between the photonic crystal VPC2 and the photonic crystal VPC1 has a bend.

[0014] Furthermore, the splicing boundary between the photonic crystal VPC2 and the photonic crystal VPC1 is one or more.

[0015] Furthermore, the optical waveguide structure supports unidirectional optical transmission and is a topology-protected boundary-state waveguide structure with an operating bandwidth of 0.63. up to 0.84 (corresponding to 190THz-240THz) and 1.35 Up to 1.73 (corresponding to 400THz-520THz), where c is the speed of light.

[0016] The terahertz valley topological photonic crystal based on a rotating elliptical dielectric pillar described in this invention achieves two topological properties and double Dirac cone degeneracy by simply rotating the dielectric pillar and controlling its rotation angle, without changing the lattice constant, the size and position of the dielectric pillar, or the background material. The structure is simple, with high transmission efficiency and strong photonic localization. Compared to previous schemes that changed the size of the dielectric pillar within the lattice to achieve unidirectional transmission of boundary states, this scheme is simpler and easier to apply in practice.

[0017] The optical waveguide structure constructed based on the valley topology photonic crystal provided by this invention, compared with the existing valley topology photonic crystal optical waveguide structure, can not only realize two types of VPC with different topological properties by rotating the elliptical dielectric pillar, but also change the photonic bandgap. In practical applications, the rotation angle can be changed according to actual needs.

[0018] The optical waveguide structure designed in this invention has a large operating bandwidth, possesses two common bandgap (high-frequency and low-frequency), exhibits high transmission rate (up to 99%), suppresses backscattering, enables robust unidirectional transmission, and enhances optical locality, making it immune to disorder, cavities, and sharp bends. It has enormous potential applications in optical communication and optical switching.

[0019] The optical waveguide structure designed in this invention does not require changing the lattice constant. Given the size of the dielectric column and the materials of the background and dielectric column, electromagnetic wave transmission through multiple paths can be achieved simply by controlling the rotation angle, making it a highly valuable application option. Attached Figure Description

[0020] Figure 1 (a), (b), and (c) are deflection angles. , and The schematic diagrams of the cross-sectional structures of the unit cells are denoted as VPC1, VPC3, and VPC2, respectively, where θ is the deflection angle. Let be the lattice constant of the unit cell. (d) The band structure corresponding to VPC3, at K and A degenerate Dirac cone appears at this point. (e)-(f) Band structures corresponding to VPC1 and VPC2, with the gray rectangular region representing their common bandwidth. The phase distribution indicates... and They have opposite chirality.

[0021] Figure 2 For the unit cell of VPC2, n, , The change of b with respect to the Dirac cone frequency The impact, including:

[0022] (a) is when , At that time, in the unit cell Refractive index with background The changing trend;

[0023] (b) When , At that time, in the unit cell With the refractive index of the medium column The changing trend;

[0024] (c) When , , At that time, the band gap width of the unit cell increases with... The trend of change, distance The farther away, the wider the band gap;

[0025] (d) When , , At that time, in the unit cell With the short half-axis of the medium column The trend of value changes.

[0026] Figure 3 (a) is a two-dimensional schematic diagram of the supercell constructed by VPC1 and VPC2; (b) is a banded dispersion curve of the supercell in (a), showing a topologically protected boundary state in the bulk band gap, located in the gray region, with the positive and negative slopes of the curves representing pseudospin-up and pseudospin-down, respectively. (c) is an equilateral triangle in (b) ) and inverted triangle ( ) at the corresponding boundary Field distribution and corresponding Poynting vector diagram.

[0027] Figure 4(a) is a two-dimensional schematic diagram of the designed optical waveguide structure. (b) is the field strength distribution diagram of the topological boundary state propagating along a straight line at a frequency of 193.28 THz. The yellow stars are chiral sources. (c) is the normalized electric field distribution diagram on the white horizontal dashed line. (d) is the normalized electric field distribution diagram on the white vertical dashed line.

[0028] Figure 5 Figures (a), (b), and (c) show the electric field distributions of three different defects—disorder, cavity, and sharp bend—constructed in the optical waveguide structure. Figures (d), (e), and (f) are magnified views of the Poynting vectors at the disorder A, cavity B, and sharp bend C, respectively. Figure (g) shows the transmittance at the boundary states of defect-free, disordered, cavity, and sharp bend conditions.

[0029] Figure 6 A tunable topological photonic crystal model was designed to adjust the propagation path of electromagnetic waves by changing the pseudospin state, which can achieve 1 Electromagnetic wave transmission using two beam splitters, "U"-shaped, and "Ω"-shaped beams was demonstrated and verified through simulation.

[0030] In the diagram: 1 represents the medium, and 2 represents the medium column. Detailed Implementation

[0031] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0032] The terahertz valley topological photonic crystal based on rotating elliptical dielectric pillars provided by this invention consists of rotating elliptical dielectric pillars arranged in a medium with a background refractive index of 1.39. The cross-sectional shape of the rotating elliptical dielectric pillars is a C3 symmetrical structure formed by three elliptical arcs connected end-to-end. The refractive index of the rotating elliptical dielectric pillars is... The ellipse has a major axis a and a minor axis b. Each rotating elliptical dielectric pillar forms a regular hexagonal unit cell, and the distance between the centers of adjacent regular hexagonal unit cells is a lattice constant. The deflection angle of the rotating elliptical medium column rotating counterclockwise about its axis Define the deflection angle when the minor axis of the elliptical arc of the rotating elliptical dielectric cylinder lies on the line connecting the axis of the dielectric cylinder and the vertex of the regular hexagonal unit cell. .

[0033] Figure 1 The diagram shows the unit cell of the terahertz topological photonic crystal structure based on a rotating elliptical dielectric pillar designed in this invention. The two-dimensional cross-section of the unit cell consists of a rotating elliptical dielectric pillar and a dielectric material with a refractive index of 1.39. The refractive index of the dielectric pillar material is... 0.22. The cross-section of the unit cell is a regular hexagon, and the distance between the centers of two adjacent unit cells is the lattice constant. The white area represents the background of the crystal structure, with a refractive index of [missing information]. . Figure 1 In the diagram, (a), (b), and (c) represent the deflection angles. , and Three valley topological photonic crystal cells; the deflection angle Starting from the positive y-axis, rotate counterclockwise around the center of the hexagon, and label them as VPC1, VPC3, and VPC2 respectively.

[0034] like Figure 1 (d) shows the deflection angle. The band structure of the valley topological photonic crystal, corresponding to the band gap at K and At this point, a degenerate Dirac cone, or energy valley, appears. If the lattice symmetry is broken, causing the deflection angle to increase or decrease, then the degenerate energy valley will be opened, resulting in a photonic bandgap.

[0035] when At this time, the valley topological photonic crystal is called VPC1, and the valley degeneracy is opened, resulting in a band gap. In the first (blue curve) and second band (green curve), the valley K( ) are defined respectively ( )and ( ). The phase of the valley decreases in a clockwise direction (as indicated by the blue rotating arrow), and we define the photon state at this point as a pseudo-spin-down state. ;and on the contrary, The phase of the valley decreases in a counterclockwise direction (as indicated by the green rotating arrow), and the photon state at this point is defined as a pseudo-spin-up state. . and The phase distribution of the energy valley can also be obtained through numerical simulation. Corresponding pseudo-spin-up state , pseudo-spin-down state .when At this time, the valley topological photonic crystal is called VPC2. At this time, the photonic band structure is exactly the same as that of VPC1, but the phase distribution is opposite. The phase of the valley decreases counterclockwise (as indicated by the green rotating arrow), and the photon state at this point is a pseudo-spin-up state. ; The phase of the valley decreases in a clockwise direction (indicated by the blue rotating arrow), at which point the photon state is a pseudo-spin-down state. .at this time Corresponding pseudospin-down state , pseudo-spin-up state .like Figure 1 As shown in (e) and (f), when respectively and At this point, the lattice symmetry is broken, the degenerate valley is opened, and a photonic bandgap appears. VPC1 and VPC2 both have two common bandgap widths, with widths of 0.63 and 0.63, respectively. up to 0.84 This corresponds to 190THz-240THz; and 1.35 Up to 1.73 This corresponds to 400THz-520THz. and The phase distribution at the valley indicates that VPC1 and VPC2 have opposite chirality.

[0036] The quantum valley Hall effect does not require breaking time reversal symmetry or constructing pseudospin; it only requires that the quantum valley Hall effect has the following properties: In a symmetric lattice, the Dirac point is positioned on an inequivalent valley, namely the K and K′ valleys, and the valley Hall effect is achieved through a phase transition mechanism. Similar to the quantum spin Hall effect, realizing the quantum valley Hall effect also requires the introduction of a degree of freedom, namely the valley degree of freedom. Currently, there are two main ways to introduce the valley degree of freedom: using electromagnetically dual valley photonic crystals or using all-dielectric valley photonic crystals.

[0037] set up ,when At that time, we analyzed several key parameters n, , The effect of changes in b on the Dirac cone frequency, such as Figure 2 As shown. When , , At that time, we found the frequency at the Dirac point. It decreases as the background refractive index n increases, such as Figure 2 As shown in (a). When , At that time, frequency With the refractive index of the medium column As it increases, it decreases, such as Figure 2 As shown in (b). When , At that time, the band gap width increases with The trend of change, distance The farther away, the wider the band gap, such as Figure 2 As shown in (c). When , , At that time, frequency With the short half-axis of the medium column It increases as the value increases.

[0038] Current valley-topological photonic crystal (VPC) structures adjust the photonic bandgap width simply by rotating the dielectric pillars, without changing the size or material of the pillars. Compared to previous structures, this offers greater freedom and is easier to fabricate. It holds immense application potential in optical communications and all-optical integrated devices.

[0039] The optical waveguide structure described in this invention is composed of a deflection angle Photonic crystal VPC2 and The photonic crystal VPC1 is formed by adjacent splicing, and the photonic crystal VPC2 has a splicing boundary parallel to the axis of the dielectric pillar between it and the photonic crystal VPC1. The optical waveguide structure has two common band gaps.

[0040] Figure 3 (a) shows a supercell of one embodiment of the optical waveguide structure. In this embodiment, the optical waveguide structure is composed of a deflection angle. Photonic crystal VPC2 and The photonic crystals VPC1 are joined together, and the photonic crystals VPC2 and VPC1 have a joint boundary parallel to the axis of the dielectric pillar. Figure 3 In the supercell shown in (a), the upper part consists of multiple layers. VPC2 is arranged in a medium with a background refractive index of 1.39, and the lower half consists of multiple layers. VPC1 is arranged in a medium with a background refractive index of 1.39. Topologically protected helical boundary states appear at the interface between two different topological properties. Figure 3 (b) is the banded dispersion curve of the supercell structure in (a). A boundary state (red curve) can be observed within the bulk bandgap. The gray rectangular area represents the operating bandwidth of this waveguide structure, which is 0.63. up to 0.81 . Figure 3 (c) is the red equilateral triangle in (b). ) and the red inverted triangle ( ) at the corresponding boundary Field distribution and corresponding Poynting vector diagram. The operating bandwidth of this optical waveguide is 0.63. up to 0.84 Corresponding to 190THz-240THz and 1.35 Up to 1.73 This corresponds to 400THz-520THz.

[0041] Figure 4(a) is a two-dimensional schematic diagram of the optical waveguide structure designed in this invention. (b) is a field strength distribution diagram of the topological boundary state propagating along a straight line at a frequency of 193.28 THz. The yellow stars are chiral sources. (c) is a normalized electric field distribution diagram on the white horizontal dashed line. It can be seen from the figure that the electromagnetic wave propagates stably in one direction along the interface of VPC1 and VPC2, and backscattering is suppressed. (d) is a normalized electric field distribution diagram on the white vertical dashed line. It can be seen from the figure that the optical flow is mainly localized at the interface.

[0042] To verify the robustness of our designed waveguide structure, we introduced disorder, cavities, and 60° volatilities into the optical waveguide structure by interchanging the positions of two adjacent topological photonic crystal cells. The system features a sharp bend, and its current structure is simulated. Its electric field distribution is also plotted. Figure 5 As shown in (a), (b), and (c). Figure 5 Figures (d), (e), and (f) are magnified views of the Poynting vectors at points A (disorder), B (cavity), and C (sharp bend). The figures show that electromagnetic waves can propagate robustly along the interfaces, are immune to the three defects of disorder, cavity, and sharp bend, and exhibit no significant backscattering or energy loss. Figure 5 In the case of (g), the transmittance of waveguides in defect-free, disordered, cavity, and sharp-bend boundary states is given.

[0043] To verify that this model can adjust the propagation path of electromagnetic waves by changing the pseudospin state, a tunable topological photonic crystal model was designed, such as... Figure 6 As shown in (a), (b), and (c), 1 was achieved. Electromagnetic wave transmission using two beam splitters, "U"-shaped, and "Ω"-shaped beams was demonstrated and verified through simulation. The yellow area represents... VPC1, the green area represents VPC2.

[0044] The above examples are merely specific embodiments of the present invention, but the present invention is not limited to the above embodiments. For example, by changing the parameters of the elliptical medium cylinder, this structure can be used to design a topology beam splitter and to use an encoder to control the transmission of optical flow paths.

[0045] The embodiments described above are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments. Any obvious improvements, substitutions or modifications that can be made by those skilled in the art without departing from the essence of the present invention shall fall within the protection scope of the present invention.

Claims

1. A terahertz valley topological photonic crystal based on a rotating elliptical dielectric pillar, characterized in that, The structure is formed by rotating elliptical dielectric cylinders arranged in a medium with a background refractive index of 1.

39. The cross-sectional shape of each rotating elliptical dielectric cylinder is a C3 symmetrical structure formed by three elliptical arcs joined end-to-end. The refractive index of the rotating elliptical dielectric cylinders is... The ellipse has a major semi-axis of a and a minor semi-axis of b. Each rotating elliptical dielectric pillar constitutes a regular hexagonal unit cell, and the distance between the centers of adjacent regular hexagonal unit cells is a lattice constant. The deflection angle of the rotating elliptical medium column rotating counterclockwise about its axis is . ,and Define the deflection angle when the minor axis of the elliptical arc of the rotating elliptical dielectric cylinder lies on the line connecting the axis of the rotating elliptical dielectric cylinder and the vertex of the regular hexagonal unit cell. .

2. The valley topological photonic crystal according to claim 1, characterized in that, The deflection angle of the rotating elliptical medium column rotating counterclockwise about its axis is: The valley topological photonic crystal has two photonic band gaps, referred to as VPC1.

3. The valley topological photonic crystal according to claim 1, characterized in that, The deflection angle of the rotating elliptical medium column rotating counterclockwise about its axis is: The valley topological photonic crystal has two photonic band gaps, referred to as VPC2.

4. The valley topological photonic crystal according to claim 1, characterized in that, The deflection angle of the rotating elliptical medium column rotating counterclockwise about its axis = At that time, the valley topological photonic crystal has a degenerate Dirac cone, referred to as VPC3.

5. The valley topological photonic crystal according to any one of claims 1-4, characterized in that, The major semi-axis of the rotating elliptical medium cylinder short half-shaft , where r is .

6. The valley topological photonic crystal according to claim 5, characterized in that, The lattice constant .

7. An optical waveguide structure based on the valley topological photonic crystal of claim 1, characterized in that, The optical waveguide structure is composed of a deflection angle of... Photonic crystal VPC2 and deflection angle of The photonic crystal VPC1 is formed by adjacent splicing, and the photonic crystal VPC2 has a splicing boundary with the photonic crystal VPC1 that is parallel to the axis of the rotating elliptical dielectric cylinder. The optical waveguide structure has two common band gaps.

8. The optical waveguide structure according to claim 7, characterized in that, The splicing boundary between the photonic crystal VPC2 and the photonic crystal VPC1 has a bend.

9. The optical waveguide structure according to claim 7, characterized in that, The splicing boundary between the photonic crystal VPC2 and the photonic crystal VPC1 is one or more.

10. The optical waveguide structure according to claim 7, characterized in that, It supports unidirectional optical transmission and features a topology-protected boundary-state waveguide structure with an operating bandwidth of 0.

63. up to 0.84 Corresponding to 190THz-240THz and 1.35 Up to 1.73 , corresponding to 400THz-520THz, where c is the speed of light.

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