High-performance silicon-based topological microcavity based on low-loss pseudo-spin polarization topological boundary state

Abstract

The invention discloses a high-performance silicon-based topological microcavity based on a low-loss pseudo-spin polarization topological boundary state. The high-performance silicon-based topological microcavity comprises a first silicon-based spin photonic crystal panel (SPC1) and a second silicon-based spin photonic crystal panel (SPC2). The SPC1 has a topological non-trivial band gap, the SPC2 has a topological trivial band gap, both the SPC1 and the SPC2 are composed of primitive cells formed by connecting rotary rectangular silicon rods and silicon rings in series, and the SPC2 completely covers the SPC1 to form a microcavity. Most of the boundary state in the topological microcavity is located below the light cone, so that the radiation loss of the microcavity is greatly reduced.

Description

Technical Field

[0001] The present invention relates to the technical fields of topological photonics and integrated photonic devices, and particularly relates to a silicon-based topological microcavity based on low-loss pseudo-spin polarized topological edge states. Background Art

[0002] Optical topological edge states have the property of topological protection, and their transmission efficiency is not easily affected by large-angle turns and defects in the boundary, providing new ideas for designing high-performance photonic devices. Photonic crystals are one of the ideal systems for realizing optical topological edge states. In two-dimensional photonic crystals, typical schemes for realizing optical topological edge states include the optical quantum Hall effect, the optical quantum spin Hall effect, and the optical quantum valley Hall effect. Considering that the realization of the optical quantum Hall effect requires magnetic materials and an external magnetic field, it is difficult to achieve in the optical frequency band; the edge states generated by the optical quantum valley Hall effect can usually only efficiently bypass a 120-degree turn, while the realization of topological edge states using the optical quantum spin Hall effect can overcome the above problems. Therefore, the optical quantum spin Hall effect has been widely studied by researchers. We call the photonic crystal that can realize the quantum spin Hall effect a spin photonic crystal.

[0003] Based on the topological edge states of spin photons, researchers have designed various topological microcavities. For example, the patent application with the publication number CN112987176A discloses a topological microcavity (attached Figures 1 - 2 ), the center of which is a hexagonal topologically trivial photonic crystal PhC1, and topologically non-trivial photonic crystals PhC2 are spliced around the hexagonal topologically trivial photonic crystal, and a zero-dimensional edge state microcavity is formed at the interface between the hexagonal topologically trivial PhC1 and the topologically non-trivial photonic crystal PhC2.

[0004] The technical defect of the existing topological microcavities is that the edge states of the existing topological microcavities designed based on spin photonic crystals are located above the light cone. Due to out-of-plane radiation, the transmission loss is large. At the frequency with the highest quality factor Q≈600, the transmission loss is about 4 db / mm. The existing radiation loss seriously affects the performance of the designed topological microcavities.

[0005] Therefore, developing a new microcavity structure that can tune the energy band of topological edge states below the light cone to fundamentally solve the radiation loss problem has become an urgent technical problem to be broken through in this field. Summary of the Invention

[0006] Aiming at the deficiencies in the prior art, the present invention provides a topological microcavity based on low-loss pseudo-spin polarized topological edge states, and most of the edge states in the topological microcavity are located below the light cone to solve the problem of large radiation loss of the existing topological microcavities.

[0007] To achieve the above object, the technical solution of the present invention provides a topological microcavity based on a low-loss pseudo-spin-polarized topological boundary state, including a first silicon-based spin photonic crystal slab, a second silicon-based spin photonic crystal slab, and a background material.

[0008] Among them, the first silicon-based spin photonic crystal slab has a topologically non-trivial bandgap; the second silicon-based spin photonic crystal slab has a topologically trivial bandgap; the background material.

[0009] Among them, the first silicon-based spin photonic crystal slab is located in the internal region of the microcavity, and the second silicon-based spin photonic crystal slab completely covers the outer surface of the first silicon-based spin photonic crystal slab to form a continuous topological boundary interface. The closed boundary between the two constitutes the topological microcavity.

[0010] Among them, both the first silicon-based spin photonic crystal slab and the second silicon-based spin photonic crystal slab are composed of a plurality of unit cells arranged periodically according to the lattice constant a, and the center distance between two adjacent unit cells is the lattice constant a.

[0011] Among them, each unit cell contains four rectangular silicon rods and a silicon ring, and the rectangular silicon rods are connected in series through the silicon ring to form an overall structure with a square xy cross-section.

[0012] Among them, the background material is filled in the gaps of the silicon-based materials.

[0013] Among them, the geometric parameters of the rectangular silicon rods satisfy: length L = 0.4a, width w = 0.25a; the geometric parameters of the silicon ring satisfy: inner radius r1 = 0.1a, outer radius r2 = 0.25a.

[0014] Among them, the upper left and lower right rectangular silicon rods in the unit cell of the first silicon-based spin photonic crystal slab are rotated by θ1 = 45° relative to the center of their respective silicon rods, and the upper right and lower left rectangular silicon rods are rotated by θ2 = -45° relative to the center of their respective silicon rods; the upper left and lower right rectangular silicon rods in the unit cell of the second silicon-based spin photonic crystal slab are rotated by θ3 = -45° relative to the center of their respective silicon rods, and the upper right and lower left rectangular silicon rods are rotated by θ4 = 45° relative to the center of their respective silicon rods.

[0015] Optionally, the rectangular silicon rods and the silicon ring are made of silicon material with a dielectric constant of 12.

[0016] Optionally, the refractive index of the background material is 1.

[0017] Optionally, the background material is air.

[0018] Optionally, the lattice constant a = 713 nm.

[0019] Optionally, the heights of the rectangular silicon rods and the silicon ring are both 500 nm.

[0020] One implementation method is that the first silicon-based spin photonic crystal slab is composed of n×n unit cells, with a square xy cross-section and a side length of n×a; the second silicon-based spin photonic crystal slab wraps the first silicon-based spin photonic crystal slab to jointly form a rectangular topological microcavity with 2n×2n units, with a square xy cross-section and a side length of 2n×a; n is an integer greater than or equal to 2.

[0021] Optionally, n = 12. At this time, the first silicon-based spin photonic crystal slab is composed of 12×12 unit cells, with a square xy cross-section and a side length of 12a; the second silicon-based spin photonic crystal slab wraps the first silicon-based spin photonic crystal.

[0022] Optionally, at the adjacent boundary of the first silicon-based spin photonic crystal slab and the second silicon-based spin photonic crystal slab, part of the silicon material of the unit cells of the first silicon-based spin photonic crystal slab and the second silicon-based spin photonic crystal slab is replaced by air.

[0023] Applying the technical solution of the present invention has the following beneficial effects: By band design, the present invention shifts the edge state below the light cone, thereby greatly reducing the radiation loss of the microcavity. Calculated by using finite element simulation software, the quality factor of the topological microcavity of the present invention is improved from Q≈600 of the traditional design to Q>3000. Description of the Drawings

[0024] Figure 1 It is the lattice structure of a topological microcavity of the prior art; Figure 2 It is the schematic structural diagram of a topological microcavity of the prior art; Figure 3 The electric field distribution diagram of the microcavity mode with the highest quality factor of the topological microcavity of the prior art; Figure 4 It is the schematic structural diagram of the topological microcavity of the embodiment of the present invention; Figure 5 It is the schematic diagram of the unit cell structure of the topological microcavity of the embodiment of the present invention. Among them, Figure 5 (a) in it is the three-dimensional schematic diagram of the SPC1 unit cell structure, Figure 5 (b) in it is the xy cross-section schematic diagram of the SPC1 unit cell structure, Figure 5 (c) in it is the three-dimensional schematic diagram of the SPC2 unit cell structure, Figure 5 (d) in it is the xy cross-section schematic diagram of the SPC2 unit cell structure; Figure 6 It is the schematic diagram of the calculation method of the rotation angle θ of the rectangular silicon rod of the unit cell of the embodiment of the present invention; Figure 7 It is the electric field distribution diagram of the microcavity mode with the highest quality factor of the topological microcavity of the embodiment of the present invention; Figure 8 Attached diagrams are the lattice structure and lattice feature analysis of the embodiments of the present invention; Figure 9 It is a figure analyzing the boundary structure of an embodiment of the present invention; Figure 10 The figure is a robustness analysis diagram of an embodiment of the present invention. DETAILED DESCRIPTION

[0025] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the accompanying drawings in the embodiments of the present invention, but this does not constitute a limitation on the protection scope of the present invention.

[0026] like Figure 4 As shown, the present invention is based on a topological microcavity of low-loss pseudospin polarized topological boundary states. The overall structure is a square photonic crystal slab in which a second silicon-based spin photonic crystal slab (SPC2) completely covers a first silicon-based spin photonic crystal slab (SPC1), forming a continuous topological boundary interface. The closed boundary between the two constitutes a topological microcavity, and the microcavity space is filled with background material.

[0027] In this embodiment, the interior of the microcavity structure is composed of 12 units*12 units of SPC1, and the whole is composed of 24 units*24 units of primitive cells.

[0028] Among them, SPC1 has a topologically nontrivial band gap, and SPC2 has a topologically trivial band gap; Among them, the first silicon-based spin photonic crystal plate and the second silicon-based spin photonic crystal plate are both composed of a plurality of unit cells arranged periodically according to the lattice constant a, and the center distance between two adjacent unit cells is the lattice constant a; wherein each unit cell comprises four rectangular silicon rods and a silicon ring, and the rectangular silicon rods are connected in series through the silicon ring to form an overall structure with a square xy cross-section; the geometric parameters of the rectangular silicon rods satisfy: length L=0.4a, width w=0.25a; the geometric parameters of the silicon ring satisfy: inner radius r1=0.1a, outer radius r2=0.25a.

[0029] Among them, the gaps outside the silicon-based material are filled with background materials, including microcavity spaces, gaps between primitive cells, and gaps inside primitive cells. Figure 5 (a) Figure 5 As shown in (b) in FIG. 1 , the rectangular silicon rods at the upper left corner and the lower right corner of the unit cell of SPC1 are rotated by θ1=-45° relative to the centers of their respective silicon rods, and the rectangular silicon rods at the upper right corner and the lower left corner are rotated by θ2=45° relative to the centers of their respective silicon rods; Figure 5 (c) Figure 5 As shown in (d), the rectangular silicon rods at the upper left and lower right corners of the SPC2 unit cell are rotated by θ3=45° relative to the centers of their respective silicon rods, and the rectangular silicon rods at the upper right and lower left corners are rotated by θ4=-45° relative to the centers of their respective silicon rods.Figure 6 The calculation method of the rotation angle θ of the rectangular silicon rod in the primitive cell, where Figure 6 (a) in it is a three-dimensional schematic diagram of the rectangular silicon rod in the primitive cell unit without rotation (for easy understanding, the silicon ring is omitted in the figure); Figure 6 (b) in it is the xy cross-sectional view of the rectangular silicon rod in the primitive cell without rotation. The square box is the primitive cell unit, and the four small rectangles represent the rectangular silicon rod (similarly, for easy understanding, the silicon ring is omitted in the figure).

[0030] Among them, as Figure 9 shown in (a) in it, in this embodiment, around the boundary where SPC1 and SPC2 are adjacent, air replaces the silicon material in the partial dotted-line frames of the first silicon-based spin photonic crystal slab primitive cell and the second silicon-based spin photonic crystal slab primitive cell.

[0031] In this embodiment, the rectangular silicon rod and the silicon ring are made of silicon material with a dielectric constant of 12, the background material is air with a refractive index of 1, the lattice constant a = 713 nm, and the heights of the rectangular silicon rod and the silicon ring are both 500 nm.

[0032] In this embodiment, each primitive cell is the smallest functional unit with topological properties. Multiple primitive cells are periodically arranged in the xy plane with a lattice constant a = 713 nm to form a slab structure with specific bandgap characteristics. The periodic arrangement of the primitive cells ensures the continuity and robustness of the topological boundary states.

[0033] Analysis and verification of technical effects: 1. Based on the finite element simulation software, the electric field distributions of the existing technology and this embodiment are simulated and analyzed: Figure 3 is the electric field distribution diagram of the microcavity mode with the highest quality factor of the existing technology topological microcavity. The center of this microcavity is a hexagonal topologically trivial photonic crystal PhC1, and a topologically non-trivial photonic crystal PhC2 is spliced around the hexagonal topologically trivial photonic crystal. A zero-dimensional boundary state microcavity is formed at the interface between the hexagonal topologically trivial photonic crystal PhC1 and the topologically non-trivial photonic crystal PhC2. The boundary state of this microcavity is above the light cone. According to the simulation, the highest quality factor Q = 590 of this microcavity at a frequency of 171.113 THz.

[0034] Figure 7 is the electric field distribution diagram of the microcavity mode with the highest quality factor of the topological microcavity in the embodiment of the present invention. According to the simulation, the highest quality factor Q = 3668 of the microcavity of the present invention at a frequency of 157.078 THz.

[0035] According to the comparison, it can be seen that the quality factor of the microcavity constructed by the present invention is one order of magnitude larger than that of the existing technology. 2. Analysis of the lattice structure and lattice characteristics: For the microcavity designed in the present invention, in the lattice structures of SPC1 and SPC2, the primitive cell consists of four rectangular silicon rods and a silicon ring embedded in an air background. The lattice constant is a = 713 nm. The length and width of the rectangular silicon rods are L = 0.4a and w = 0.25a respectively. The inner radius and outer radius of the silicon ring are r1 = 0.1a and r2 = 0.25a respectively. The height of the rectangular silicon rods and the silicon ring is h = 500 nm. The relative permittivity of the rectangular silicon rods is ε = 12. In order to achieve topological edge states in the primitive cell, two photonic crystals with different rotation methods of the silicon rods are selected to construct the boundary. Figure 8 (a) in Figure 8 and (b) in show their energy bands. The inset shows the

[0036] III. Analysis of the microcavity boundary structure: The method is to construct the boundary by combining SPC1 and SPC2, as shown in Figure 9 (a) in Figure 9 . The constructed boundary is a rectangular structure, where the primitive cell takes 1 period in the x direction and expands 10 periods in the y direction. The above boundary structure is equally divided into two regions, and the boundary line between the two regions is parallel to the x axis. In order to increase the frequency of the edge state below the light cone, through the perturbation of the permittivity, part of the silicon material of SPC1 and SPC2 in the dashed box in Figure 9 (a) is replaced by air. The finite element simulation software is used to calculate the eigenfrequency in the kx direction. The wave vector scanning direction is Γ - M, and the scanning range is from 0 to 1. The result is shown in Figure 8 (b) in Figure 8 . It can be seen that due to the band inversion at the M point, see

[0037] Figure 9 (a) and

[0038] Figure 9 (b) in , SPC1 and SPC2 have different spin Chern numbers, so there is a pair of topological edge states. (c) in

[0038] Figure 9 is a comparison chart of the transmission loss of the edge state below the light cone and the edge state above the light cone. The transmission loss of the edge state below the light cone can be ignored.

[0038] Figure 9 (d) and (e) in are the transmission field distributions of different edge states under the excitation of an electric dipole at the same frequency and the same length respectively. The transmission of the edge state below the light cone has no attenuation under the excitation of 164.0 THz, while the transmission of the edge state above the light cone shows obvious loss under the excitation of 164.0 THz, and the localization of the edge state below the light cone is better.

[0039] IV. Based on the finite element simulation software, the robustness analysis of the microcavity structure of the present invention is carried out: Figure 10 As shown in (a) in [reference], it is the microcavity structure after introducing corner defects. Based on the finite element simulation software, the highest quality factor of the corner defect microcavity mode is still 3322, as shown in Figure 10 (b) in [reference]. Figure 10 (c) in [reference] shows the microcavity structure after introducing boundary defects. Based on the finite element simulation software, the highest quality factor of the boundary defect microcavity mode is still 3668, as shown in Figure 10 (d) in [reference].

[0040] The above is the preferred embodiment of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements are also regarded as the protection scope of the present invention.

Claims

1. A high-performance silicon-based topological microcavity based on low-loss pseudo-spin polarized topological edge states, characterized in that, Including: The first silicon-based spin photonic crystal slab, having a topologically non-trivial bandgap; The second silicon-based spin photonic crystal slab, having a topologically trivial bandgap; Background material; Wherein: The first silicon-based spin photonic crystal slab is located in the inner region of the microcavity, and the second silicon-based spin photonic crystal slab completely coats the outer surface of the first silicon-based spin photonic crystal slab to form a continuous topological boundary interface, and the closed boundary between the two constitutes a topological microcavity; Both the first silicon-based spin photonic crystal slab and the second silicon-based spin photonic crystal slab are composed of a plurality of unit cells arranged periodically according to the lattice constant a, and the center distance between two adjacent unit cells is the lattice constant a; The unit cell includes four rectangular silicon rods and a silicon ring, and the rectangular silicon rods are connected in series through the silicon ring to form an overall structure with a square xy cross-section; The background material is filled in the gaps of the silicon-based material; The geometric parameters of the rectangular silicon rod satisfy: length L = 0.4a, width w = 0.25a; The geometric parameters of the silicon ring satisfy: inner radius r1 = 0.1a, outer radius r2 = 0.25a; In the unit cell of the first silicon-based spin photonic crystal slab, the upper left and lower right rectangular silicon rods are rotated by θ1 = 45° relative to the center of their respective silicon rods, and the upper right and lower left rectangular silicon rods are rotated by θ2 = -45° relative to the center of their respective silicon rods; In the unit cell of the second silicon-based spin photonic crystal slab, the upper left and lower right rectangular silicon rods are rotated by θ3 = -45° relative to the center of their respective silicon rods, and the upper right and lower left rectangular silicon rods are rotated by θ4 = 45° relative to the center of their respective silicon rods.

2. The high-performance silicon-based topological microcavity based on low-loss pseudo-spin polarized topological edge states according to claim 1, characterized in that, The rectangular silicon rod and the silicon ring are made of silicon material with a dielectric constant of 12.

3. The high-performance silicon-based topological microcavity based on low-loss pseudo-spin polarized topological boundary states according to claim 1, wherein The refractive index of the background material is 1.

4. The high-performance silicon-based topological microcavity based on low-loss pseudo-spin polarized topological boundary states according to claim 3, characterized in that The background material is air.

5. The high-performance silicon-based topological microcavity based on low-loss pseudo-spin polarized topological edge states according to claim 1, wherein The lattice constant a = 713 nm.

6. The high-performance silicon-based topological microcavity based on low-loss pseudo-spin polarized topological boundary states according to claim 1, characterized in that The height of the rectangular silicon rod and the silicon ring is both 500 nm.

7. The high-performance silicon-based topological microcavity based on low-loss pseudo-spin polarized topological boundary states according to claim 1, wherein The first silicon-based spin photonic crystal slab is composed of n×n unit cells, with a square xy cross-section and a side length of n×a; the second silicon-based spin photonic crystal slab wraps the first silicon-based spin photonic crystal slab to jointly form a cuboid topological microcavity of 2n×2n units, with a square xy cross-section and a side length of 2n×a; n is an integer greater than or equal to 2.

8. The high-performance silicon-based topological microcavity based on low-loss pseudo-spin polarized topological edge states according to claim 7, characterized in that The n = 12.

9. The high-performance silicon-based topological microcavity based on low-loss pseudo-spin polarized topological boundary states according to claim 8, characterized in that At the adjacent boundary of the first silicon-based spin photonic crystal slab and the second silicon-based spin photonic crystal slab, part of the silicon material of the unit cell of the first silicon-based spin photonic crystal slab and the unit cell of the second silicon-based spin photonic crystal slab is replaced by air.

Images