High-performance silicon-based topological microcavity based on low-loss pseudospin-polarized topological boundary states

Abstract

This invention discloses a high-performance silicon-based topological microcavity based on low-loss pseudospin-polarized topological boundary states. The microcavity comprises a first silicon-based spin photonic crystal slab (SPC1) and a second silicon-based spin photonic crystal slab (SPC2). SPC1 has a topologically nontrivial band gap, while SPC2 has a topologically trivial band gap. Both are constructed from a unit cell formed by a series of rotated rectangular silicon rods and silicon rings. SPC2 completely encapsulates SPC1 to form the microcavity. The boundary states in the topological microcavity of this invention are mostly located below the light cone, significantly reducing the microcavity's radiation losses.

Description

Technical Field

[0001] The present invention relates to the technical field of topological photonics and integrated photonic devices, and in particular to a silicon-based topological microcavity based on low-loss pseudospin-polarized topological boundary states. Background Art

[0002] Optical topological boundary states possess topologically protected properties, and their transmission efficiency is not easily affected by large-angle turns and defects in the boundaries, providing new ideas for designing high-performance photonic devices. Photonic crystals are one of the ideal systems for realizing optical topological boundary states. In two-dimensional photonic crystals, typical schemes for realizing optical topological boundary states include the optical quantum Hall effect, the optical quantum spin Hall effect, and the optical quantum valley Hall effect. However, since the optical quantum Hall effect requires magnetic materials and an external magnetic field, it is difficult to achieve in the optical frequency band. The boundary states generated by the optical quantum valley Hall effect can usually only efficiently bypass 120-degree turns. However, using the optical quantum spin Hall effect to realize topological boundary states can overcome these problems, and therefore the optical quantum spin Hall effect has been widely studied by researchers. We call photonic crystals that can realize the quantum spin Hall effect spin photonic crystals.

[0003] Based on the topological boundary states of spin photons, researchers have designed a variety of topological microcavities. For example, the patent application with publication number CN112987176A discloses a topological microcavity (attached Figure 1-Figure 2 ), with a hexagonal topologically trivial photonic crystal PhC1 as its center, and a topologically non-trivial photonic crystal PhC2 spliced around the hexagonal topologically trivial photonic crystal, forming a zero-dimensional boundary state microcavity at the interface between the hexagonal topologically trivial PhC1 and the topologically non-trivial photonic crystal PhC2.

[0004] The technical drawbacks of existing topological microcavities are that the boundary states of 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 approximately 4dB / mm. This radiation loss seriously affects the performance of the designed topological microcavity.

[0005] Therefore, developing a new microcavity structure that can regulate the topological boundary state energy band to below the light cone and fundamentally solve the radiation loss problem has become a technical problem that urgently needs to be overcome in this field. Summary of the Invention

[0006] In response to the shortcomings of the existing technology, the present invention provides a topological microcavity based on low-loss pseudospin-polarized topological boundary states. Most of the boundary states in the topological microcavity are located below the light cone, which is used to solve the problem of high radiation loss in existing topological microcavities.

[0007] To achieve the above objectives, the technical solution of the present invention provides a topological microcavity based on low-loss pseudospin-polarized topological boundary states, comprising a first silicon-based spin photonic crystal slab, a second silicon-based spin photonic crystal slab and background materials.

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

[0009] Among them, the first silicon-based spin photonic crystal slab is located in the internal area 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, forming a continuous topological boundary interface. The closed boundary between the two constitutes a topological microcavity.

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

[0011] 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] The background material is filled in the gaps of the silicon-based material.

[0013] 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.

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

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

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

[0017] Optionally, the background material is air.

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

[0019] Optionally, the height of the rectangular silicon rod 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 an xy cross-section of a square 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 form a 2n×2n unit rectangular topological microcavity, with an xy cross-section of a square and a side length of 2n×a; n is an integer greater than or equal to 2.

[0021] Optionally, n=12, in which case 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 boundary between the first silicon-based spin photonic crystal slab and the second silicon-based spin photonic crystal slab, part of the silicon material of the first silicon-based spin photonic crystal slab unit cell and the second silicon-based spin photonic crystal slab unit cell is replaced by air.

[0023] The technical solution of this invention has the following beneficial effects: Through band design, the invention shifts the edge states below the light cone, significantly reducing microcavity radiation losses. Calculations using finite element simulation software show that the quality factor of the topological microcavity of this invention is improved from Q≈600 in conventional designs to Q>3000. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 A lattice structure of a prior art topological microcavity;

[0025] Figure 2 Schematic diagram of the structure of a prior art topological microcavity;

[0026] Figure 3 The electric field distribution diagram of the highest quality factor microcavity mode of the existing topological microcavity;

[0027] Figure 4 A schematic diagram of the structure of a topological microcavity according to an embodiment of the present invention;

[0028] Figure 5 Schematic diagram of the primitive cell structure of the topological microcavity according to an embodiment of the present invention, wherein: Figure 5 (a) is a three-dimensional schematic diagram of the SPC1 primitive cell structure. Figure 5 (b) is a schematic diagram of the xy cross-section of the SPC1 primitive cell structure. Figure 5 (c) is a three-dimensional schematic diagram of the SPC2 primitive cell structure. Figure 5 (d) is a schematic diagram of the xy cross-section of the SPC2 primitive cell structure;

[0029] Figure 6 Schematic diagram of a method for calculating the rotation angle θ of a unit cell rectangular silicon rod according to an embodiment of the present invention;

[0030] Figure 7 This is the electric field distribution diagram of the highest quality factor microcavity mode of the topological microcavity according to an embodiment of the present invention;

[0031] Figure 8 Attached diagrams are analysis diagrams of the lattice structure and lattice characteristics of an embodiment of the present invention;

[0032] Figure 9 Attached diagram is an analysis of the boundary structure of an embodiment of the present invention;

[0033] Figure 10 FIG2 is a diagram showing the robustness analysis of an embodiment of the present invention. DETAILED DESCRIPTION

[0034] The technical solutions in the embodiments of the present invention will be described clearly and completely below with reference to 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.

[0035] like Figure 4 As shown, the present invention is based on a topological microcavity with low-loss pseudospin-polarized topological boundary states. The overall structure is a square photonic crystal slab in which the second silicon-based spin photonic crystal slab (SPC2) completely covers the 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.

[0036] In this embodiment, the interior of the microcavity structure is composed of 12 units*12 units of SPC1, and the entire structure is composed of 24 units*24 units of primitive cells.

[0037] Among them, SPC1 has a topologically nontrivial band gap, and SPC2 has a topologically trivial band gap;

[0038] Among them, the first silicon-based spin photonic crystal slab and the second silicon-based spin photonic crystal slab are both composed of multiple 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 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; 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.

[0039] Among them, the gaps outside the silicon-based material are filled with background materials, including microcavity space, gaps between unit cells and gaps inside unit cells. Figure 5 (a) Figure 5As shown in (b) in the figure, the rectangular silicon rods at the upper left and lower right corners of the SPC1 unit cell are rotated by θ1=-45° relative to their respective silicon rod centers, and the rectangular silicon rods at the upper right and lower left corners are rotated by θ2=45° relative to their respective silicon rod centers; 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 their respective silicon rod centers, and the rectangular silicon rods at the upper right and lower left corners are rotated by θ4=-45° relative to their respective silicon rod centers. Figure 6 The calculation method of the rotation angle θ of the unit cell rectangular silicon rod is represented by: Figure 6 (a) Schematic diagram of the unit cell rectangular silicon rod when it is not rotated (the silicon ring is omitted in the figure for ease of understanding); Figure 6 (b) is the xy cross-section of the unit cell rectangular silicon rod when it is not rotated. The square box is the unit cell unit, and the four small rectangles represent the rectangular silicon rod (also for ease of understanding, the silicon ring is omitted in the figure).

[0040] Among them, such as Figure 9 As shown in (a), in this embodiment, air replaces the silicon material in the dotted box of the first silicon-based spin photonic crystal slab unit cell and the second silicon-based spin photonic crystal slab unit cell around the adjacent boundaries of SPC1 and SPC2.

[0041] 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 height of the rectangular silicon rod and the silicon ring are both 500 nm.

[0042] In this example, each unit cell is the smallest functional unit of topological properties. Multiple units are periodically arranged in the xy plane with a lattice constant of a = 713 nm, forming a planar structure with specific bandgap characteristics. This periodic arrangement of units ensures the continuity and robustness of topological boundary states.

[0043] Technical effect analysis and verification:

[0044] 1. Based on finite element simulation software, the electric field distribution of the prior art and this embodiment is simulated and analyzed:

[0045] Figure 3 This diagram shows the electric field distribution of the highest-quality microcavity mode of a conventional topological microcavity. The microcavity consists of a hexagonal topologically trivial photonic crystal (PhC1) at its center, surrounded by a topologically nontrivial photonic crystal (PhC2). A zero-dimensional boundary state microcavity is formed at the interface between the hexagonal topologically trivial and nontrivial photonic crystals (PhC1 and PhC2). This microcavity boundary state lies above the light cone. Simulations show that this microcavity achieves a maximum quality factor (Q) of 590 at a frequency of 171.113 THz.

[0046] Figure 7 : This is the electric field distribution diagram of the highest quality factor microcavity mode of the topological microcavity according to an embodiment of the present invention. According to simulation, the highest quality factor Q of the microcavity of the present invention is 3668 at a frequency of 157.078 THz.

[0047] According to the comparison, the quality factor of the microcavity constructed by the present invention is one order of magnitude greater than that of the prior art.

[0048] In the lattice structures of the microcavities SPC1 and SPC2 designed in the present invention, the unit 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 silicon ring is h = 500 nm, and the relative dielectric constant of the rectangular silicon rods is ε = 12. In order to realize topological boundary states in the unit cell, two photonic crystals with different silicon rod rotation modes are selected to construct the boundaries. Figure 8 (a) and Figure 8 (b) shows their energy bands, and the inset shows the characteristic modes of the M point. We can see that both SPC1 and SPC2 have a complete band gap, with a band gap size of 8.6%, as shown by the rectangle.

[0049] 3. Analysis of the microcavity boundary structure:

[0050] The method is to construct the boundary by combining SPC1 and SPC2, such as Figure 9 As shown in (a) in the figure. The constructed boundary is a rectangular structure, in which the unit cell takes 1 period in the x direction and extends 10 periods in the y direction. The above boundary structure is divided into two equal areas, and the boundary line between the two areas is parallel to the x axis. In order to increase the frequency of the boundary state below the light cone, the dielectric constant is perturbed and the dielectric constant is replaced by air. Figure 9 The silicon material of SPC1 and SPC2 in the dashed box in (a) is shown in Figure 1. The eigenfrequency in the kx direction is calculated using finite element simulation software. The wave vector scanning direction is Γ-M and the scanning range is 0 to 1. The results are shown in Figure 1. Figure 9 As shown in (b) in the figure, it can be seen that due to the band inversion at point M, Figure 8 (a) and Figure 8 In (b), SPC1 and SPC2 have different spin Chern numbers, so there is a pair of topological boundary states.

[0051] Figure 9(c) is a comparison of the transmission losses of the boundary states below the light cone and above the light cone. The transmission loss of the boundary states below the light cone can be ignored.

[0052] Figure 9 Figures (d) and (e) show the transmission field distributions of different edge states under electric dipole excitation at the same frequency and length. Under 164.0 THz excitation, the transmission of the edge states below the light cone is unattenuated, while under 164.0 THz excitation, the transmission of the edge states above the light cone exhibits significant loss, and the edge states below the light cone are more localized.

[0053] 4. Based on finite element simulation software, the robustness analysis of the microcavity structure of the present invention is carried out:

[0054] Figure 10 (a) shows the microcavity structure after the corner defect is introduced. Based on the finite element simulation software, the highest quality factor of the corner defect microcavity mode is still 3322, see Figure 10 (b) in the. Figure 10 (c) shows the microcavity structure after the boundary defect is introduced. Based on the finite element simulation software, the highest quality factor of the boundary defect microcavity mode is still 3668, see Figure 10 (d) in.

[0055] The above is a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. High-performance silicon-based topological microcavity based on low-loss pseudospin-polarized topological boundary states, characterized by: include: The first silicon-based spin photonic crystal slab with a topologically nontrivial band gap; The second silicon-based spin photonic crystal slab has a topologically trivial band gap; Background information; in: 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 covers 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; The first silicon-based spin photonic crystal slab and the second silicon-based spin photonic crystal slab are both composed of a plurality of unit cells arranged periodically according to a lattice constant a, and the center distance between two adjacent unit cells is the lattice constant a; The unit cell comprises four rectangular silicon rods and a silicon ring, wherein 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 between the silicon-based materials; The geometric parameters of the rectangular silicon rod satisfy: length L=0.4a, width w=0.25a; The geometric parameters of the silicon ring meet the following requirements: inner radius r1=0.1a, outer radius r2=0.25a; The rectangular silicon rods at the upper left corner and the lower right corner of the unit cell of the first silicon-based spin photonic crystal slab are rotated by θ1=45° relative to the centers of the 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 the respective silicon rods; The rectangular silicon rods at the upper left and lower right corners of the unit cell of the second silicon-based spin photonic crystal slab are rotated by θ3=-45° relative to their respective silicon rod centers, and the rectangular silicon rods at the upper right and lower left corners are rotated by θ4=45° relative to their respective silicon rod centers.

2. The high-performance silicon-based topological microcavity based on low-loss pseudospin-polarized topological boundary 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 pseudospin-polarized topological boundary states according to claim 1, characterized in that: The background material has a refractive index of 1.

4. The high-performance silicon-based topological microcavity based on low-loss pseudospin-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 pseudospin-polarized topological boundary states according to claim 1, characterized in that: The lattice constant a=713nm.

6. The high-performance silicon-based topological microcavity based on low-loss pseudospin-polarized topological boundary states according to claim 1, characterized in that: The heights of the rectangular silicon rods and silicon rings are both 500 nm.

7. The high-performance silicon-based topological microcavity based on low-loss pseudospin-polarized topological boundary states according to claim 1, characterized in that: The first silicon-based spin photonic crystal slab is composed of n×n unit cells, with an xy cross-section of a square 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 form a 2n×2n unit rectangular topological microcavity, with an xy cross-section of a square 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 pseudospin-polarized topological boundary states according to claim 7, characterized in that: Said n=12.

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

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