Broadband low-dispersion slow-light waveguide based on valley photonic crystal

Abstract

The invention discloses a broadband low-dispersion slow light waveguide based on valley photonic crystals, which comprises A-type and B-type silicon-based two-dimensional valley photonic crystals, and beard-type interface waveguides are formed between the A-type and B-type silicon-based two-dimensional valley photonic crystals. A plurality of rows of regular triangular air holes tria and inverted triangular air holes trib which take the center line of the valley photonic crystal as a symmetry axis are respectively and sequentially arranged and etched on the planes of the A type silicon-based two-dimensional valley photonic crystal and the B type silicon-based two-dimensional valley photonic crystal along the direction of the long side of the valley photonic crystal; a plurality of rows of inverted triangular air holes tria are sequentially arranged and etched between every two adjacent rows of regular triangular air holes tria along the direction of the long side of the valley photonic crystal; and a plurality of rows of regular triangular air holes trib are sequentially arranged and etched between the adjacent rows of inverted triangular air holes trib along the direction of the long side of the valley photonic crystal. According to the invention, the problem that light pulses are broadened or distorted in the propagation process due to the fact that the slow light waveguide normalization delay bandwidth product is relatively low in the prior art is solved.

Description

Technical Field

[0001] The invention belongs to the technical field of integrated photonics, and in particular relates to a broadband low-dispersion slow light waveguide based on valley photonic crystals. Background Art

[0002] Integrated optical waveguides based on two-dimensional topological photonic crystals have attracted widespread attention due to their potential for robust optical transmission. Among various two-dimensional topological photonic crystals, valley photonic crystal (VPhC) waveguides can achieve efficient optical transmission through sharp waveguide bends and can be implemented based on common dielectrics such as silicon, making them compatible with today's mainstream complementary metal oxide semiconductor (CMOS) process technology.

[0003] By adjusting the structural parameters of the VPhC waveguide, a slow light effect with a wide low group velocity dispersion bandwidth can be generated. and low group velocity dispersion bandwidth There is a trade-off between the two, so the performance of broadband low-dispersion slow-light waveguides is usually evaluated by the normalized delay-bandwidth product (NDBP), which is defined as If it is possible to achieve larger and NDBP will be very beneficial to the development of key devices such as highly nonlinear devices and compact modulators.

[0004] At present, VPhC slow light waveguide maintains significant slow light properties ( ) is still relatively limited. The NDBP values ​​reported in public reports are only 0.22 (Chinese Optics Letters, 2024, 22(5): 053602.) and 0.26 (2019 In 66th Japan Society of Applied Physics Spring Meeting, March 26-29, 2019, Tokyo, Japan: JSAP Annual Meetings Extended Abstracts, 933 and Opticsexpress, 2024, 32(4): 6382-6390.). Therefore, the broadband low-dispersion performance of VPhC slow light waveguides still needs to be further improved. Summary of the invention

[0005] The purpose of the present invention is to provide a broadband low-dispersion slow light waveguide based on valley photonic crystals, which solves the problem in the prior art that the normalized delay-bandwidth product of the slow light waveguide is low, resulting in broadening or distortion of light pulses during propagation.

[0006] The technical solution adopted by the present invention is that a broadband low-dispersion slow light waveguide based on valley photonic crystals includes A-type and B-type silicon-based two-dimensional valley photonic crystals, a whisker-type interface waveguide is formed between the A-type silicon-based two-dimensional valley photonic crystal and the B-type silicon-based two-dimensional valley photonic crystal, a plurality of rows of regular triangular air holes tri_a are sequentially arranged and etched along the long side of the valley photonic crystal on the plane of the A-type silicon-based two-dimensional valley photonic crystal, and a plurality of rows of inverted triangular air holes tri_a are sequentially arranged and etched along the long side of the valley photonic crystal between adjacent rows of regular triangular air holes tri_a; On the plane of the B-type silicon-based two-dimensional valley photonic crystal, a plurality of rows of inverted triangle air holes tri_b are sequentially arranged and etched along the direction of the long side of the valley photonic crystal with the center line of the valley photonic crystal as the symmetry axis, and between adjacent rows of inverted triangle air holes tri_b, a plurality of rows of regular triangle air holes tri_b are sequentially arranged and etched along the direction of the long side of the valley photonic crystal; The equilateral triangle air hole tri_a and the inverted triangle air hole tri_a, the equilateral triangle air hole tri_b and the inverted triangle air hole tri_b all constitute unit cells on the honeycomb lattice, and the lattice constant is a.

[0007] The present invention is also characterized in that The side lengths of the inverted triangle air hole tri_a and the regular triangle air hole tri_b are .

[0008] The side lengths of the equilateral triangle air hole tri_a and the inverted triangle air hole tri_b are .

[0009] The beard-type interface waveguide includes a plurality of equilateral triangular air holes tri_a and inverted triangular air holes tri_b, wherein the plurality of equilateral triangular air holes tri_a and inverted triangular air holes tri_b form a row, and the equilateral triangular air holes tri_a and inverted triangular air holes tri_b are alternately arranged in sequence along the direction of the long side of the valley photonic crystal; The side lengths of the regular triangle air holes tri_a and the inverted triangle air holes tri_b are .

[0010] The side lengths of the first row of inverted triangle air holes tri_a and regular triangle air holes tri_b adjacent to the whisker-type interface waveguide are .

[0011] The side lengths of the second row of regular triangle air holes tri_a and inverted triangle air holes tri_b adjacent to the whisker-type interface waveguide are .

[0012] The lattice constant a=ω×λ, where ω is the frequency and λ is the wavelength.

[0013] In the valley photonic crystal slow light waveguide, the normalized delay-bandwidth product is introduced, and the calculation formula is as follows: ; In the formula, is the slow light working center wavelength, is the bandwidth, is the group refractive index; Group refractive index The calculation is as follows: ; ; In the formula, is the frequency, k is the wave number, is the speed of light in a vacuum; When calculating the waveguide transmission spectrum, the two-dimensional time-domain finite difference method is used, and the calculation formula is as follows: .

[0014] The beneficial effects of the present invention are: (1) The present invention is based on a broadband low-dispersion slow light waveguide of a honeycomb lattice valley photonic crystal composed of equilateral triangle air holes. The honeycomb lattice has C 6v Symmetry, side length of triangular air hole Afterwards, the spatial inversion symmetry is broken, and a topological band gap is generated between the two lowest energy bands.

[0015] And the present invention adjusts the lattice constant a The ratio of the wavelength to the side length of the air hole effectively adjusts the dispersion characteristic curve of the waveguide boundary state and achieves optimal control of the group velocity and flatness.

[0016] (2) Considering that the electromagnetic field of the waveguide boundary state is mainly localized within the range of about three rows of air holes near the interface, the present invention focuses on optimizing the size of the air holes in the interface area. This targeted optimization can significantly reduce the scattering loss of light waves during propagation and improve the dispersion characteristics, thereby obtaining a higher NDBP value (NDBP=0.356). Through this design method, a relatively significant slow light characteristic ( ) and wider low-dispersion bandwidth ( ) waveguide structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a schematic structural diagram of a broadband low-dispersion slow light waveguide based on valley photonic crystals of the present invention; Figure 2 It is a schematic diagram of the structure of two valley photonic crystal unit cells of the present invention; Figure 3It is a parameter schematic diagram of the broadband low-dispersion slow light waveguide based on valley photonic crystal of the present invention; Figure 4 is a topological boundary state dispersion curve diagram of the present invention; Figure 5 is a graph of the refractive index of the topological boundary state group of the present invention; Figure 6 is the transmission spectrum of the linear waveguide constructed in the present invention; Figure 7 It is a schematic diagram of the Z-type waveguide constructed by the present invention; Figure 8 It is the transmission spectrum of the Z-waveguide constructed by the present invention; DETAILED DESCRIPTION The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0018] Example 1 The present invention is based on the broadband low dispersion slow light waveguide of valley photonic crystal, such as Figure 1 As shown, it includes type A and type B silicon-based two-dimensional valley photonic crystals, and a bearded interface waveguide is formed between the type A silicon-based two-dimensional valley photonic crystal and the type B silicon-based two-dimensional valley photonic crystal. Figure 2 As shown, the silicon-based two-dimensional valley photonic crystals of type A and type B are honeycomb lattices formed by silicon and equilateral triangular air holes. The lattice constant of the honeycomb lattice is a It is 376nm.

[0019] Specifically, a plurality of rows of regular triangular air holes tri_a are sequentially arranged and etched along the long side of the valley photonic crystal on the plane of the A-type silicon-based two-dimensional valley photonic crystal, with the center line of the valley photonic crystal as the symmetry axis, and a plurality of rows of inverted triangular air holes tri_a are sequentially arranged and etched along the long side of the valley photonic crystal between adjacent rows of regular triangular air holes tri_a; On the plane of the B-type silicon-based two-dimensional valley photonic crystal, a plurality of rows of inverted triangle air holes tri_b are sequentially arranged and etched along the direction of the long side of the valley photonic crystal with the center line of the valley photonic crystal as the symmetry axis, and between adjacent rows of inverted triangle air holes tri_b, a plurality of rows of regular triangle air holes tri_b are sequentially arranged and etched along the direction of the long side of the valley photonic crystal; The equilateral triangle air hole tri_a and the inverted triangle air hole tri_a, the equilateral triangle air hole tri_b and the inverted triangle air hole tri_b all constitute unit cells on the honeycomb lattice, and the lattice constant is a.

[0020] Example 2 The broadband low-dispersion slow light waveguide based on valley photonic crystals of the present invention comprises A-type and B-type silicon-based two-dimensional valley photonic crystals, wherein the silicon-based two-dimensional valley photonic crystals are in the form of two-dimensional sheets, and a whisker-type interface waveguide is formed between the A-type silicon-based two-dimensional valley photonic crystals and the B-type silicon-based two-dimensional valley photonic crystals, and a plurality of rows of regular triangular air holes tri_a are sequentially arranged and etched along the long side of the valley photonic crystal on the plane of the A-type silicon-based two-dimensional valley photonic crystal, and a plurality of rows of inverted triangular air holes tri_a are sequentially arranged and etched along the long side of the valley photonic crystal between adjacent rows of regular triangular air holes tri_a; On the plane of the B-type silicon-based two-dimensional valley photonic crystal, a plurality of rows of inverted triangle air holes tri_b are sequentially arranged and etched along the direction of the long side of the valley photonic crystal with the center line of the valley photonic crystal as the symmetry axis, and between adjacent rows of inverted triangle air holes tri_b, a plurality of rows of regular triangle air holes tri_b are sequentially arranged and etched along the direction of the long side of the valley photonic crystal; The equilateral triangle air hole tri_a and the inverted triangle air hole tri_a, the inverted triangle air hole tri_b and the equilateral triangle air hole tri_b all constitute unit cells on the honeycomb lattice, and the lattice constant is a.

[0021] like Figure 2 As shown, the side lengths of the inverted triangle air hole tri_a and the regular triangle air hole tri_b are The side lengths of the equilateral triangle air hole tri_a and the inverted triangle air hole tri_b are .

[0022] In this embodiment, the sizes of the three rows of air holes corresponding to the two sides of the interface are optimized with the waveguide interface as the center. The beard-shaped interface waveguide includes a plurality of equilateral triangular air holes tri_a and inverted triangular air holes tri_b. The plurality of equilateral triangular air holes tri_a and inverted triangular air holes tri_b form a row, and the equilateral triangular air holes tri_a and inverted triangular air holes tri_b are alternately arranged in sequence along the direction of the long side of the valley photonic crystal. like Figure 3 As shown, the side lengths of the row of regular triangle air holes tri_a and inverted triangle air holes tri_b are .

[0023] Example 3 In this embodiment, based on the second embodiment, the side lengths of the first row of inverted triangle air holes tri_a and regular triangle air holes tri_b adjacent to the whisker-type interface waveguide are .

[0024] Example 4 In this embodiment, based on the third embodiment, the side lengths of the second row of regular triangle air holes tri_a and inverted triangle air holes tri_b adjacent to the whisker-type interface waveguide are .

[0025] Example 5 In this embodiment, based on the fourth embodiment, the lattice constant a=ω×λ, wherein ω is the frequency and λ is the wavelength.

[0026] In the valley photonic crystal slow light waveguide, the normalized delay-bandwidth product is introduced, and the calculation formula is as follows: ; In the formula, is the slow light working center wavelength, is the bandwidth, is the group refractive index; Group refractive index The calculation is as follows: ; ; In the formula, is the frequency, k is the wave number, is the speed of light in a vacuum; When calculating the waveguide transmission spectrum, the two-dimensional time-domain finite difference method is used, and the calculation formula is as follows: .

[0027] Example 6 The present invention is based on the broadband low dispersion slow light waveguide of valley photonic crystal, such as Figure 1 As shown, it includes type A and type B silicon-based two-dimensional valley photonic crystals, and a whisker-type interface waveguide is formed between the type A and type B silicon-based two-dimensional valley photonic crystals.

[0028] Furthermore, the A-type and B-type silicon-based two-dimensional valley photonic crystals are honeycomb lattices formed by silicon and equilateral triangular air holes. The lattice constant of the honeycomb lattice is a It is 376nm.

[0029] On the plane of the A-type silicon-based two-dimensional valley photonic crystal, several rows of equilateral triangular air holes tri_a are sequentially arranged along the long side of the valley photonic crystal with the center line of the valley photonic crystal as the symmetry axis, and several rows of inverted triangular air holes tri_a are sequentially arranged along the long side of the valley photonic crystal between adjacent rows of equilateral triangular air holes tri_a.

[0030] On the plane of the B-type silicon-based two-dimensional valley photonic crystal, several rows of inverted triangular air holes tri_b are sequentially arranged along the long side of the valley photonic crystal with the center line of the valley photonic crystal as the symmetry axis, and several rows of regular triangular air holes tri_b are sequentially arranged along the long side of the valley photonic crystal between adjacent rows of inverted triangular air holes tri_b.

[0031] The side length of the regular triangle air hole tri_a and the inverted triangle air hole tri_b is 152nm. The side length of the inverted triangle air hole tri_a and the regular triangle air hole tri_b is 282.2nm.

[0032] The side length of the equilateral triangle air hole tri_a and the inverted triangle air hole tri_b of the beard-type waveguide interface is 162.7nm, the side length of the first row of inverted triangle air holes tri_a and the equilateral triangle air holes tri_b adjacent to the beard-type interface waveguide is 292.5nm, and the side length of the first row of inverted triangle air holes tri_a and the equilateral triangle air holes tri_b adjacent to the beard-type interface waveguide is 22.5nm.

[0033] The dispersion curve of waveguide topological boundary states calculated by two-dimensional plane wave expansion (PWE) is shown in Figure 4 As shown in the figure, the bold segment is the broadband low dispersion range, and the calculation formulas are shown in formula (1) and formula (2): (1); (2); In the formula is the frequency, k is the wave number, the group velocity is the first derivative of the dispersion characteristic curve, the group refractive index is the speed of light in a vacuum and The ratio of the calculated group refractive index Curve like Figure 5 As shown, the group refractive index in the low dispersion region is obtained It is 21.89, change The frequency range is from 0.240619 to 0.244569. According to formula (3), the wavelength range is 1537.39 to 1562.63 nm, and the bandwidth is The central wavelength is 25.24nm It is 1550nm.

[0034] (3); The normalized delay bandwidth product is introduced and the calculation formula is as shown in formula (5). The NDBP is calculated to be 0.356.

[0035] (4); The transmission spectrum of a linear waveguide calculated using the two-dimensional finite-difference time-domain method (FDTD) is shown in Figure 6 As shown, a flat transmittance curve is observed in the broadband low dispersion region (grey shaded area). Calculated by formula (5), the average transmission coefficient is 0.999 in the entire 25.24nm width, which is very close to the ideal lossless transmission coefficient of 1. Formula (5) is as follows: (5); In order to verify the robustness of transmission at sharp corners, the transmission characteristics of the Z-type waveguide are analyzed. The schematic diagram of the Z-type waveguide structure is shown in Figure 7 The calculated transmission spectrum is shown in Figure 8 As shown, 1536nm is the boundary between the topological state (>1536nm) and the ordinary state (<1536nm). The ordinary state has obvious losses in the Z-type waveguide due to reflections at sharp corners, while the topological state shows high transmittance, with an average transmission coefficient of 0.998 over the entire 25.24nm width, which is also very close to the transmission coefficient of 1 for ideal lossless transmission.

[0036] The broadband low-dispersion slow light waveguide based on valley photonic crystal of the present invention can realize a valley photonic crystal slow light waveguide with a group refractive index of 21.89, a low group velocity dispersion bandwidth of 25.24nm, and an NDBP of 0.356, thereby improving the broadband low-dispersion performance of the valley photonic crystal slow light waveguide.

[0037] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0038] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present application. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A broadband low-dispersion slow light waveguide based on valley photonic crystals, characterized in that: It comprises A-type and B-type silicon-based two-dimensional valley photonic crystals, wherein a whisker-type interface waveguide is formed between the A-type silicon-based two-dimensional valley photonic crystal and the B-type silicon-based two-dimensional valley photonic crystal, and a plurality of rows of regular triangular air holes tri_a are sequentially arranged and etched on the plane of the A-type silicon-based two-dimensional valley photonic crystal along the direction of the long side of the valley photonic crystal, and a plurality of rows of inverted triangular air holes tri_a are sequentially arranged and etched along the direction of the long side of the valley photonic crystal between adjacent rows of regular triangular air holes tri_a; On the plane of the B-type silicon-based two-dimensional valley photonic crystal, a plurality of rows of inverted triangle air holes tri_b are sequentially arranged and etched along the direction of the long side of the valley photonic crystal with the center line of the valley photonic crystal as the symmetry axis, and between adjacent rows of inverted triangle air holes tri_b, a plurality of rows of regular triangle air holes tri_b are sequentially arranged and etched along the direction of the long side of the valley photonic crystal; The equilateral triangle air hole tri_a and the inverted triangle air hole tri_a, the equilateral triangle air hole tri_b and the inverted triangle air hole tri_b all constitute unit cells on the honeycomb lattice, and the lattice constant is a.

2. The broadband low-dispersion slow light waveguide based on valley photonic crystal according to claim 1, characterized in that: The side lengths of the inverted triangle air hole tri_a and the regular triangle air hole tri_b are .

3. The broadband low-dispersion slow light waveguide based on valley photonic crystal according to claim 1, characterized in that: The side lengths of the regular triangle air hole tri_a and the inverted triangle air hole tri_b are .

4. The broadband low-dispersion slow light waveguide based on valley photonic crystal according to claim 1, characterized in that: The beard-type interface waveguide comprises a plurality of equilateral triangular air holes tri_a and inverted triangular air holes tri_b, wherein the plurality of equilateral triangular air holes tri_a and inverted triangular air holes tri_b form a row, and the equilateral triangular air holes tri_a and inverted triangular air holes tri_b are arranged alternately in sequence along the direction of the long side of the valley photonic crystal; The side lengths of the regular triangle air holes tri_a and the inverted triangle air holes tri_b in this row are .

5. The broadband low-dispersion slow light waveguide based on valley photonic crystal according to claim 1, characterized in that: The side lengths of the first row of inverted triangle air holes tri_a and regular triangle air holes tri_b adjacent to the whisker-type interface waveguide are .

6. The broadband low-dispersion slow light waveguide based on valley photonic crystal according to claim 1, characterized in that: The side lengths of the second row of regular triangle air holes tri_a and inverted triangle air holes tri_b adjacent to the whisker-type interface waveguide are .

7. The broadband low-dispersion slow light waveguide based on valley photonic crystal according to claim 1, characterized in that: The lattice constant a=ω×λ, wherein ω is the frequency and λ is the wavelength.

8. The broadband low-dispersion slow light waveguide based on valley photonic crystal according to claim 1, characterized in that: In the valley photonic crystal slow light waveguide, the normalized delay-bandwidth product is introduced, and the calculation formula is as follows: ； In the formula, is the slow light working center wavelength, is the bandwidth, is the group refractive index; Group refractive index The calculation is as follows: ； ； In the formula, is the frequency, k is the wave number, is the speed of light in a vacuum; When calculating the waveguide transmission spectrum, the two-dimensional time-domain finite difference method is used, and the calculation formula is as follows: 。

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