Visible light band hexagonal boron nitride topological unidirectional slow light transmission structure

Abstract

The present application belongs to the field of topological photonics and optical communication system, and discloses a visible light band hexagonal boron nitride topological unidirectional slow light transmission structure, which comprises a two-dimensional hexagonal boron nitride substrate, and a plurality of air holes are etched on the substrate; with the interface line parallel to the light incidence direction as the boundary, the air holes on both sides of the interface line are periodically arranged in a triangular lattice to form a first energy valley photonic crystal structure and a second energy valley photonic crystal structure, and the air holes in the two energy valley photonic crystal structures are mirror set relative to the interface line, and the two rows of air holes on both sides of the interface line form a topological optical waveguide. The present application can realize unidirectional slow light transmission of circularly polarized light in the visible light band, and by adding liquid crystal material in the air holes of the topological optical waveguide, the slow light wavelength tuning function can also be realized by adjusting the external electric field intensity, which opens up new possibilities for designing visible light unidirectional transmission equipment, and can be widely applied in optical communication and quantum optics.

Description

Technical Field

[0001] This invention belongs to the field of topological photonics and optical communication systems, specifically relating to a hexagonal boron nitride topological unidirectional slow light transmission structure in the visible light band. Background Technology

[0002] Photonic devices with slow-light characteristics are widely used in optical nonlinearity, optical switching, pulse delay, quantum optics, optical storage, and optical gain. Among these, optical delay lines are key components in integrated optics and optical communication, functioning to temporarily store optical signals for a sufficient time before using them as optical buffers in integrated optical paths. Advances in integrated photonics have facilitated the miniaturization of optical delay lines, placing higher demands on stability, tuning speed, and power consumption. Key performance indicators for slow-light photonic crystal waveguides include low group velocity, high group refractive index, normalized delay-bandwidth product within a certain range, low transmission loss (high transmittance), and good dispersion characteristics.

[0003] Photonic crystal nanostructures can be used to reduce the size of optical delay lines, making them suitable for on-chip integration. Photonic crystal delay lines come in several types, including photonic crystal waveguides, optical waveguides based on photonic crystal cavity-coupled resonators, and photonic crystal microrings. In 2021, researchers at Yokohama National University designed a micro-nano-sized silicon photonic crystal slow-light waveguide, enabling slow light transmission in the optical communication band with a group refractive index of 20 and a normalized delay bandwidth product of 0.45 [Siphotonic crystal slow-light waveguides optimized through informaticstechnology. Optics Letters, 2021, 46(17):4422-4425]. To date, most slow-light photonic crystal waveguide structures operate in the optical communication band, often using silicon to achieve a wide photonic bandgap for high transmission. However, the feasibility of using materials with lower absorption in the visible light band to achieve unidirectional slow-light transmission in photonic crystals remains to be studied.

[0004] Compared with traditional photonic crystal slow light devices, valley photonic crystals have the advantages of high transmittance, unidirectional transmission and compact structure. Slow light transmission in valley photonic crystal slow light waveguides has been confirmed in different wavelength ranges, including near-infrared, optical communication and G-Hertz band. In 2021, researchers at the University of Tokyo reported an experiment embedding a single-photon source in a valley photonic crystal waveguide, which confirmed that the single-photon source can realize slow light transmission in edge states, with a group refractive index greater than 20 near the near-infrared wavelength of 900 nm [Topologically-protected single-photon sources with topological slow light photonic crystal waveguides. Laser & Photonics Reviews, 2021, 16(8): 2200077]. Studies have also reported that valley photonic crystal slow light waveguides can achieve unidirectional anti-scattering slow light transmission near the near-infrared wavelength of 1500 nm, with a size of approximately 15 μm × 10 μm [Experimental demonstration of topological slow light waveguides in valley photonic crystals. Optics Express, 2021, 29(9): 13441-13450]. In 2022, researchers at Jiangnan University proposed a sandwiched photonic crystal topological slow light waveguide structure that can achieve slow light transmission with a normalized delay-bandwidth product of 0.2694 and a group refractive index of 12.85 [Zero-GVDslow light of coupled topological edge states in a sandwiched photonic crystal waveguide. Optical Materials Express, 2022, 12(11): 4252-4260]. Different group velocities and group refractive indices were achieved by changing the effective refractive index of the edge state structure. Currently, most research on optical delay lines and slow optical waveguides focuses on the microwave and near-infrared bands, while topological slow optical waveguides in the visible light band have been rarely studied. Summary of the Invention

[0005] The present invention overcomes the shortcomings of the prior art, and the technical problem to be solved is: to provide a hexagonal boron nitride topology unidirectional slow light transmission structure in the visible light band, so as to realize unidirectional slow light transmission in the visible light band.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: a visible light band hexagonal boron nitride topological unidirectional slow light transmission structure, comprising a two-dimensional hexagonal boron nitride substrate, wherein multiple air holes are etched on the two-dimensional hexagonal boron nitride substrate; taking a boundary line parallel to the incident light direction as the boundary, the multiple air holes on one side of the boundary line are arranged in a triangular lattice periodically to form a first valley photonic crystal structure, and the multiple air holes on the other side of the boundary line are arranged in a triangular lattice periodically to form a second valley photonic crystal structure, wherein the air holes in the first valley photonic crystal structure and the second valley photonic crystal structure are mirror images of the boundary line, and the two rows of air holes on both sides of the boundary line form a topological optical waveguide.

[0007] The air hole is circular, and its radius r ranges from 0.22a to 0.27a, where a represents the distance between two adjacent air holes in the first valley photonic crystal structure.

[0008] The value of 'a' ranges from 180 to 260 nm.

[0009] The distance h between the geometric centers of the two rows of air holes forming the topological waveguide ranges from 105 to 150 nm.

[0010] The depth of the air hole is equal to the thickness of the two-dimensional hexagonal boron nitride substrate, and it penetrates the two-dimensional hexagonal boron nitride substrate, the thickness of which is 200-1000 nm.

[0011] In the visible light band, the refractive index of the two-dimensional hexagonal boron nitride substrate is a dispersive refractive index in both the x and y directions, and the refractive index in the z direction is 1.84. Here, the xy plane is the plane in which the two-dimensional hexagonal boron nitride substrate is located, and z is the direction perpendicular to the two-dimensional hexagonal boron nitride substrate; the refractive index of the air hole is 1.

[0012] The visible light band hexagonal boron nitride topology unidirectional slow light transmission structure further includes liquid crystal pillars disposed in two rows of air holes forming the topological waveguide. The liquid crystal pillars are formed by injection and are used to achieve tuning of the working wavelength under an applied electric field.

[0013] The liquid crystal pillar is made of nematic liquid crystal material or cholesteric liquid crystal material.

[0014] The direction of the applied electric field is perpendicular to the extension direction of the topological optical waveguide.

[0015] The aforementioned two-dimensional hexagonal boron nitride tunable topology unidirectional slow light transmission structure in the visible light band operates in the visible light band.

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

[0017] This invention provides a hexagonal boron nitride topological unidirectional slow light transmission structure for the visible light band, achieving unidirectional transmission with a forward transmittance higher than 0.68 in the visible light band (636nm-646nm), and a forward transmittance of 0.75 at the peak wavelength of 650nm. Furthermore, by filling the topological waveguide with liquid crystal material, simulations demonstrate the influence of changes in the optical properties of the liquid crystal material under applied voltage on the edge state dispersion characteristics of the valley photonic crystal, thus enabling tunable unidirectional slow light transmission with backscatter suppression. Attached Figure Description

[0018] Figure 1 This invention provides a visible light band hexagonal boron nitride topology unidirectional slow light transmission structure.

[0019] Figure 2 This is the energy band diagram of the first valley photonic crystal structure in this embodiment of the invention, where the shaded area is the light cone;

[0020] Figure 3 The diagram shows the energy band structure (a) and the distribution of group refractive index and group velocity as a function of wave vector at the interface edge states of the first valley photonic crystal structure and the second valley photonic crystal structure in this embodiment of the invention (b).

[0021] Figure 4 This is a transmittance diagram of right-handed circularly polarized light propagating in the structure of this invention;

[0022] Figure 5 The figures (a) and (b) show the local dispersion curves of the edge state bands under different voltages in the embodiments of the present invention, and the variation of slow light frequency (wavelength) with voltage.

[0023] In the figure: 1 is the hBN substrate, 2 is the air hole, 3 is the topological waveguide, 4 is the first valley photonic crystal structure, 5 is the second valley photonic crystal structure, 6 is the boundary line, and 7 is the liquid crystal pillar. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0025] like Figure 1As shown, this embodiment of the invention provides a visible light band hexagonal boron nitride topological unidirectional slow light transmission structure, including a two-dimensional hexagonal boron nitride substrate 1, on which multiple air holes 2 are etched; with a boundary line 6 parallel to the light incident direction as the boundary, the multiple air holes 2 on one side of the boundary line 6 are arranged in a triangular lattice periodically to form a first valley photonic crystal structure 4, and the multiple air holes 2 on the other side of the boundary line 6 are arranged in a triangular lattice periodically to form a second valley photonic crystal structure 5, and the air holes 2 in the first valley photonic crystal structure 4 and the second valley photonic crystal structure 5 are arranged in a mirror symmetrical arrangement with respect to the boundary line 6. The two rows of air holes 2 on both sides of the boundary line 6, namely the row of air holes in the first valley photonic crystal structure 4 near the boundary line 6 and the row of air holes in the second valley photonic crystal structure 5 near the boundary line, form a topological optical waveguide 3.

[0026] Specifically, in this embodiment, the air hole 2 is circular, and its radius r ranges from 0.22a to 0.27a, where a represents the distance between two adjacent air holes 2 in the first valley photonic crystal structure 4. Specifically, the value of a ranges from 180 to 260 nm.

[0027] Specifically, in this embodiment, the distance h between the geometric centers of the two rows of air holes 2 forming the topological waveguide 3 ranges from 105 to 150 nm.

[0028] Specifically, in this embodiment, the depth of the air hole 2 is equal to the thickness of the two-dimensional hexagonal boron nitride substrate 1, and the air hole 2 penetrates the two-dimensional hexagonal boron nitride substrate 1. The thickness of the two-dimensional hexagonal boron nitride substrate 1 is d = 200~1000nm.

[0029] Furthermore, in this embodiment, the radius of the air hole 2 is r = 60 nm, and the distance 'a' between any two adjacent air holes 2 in the first valley photonic crystal structure 4 and the second valley photonic crystal structure 5 is a = 230 nm. The thickness of the hBN substrate 1 is 220 nm. The distance between the geometric centers of the upper and lower rows of air holes forming the topological waveguide is h = 133 nm.

[0030] Specifically, in this embodiment, within the visible light band, the refractive index of the two-dimensional hexagonal boron nitride substrate 1 is a dispersive refractive index in both the x and y directions, and the refractive index in the z direction is 1.84. Here, the xy plane is the plane where the two-dimensional hexagonal boron nitride substrate 1 is located, and z is the direction perpendicular to the two-dimensional hexagonal boron nitride substrate 1; the refractive index of the air hole 2 is 1.

[0031] Furthermore, the visible light band hexagonal boron nitride topological unidirectional slow light transmission structure of this embodiment also includes liquid crystal pillars 7 disposed within two rows of air holes 2 forming the topological waveguide 3. The liquid crystal pillars 7 are formed by injecting liquid crystal material and are used to achieve tuning of the operating wavelength under an applied electric field. Specifically, the material of the liquid crystal pillars 7 is a nematic liquid crystal material or a cholesteric liquid crystal material. Specifically, the direction of the applied electric field is perpendicular to the extension direction of the topological waveguide 3, that is, perpendicular to the straight line direction where the boundary line 6 is located.

[0032] This invention discloses a two-dimensional hexagonal boron nitride valley photonic crystal structure, fabricated as follows: First, an hBN thin film is peeled onto a grooved silicon substrate, followed by the deposition of a 15 nm tungsten layer. Then, polymethyl methacrylate (PMMA) is spin-deposited onto the tungsten layer. Next, a pattern for the structure is fabricated on the PMMA using electron beam lithography. After transfer, the pattern is transferred to a tungsten mask via reactive ion etching. Using the tungsten layer as a mask, the hBN structure is then etched using electron beam induction. Finally, the tungsten mask is removed using hydrogen peroxide to obtain the complete hBN photonic crystal structure.

[0033] The band structure of the hBN photonic crystal structure with circular lattice points in a honeycomb lattice and VPC1 were calculated using the finite-difference time-domain (FDTD) method, as follows: Figure 2 As shown in the band structure diagram, the hBN photonic crystal structure with a circular honeycomb lattice exhibits conical dispersion curves in the K-valley of the Brillouin zone due to the C6 wave group symmetry of the hexagonal lattice. The intersection of these curves in the K-valley is the Dirac point. By adjusting the radii of the air holes spaced in the three directions within the unit cell until the radii of the air holes are reduced to zero, the first valley photonic crystal structure 4 and the second valley photonic crystal structure 5 are formed, respectively. Since the lattice structure decreases from C6 symmetry to C3 symmetry, the Dirac point opens, resulting in a complete band gap ranging from 0.345 to 0.362 a / λ (635.5 nm to 667 nm). Figure 2 The bandgap portion is shown.

[0034] Subsequently, after splicing the first valley photonic crystal structure 4 and the second valley photonic crystal structure 5 together, topologically protected edge states are generated at their boundary, as shown in the energy band diagram. Figure 3 As shown in (a), the edge state structure exhibits a passband from 0.345–0.362 a / λ (635.5 nm–667 nm), which is consistent with... Figure 2 The band gaps of the two structures share a common wavelength range, indicating that light waves are in the passband at the edge states and in the bandgap of VPC1 and VPC2. Therefore, light waves can pass through the edge interfaces of the structure. The propagation speed of light, v... g The formula for calculating the slope of the dispersion curve (v) is as follows: g=dω / dk=c / n g .from Figure 3 As shown in (a), the inflection points of the dispersion curve are located at the frequencies where the group velocity is minimum, specifically at wave vector k = 0 and k = ±0.14. The tangents point horizontally (black arrows), indicating that lower light propagation speeds can be achieved near these frequencies, suggesting the possibility of slow light propagation. Based on the distribution of group refractive index and group velocity within the range of k = ±0.12 under different wave vectors, it can be seen that... Figure 3 In the dashed box (a), the group velocities on both sides of wave vector k=0 exhibit opposite directions but the same trend of change. The group refractive index at wave vector k=0 can reach a relatively large value (>1000), such as... Figure 3 As shown in (b). Theoretically, the position where the wave vector k = 0 is the point where the group velocity direction changes. The group refractive index at this point with a wavelength of 645.3 nm can reach infinity, and the group velocity is close to zero.

[0035] In this embodiment, a hexagonal boron nitride topological unidirectional slow light transmission structure for the visible light band is provided. The forward and reverse transmission power of right-hand circularly polarized light in the structure are respectively represented by T... F and T B The transmission contrast ratio is defined as C = (T F -T B ) / (T F +T B The transmission spectrum is calculated using the finite-difference time-domain (FDTD) method, such as... Figure 4 We define the direction of light propagation as positive (rightward) and the direction of light propagation as negative (leftward). Using monitors at both receiving ends, we obtain the forward transmittance T. F and reverse transmittance T B The forward transmittance is higher than -1.67 dB (0.68) and the reverse transmittance is lower than -8.53 dB (0.14) within the operating bandwidth from 637 nm to 644 nm. At the peak wavelength of 650 nm, the forward transmittance is -0.63 dB (0.89) and the reverse transmittance is -9.20 dB (0.12), indicating that the slow waveguide structure based on valley photonic crystals of this invention can realize unidirectional transmission of visible light waves.

[0036] When nematic or cholesteric liquid crystal material is injected into the two rows of air holes of the topological waveguide to form liquid crystal pillars, the birefringence Δn of the liquid crystal changes from the unusual light refractive index n. e With ordinary refractive index n o The difference determines (Δn=n) e -n o When nematic liquid crystal material is injected, without an applied electric field, n o =1.51, n e=1.73. In this embodiment, a transparent electrode (ITO) or a metal electrode (Au) is applied to the upper first valley photonic crystal surface and the lower second valley photonic crystal surface of the topological waveguide. By applying a voltage to the electrodes, an electric field can be formed on the entire topological waveguide. The direction of the electric field is perpendicular to the extension direction of the topological waveguide. The larger the applied voltage, the larger the spatial electric field.

[0037] like Figure 5 As shown, with the continuous increase of voltage, the unusual light refractive index decreases until it approaches the ordinary light refractive index. During the gradual increase of the applied electric field, the slow light frequency at the lowest point of the dispersion curve changes from 0.339 a / λ (678 nm) at 0 V to 0.343 a / λ (671 nm) at 3 V, exhibiting a slow light tuning range of 8 nm. Figure 5 As shown in (a) and (b), the above conclusions indicate that in this embodiment, the slow light wavelength undergoes a blue shift with increasing voltage, enabling slow light tuning within the visible light range of 671nm to 678nm. It should be noted that adding liquid crystal material to the air hole of the topological waveguide 3 affects the wavelength range of unidirectional slow light transmission, causing a shift in its operating wavelength, but does not affect its unidirectional slow light output effect. Furthermore, wavelength tuning within the visible light transmission band can be achieved under the influence of an external electric field.

[0038] In summary, this invention provides a hexagonal boron nitride topological unidirectional slow light transmission structure in the visible light band, which realizes efficient unidirectional transmission of right-hand circularly polarized light waves. Moreover, by injecting liquid crystal material and adjusting the electric field strength of the environment in which the structure is located, the operating wavelength can also be tuned. This invention has achieved a breakthrough in principle and can be widely applied to other optical integrated communication and information processing devices based on hBN materials.

[0039] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A hexagonal boron nitride topological unidirectional slow light transmission structure in the visible light band, characterized in that, The structure includes a two-dimensional hexagonal boron nitride substrate (1), on which multiple air holes (2) are etched. Using a boundary line (6) parallel to the light incident direction as a boundary, the multiple air holes (2) on one side of the boundary line (6) are arranged in a triangular lattice periodically to form a first valley photonic crystal structure (4), and the multiple air holes (2) on the other side of the boundary line (6) are arranged in a triangular lattice periodically to form a second valley photonic crystal structure (5). The first valley photonic crystal structure... The air holes (2) in the crystal structure (4) and the second valley photonic crystal structure (5) are mirror images of the boundary line (6), and the two rows of air holes (2) on both sides of the boundary line (6) form a topological optical waveguide (3); the air holes (2) are circular, and the radius r ranges from 0.22a to 0.27a, where a represents the distance between two adjacent air holes (2) in the first valley photonic crystal structure (4); the value of a ranges from 180 to 260 nm.

2. The visible light band hexagonal boron nitride topological unidirectional slow light transmission structure according to claim 1, characterized in that, The distance h between the geometric centers of the two rows of air holes (2) forming the topological waveguide (3) ranges from 105 to 150 nm.

3. The visible light band hexagonal boron nitride topological unidirectional slow light transmission structure according to claim 1, characterized in that, The depth of the air hole (2) is equal to the thickness of the two-dimensional hexagonal boron nitride substrate (1), and it penetrates the two-dimensional hexagonal boron nitride substrate (1). The thickness of the two-dimensional hexagonal boron nitride substrate (1) is 200~1000 nm.

4. The visible light band hexagonal boron nitride topological unidirectional slow light transmission structure according to claim 3, characterized in that, In the visible light band, the refractive index of the two-dimensional hexagonal boron nitride substrate (1) is a dispersive refractive index in both the x and y directions, and the refractive index in the z direction is 1.

84. The xy plane is the plane in which the two-dimensional hexagonal boron nitride substrate (1) is located, and z is the direction perpendicular to the two-dimensional hexagonal boron nitride substrate (1). The refractive index of the air hole (2) is 1.

5. The visible light band hexagonal boron nitride topological unidirectional slow light transmission structure according to claim 1, characterized in that, It also includes liquid crystal pillars (7) disposed in two rows of air holes (2) forming the topological waveguide (3), the liquid crystal pillars (7) being formed by injection and used to achieve tuning of the working wavelength under an applied electric field.

6. The visible light band hexagonal boron nitride topological unidirectional slow light transmission structure according to claim 5, characterized in that, The liquid crystal column (7) is made of nematic liquid crystal material or cholesteric liquid crystal material.

7. The visible light band hexagonal boron nitride topological unidirectional slow light transmission structure according to claim 6, characterized in that, The direction of the applied electric field is perpendicular to the extension direction of the topological optical waveguide (3).

8. The visible light band hexagonal boron nitride topological unidirectional slow light transmission structure according to claim 1, characterized in that, Its operating wavelength is the visible light band.

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