Electronic control topology photon state coupling based on liquid crystal and dynamic regulation and control method thereof

Abstract

The invention provides liquid crystal-based electronic control topology photon state coupling and a dynamic regulation and control method thereof. According to the method, a photonic lattice is immersed in liquid crystal, and an external bias voltage is utilized to actively modulate a topological boundary state and a topological angular state of the photonic lattice, so that Fano-like linetype selective coupling between high-order topological states is realized. As the liquid crystal shows different refractive indexes under different bias voltages, the electronic control switching of the background refractive index of the photonic crystal can be realized. On the basis, spectrum overlapping of a topological boundary state and a topological angular state can be realized, so that coupling between high-order topological states is realized in a photonic lattice with a determined structure. The invention provides an effective method for realizing a high-performance tunable topological photonic device, and the method has the advantages of dynamic regulation and control, programmability, high efficiency, flexibility and the like.

Description

Technical Field

[0001] The present invention relates to the field of topological photonic devices, and in particular to a liquid crystal-based electrically controlled topological photonic state coupling and a dynamic regulation method thereof. Background Art

[0002] Topological photonic insulators that support robust low-dimensional topological boundary states have attracted great interest. Thanks to the robustness of topologically protected boundary states, a series of new applications such as lasers, filters, sensors and quantum teleportation have been developed and studied. In recent years, coupled resonant photonic devices based on different topological states have been proposed, which greatly enriched the propagation and localization of light in integrated photonics. By combining different topological states, higher quality nanocavities and more flexible energy conversion methods can be achieved. However, traditional topological photonic devices require the introduction of complex designs, and once the design is determined, the structure is usually fixed, which limits the transmission and programmable control of light.

[0003] In order to explore the dynamic adjustability of photonic topological devices, introducing dielectric materials with adjustable refractive index has been shown to be a very feasible method. Among them, liquid crystal is one of the best choices, because the molecules of different principal axes of liquid crystal have different refractive indices, so that their refractive index can be adjusted by external voltage. Summary of the invention

[0004] In view of the above problems existing in the prior art, an object of the present invention is to provide a liquid crystal-based electrically controlled topological photon state coupling and a dynamic regulation method thereof.

[0005] The technical solution adopted by the present invention is as follows:

[0006] A liquid crystal-based electrically controlled topological photonic state coupling and a dynamic regulation method thereof, specifically: immersing a photonic lattice in liquid crystal, and using an external bias voltage to actively modulate the topological boundary states and topological corner states of the photonic lattice, thereby achieving selective coupling with a Fano-like line shape between high-order topological states.

[0007] Furthermore, when no voltage is applied to the liquid crystal, the long axes of the liquid crystal molecules are arranged horizontally, and the refractive index is 1.45 at this time; when the voltage is high enough, the liquid crystal molecules will tilt vertically, and the refractive index is 1.75 at this time.

[0008] Furthermore, the photonic lattice includes a topological phase photonic crystal and a non-topological phase photonic crystal, both of which are composed of a periodic arrangement of cylindrical dielectric columns; for the topological phase photonic crystal, the dielectric column is located at the center of the unit cell, and for the non-topological phase photonic crystal, a quarter dielectric column with the same radius is located at the corner of the unit cell.

[0009] Furthermore, the materials of the topological phase photonic crystal and the non-topological phase photonic crystal are both silicon.

[0010] Furthermore, the relative dielectric constant of silicon is 11.7.

[0011] Furthermore, the lattice constants of the topological phase photonic crystal and the non-topological phase photonic crystal are both a.

[0012] Furthermore, the base radius of the dielectric columns of the topological phase photonic crystal and the non-topological phase photonic crystal are both 0.22a.

[0013] Furthermore, the dielectric columns of the topological phase photonic crystal and the non-topological phase photonic crystal are arranged in a square lattice.

[0014] The present invention proposes an effective method for realizing high-performance tunable topological photonic devices, which has the following beneficial effects:

[0015] (1) Dynamic control: By adjusting the external bias voltage, the topological edge states and corner states of the photonic lattice can be dynamically adjusted to achieve flexible control of the optical path.

[0016] (2) Programmability: Different topological states can be selectively coupled as needed to achieve programmability of the optical path.

[0017] (3) Efficient and flexible: The present invention provides an efficient and flexible method to manipulate optical transmission and localization with topological robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 Schematic diagram of the energy band structure and topological phase transition of the photonic crystal based on liquid crystal of the present invention, (a) schematic diagram of the photonic crystal structure, (b) schematic diagram of the adjustment of the arrangement of liquid crystal molecules, (c) diagram of the energy band structure of the photonic crystal, and (d) diagram of the electric field distribution of the photonic crystal.

[0019] Figure 2 Schematic diagram of the projected energy band structure and topological boundary state of the present invention, (a) schematic diagram of the photonic lattice structure, (b) electric field distribution diagram of the photonic lattice, (c) projected energy band diagram of the photonic lattice, (d) electromagnetic wave propagation diagram when the voltage is off, and (e) electromagnetic wave propagation diagram when the voltage is on.

[0020] Figure 3 The present invention is based on the square splicing structure of liquid crystal (a) eigenmode calculation schematic diagram, (b) topological boundary state electric field distribution diagram excited when the voltage is turned off, (c) topological corner state electric field distribution diagram excited when the voltage is turned on.

[0021] Figure 4 Schematic diagram of Fano-like resonance of electrically controlled topological state coupling of the present invention, (a) schematic diagram of composite photonic lattice structure, (b) and (c) are the electric field E at the resonant frequency under different external voltage conditionsz Distribution diagram, (d) and (e) are the integrated diagrams of the electric field intensity in specific areas in Figures (b) and (c), respectively.

[0022] Figure 5 Schematic diagram of the present invention achieving coupling by selectively exciting different topological angular states, (a) electric field intensity integral diagram, (b) electric field distribution diagram of each topological angular state of a single square splicing structure, (c) electric field distribution diagram of each topological angular state of the composite photonic lattice structure being excited. DETAILED DESCRIPTION

[0023] The present invention provides a method for electrically controlled topological photon state coupling based on liquid crystal and its dynamic regulation. By utilizing the different refractive indices exhibited by liquid crystal under different bias voltages, electrically controlled switching of the background refractive index of the photonic crystal can be achieved. On this basis, spectral overlap of topological boundary states and topological corner states can be achieved, thereby achieving coupling between high-order topological states in a photonic lattice with a determined structure. Specifically, the present invention designs an electrically controlled resonant device with coupling between topological states, immerses it in liquid crystal, and uses an external bias voltage to actively modulate the topological boundary state and the topological corner state, thereby achieving Fano-like selective coupling between the waveguide and the corner cavity under electrically controlled drive in the electrically controlled resonant device with a determined structure, while maintaining the robustness of the topological state.

[0024] The control method of this embodiment specifically includes the following steps: first, design and construct a two-dimensional photonic lattice, which is composed of all-dielectric photonic crystals with different topological phases; then, immerse the two-dimensional photonic lattice in a liquid crystal environment, and adjust the refractive index of the liquid crystal by applying an external bias voltage, thereby dynamically adjusting the topological boundary state and topological angle state of the photonic lattice. The present invention can selectively couple different topological states by designing an electrically controlled coupled resonant device to achieve flexible control of light transmission.

[0025] This embodiment is based on the Su-Schrieffer-Heeger (SSH) model (WP Su, JRSchrieffer, and A.J.Heeger, "Solitons in polyacetylene," Phys. Rev. Lett. 42 (25), 1698-1701 (1979)) The two-dimensional lattice of C4 symmetry is extended, and two types of two-dimensional square photonic crystals composed of periodically arranged dielectric columns (silicon) with different topological phases are proposed. The photonic lattice considered is formed by splicing these two types of photonic crystals, and all are completed by COMSOL Multiphysics numerical simulation. In the simulation software, the material is set to silicon (Si), cylindrical, with a relative dielectric constant of 11.7, a lattice constant, and a base radius of 0.22a.

[0026] Figure 1 The figure shows the energy band structure and topological phase transition of photonic crystal based on liquid crystal. Figure 1 As shown in (a), the right part is in the topological phase and the left part is in the non-topological phase, both of which are embedded in the liquid crystal environment (such as Figure 1 (b)). The lattice constant of the two types of photonic crystals is a, and the relative dielectric constant of the dielectric pillars is set to 11.7 in the frequency range of interest. For the non-topological part of the lattice, a cylindrical pillar with a radius of r = 0.22a is located at the center of the unit cell, while for the topological part, four quarter-circular pillars with a radius of r are located at the corners of the unit cell, as shown in Figure 1 As shown in the upper part of (d). In the absence of external voltage, the long axes of all liquid crystal molecules are aligned horizontally, resulting in a refractive index of 1.45 (Y. Wang, W. Zhang, and X. Zhang, "Tunable topological valley transport in two-dimensional photonic crystals," New J. Phys. 21 (23), 233903 (2019)). Under a sufficiently high external voltage, the liquid crystal molecules tilt vertically, causing the refractive index of the liquid crystal to switch from 1.45 to 1.75. Figure 1 (c) shows the band structures of topological and non-topological photonic crystals in air background, represented by red triangles and blue circles, respectively. In order to clearly illustrate the different topological properties of these two photonic crystals, this example calculates their electric field distribution, such as Figure 1 (d) is shown. Points X1 and X2 represent the high symmetry points X of the first and second energy bands, respectively. The isolated s state has even parity (marked with "+"), and the degenerate p state has odd parity (marked with "-"). Obviously, as the photonic crystal structure changes, the parity of the energy band at point X is reversed, although the band graphs for both cases are the same.

[0027] Figure 2 The diagram shows the projected band structure and topological boundary state. The topological boundary state can be realized along the x or y direction at the interface between two photonic crystals with different topological phases. Figure 2 As shown in (a), the proposed photonic lattice is composed of dielectric pillars immersed in a liquid crystal environment and enclosed between conductive electrodes. The lattice consists of a topological two-dimensional photonic crystal and a non-topological photonic crystal. Through numerical simulation, this embodiment plots the projected energy bands of the photonic lattice when the background refractive index is 1.45 and 1.75, respectively, as shown in Figure 2As shown in the left and right puzzles in (c). It is obvious that the frequency of the band gap changes when the refractive index of the liquid crystal is changed. When the applied voltage causes the background refractive index to be 1.75, the frequency of the edge state in the band gap is lower than that when no voltage is applied due to the reduced refractive index contrast between the dielectric column and the background, which provides an opportunity to effectively control the topological edge state. Figure 2 As shown in (a), the position of the probe is set as the excitation source. When the voltage is turned off, the electromagnetic wave excited at a frequency of 0.2740 (c / a) propagates smoothly along the boundary, as shown in Figure 2 As shown in (d), this is because the frequency of the excitation source is the same as the frequency of the boundary state. If a voltage is applied, the excitation source frequency 0.2740 (c / a) cannot match the frequency of the boundary state, and the electromagnetic wave cannot propagate along the boundary, as shown in Figure 2 This effect provides the potential for realizing photonic devices based on dynamic control of optical switches.

[0028] Figure 3 The topological corner states can also be effectively tuned by applying an external bias voltage. Figure 3 The illustration in (a) shows a square tiling structure in which a topological two-dimensional square photonic crystal with 6×6 units is surrounded by three layers of non-topological photonic crystals. Figure 3 In (a), the eigenfrequencies of the structures corresponding to the liquid crystal refractive index of 1.45 and 1.75 are represented by triangular solid points and circular solid points, respectively, where the black ( / blue / red) points represent the corresponding body ( / edge / corner) topological states. When the voltage is turned off, a topological boundary state with a frequency of 0.2800 (c / a) can be excited, and its electric field distribution diagram is shown in Figure 3 When voltage is applied, the band frequency shifts due to the change in the background dielectric constant, and the corresponding topological corner state can be excited at the same frequency of 0.2800 (c / a), as shown in (b). Figure 3 as shown in (c).

[0029] Figure 4 Shown is a schematic diagram of Fano-like resonance with electrically controlled topological state coupling. Figure 3 Dynamic mode modulation in the frequency domain provides an effective way to control mode coupling in high-order photonic topological insulators. This is demonstrated by designing a composite photonic lattice. Figure 4 As shown in (a), the entire structure is filled with liquid crystals, and the excitation source is located at the position marked by the red star. The blue-shaded area 1 (voltage) consists of a topological photonic crystal with a 6×6 unit cell, surrounded by a three-layer non-topological photonic crystal. The gray-shaded area 2 (no voltage) consists of two different topological photonic crystals with the same geometric parameters as area 1, and their boundaries simulate line waveguides. Figure 4(b) and (c) show the electric field E at the resonant frequency under different external voltage conditions. z In order to further study the intensity of the coupled energy, this embodiment calculates the electric field intensity integrals of the specific areas marked by white dashed lines in the two regions, and the results are as follows: Figure 4 The black and red curves in (d) and (e) are shown in FIG. By modulating the refractive index, the energy of the waveguide mode at the resonant frequency can be transferred to the topological state in region 1. Due to the interaction between the so-called waveguide mode in region 1 and the topological state in region 2, it can be found that the red curve has a Fano-like line shape.

[0030] Figure 5 The figure shows a schematic diagram of coupling achieved by selectively exciting different topological corner states. Figure 5 In (a), there are four peaks C1, C2, C3, and C4 in the frequency range of 0.2780 (c / a) to 0.2840 (c / a). In order to confirm whether different topological corner states are excited, the eigenmode of a single square splicing structure is first numerically simulated, and the electric field E of each topological corner state is plotted. z The distribution is compared, such as Figure 5 Correspondingly, the electric field E of the linear waveguide and the corner cavity at the resonant frequencies C1, C2, C3 and C4 was numerically simulated by COMSOL Multiphysics. z Distribution, such as Figure 5 As shown in (c). By applying the electric field E z By comparing the distributions, the line waveguide can effectively excite four different types of topological corner states.

[0031] The above embodiments are merely illustrative of the principles and effects of the present invention, rather than limiting the present invention. Any insubstantial replacement or modification that does not exceed the essential spirit of the present invention shall fall within the protection scope of the present invention.

Claims

1. A liquid crystal-based electrically controlled topological photon state coupling and a dynamic control method thereof, characterized in that: The photonic lattice is immersed in liquid crystal, and an external bias voltage is used to actively modulate the topological edge states and topological corner states of the photonic lattice, thereby achieving selective coupling with Fano-like line shapes between high-order topological states.

2. According to claim 1, a liquid crystal-based electrically controlled topological photon state coupling and its dynamic control method is characterized in that: When no voltage is applied to the liquid crystal, the long axes of the liquid crystal molecules are arranged horizontally, and the refractive index is 1.45 at this time; when the voltage is high enough, the liquid crystal molecules will tilt vertically, and the refractive index is 1.75 at this time.

3. The method for electrically controlled topological photon state coupling and dynamic regulation thereof based on liquid crystal according to claim 1, characterized in that: The photonic lattice includes a topological phase photonic crystal and a non-topological phase photonic crystal, both of which are composed of a periodic arrangement of cylindrical dielectric columns; for the non-topological phase photonic crystal, the dielectric column is located at the center of the unit cell, and for the topological phase photonic crystal, a quarter dielectric column with the same radius is located at the corner of the unit cell.

4. The method for electrically controlled topological photon state coupling and dynamic regulation thereof based on liquid crystal according to claim 3, characterized in that: The materials of the topological phase photonic crystal and the non-topological phase photonic crystal are both silicon.

5. The method for electrically controlled topological photon state coupling and dynamic regulation thereof based on liquid crystal according to claim 4, characterized in that: The relative dielectric constant of silicon is 11.

7.

6. The method for electrically controlled topological photon state coupling and dynamic regulation thereof based on liquid crystal according to claim 3, characterized in that: The lattice constants of the topological phase photonic crystal and the non-topological phase photonic crystal are both a.

7. The method for electrically controlled topological photon state coupling and dynamic regulation thereof based on liquid crystal according to claim 6, characterized in that: The base radius of the dielectric columns of the topological phase photonic crystal and the non-topological phase photonic crystal is 0.22a.

8. The method for electrically controlled topological photon state coupling and dynamic regulation thereof based on liquid crystal according to claim 3, characterized in that: The dielectric columns of the topological phase photonic crystal and the non-topological phase photonic crystal are arranged in a square lattice.

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