CN113391378A

CN113391378A - High-quality second harmonic enhancer based on topological angular state

Info

Publication number: CN113391378A
Application number: CN202110526065.XA
Authority: CN
Inventors: 郭凯; 郭忠义; 吴金涛
Original assignee: Hefei University of Technology
Current assignee: Hefei University of Technology
Priority date: 2021-05-14
Filing date: 2021-05-14
Publication date: 2021-09-14
Anticipated expiration: 2041-05-14
Also published as: CN113391378B

Abstract

The invention discloses a high-quality second harmonic enhancer based on a topological angular state, wherein the topological angular state is widely concerned due to high locality and robustness, and the topological angular state with a high Q factor can be obtained at the intersection of two boundaries of an Armchair type and a Broken-zigzag type in a photonic crystal. The second harmonic is enhanced by using a topological angular state, and because the highly localized second harmonic is highly localized at an angle, the second harmonic is significantly enhanced and exhibits directional radiation, and more importantly, the enhanced second harmonic has robustness to defects.

Description

High-quality second harmonic enhancer based on topological angular state

Technical Field

The invention relates to the technical field of novel all-dielectric photonic crystals, in particular to a high-quality second harmonic enhancer based on topological angular states.

Background

Topological states originating from condensed state physics have found widespread use in photonics because they can provide novel approaches to optical engineering with topological protective properties such as resistance to backscattering and suppression of scattering losses. Recently, high-order topological insulators are developed, and the traditional body-edge correspondence is broken through. It has been demonstrated that a higher order topological insulator can support topological states that are two or more dimensions lower than the system itself. For example, a two-dimensional high order topology insulator can support zero-dimensional topological angular states, which have a very high Q factor and therefore can capture a small volume of light at the corners. The topological angular state has robustness to defects and has wide application prospect in the fields of nano laser and the like.

Also, topophotonics, in combination with nonlinear optical effects, reveals a few interesting phenomena and functions in condensed state physics. The emerging field of nonlinear topological photonics can be divided into two main areas: the impact of topographies on nonlinearities and the impact of nonlinearities on topological states. On the one hand, the non-linearity changes the topology neutral state to a non-neutral state, resulting in a topology protected mode. On the other hand, the topological state has the characteristics of no scattering, low loss and high localization, and provides a shortcut for researching nonlinear optics. Nonlinear responses in topological photonics open up a way to achieve advanced functions such as nonlinearity, nonreciprocity, and frequency conversion. We have observed that nonlinear light can be enhanced by topological boundary states and show robustness to various perturbations and controllable unidirectional excitation. Recently, the all-dielectric-photonic valley hall effect has been designed to achieve tunable and bi-directional phase-matched second harmonic generation. Clearly, these results demonstrate the superiority of exploiting photonics in nonlinear photon generation due to the unique properties of topological states.

Disclosure of Invention

The invention aims to make up for the defects of the prior art, and provides a topological angular state-based high-quality second harmonic enhancer, which enhances the second harmonic through the high locality and robustness of the topological angular state, directionally radiates the second harmonic through a photonic crystal, and obtains the radiation direction of the second harmonic through carrying out Fourier transform on the field intensity of the second harmonic, wherein the radiation direction is vertical to the surface of the photonic crystal. And introducing some defects into the photonic crystal demonstrates the robustness of the topological corner states to defects.

The invention is realized by the following technical scheme:

a high-quality second harmonic enhancer based on topological angular states is used for constructing photonic crystals, constructing pseudo spins by using the symmetry of photonic crystal lattices, exciting the topological angular states by lattice contraction and expansion to realize topological phase change, locally enhancing second harmonics by using the excited topological angular states, and directionally radiating the enhanced second harmonics.

The photonic crystal is constructed by adopting all-dielectric materials, and when the dielectric columns in the photonic crystal lattice shrink inwards, the photonic crystal is in a topological mediocre state; when the dielectric columns in the photonic crystal lattice shrink outwards, the photonic crystal is in a topological indifferent state, and the topological indifferent state and the lattice of the topological indifferent state are arranged in order to obtain the photonic crystal.

An Armchair type boundary and a Broken-zigzag type boundary are constructed between lattices in topological mediocre states and topological non-mediocre states in the photonic crystal, a topological angular state with a high Q factor is excited at the center of a cross structure consisting of the Armchair type boundary and the Broken-zigzag type boundary, and second harmonics are enhanced and directionally radiated through the high locality of the topological angular state.

The radiation direction of the second harmonic is perpendicular to the surface of the photonic crystal, which is obtained by fourier transformation of the second harmonic field strength.

The invention has the advantages that: the invention constructs Armchair type and Broken-zig type boundaries between topologically meditative and topologically non-meditative lattices in photonic crystals, and by the intersection of the two boundaries, a Q factor as high as 1.65 x 10 can be obtained at the intersection point⁸Topological angular state of (1); the second harmonic is enhanced by utilizing the locality of the topological angular state, the intensity of the generated second harmonic can be improved, the second harmonic is radiated out in a directional mode, the subsequent use of the second harmonic is facilitated, and the robustness of the topological angular state to defects is verified by introducing some defects.

Drawings

FIG. 1 is a schematic diagram of a photonic crystal structure. (FIG. 1(a) is a structural view of the entire photonic crystal, and FIG. 1(b) is a structural view of each lattice constituting the photonic crystal)

FIG. 2 is a graph of the two types of boundary and excited topological angular state field distributions in a photonic crystal structure and their corresponding Q-factors. (FIG. 2(a) is a crystal structure diagram obtained by amplifying an Armchair type boundary, FIG. 2(b) is a crystal structure diagram obtained by amplifying a Broken-zig type boundary, FIG. 2(c) is a topological angle state diagram, and FIG. 2(d) is a Q factor diagram of a topological angle state.)

FIG. 3 is a graph of the excited fundamental and second harmonic intensities and second harmonic field distributions and directional radiation patterns. (FIG. 3(a) is a graph of the fundamental wave after excitation, FIG. 3(b) is a graph of the field intensity of the second harmonic, and FIG. 3(c) is a far-field radiation pattern)

FIG. 4 is a graph of robustness tests for various defects for topological corners. (FIG. 4(a) is a view showing a structure in which a lattice within a dotted line is removed, FIG. 4(b) is a view showing an eigenmode field pattern in which a lattice within a dotted line is removed, FIG. 4(c) is a view showing a structure in which one boundary is bent, and FIG. 4(d) is a view showing an eigenmode field pattern in which one boundary is bent)

Detailed Description

The invention is based on the optical quantum spin Hall effect, adopts all-dielectric materials to construct photonic crystals, utilizes lattice symmetry to construct pseudo spin, and realizes topological phase change through lattice contraction or expansion. The boundaries of the Armchair and Broken-zig zag types are formed between topologically mediocre and topologically mediocre lattices in photonic crystals, exciting a topological angular state of high Q-factor at the boundary intersections. The topological angular state is utilized to carry out local enhancement on the second harmonic wave, and the enhanced second harmonic wave is subjected to directional radiation, so that the subsequent application of the second harmonic wave is facilitated. And the robustness of the topological corner state to the defect is verified by introducing some defects.

The specific implementation mode of the invention is as follows:

the structure of the entire photonic crystal is shown in fig. 1(a), in which each lattice structure constituting the photonic crystal is shown in fig. 1 (b). Where the lattice constant is 1 micron (the lattice constant is the distance from one lattice center to another), the dielectric pillar radius is 1/11 microns, the lattice radius is L (the lattice radius refers to the distance from the dielectric pillar center to the lattice center), and L varies. When L is a/4.25 microns, the dielectric columns in the crystal lattice shrink inwards at this time, and the photonic crystal is in a topologically mediocre state; when L is a/2.5 μm, the dielectric pillars shrink outward at this time, band inversion occurs due to orbital-spin coupling, and the photonic crystal becomes topologically unsmooth. When topologically mediocre and non-mediocre lattices are arranged in air in accordance with the structure shown in fig. 1(a), a photonic crystal can be obtained. Note that only a portion of the photonic crystal is shown in fig. 1, and the complete photonic crystal has approximately 20 x 20 crystal lattices.

As shown in FIG. 1(a), two different boundaries, called Armchair and Broken-zig, are constructed along the X-axis and Y-axis, respectively, and enlarged to obtain the structure shown in FIGS. 2(a) - (b).

Now, a variable is needed to represent the topological phase change of the crystal lattice so as to judge whether the topological angular state can be excited. Using quadrupole moment Q here^cTo represent the topological corner charge. First, Q is obtained^cPreviously, a dipole moment P had to be solved. Point C where high symmetry of dipole moment is required₂The eigenvalue of the rotation is determined, and the specific formula is as follows:

where eta is_n(K) Is that the nth energy band is at the K point (high symmetry point) C₂The characteristic value of the rotation can only be ± 1.

Is the dipole moment at the X or Y boundary. In addition, only three energy bands below the band gap need be calculated. It is calculated that when the photonic crystal is topologically sound, all dipole moments P are zero; but if the photonic crystal is topologically non-trivial, the dipole moments are 1/2, 1/2, and 0, respectively, on each band from bottom to top. Now the dipole moment of only one side of the corner, the other dipole moment of the corner is needed. Since the lattice has C_6vPoint group symmetry so that dipole moment is satisfied

Only one dipole moment needs to be calculated. Second, a quadrupole moment is required to represent the topological corner charge, as follows:

by calculation, the photonic crystal in the mediocre state is Q^o0, which is not in the plain state, is Q^o1/2. This non-zero Q^oThe existence of topological angular states in the photonic crystal can be ensured.

And scanning the eigenmode of the designed photonic crystal by using simulation software, wherein the scanning result consists of a body state, a boundary state and an angle state. FIG. 2(c) shows the topological corner state. As can be seen from the figure, the topological angular state has strong field distribution and good locality, which is very beneficial to future utilization. The star at the highest point in fig. 2(d) is the Q factor corresponding to the topological angular state. It can be seen from the figure that the value of the Q factor is very large, 1.65X 10⁸This again demonstrates the good locality and robustness of the topological corners.

Due to the nonlinear material used in the fabrication of photonic crystals, second harmonics are generated due to nonlinear effects when a signal is input. As mentioned above, the topological corner states have good locality. In the topological angular state excitation region, the photonic crystal has high photonic state density and strong field distribution. Therefore, when a sinusoidal signal having the same frequency as the topological angular state is input, the second harmonic will be excited and enhanced, as shown in fig. 3 (a). As can be seen from the figure, the intensity of the excited fundamental wave is 0.57X 10¹⁰The doubling strength is 0.65 × 10 °, and the ratio of the latter to the former is about 1/10. Therefore, the enhancement effect of the topological angular state on the second harmonic is obvious.

The enhanced second harmonic is then radiated for subsequent use. First, the fundamental wave and the second harmonic are separated to obtain respective field intensity graphs. Fig. 3(b) is a field intensity diagram of the second harmonic. Next, the amplitude and phase data in fig. 3(b) are fourier transformed to obtain the far-field radiation pattern in fig. 3 (c). The far-field diagram shows that after the second harmonic generated on the surface of the photonic crystal is radiated at a certain distance, although the radiation direction of a small part of the second harmonic is slightly deviated from the central direction, the majority of the second harmonic is still concentrated on the central position of the photonic crystal and radiates along the direction vertical to the photonic crystal. This provides convenience for subsequent application of the second harmonic. Whether in imaging, laser or future new application areas, the enhancement of frequency doubling and directional radiation will have a tremendous push to these areas.

As described in the foregoing, the topological corner states are robust to defects. Some drawbacks are now introduced and their robustness is observed. In fig. 4(a), the lattice within the red dotted line is removed, and in fig. 4(c), one of the boundaries is curved. Fig. 4(b) and 4(d) are the eigenmode field diagrams for the two cases described above, respectively. From the above results, it can be seen that the topological angular state can be excited normally regardless of the kind of defect added. The superior performances of topological angular states have important significance on the development of topological photonics and nonlinearity.

Claims

1. A high-quality second harmonic enhancer based on topological angular state is characterized in that: the method comprises the steps of constructing a photonic crystal, constructing pseudo spin by utilizing the symmetry of photonic crystal lattices, exciting topological angular states by lattice contraction and expansion to realize topological phase change, locally enhancing second harmonics by utilizing the excited topological angular states, and directionally radiating the enhanced second harmonics.

2. The topological corner state-based high-quality second harmonic enhancer as claimed in claim 1, wherein: the photonic crystal is constructed by adopting all-dielectric materials, and when the dielectric columns in the photonic crystal lattice shrink inwards, the photonic crystal is in a topological mediocre state; when the dielectric columns in the photonic crystal lattice shrink outwards, the photonic crystal is in a topological non-trivial state, and the topological non-trivial state and the lattice of the topological non-trivial state are arranged in order to obtain the photonic crystal.

3. The topological corner state-based high-quality second harmonic enhancer as claimed in claim 2, wherein: an Armchair type boundary and a Broken-zigzag type boundary are constructed between lattices in topological mediocre states and topological non-mediocre states in the photonic crystal, a topological angular state with a high Q factor is excited at the center of a cross structure consisting of the Armchair type boundary and the Broken-zigzag type boundary, and second harmonics are enhanced and directionally radiated through the high locality of the topological angular state.

4. The topological corner state-based high-quality second harmonic enhancer of claim 3, wherein: the radiation direction of the second harmonic is perpendicular to the surface of the photonic crystal by fourier transforming the field strength of the second harmonic.