CN113219584B - Second harmonic control device based on high-order topological photonic crystal - Google Patents

Abstract

The invention discloses a second harmonic control device based on a high-order topological photonic crystal, comprising a topological angular state resonant cavity and a topological boundary state waveguide based on a photon quantum spin Hall effect. The two-dimensional high-order topological photonic crystals are obtained by combining the state waveguides to handle the flow of nonlinear light. The invention designs a topological angular resonator based on the quantum spin Hall effect, and proves that the high localization of the resonator to photons can significantly enhance the optical frequency doubling response. The topological boundary state waveguide for robust transmission finally realizes the frequency-doubling signal enhanced by the angular resonator, and the enhanced frequency-doubling signal has lower loss during transmission in the presence of the topologically protected boundary state waveguide. , this design combines the advantages of angular state resonators and boundary state waveguides, demonstrating the potential applications of topological photonic devices in optical communication and optical computing technologies.

Description

A Second Harmonic Control Device Based on High-Order Topological Photonic Crystal

technical field

The invention relates to the technical field of topological photonic crystals in condensed matter physics, in particular to a second harmonic control device based on high-order topological photonic crystals.

Background technique

Over the past decade, topological photonic crystals have provided a new engineering platform for the control of light. Topological guard bands contain various new physical properties and optical phenomena, further promoting the development of the field of topological photonic crystals. Topological photonics is proposed based on topological phases in condensed matter physical systems. Despite the fundamental differences between Fermi and Bose systems, many topological features in condensed matter physics have been realized in topological photonics. So far, researchers have studied topological photonics in different optical systems, and obtained special optical phenomena such as unidirectional transmission, zero-order Landau level, as well as topological lasers, topological optical routing and topological all-optical logic devices, etc. Multiple functions. At present, the research of topological photonics mainly focuses on optical systems such as coupled resonant optical microcavities, coupled helical waveguides, topological artificial surface plasmon crystals, and resonant lattices.

Nonlinear optics are one of the key issues in metamaterials and photonic crystals, as they enable the present invention to manipulate light-light interactions at subwavelength scales and potentially facilitate the development of optical information and computing technologies. So far, much work has focused on bridging topological photonics and nonlinear optics. These efforts can be mainly divided into two categories. On the one hand, most of the problems are that nonlinear effects may change the topological phase at high light intensities. For linear topological photonics, the band topology can be determined by the system itself, whereas the band topology of nonlinear photonic crystals is not intuitive. Using one-dimensional Su-Schrieffer-Heeger (SSH), Xia et al. demonstrate the nonlinear coupling of light with topologically protected boundary states. Maczewsky et al. demonstrated that when the input signal strength is high, the nonlinearity leads to a topological phase transition, from trivial to topologically nontrivial. However, due to different experimental conditions, the interaction of nonlinearity with topological photonics is still in its infancy. On the other hand, the enhancement of nonlinear optical signals is achieved by exploiting the localization of the electric field in topological states and the robustness to defects. In a simple topologically sawtooth array of nanodiscs, a third-harmonic signal is observed at topological boundary states, demonstrating the topologically enhanced nonlinearity. Furthermore, using the enhanced third harmonic method, topological states that cannot be detected by the linear far-field method are directly probed. However, since the nonlinear optical flow in topological photonic crystals mostly obeys the bulk-boundary correspondence, the manipulation in multiple dimensions has obvious limitations.

In recent years, a new class of high-order topological photonic crystals has been extensively studied. Compared with topological photonic crystals with bulk-boundary counterparts, higher-order topological photonic crystals support lower-dimensional topological states, thereby providing the present invention with additional degrees of freedom to manipulate optical flow. At present, it has been found that second-order topological photonic crystals can support 0-dimensional angular state resonators, which are highly localized and non-radiative. This property makes the angular state a potential platform for lasing and nonlinear enhancement. At the same time, these second-order topological photonic crystals also support topological boundary state transmission along the boundary and have topological protection. Therefore, it is a very meaningful problem to process the light of the angle state and the boundary state, and it is also of great significance to the light information processing.

SUMMARY OF THE INVENTION

Based on the technical problems existing in the background art, the present invention proposes a second harmonic control device based on a high-order topology photonic crystal.

A second harmonic control device based on a high-order topological photonic crystal proposed by the present invention includes a topological angular state resonant cavity and a topological boundary state waveguide generated based on the optical quantum spin Hall effect. The two-dimensional high-order topological photonic crystals are obtained by combining the state waveguides to handle the flow of nonlinear light.

Preferably, by constructing the pseudo-time-reversal symmetry of the photonic crystal, a highly localized field is obtained so that the photons are confined to a small range.

Preferably, the pseudo-time-reversal symmetry of the constructed photonic crystal is the lattice symmetry of the constructed topological crystal insulator.

Preferably, the topological angular resonator is periodically arranged using regular triangular dielectric columns, the center wavelength is 1550 nm, and the resonator has a high Q factor.

Preferably, the topological boundary state derivation occurs in a high frequency energy band, the center wavelength is 775 nm, and the transmission is robust.

Compared with the prior art, the present invention has the beneficial effects of: combining the topological advantages of the 0-dimensional angular state resonant cavity and the 1-dimensional boundary state waveguide, a two-dimensional high-order topological photonic crystal is designed to handle the flow of nonlinear light; The nonradiative nature of the angular state resonator enhances the localized strength of the field, while the topologically protected transmission of the boundary state waveguide is used for harmonic signals with relatively low transmission losses. In addition, the present invention introduces defects, demonstrating the topological protection of angular state resonators and boundary state waveguides. The present invention utilizes the control flow concept of nonlinear light, which can pave the way for the practical application of topological photonics in optical information and computing technology, and topological photonic crystals are more immune to manufacturing defects than nonlinear metamaterials and metasurfaces.

Description of drawings

Figure 1. Structure and energy band change diagram of topological photonic crystal;

Figure 2 is a schematic diagram of the intrinsic electric field of the topological angular resonator and the principle of the resonator;

Fig. 3 Schematic diagram of angular resonator enhanced second harmonic and second harmonic scattering;

Fig. 4 Schematic diagram of frequency doubling effect of angular state resonator and topological protection transmission of boundary state waveguide;

Fig. 5 Schematic diagram of topology protection of lattice defects during second harmonic signal enhancement and transmission;

Fig. 6 Schematic diagram of the loss during the transmission of the second harmonic along the waveguide.

Detailed ways

The present invention will be further explained below in conjunction with specific embodiments.

The specific embodiment of the topological nonlinear control device of the present invention is as follows:

本发明用它们来构造赝自旋，得到了两种不同的赝自旋态p_±和d_±：(1) This paper proposes a two-dimensional C ₆ -symmetric topological photonic crystal, which consists of a honeycomb lattice containing six dielectric pillars. The characteristic modes are the two sets of orbitals of the dipole mode and the quadrupole mode, denoted as p _x (p _y ) and

The present invention uses them to construct pseudospins, and obtains two different pseudospin states p _± and d _± :

These combinations will form pseudospins that preserve pseudotime-reversal symmetry. When the beam passes through a non-uniform medium, the pseudospin photons with the above-mentioned two opposite phases are separated from each other in the direction perpendicular to the incident plane, resulting in a spin-induced split beam. That is, spin-momentum locking is achieved. The band folding of the honeycomb lattice folds the Dirac points at the K corner and K' towards the center, resulting in two quadruple degenerate Dirac points at the Γ point in the Brillouin zone. The present invention uses a tight-binding model (TBM) to describe intercellular coupling, where long-range interactions between particles are negligible. The present invention uses intercellular coupling (t _inter ) and intracellular coupling (t _intra ) to describe the coupling strength of the dielectric pillars, which are determined by the distance between the dielectric pillars. By adjusting the two coupling strengths, an energy band with a full band gap can be obtained. If t _inter = t _intra , two degenerate Dirac points are found in the energy band. The topological phase appears when t _inter /t _intra > 1 (contracted lattice with two topologically trivial band gaps) becomes t _inter /t _intra < 1 (extended lattice with two topologically non-trivial band gaps) Variations, the present invention describes the structure in detail while describing it.

The lattice constant is set to a ₀ =835 nm, the initial side length of the triangular dielectric column is d ₀ =230 nm, and the surrounding medium is air (as shown in Fig. 1a). The coupling strength t _intra (t _inter ) in the tight-binding model is governed by the intra-element (inter-element) spacing between adjacent columns r ₁ (r ₂ ), 2r ₁ +r ₂ =a ₀ . When r ₁ =r ₂ =r ₀ and r ₀ =a ₀ /3, two quadruple degenerate points appear, which the present invention labels as A and B (as shown in Figure 1c). It can be observed that they are all located at the Γ point of the two-dimensional Brillouin zone. When r ₁ /r ₂ is not equal to 1, a band gap can be observed near A and B. Figures 1c and 1d show that r ₁ /r ₂ =0.85r ₀ /1.15r ₀ <1(t _inter /t _intra >1) and r ₁ /r ₂ =1.15r ₀ /0.85r ₀ >1(t _inter Band structure in the case of /t _intra <1). Figures 1b and 1d plot the distribution of the electric field along the z-direction. It is found that the upper and lower energy bands of points A and B have undergone an on-off-on energy band inversion process, and r ₁ /r ₂ increases from 0.85r ₀ /1.15r ₀ to 1.15r ₀ /0.85r ₀ , The phase transitions near points A and B are shown in Fig. 1e and Fig. 1f.

(2) In order to realize the topological angular state resonator, the structure designed by the present invention includes trivial and topologically non-trivial photonic crystals, as shown in Fig. 2a. There are two armchair edges between the two photonic crystals, and a 0-dimensional high-order topological angular state may appear at the intersection of the two edges. The specific principles of cavity formation will be discussed below.

First, the system of the present invention is based on the original model of a C ₆ symmetric hexagonal lattice (Fig. 2b), and there is a sub-nearest-neighbor coupling represented by the black line. The present invention knows that the angular state is closely related to the Wannier center, which corresponds to the maximum Wyckoff position by mapping it from momentum space to real space (Figures 2b and 2c). Therefore, the present invention denote the three maximum Wyckoff positions in the model as c, c', c", and the corresponding Wannier centers at points K, K', K" in the momentum space. After that, the present invention has the following formula to calculate [Πp] of high symmetry points K, M and Γ in the momentum space:

[Π _p ]＝#Π _p -#Γ _p (3)

#Π _p denotes the number of energy bands below the Fermi level, at Π, and p denotes a point of high symmetry.

When t _intra < 1, the first-order and second-order topological phases are characterized by P _x(y) ⁽⁶⁾ and Q _corner , respectively, and the following formulas can be obtained:

Since the Wannier center is located at K, K', K", the present invention has [M]=2 and [K]=[K']=[K"]=0 in the same topological class, resulting in a vanishing dipole moment P =(0,0) and the non-trivial second-order topologically insulated phase Q _corner = 0.5. Conversely, when t _intra > 1, the model is trivial, [M] = [K] = 0, Q _corner = 0, preventing unnecessary scattering of energy in structures with t _intra < 1, as shown in Figure 2(a) shown.

A typical feature of such angular resonators is the high localization of photons, which can be demonstrated with a more vivid image. Figure 2e is the numerical calculation result of the out-of-plane electric field, the photons are mainly concentrated in the angular state and decay rapidly in the region outside the angular state. In a sense, the 0-dimensional corner state can be regarded as the boundary of the 1-dimensional boundary state, which is called the edge-corner correspondence.

In order to further study the properties of the angular resonator, the present invention analyzes the energy band structure near the working wavelength, as shown in Fig. 2e. As expected, the pseudospin-dependent boundary states exist in the forbidden band, while the angular states inside the forbidden band appear in the gap between the two boundary states, the intrinsic properties of the angular states are marked with red dashed lines in the figure frequency. The eigenvalues in the designed structure (Fig. 2c) are numerically calculated as shown in Fig. 2f. It can be observed that a 1-D boundary state (indicated by a dashed line) and a 0-D angular state (indicated by a pentagram) appear between the bulk states (indicated by a square). In addition, in order to quantify the high localization of the angular state, the present invention also calculates the quality factor Q of the body state, the boundary state and the angular state, as shown in Fig. 2g. The body and boundary state quality factors Q can be up to 2500, while the angular state quality factor Q is about 25000. The resonant properties of the topological angular state, along with its topological protection, offer opportunities to enhance photon-photon interactions, making it a potential platform for improving lasing and nonlinear conversion rates. It should be noted that the discussion of the corner state in the present invention is all at point A (Fig. 2d), there is no corner state at point B, but two boundary states are observed, which will be discussed in the next section.

In order to study the effect of angular state on nonlinear harmonics, the present invention takes the second harmonic as an example to carry out numerical simulation calculation. To excite the angular state, a point source with frequency Freq=193.4 THz was used as the excitation source. Figure 3a shows the electric field near the corner when the electric field distribution tends to stabilize. The five-pointed star indicates the location of the excitation source. It can be seen that the electric field is highly enhanced and localized at the angular states. Therefore, the frequency-doubled emission of the angular state resonator will be enhanced. The invention extracts the electric field of the resonance peak of the resonant cavity and performs Fourier transform. The peak appears at the second harmonic frequency on the Fourier coefficient spectrum, as shown in Fig. 3b. A question naturally arises: how does the present invention take advantage of the cavity-enhanced frequency-doubling response? Figures 3c and 3d show two representative results for harmonic scattering: in Figure 3c, the second harmonic frequency corresponds to the bulk state, while in Figure 3d, the second harmonic frequency corresponds to the band gap. Figure 3c shows that the harmonic field will diffuse towards the bulk state and its intensity decays significantly, making it difficult to collect the harmonic signal. Figure 3d shows that the harmonics are confined to the corners. In both cases, it is not easy to take full advantage of the frequency doubling of the angular resonator. In other words, the band structure must be designed so that there is an ideal field interaction at the fundamental and second harmonic frequencies.

In the following, the present invention investigates the control of fundamental and frequency-doubling light by manipulating the structural parameters of topological photonic crystals. As mentioned above, the present invention finds two Dirac degeneracy A and B in the low energy band and the high energy band, respectively. The characteristic mode of the electric field near point B is different from that near point A. As shown in Fig. 4(a ₁ ), a topologically protected angular state resonator (marked with a dashed line) can be observed near the Dirac degenerate point A. Meanwhile, Fig. 4(a ₂ ) shows that a boundary state with a tiny energy gap can be clearly observed near the Dirac degeneracy point B. It is well known that the band structure of topological photonic crystals depends on its geometrical parameters. By tuning the structural parameters, the frequency of the boundary state near point B is about twice the frequency of the angular state near point A, which provides a way for the present invention to manipulate light at the fundamental and second harmonic frequencies. To this end, the present invention has carried out numerical simulation on photonic crystals with different geometric parameters: a ₀ =835nm, d ₀ =230nm, as shown in Figure 4(a ₁ -a ₂ ), a ₀ =770nm, d ₀ =240nm, as shown in Figure 4(a 1 -a 2 ) 4(b ₁ -b ₂ ), and a ₀ =720 nm, d ₀ =255 nm, see Figure 4(c ₁ -c ₂ ). For these different geometric parameters, the frequency of the angular state is located around the frequency of 193 THz and does not show a significant shift, see Fig. 4(a ₁ -c ₁ ), while the frequency of the boundary state is shifted from about 402 THz to about 387 THz, See Figure 4(a ₂ -c ₂ ). In addition, the forbidden band width of the high frequency energy band studied in the present invention is gradually compressed to be close to zero. In these three cases, the frequency-doubled signal state enhanced from the fundamental angular state of the resonator may undergo a transition from diffused to bulk, localized to be unable to exit at the corners, to propagating along the boundary state.

Figure 4(d) plots the calculated transmission loss for topological boundary waveguides (straight, curved, defective), which is defined as the ratio of the transmitted energy at the entrance and exit (marked by white dashed lines). The present invention plots the transmission spectrum in Figure 4(d) for comparison. As shown in the frequency range 381-398THz (blue area), the difference in the transmitted energy can be seen compared to the case of the unbounded state, indicating that the energy dissipation of the second harmonic enhanced by the fundamental angular state along the waveguide is less than Low. The present invention also compares the transmission spectra of straight waveguides, two 120° curved waveguides and waveguides carrying lattice defects, and the results show that they have similar transmission efficiencies, proving that the boundary state waveguides have good robustness to structural defects . The electric field of light propagating along the boundary state waveguide is shown in Fig. 4(e-g), and the white arrows indicate the location and direction of the incident plane wave source.

In order to better illustrate how to manipulate the behavior of light, the present invention simulates the excitation of the fundamental frequency angular state resonator and the process of the second harmonic transmitted along the boundary state waveguide. The simulation details are given in the Methods section at the end of this paper. To demonstrate the topological protection of angular state resonators and boundary state waveguides, the present invention introduces the same type of lattice defects at different locations. In these cases, the geometric parameters are a ₀ =720 nm and d ₀ =255 nm. Figure 5(a ₁ -e ₁ ) shows that the fundamental frequency electric field can be highly localized at the angular resonator, and Figure 5(a ₂ -e ₂ ) shows that the second harmonic propagates along the curved boundary waveguide without significant attenuation. In addition, lattice defects have little effect on harmonic transmission. The present invention extracts the frequency-amplitude relationship of the excitation electric field of the resonator cavity, and performs Fourier transform on it, as shown in Fig. 5(a ₃ -e ₃ ). The results show that even if there are defects in the angular resonator, the frequency doubling effect is not significantly affected.

The results in Figure 5 show the advantages of the design of the present invention. Compared with the case where the second harmonic frequency corresponds to the bulk state (Fig. 3c), the enhanced second harmonic energy of the angular state resonator can be transmitted along the boundary state waveguide without scattering into the bulk state. Compared with the case where the second harmonic frequency corresponds to the forbidden band (Fig. 3d), the enhanced second harmonic energy can reach the structure boundary and be output, which provides an exploration direction for the present invention to further enhance the interaction of light.

The present invention also measured the loss of the _second harmonic energy transmitted along the boundary state waveguides P1 and P2, as shown in _Fig . 6a. The measurement locations are located around the two output ports, and the measurement results are shown in Figure 6b. The labels of “a, b, c, d, e” correspond to the cases of a ₂ , b ₂ , c ₂ , d ₂ and e ₂ in FIG. 5 , respectively, and the label of “initial” indicates that the second harmonic frequency corresponds to in the case of an energy gap (a ₀ =835 nm and d ₀ =230 nm). Compared with the initial structure, the designed structure enables the harmonic energy to effectively propagate along the boundary state waveguide, and the structural defects have less influence on the harmonic signal transmission, which further demonstrates the superior performance of the device designed in the present invention.

The above description is only a preferred embodiment of the present invention, but the protection scope of the present invention is not limited to this. The equivalent replacement or change of the inventive concept thereof shall be included within the protection scope of the present invention.

Claims (3)

1. A second harmonic control device based on a high-order topological photonic crystal is characterized by comprising a topological angular state resonant cavity and a topological boundary state waveguide which respectively generate a light quantum spin Hall effect based on two frequencies at the same time, and the two-dimensional high-order topological photonic crystal is obtained by combining the topological angular state resonant cavity and the topological boundary state waveguide and is used for regulating and controlling nonlinear light.

2. The higher order topological photonic crystal based second harmonic control device according to claim 1, wherein the electric field is highly enhanced and localized at the angular state, and the quality factor of the bulk state and the boundary state can reach 25000, so that the frequency doubled emission of the angular resonator cavity will be enhanced.

3. The higher-order topological photonic crystal-based second harmonic control device according to claim 1, wherein the topological angular resonator is periodically arranged by using triangular dielectric pillars, and the eigenmode of the second harmonic frequency can be adjusted by adjusting the relationship between the side length and the lattice constant of the triangular dielectric pillars, and the second harmonic propagates along the curved boundary waveguide without significant attenuation.

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