CN113219584B - Second harmonic control device based on high-order topological photonic crystal - Google Patents
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Abstract
The invention discloses a second harmonic control device based on a high-order topological photonic crystal, which comprises a topological angular state resonant cavity and a topological boundary state waveguide which are generated based on a photon quantum spin Hall effect, wherein a 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 processing the flow of nonlinear light. The invention designs a topological angular state resonant cavity based on quantum spin Hall effect, and proves that the resonant cavity can remarkably enhance optical frequency doubling response to the high localization of photons, and in addition, a topological boundary state waveguide which enables frequency doubling second harmonic signals to be robustly transmitted is designed, so that the frequency doubling signals enhanced by the angular state resonant cavity are finally realized, and the enhanced frequency doubling signals have lower loss in the transmission process under the condition that the topological boundary state waveguide is protected.
Description
Technical Field
The invention relates to the technical field of topological photonic crystals in condensed physical, in particular to a second harmonic control device based on a high-order topological photonic crystal.
Background
In the last decade, topological photonic crystals have provided a new engineering platform for light control. The topological protective energy band comprises various new physical properties and optical phenomena, and further promotes the development of the field of topological photonic crystals. Topological photonics is proposed based on topological phases in condensed physical systems. Despite the fundamental differences between fermi and bose systems, many topological features in condensed state physics have been realized in topological photonics. Researchers have studied topological photonics in different optical systems to date, and have obtained special optical phenomena such as unidirectional transmission, zero-order Landau energy levels, and multiple functions such as topological lasers, topological optical routing, and topological all-optical logic devices. 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, resonant lattices and the like.
Nonlinear optics is one of the key issues in metamaterials and photonic crystals, as they enable the present invention to manipulate light-to-light interactions on a sub-wavelength scale and potentially facilitate the development of optical information and computational techniques. To date, much work has focused on the bridge of topological photonics and nonlinear optics. These efforts fall largely into two categories. On the one hand, most 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, while the band topology of a nonlinear photonic crystal is not intuitive. Xia et al demonstrate nonlinear coupling of light with topologically protected boundary states using a one-dimensional Su-Schrieffer-Heeger (SSH). Maczewsky et al demonstrate that when the input signal strength is high, the nonlinearity can cause topological phase transitions, from trivial to topologically non-trivial. However, due to the different experimental conditions, the interaction of nonlinearity with topophotonics is still in the first order. On the other hand, the enhancement of the nonlinear optical signal is realized by utilizing the localization of the electric field in a topological state and the robustness to the defect. In a simple nano-disc topological sawtooth array, a third harmonic signal is observed under a topological boundary state, and the nonlinearity of topological enhancement is proved. In addition, the topological state which cannot be detected by a linear far-field method is directly detected by using an enhanced third harmonic method. However, since the nonlinear optical flow in topological photonic crystals mostly follows the volume boundary correspondence, manipulation in multiple dimensions has significant limitations.
In recent years, a new class of high-order topological photonic crystals has been widely studied. Higher order topological photonic crystals support topological states with lower dimensions than topological photonic crystals with volume boundary correspondences, thereby providing the present invention with an additional degree of freedom to manipulate the optical flow. At present, the second-order topological photonic crystal can support a 0-dimensional angular state resonant cavity, and has the characteristics of high localization and non-radiation. This property makes the angular state a potential platform for laser and nonlinear enhancement. Meanwhile, the second-order topological photonic crystals also support the transmission of topological boundary states along the boundary and have topological protection. Therefore, it is a significant problem to process the light in the angle state and the boundary state, and it is also significant to process the light information.
Disclosure of Invention
Based on the technical problems in the background art, the invention provides a second harmonic control device based on a high-order topological photonic crystal.
The invention provides a second harmonic control device based on a high-order topological photonic crystal, which comprises a topological angular state resonant cavity and a topological boundary state waveguide which are generated based on a photon quantum spin Hall effect, wherein a 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 processing the flow of nonlinear light.
Preferably, by constructing the pseudotime reversal symmetry of the photonic crystal, a highly localized field is obtained such that the photons are confined to a small range.
Preferably, the pseudotime reversal symmetry of the structured photonic crystal is lattice symmetry of a structured topological crystal insulator.
Preferably, the topological angular resonant cavity is periodically arranged by using regular triangular dielectric cylinders, the central wavelength is 1550nm, and the Q factor of the resonant cavity is high.
Preferably, the topological boundary state waveguide appears on a high-frequency energy band, the center wavelength is 775nm, and the transmission is robust.
Compared with the prior art, the invention has the beneficial effects that: by 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 process the flow of nonlinear light; the non-radiative property of the angular resonant cavity is also utilized to enhance the local strength of the field, and the topological protection transmission of the boundary state waveguide is used for transmitting harmonic signals with relatively low loss. In addition, the invention also introduces defects to prove the topological protection of the angular state resonant cavity and the boundary state waveguide. The invention utilizes the control flow concept of nonlinear light, can pave the way for the practical application of topological photonics in optical information and computing technology, and the topological photonic crystal can more immune manufacture defects than nonlinear metamaterials and metamaterials.
Drawings
FIG. 1 is a graph of the structure and energy band variation of a topological photonic crystal;
FIG. 2 is a schematic diagram of the intrinsic electric field of a topological angular resonator and the principle of the resonator generation;
FIG. 3 is a schematic diagram of an angular resonator enhancing the second harmonic and scattering of the second harmonic;
FIG. 4 is a schematic diagram of the frequency doubling effect of an angular resonator and the topological guard transmission of a boundary waveguide;
FIG. 5 is a schematic view of the topological protection of lattice defects during second harmonic signal enhancement and transmission;
fig. 6 is a schematic diagram of losses during transmission of the second harmonic along a waveguide.
Detailed Description
The present invention will be further illustrated with reference to the following specific examples.
The specific implementation mode of the topological nonlinear regulation device is as follows:
(1) this document presents two-dimensional C 6 A symmetrical topological photon crystal is composed of a honeycomb lattice containing six dielectric columns. Two sets of tracks with characteristic patterns of dipole mode and quadrupole mode, respectively, are denoted as p x (p y ) And
the invention constructs pseudo spin by using the pseudo spin model to obtain two different pseudo spin states p ± And d ± ：
These combinations will form pseudospins that retain pseudotime-reversal symmetry. When the beam passes through the inhomogeneous medium, the pseudo spin photons with the two opposite phases are separated from each other in the direction perpendicular to the incident plane to produce spin-induced split beam. That is, spin momentum locking is achieved. The band folding of the honeycomb lattice causes the Dirac points at the K angle and K' to fold toward the center, creating two quadruple degenerate Dirac points at the brillouin zone Γ point. The present invention uses a Tight Bound Model (TBM) to describe intercellular coupling, where long-range interactions between particles are negligible. The 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, a band with a complete band gap can be obtained. If t is inter ＝t intra Two degenerate Dirac points were found in the energy bands. When t is inter /t intra >1 (contracted lattice with two topologically trivial bandgaps) to t inter /t intra <1 (extended lattice with two topologically non-trivial bandgaps), a topological phase transition occurs, which is elaborated upon while describing the structure.
Lattice constant is set as a 0 835nm, triangular dielectric cylinder initial side length d 0 230nm, and the surrounding medium is air (as shown in fig. 1 a). Coupling strength t in tight bound model intra (t inter ) From adjacent columns r 1 (r 2 ) Inter-cell (inter-cell) spacing control of 2r 1 +r 2 ＝a 0 . When r is 1 ＝r 2 ＝r 0 And r is 0 ＝a 0 At/3, two fourfold degeneracy points occur, which are labeled A and B by the present invention (as shown in FIG. 1 c). They were observed to both lie at the Γ point of a two-dimensional brillouin zone. When r is 1 /r 2 When not equal to 1, a band gap can be observed around a and B. FIGS. 1c and 1d show r, respectively 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 /t intra <1) The band structure of the case. Fig. 1b and 1d plot the distribution of the electric field along the z-direction. It was found that the upper and lower bands at points A and B underwent an on-off-on band inversion process, r 1 /r 2 From 0.85r 0 /1.15r 0 Increased to 1.15r 0 /0.85r 0 The phase transitions near points a and B are shown in fig. 1e and 1 f.
(2) In order to realize a topological angular resonator, the structure designed by the invention comprises a trivial and a topological non-trivial photonic crystal, as shown in fig. 2 a. Two armchairs (armchair) type edges are arranged between the two photonic crystals, and a 0-dimensional high-order topological angular state can appear at the intersection of the two edges. The specific principle of the formation of the resonant cavity will be discussed below.
First, the system of the present invention is based on C 6 The original model of a symmetric hexagonal lattice (fig. 2b), and there is a next-nearest-neighbor coupling represented by the black lines. The present invention knows that the angular state is closely related to the Wannier center, which corresponds to the maximum Wyckoff position (fig. 2b and 2c) by mapping it from the vector space to the real space. Therefore, the present invention represents the three maximum Wyckoff positions in the model as c, c ', c "and the corresponding Wannier centers at the K, K', K" points in the momentum space. Then, the present invention has the following formula to calculate [ Π p ] of high symmetry points K, M and Γ in momentum space]：
[Π p ]＝#Π p -#Γ p (3)
#Π p Representing the number of bands below the fermi level, at Π, and p representing the high symmetry point.
When t is intra <1, the first and second topological phases are respectively composed of P x(y) (6) And Q corner Characterization, the following formula can be obtained:
since the Wannier center is positioned at K, K 'and K', the invention has [ M ] in the same topological class]2 and [ K]＝[K’]＝[K”]0, resulting in a vanishing dipole moment P (0, 0) and a non-trivial second-order topological isolated phase Q corner 0.5. On the contrary, when t is intra >At 1, the model is trivial, [ M]＝[K]＝0，Q corner T is 0, prevent intra <1, as shown in fig. 2 (a).
A typical feature of such angular resonators is the high localization of photons, which can be demonstrated by more visual images. Fig. 2e is a numerical calculation of the out-of-plane electric field, with photons concentrated primarily at the angular state and decaying rapidly in regions outside the angular state. In a sense, a 0-dimensional corner state can be considered as a boundary of a 1-dimensional boundary state, which is called an edge-corner correspondence.
To further investigate the properties of the angular cavity, the present invention analyzed the band structure around the operating wavelength, as shown in FIG. 2 e. As expected, pseudo spin-dependent boundary states exist in the forbidden band, while angular states within the forbidden band occur in the gap between two boundary states, the eigenfrequencies of the angular states being marked with a red dashed line in the figure. The eigenvalues in the designed structure (fig. 2c) are numerically calculated as shown in fig. 2 f. It can be observed that the 1-dimensional boundary states (represented by the dashed lines) and the 0-dimensional angular states (represented by the pentagram) occur between the body states (represented by the squares). In addition, to quantify the high localization of the angular states, the present invention also calculates the quality factors Q for the bulk, boundary and angular states, as shown in fig. 2 g. The bulk and boundary state quality factors Q can reach 2500 a maximum, while the angular state quality factor Q is about 25000. The resonance characteristic of the topological angular state and the topological protection thereof provide opportunities for improving the interaction of photons, so that the topological angular state and the topological protection thereof become potential platforms for improving the conversion rate of laser and nonlinearity. It should be noted that the present invention discusses the corner point states as being at point a (fig. 2d) and no corner state at point B, but two boundary states are observed, which will be discussed in the next section.
In order to research the effect of the angular state on the nonlinear harmonic, the invention takes the second harmonic as an example to carry out numerical simulation calculation. To excite the angular states, a point source with frequency Freq 193.4THz is used as the excitation source. Fig. 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 resonator will be enhanced. The invention extracts the electric field of the resonant cavity resonant peak and performs Fourier transform. The peaks occur at the second harmonic frequencies on the fourier coefficient spectrum as shown in fig. 3 b. One problem occurs naturally: how does the present invention take advantage of the enhanced frequency doubling response of the resonator? Fig. 3c and 3d show two representative results of harmonic scattering: in fig. 3c, the second harmonic frequency corresponds to the body state, while in fig. 3d, the second harmonic frequency corresponds to the bandgap. Fig. 3c shows that the harmonic field will diffuse towards the body state and its intensity is significantly attenuated, making it difficult to collect the harmonic signal. Fig. 3d shows that the harmonics are limited in angle. In both cases, it is not easy to fully utilize the advantage of the frequency doubling of the angular resonator. In other words, the structure of the energy bands must be designed to achieve a desired field interaction at the fundamental and second harmonic frequencies.
In the following, the present invention researches the control of fundamental frequency and frequency doubled light by regulating and controlling the structural parameters of topological photonic crystals. As described above, the present invention found two Dirac degenerations 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 ) As shown, a topologically protected angular cavity (marked with a dashed line) can be observed near the Dirac degeneracy point A. Meanwhile, FIG. 4 (a) 2 ) It is shown that a boundary state with a small energy gap can be observed clearly near the Dirac degeneracy point B. It is well known that the band structure of a topological photonic crystal depends on its geometrical parameters. By structural parameter manipulation, the boundary state frequency near point B is about twice the angular state frequency near point a, which provides a way for the present invention to manipulate light at fundamental and second harmonic frequencies. To this end, the invention isThe photonic crystals with different geometrical parameters are subjected to numerical simulation: a is a 0 ＝835nm，d 0 230nm, as shown in fig. 4 (a) 1 -a 2 )，a 0 ＝770nm，d 0 240nm, as shown in fig. 4 (b) 1 -b 2 ) And a is 0 ＝720nm，d 0 255nm, see fig. 4 (c) 1 -c 2 ). For these different geometric parameters, the frequency of the angular state lies around the frequency of 193THz and shows no significant shift, see fig. 4 (a) 1 -c 1 ) While the frequency of the boundary state moves from about 402THz to about 387THz, see fig. 4 (a) 2 -c 2 ). In addition, the forbidden band width of the high-frequency band studied by the invention is gradually compressed to be close to zero. In these three cases, the frequency-doubled signal state enhanced from the fundamental angular resonator may undergo a transition from diffuse to bulk, locally not exiting at an angle, to propagating along a boundary state.
Fig. 4(d) plots the calculated transmission loss for the topological boundary waveguide (straight waveguide, curved waveguide, defective waveguide), which is defined as the ratio of the transmitted energy at the entrance and exit (marked with white dashed lines). The invention plots the transmission spectra for comparison in fig. 4 (d). As shown in the frequency range 381-398THz (blue region), the difference in transmitted energy can be seen compared to the case of the borderless state, indicating a low dissipation of energy transmitted along the waveguide by the second harmonic enhanced by the angular state of the fundamental frequency. The invention also compares the transmission spectra of the straight waveguide, the two 120-degree bent waveguides and the waveguide carrying the lattice defect, and the results show that the straight waveguide, the two 120-degree bent waveguides and the waveguide carrying the lattice defect have similar transmission efficiency, thereby proving that the boundary state waveguide has good robustness to the structural defect. The electric field of light as it propagates along the boundary state waveguide is shown in fig. 4(e-g), with white arrows indicating the location and direction of the incident plane wave source.
To better illustrate how light is manipulated, the present invention simulates the process of excitation of a fundamental angular resonator and the second harmonic propagating along a boundary waveguide. The simulation details are finally given in the method section herein. In order to prove the topological protection of the angular state resonant cavity and the boundary state waveguide, the invention introduces the same type of lattice defects at different positions. In these casesThe geometric parameter is a 0 ＝720nm，d 0 255 nm. FIG. 5 (a) 1 -e 1 ) Showing that the fundamental electric field can be highly localized at the angular resonator, FIG. 5 (a) 2 -e 2 ) It is shown that the second harmonic propagates along the curved boundary waveguide without significant attenuation. In addition, the influence of lattice defects on harmonic transmission is also small. The invention extracts the frequency-amplitude relation of the resonant cavity excitation electric field and performs Fourier transform on the relation, as shown in figure 5 (a) 3 -e 3 ) As shown. The results show that even if there is a defect in the angular resonator, the frequency doubling effect is not significantly affected.
The results in fig. 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 resonator can be transmitted along the boundary state waveguide without scattering to the bulk state. The enhanced second harmonic energy can reach the structural boundaries and be output, providing the present invention with a direction to explore further enhanced light interaction, as compared to the case where the second harmonic frequency corresponds to the forbidden band (fig. 3 d).
The invention also measures the boundary state waveguide P 1 And P 2 The loss of the transmitted second harmonic energy as shown in figure 6 a. The measurement positions are located around the two output ports and the measurement results are shown in fig. 6 b. Labels of "a, b, c, d, e" correspond to a in FIG. 5, respectively 2 、b 2 、c 2 、d 2 And e 2 And the label of "initial" indicates that the second harmonic frequency corresponds to the energy gap (a) 0 835nm and d 0 230 nm). Compared with the initial structure, the designed structure enables harmonic energy to be effectively transmitted along the boundary state waveguide, the influence of the structural defects on the transmission of harmonic signals is small, and the superior performance of the device designed by the invention is further revealed.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art should be considered as the technical solutions and the inventive concepts of the present invention within the technical 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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| CN113391378B (en) * | 2021-05-14 | 2022-03-11 | 合肥工业大学 | High-quality second harmonic enhancer based on topological angular state |
| CN113900161B (en) * | 2021-09-09 | 2023-02-17 | 江苏大学 | Topological photonic crystal structure based on isosceles triangle dielectric cylinder and optical waveguide |
| CN114637073A (en) * | 2022-02-09 | 2022-06-17 | 江苏大学 | Topological optical communication device supporting one-dimensional topological boundary state optical waveguide and/or zero-dimensional topological angular state optical local |
| CN114966982B (en) * | 2022-04-25 | 2024-03-19 | 江苏大学 | Topological optical communication resonant device capable of realizing waveguide-cavity coupling |
| CN115524791B (en) * | 2022-10-25 | 2024-07-26 | 苏州城市学院 | Topological photonic crystal optical waveguide structure based on honeycomb photonic crystal |
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