Second‐Harmonic Generation Based on the Dual‐Band Second‐Order Topological Corner States

Abstract

Coherent frequency conversions using multiband topological edge states in photonic structures made of nonlinear optical materials have been extensively investigated. In practice, however, coherent sources localized at the subwavelength scale are of great importance. Herein, efficient second‐harmonic generation (SHG) using dual‐band second‐order topological corner states is reported. By properly adjusting the structural parameters, dual‐band corner states can be obtained in the first and second bandgaps, when the eigenfrequency of the corner state in the higher bandgap is twice that of the corner one in the lower gap. In a square lattice made of tellurium as an example, high SHG efficiency in the order of 10−1% can be obtained for a peak pump intensity of around 20 GW cm−2. The results presented provide the realizability of subwavelength‐scale coherent sources, which are robust against the structural disorder or defects.

Simultaneous Appearance of Different Topological Phases in a Single Photonic System: Coexisting Phases Characterized by Bulk Polarization and Valley‐Chern Number Enabling Dual‐Band Second‐Order Topological States

“…The lowered symmetry of the system gives larger frequency splitting of the corner states compared with previous results. [ 8,30 ] The distributions of are shown in Figure 2b for the edge and corner states at the frequencies denoted as A (0.3892) and B (0.4021) in Figure 2a, respectively. In the fourth bandgap, however, only a single corner state appears (Figure 2c) similar to the previous results.…”

“…This is the first exhibition of the simultaneous appearance of two different topologies in the single photonic system, providing a deep understanding for an unprecedented behavior of higher‐order photonic topological insulators. This new mechanism has also advantages in practice, including nonlinear frequency conversion [ 26,30 ] for the multiband characteristics of square lattice photonic crystals with low‐symmetric components shown in the study by Kim et al [ 20 ]…”

“…[ 22,23 ] The recently proposed multiband topological states [ 5,23–27 ] can be applied for topological nonlinear frequency conversion. [ 28–30 ]…”

A brief review of topological photonics in one, two, and three dimensions

“…The corner states can exist in multiband gaps simultaneously [253,254], providing the opportunity to realize highly efficient nonlinear frequency conversion protected by topology. Indeed, double-resonant corner modes have been exploited to significantly boost the second harmonic generation [255,256], e.g., in [255], by matching two corner states within two different frequency bandgaps, efficiency that is robust against defects and as high as 5.4×10 −3 W −1 has been demonstrated (see Fig. 8g).…”

Dual Band Second‐Order Topological Corner States in 2D Valley‐Hall Hexagonal Photonic Crystals

“…[1][2][3][4][5] Valley contrasting in such photonic crystals results in valley-protected backscattering suppression, [3] enabling photonic applications such as topological waveguides, [5] topological lasing, [6,7] parity-time symmetric photonic topological coupled waveguides, [8] and topological nonlinear photonics. [9] In the meantime, higher-order topological insulators [10][11][12][13][14][15][16] have recently been discovered by generalizing the conventional topological concept to the lower dimensional topological boundary states and have shortly been introduced to topological photonics, [17][18][19][20][21][22][23][24][25][26][27][28][29] mainly focusing on the corner states in 2D second-order photonic crystals. They have found wide applications for realizing ultrahigh-Q nanocavity, [19] low threshold topological laser, [30,31] and topological Fano resonance.…”