Topology-optimized photonic topological crystalline insulators with multiband helical edge states

Photonic topological crystalline insulators (PTCIs) with helical edge states provide an alternative way to achieve robust electromagnetic wave transport and processing. However, most existing PTCIs only involve a single topological bandgap, and generally support a pair of gapped helical edge states, restricting the scope of applications in various fields such as multiband waveguides, filters, and communication systems. Here, we design dual-band PTCIs, in which multiple helical edge modes appear within two distinct bulk gaps, for transverse electric (TE) and transverse magnetic (TM) modes, respectively, by introducing the topology optimization method into the photonic crystals with glide symmetry. For PTCIs with TE modes, the mismatched frequency ranges of edge modes hosted by two orthometric boundaries offer an opportunity to realize a photonic demultiplexer. For PTCIs with TM modes, we show the enhanced second harmonic (SH) generation through the coupling of multiband edge modes by matching the frequency ranges of edge modes within the first and second bandgaps to fundamental and SH waves, respectively. This work provides a new way for designing multiband PTCIs with helical edge states, having promising potentials in developing multiband topological photonic devices for both linear and nonlinear applications.