Topological photonics aims to utilize topological photonic bands and corresponding edge modes to implement robust light manipulation, which can be readily achieved in the linear regime of light-matter interaction. In this talk, I will review some recent results regarding nonlinear interactions of one-way edge-modes in frequency mixing processes in topological photonic crystals (PhCs) and graphene metasurfaces. In particular, I will demonstrate SHG via nonlinear interaction of double topological valley-Hall kink modes in PhCs with hexagonal lattice. I will first show that two topological frequency band gaps can be created around a pair of frequencies, ω0 and 2ω0, by gapping out the corresponding Dirac points. Importantly, I demonstrate that tunable, bidirectional phase-matched SHG via nonlinear interaction of the valley-Hall kink modes inside the two band gaps can be achieved. More specifically, by using Stokes parameters associated with the magnetic part of the valley-Hall kink modes, we introduce the concept of SHG directional dichroism, which is employed to characterize optical probes for sensing chiral molecules. I also show that these ideas can be extended to graphene metasurfaces, where the Kerr-type nonlinearity of graphene can be used to control the light transmission in topological domain-interface waveguides. In the second part of my talk I will illustrate how bound states in the continuum (BICs) of certain silicon nitride PhC slabs, engineered to possess sharp resonances with high quality factors at both the fundamental-frequency and second-harmonic, can be used to achieve an orders-of-magnitude enhancement of the SHG. Certain connections between the topological charge of the BICs and the properties of the nonlinear optical interaction (SHG) are also revealed.
In this paper, optically controllable and topologically protected plasmon transport is implemented via a topological nanohole plasmonic waveguide coupled to a standard edge mode of a graphene metasurface. By introducing nanoholes with different sizes in the unit cell, one breaks the spatial-inversion symmetry of a graphene metasurface in which the topological waveguide is constructed, leading to the emergence of topologically protected modes located in a nontrivial band-gap. Based on the strong Kerr effect and tunable optical properties of graphene, the coupling between the edge and topological interface modes can be efficiently controlled by optical means provided by an optical pump beam injected in a bulk mode. In particular, by tuning the power inserted in the bulk mode, one can control the difference between the wave-vectors of the topological and edge modes and consequently the optical power coupled in the topological mode. Our results show that when the pump power approaches a specific value, the edge and topological modes become phase-matched and the topological waveguide mode can be efficiently excited. Finally, we demonstrated that the optical coupling is strongly dependent on the group-velocity of the pump mode, a device feature that can be important in practical applications.
Topologically protected plasmonic states with wide topological band gaps provide unprecedented robustness against disorder-induced backscattering. In this study, we design a graphene bi-layer metasurface that possesses valley-Hall topological plasmonic modes in a nontrivial bandgap. In particular, the breaking of mirror symmetry of two graphene layers is achieved via a horizontal shift of the hole lattice of the top layer, which leads to topologically protected edge modes in the nontrivial bandgap. The corresponding band dispersion of the topological edge modes shows unidirectional propagation features. Moreover, we have designed a sensitive molecular sensor based on such graphene bi-layer metasurfaces, using the fact that the chemical potential of graphene varies upon adsorption of gas molecules. This effect leads to a marked variation of the transmission of the topological mode, and thus a sensing device with large sensitivity can be realized.
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