Topological Bound Modes With Orbital Angular Momentum in Optical Waveguide Arrays

Coupled optical waveguide arrays, in which the wave tunnelling dynamics resembles that of electrons in crystals, have been utilized as a versatile tool to demonstrate topological phenomena. So far, the study of topological phases in waveguide arrays mostly focused on the supermodes constituted by the fundamental modes of single waveguide while the high-order modes with orbital angular momentum (OAM) are rarely considered. Here the topological bound modes are investigated in a zigzag chain composed of evanescently coupled waveguides that support OAM modes. We show the topological propagation is aroused by OAM without discovering any bound modes generated by fundamental modes. The reason lies in the coupling of OAM modes between adjacent waveguides naturally gives rise to synthetical gauge fields, significantly different from fundamental modes. Furthermore, we study the coupling mechanism of elliptical waveguides and show the orientation angle of ellipses serves as gauge fields as well, which provides an additional degree of freedom to control topological bound modes.