Thresholdless crescent waves in an elliptical ring

By introducing the symmetry-breaking in geometry, we reveal the existence of thresholdless crescent waves, i.e., nonlinear surface modes pinged to the boundary of a curvature, in an elliptical ring. An effective nonlinear Schrödinger equation along the azimuthal direction is derived by taking the transformation in the curvilinear coordinate of elliptical symmetry, which illustrates the formation of trapping potentials (barriers) along the semimajor (minor) axis. Our results demonstrate an alternative but efficient approach to access optical surface modes with a variety of micro-structures.