By introducing symmetry-breaking in geometry, we reveal the existence of thresholdless crescent waves, i.e., nonlinear diffractionless 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 semi-major (minor) axis. Our results demonstrate an alternative but efficient approach to access optical modes with a variety of inhomogeneous potentials.
© 2013 Optical Society of America
Original Manuscript: November 26, 2012
Revised Manuscript: February 8, 2013
Manuscript Accepted: February 25, 2013
Published: March 21, 2013
Kuan-Hsien Kuo, YuanYao Lin, and Ray-Kuang Lee, "Thresholdless crescent waves in an elliptical ring," Opt. Lett. 38, 1077-1079 (2013)