Bulk Vortex and Horseshoe Surface Modes in Parity-Time Symmetric Media

Department of Physical Electronics, School of Electrical Engineering,Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel(Dated: March 20, 2014)We demonstrate that in-bulk vortex localized modes, and their surface half-vortex (“horseshoe”)counterparts (which were not reported before in truncated settings) self-trap in two-dimensional(2D) nonlinear optical systems with PT -symmetric photonic lattices (PLs). The respective stabilityregions are identified in the underlying parameter space. The in-bulk states are related to truncatednonlinear Bloch waves in gaps of the PL-induced spectrum. The basic vortex and horseshoe modesare built, severally, of four and three beams with appropriate phase shifts between them. Theirstable complex counterparts, built of up to 12 beams, are reported too.