Stable vortices with topological charge of 3 and 4 are examined numerically and analytically in photonic quasicrystals created by interference of 5 as well as 8 beams, in the cases of cubic as well as saturable nonlinearities. These structures are ex
perimentally realizable, including a prototypical example of a stable charge 4 vortex. Direct numerical simulations corroborate the analytical and numerical linear stability analysis predictions.
We investigate the existence and stability of gap vortices and multi-pole gap solitons in a Kagome lattice with a defocusing nonlinearity both in a discrete case and in a continuum one with periodic external modulation. In particular, predictions are
made based on expansion around a simple and analytically tractable anti-continuum (zero coupling) limit. These predictions are then confirmed for a continuum model of an optically-induced Kagome lattice in a photorefractive crystal obtained by a continuous transformation of a honeycomb lattice.
