Christian, JM, McDonald, GS, Potton, RJ and Chamorro-Posada, P 2007, 'Helmholtz solitons in power-law optical materials' , Physical Review A (PRA), 76 (3) , 033834.

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Abstract

A nonlinear Helmholtz equation for optical materials with regimes of power-law type of nonlinearity is proposed. This model captures broad beam evolution at any angle with respect to the reference direction in a wide range of media, including some semiconductors, doped glasses and liquid crystals. Novel exact analytical soliton solutions are presented for a generic nonlinearity, within which known Kerr solitons comprise a subset. Three conservation laws are also reported and numerical simulations examine the stability of the Helmholtz power-law solitons. These simulations have led to the identification of a new propagation feature associated with spatial solitons in power-law media, constituting a new class of oscillatory solution.

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