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Angular configurations play a fundamental role in essentially all nonlinear photonic architectures: from beam multiplexing applications, to scattering at a single interface, to evolution inside patterned optical structures. Equations of the nonlinear Helmholtz type are ideally suited to describing scalar oblique-propagation contexts. Knowledge of their exact solitons facilitates novel device designs, and the pursuit of these classes of solution is a key research objective of our collaboration.\ud \ud Saturation under high-intensity illumination is a property of many photonic materials. Phenomenological descriptions of a saturable refractive index must go beyond polynomial-type expansions in the (local) light intensity [e.g., the cubic-quintic approximation (Pushkarov et al., Quantum Electron. 11, 471 (1979)], which eventually break down. However, such approaches almost always result in a governing equation that does not possess exact soliton solutions. A notable exception is the model proposed by Wood et al. [Opt. Commun. 69, 156 (1988)].\ud \ud We will present, for the first time, exact dark spatial solitons for a Helmholtz equation with a self-defocusing saturable nonlinearity. These novel solutions have been obtained by deploying a unified combination of analytical techniques (symmetry reduction, coordinate transformations, and direct integration). Multi-parameter asymptotic analysis recovers the predictions of conventional (paraxial) theory [Krolikowski and Luther-Davies, Opt. Lett. 18, 188 (1993)], while convergence to its Kerr counterpart [Chamorro-Posada and McDonald, Opt. Lett. 28, 825 (2003)] has been found in the limit of low light intensities. Computations involving perturbed initial-value problems have demonstrated that Helmholtz saturable dark solitons are highly robust nonlinear waves surrounded by wide basins of attraction. |
