Abstract

Experiments on discrete trapping are generally based on photonic lattices made from etched waveguide arrays or created through optical induction in photorefractive media [1]. Studies have spanned a wide variety of physical mechanisms affecting solitons, but, at present, the soliton has always evolved in a fixed linear/nonlinear pattern, in conditions in which the lattice is not appreciably affected by the wave. We here study an entirely opposite condition: solitons that form in a lattice nonlinearity. A lattice nonlinearity is a periodic variation in the nonlinear response that is in turn negligible in the linear response. This means the lattice itself depends on the soliton, and both lattice and soliton are strongly interacting during propagation. This fundamental difference with respect to previous experiments is illustrated in Fig. 1(left), where the optical propagation in a photonic lattice is compared with that in a lattice nonlinearity. In the standard condition (Fig. 1(a)) while the nonlinear waves evolve into a lattice-dependent trapped state, the lattice remains almost completely unaffected by the waves dynamics. On the contrary, if the beam and lattice are mutually nonlinear, the propagation modifies spatially the underlying periodic pattern itself (Fig. 1(b)). We report the first observation of continuous solitons in a lattice nonlinearity. The effect is achieved in a microstructured ferroelectric crystal of KLTN with periodic variation in the low-frequency dielectric constant [2]. An electric field can turn this grating into an index modulation through the quadratic electro-optic effect. The lattice nonlinearity arises when this electric field is optically-induced, as occurs for the photorefractive nonlinearity. Results are shown in Fig. 1(right) and prove that the continuous behaviour has roots in the coupling between periodic and non-periodic terms in the supporting nonlinearity. Indeed, simulations demonstrate an index variation losing the sinusoidal behaviour in the soliton region; the screening field locally leads the underlying lattice into a latent state independently both of the beam width and of the wave size. This picture is expected to change if the electro-optical lattice can be decoupled from the photorefractive response. Since these two responses act on different time scales this can be done dynamically studying transient states after the soliton formation. In this case the space-charge field remains unshielded and the beam experiences transient discrete diffraction and self-trapping. In conclusion, we have demonstrated continuous on-axis soliton propagation in a “variable” photonic lattice characterized by the coupling with the soliton supporting nonlinearity [3]. Our results point out how the periodic properties of a media can be made to not emerge in the propagating waveform if they are filtered out by a strong nonlinear interaction. The lattice nonlinearity opens up new perspectives for exploring nonlinear waves in nonlinear lattices, such as physical correlation between the two nonlinearities.

© 2015 IEEE