Reduced-Symmetry Two-Dimensional Solitons in Photonic Lattices

We demonstrate theoretically and experimentally a novel type of localized beam supported by the combined effects of total internal and Bragg reflection in nonlinear two-dimensional square periodic structures. Such localized states exhibit strong anisotropy in their mobility properties, being highly mobile in one direction and trapped in the other, making them promising candidates for optical routing in nonlinear lattices.

Figure 1

(a), (b) Band gap spectrum and intensity distribution of the 2D square lattice. The horizontal axis in (a) corresponds to a contour shown in the inset. (c),(d) Calculated intensity and phase distribution of the Bloch wave from the $X$ point of the second band of the spectrum (a).

Figure 2

Families of gap solitons shown as normalized soliton power vs the propagation constant. (a)–(d) Examples of four types of gap solitons for $\beta =-2.04$. Lines show the position of the lattice maxima.

Figure 3

Focusing of a beam corresponding to the $X$ point of the second band: (top) width at the crystal output in experiment (dots) and theory (lines). Solid line and dots—widths along $x$; Dashed line and triangles—widths along $y$. (a)–(c) experimental, (d)–(f) numerical results: (a),(d) input beam profile; (b),(e) output beam profiles at low power; (c),(f) localized states at high power. Inset—optical lattice.

Figure 4

(a)–(d) Numerically calculated output beam profiles for different initial tilts of the beam. (a) no tilt, (b) 20 mrad tilt along $x$, (c) 20 mrad tilt along $y$, (d) 20 mrad tilt along $x$ and $y$. White bars mark lattice periods. (e),(f) show two experimental examples for the mobility along $x$, the cross marking the beam center at the crystal front face.