Controlled Generation and Steering of Spatial Gap Solitons

We demonstrate the first fully controlled generation of immobile and slow spatial gap solitons in nonlinear periodic systems with band-gap spectra, and observe the key features of gap solitons that distinguish them from discrete solitons, including a dynamical transformation of gap solitons due to nonlinear interband coupling. We also describe theoretically and confirm experimentally the effect of the anomalous steering of gap solitons in optically induced photonic lattices.

Figure 1

(a) Dispersion of Bloch waves in an optically induced photonic lattice; the spectrum bands are shaded. (b) Profiles of the Bloch waves (solid lines) and the leading-order Fourier components (dashed lines) superimposed on top of the normalized refracted index profile of the periodic lattice (shown with shading) for gap edges indicated by arrows.

Figure 2

Numerical results for the soliton families: Power (top) and width (middle) vs the propagation constant. Bottom: soliton profiles (solid lines) corresponding to the marked points (a–d) in the upper plots; shadings mark the lattice minima. Arrows illustrate the direction of the input beams, whose interference pattern (dashed lines) approximates the soliton profile.

Figure 3

Numerical results. Dynamics of the Bloch waves excited through the two-beam interference: (a) linear diffraction at low power ($I_0\simeq 0$), (b) excitation of a gap soliton in the nonlinear regime ($I_0=0.048$), (c) beam breakup and the formation of a quasiperiodic breathing state at higher powers ($I_0=0.29$). Left: variation of intensity along the propagation direction. Right: beam profiles at the crystal output ($z=15\mathrm{m}\mathrm{m}$) normalized to $I_0$.

Figure 4

Experimental results. Top: Excitation scheme (left) and input intensity profile (right). Bottom: output for various beam powers. Left: mutual focusing and gap-soliton formation when interference maxima are aligned with the lattice minima. Right: Self-defocusing when interference maxima are at the lattice maxima. Dashed curves: The beam profiles at the indicated intensity when the grating is erased.

Figure 5

(a) Schematic demonstration of anomalous gap-soliton steering induced by a tilt of the lattice; dashed line shows the propagation direction of a gap soliton; arrows indicate the directions of the input beams. (b),(c) Output soliton profile for a lattice tilt in the direction of larger $x$ by 20% of the Bragg angle with respect to normal; dashed lines show the beam profiles when the lattice is absent.