Observation of Nonlinear Self-Trapping of Broad Beams in Defocusing Waveguide Arrays

We demonstrate experimentally the localization of broad optical beams in periodic arrays of optical waveguides with defocusing nonlinearity. This observation in optics is linked to nonlinear self-trapping of Bose-Einstein-condensed atoms in stationary periodic potentials being associated with the generation of truncated nonlinear Bloch states, existing in the gaps of the linear transmission spectrum. We reveal that unlike gap solitons, these novel localized states can have an arbitrary width defined solely by the size of the input beam while independent of nonlinearity.

Figure 1

(a) Band-gap spectrum. (b),(c) Examples of two truncated nonlinear Bloch waves of different widths.

Figure 2

(a) Dependence of the output intensity profile on the nonlinearity $\gamma$. The beam spreading is arrested at a critical nonlinearity, $\gamma \approx 0.15$. (b),(c) Output beam profiles [as marked in (a)] showing localization. (d) Variation of the output beamwidth (defined as the width between the sharp boundaries) with the input beam full width at half maximum (FWHM) for different values of the nonlinear coefficient $\gamma$.

Figure 3

Output beamwidth (estimated as the width containing 50% of the total light) vs time (nonlinear index change). Dashed line—the width of 75% of the input beam. (a) Input beam profile; (b) linear diffraction at the output. (c) Nonlinear defocusing at low nonlinearity (time), (d) beam localization at high nonlinearity. Beam power, 1 mW.

Figure 4

Beam profiles at the array input (dotted line) and output (solid line) for (a) linear ($t\sim 0$) and (b) nonlinear ($t=10$ hours) propagation, corresponding to Figs. 3b, 3d. Insets: Fourier spectrum of the output beams. $\pm \pi$ indicate the edges of the Brillouin zone of the lattice.

Figure 5

Output beamwidth (estimated as the width containing 30% of the total light) vs time (nonlinear index change). Dashed line indicates the width of 65% of the input beam. Beam power, 1 mW.