Observation of Second-Band Vortex Solitons in 2D Photonic Lattices

We demonstrate second-band bright vortex-array solitons in photonic lattices. This constitutes the first experimental observation of higher-band solitons in any 2D periodic system. These solitons possess complex intensity and phase structures, yet they can be excited by a simple highly localized vortex-ring beam. Finally, we show that the linear diffraction of such beams exhibits preferential transport along the lattice axes.

Figure 1

(a) The first two bands of the band structure in a 2D square lattice with $D=10$. The four thick dots mark the $X$-symmetry points. (b) High symmetry points of the reciprocal lattice. (c) Phase structure of a counterrotating vortex array, with the arrow in each vortex showing the direction of increasing phase.

Figure 2

Simulated propagation of a second-band vortex lattice soliton as calculated from self-consistency (upper row), and compared with a simulated evolution of a vortex ring with a simple (single-vortex) phase structure into a second-band vortex lattice soliton (lower row). Upper row: (a), (b) intensity and phase structure of the soliton as calculated via the self-consistency procedure, and used as the initial condition at the input plane of the lattice. (c) Linear diffraction (nonlinearity off) after 5 mm of propagation. (d), (e) Intensity and phase of the second-band vortex lattice soliton. (d), (e) are similar to (a), (b), thus confirming the beam is indeed a second-band lattice soliton. Lower row: (f), (g) intensity (superimposed on the lattice) and phase structures of the input ring beam bearing a single vortex. (h) Linear diffraction (nonlinearity off) after 5 mm of propagation. (i), (j) Intensity and phase of the emerging output beam under appropriate nonlinear conditions. The simple ring excitation of (f), (g) evolves into a structure (i), (j) that is almost identical to the ideal structure of a the second-band vortex lattice soliton.

Figure 3

Experimental observation of a second-band vortex lattice soliton. (a) Intensity distribution of the input vortex-ring beam photographed (for size comparison) on the background of the optically induced lattice. (b) Output intensity distribution of a low-intensity ring beam experiencing linear diffraction in the lattice. (c) Output intensity distribution of a high intensity ring beam, which has evolved into a second-band vortex soliton in the same lattice as in (b).

Figure 4

Experimental observation of the phase structure of a second-band vortex lattice soliton. The phase information is obtained by interference with a weakly diverging Gaussian beam. (a) Phase distribution of the input vortex-ring beam. (b) Output phase distribution of a high intensity ring beam that has evolved into a second-band vortex soliton [interference pattern between the soliton whose intensity is presented in Fig. 3c and a weakly diverging Gaussian beam]. (c) Numerical validation of the phase information in (b).

Figure 5

Power spectrum of the input (a) and output (b) beams. The formation of the second-band vortex soliton reshapes the power spectrum. (c) Calculated power spectrum of the second-band vortex soliton. For comparison, (d), (e) show the measured and calculated power spectrum of the first-band vortex lattice solitons of 16, respectively. In all pictures, the “corners” of the first BZ are the four lattice-forming beams, represented in the Fourier picture as four dots, marked with white circles.