Multiband Vector Lattice Solitons

We predict multiband vector solitons in nonlinear periodic systems, using photonic lattices as a prime example. The solitons consist of two optical fields arising from different bands of the transmission spectrum, which involve both bound state and radiation mode components.

Figure 1

Confined mode of a single waveguide and its evanescent coupling to the adjacent waveguides (a). Structure of FB waves in the first band at the center (b) and edge (c) of the first Brillouin zone, and also of FB waves in the second band, at the center (d) and the edge (e).

Figure 2

Multiband vector lattice soliton in focusing waveguide array. (a),(b) Wave functions of the first $u_1$ and second $u_2$ components. (c) Dispersion relation of the first two bands of the linear array, with the propagation constants of the two soliton components marked by dots. First (d) and second (e) component intensities launched with white noise (top) and at the output (bottom) superimposed on the unperturbed profiles obtained through self-consistency (dotted line), showing that the output intensities of both components are almost indistinguishable from those of the ideal vector soliton. (f),(g) Self-trapped propagation of the components $u_1$ and $u_2$ of the vector soliton. (h),(i) Linear diffraction of $u_1$ and $u_2$, respectively, when the nonlinearity is zero. (j) Nonstationary propagation of $u_1$ with the nonlinearity “on” and $u_2$ absent, and vice versa (k).

Figure 3

Propagation constants (a) and widths (b) of the two components of a multiband vector self-trap solution in self-focusing media vs the peak intensity of the second component, $I_2$. The different lines correspond to different peak intensities (between 0 and 1) of the first component, $I_1$.

Figure 4

Multiband lattice vector soliton in defocusing waveguide array. (a),(b) Wave functions of the first ($u_1$) and second ($u_2$) components. (c) Dispersion relation of the first two bands of the linear array, with the propagation constants of the two soliton components marked by dots. (d),(e) Self-trapped propagation of $u_1$ and $u_2$ of the vector soliton. (f),(g) Linear diffraction of $u_1$ and $u_2$, respectively, when the nonlinearity is set to zero. (h) Nonstationary propagation of $u_1$ with the nonlinearity on and $u_2$ absent, and vice versa (i).