Existence of solitons in infinite lattice.

We consider necessary conditions for existence of optical solitons in one-dimensional nonlinear periodic layered array. We show analytically that in the array with the cubic-quintic nonlinearity bistable solitons are possible whereas for the Kerr nonlinearity they never exist. We investigate asymptotic behavior of the soliton amplitude at infinity.

Finite-band solitons in the Kronig-Penney model with the cubic-quintic nonlinearity.

We present a model combining a periodic array of rectangular potential wells [the Kronig-Penney (KP) potential] and the cubic-quintic (CQ) nonlinearity. A plethora of soliton states is found in the system: fundamental single-humped solitons, symmetric and antisymmetric double-humped ones, three-peak solitons with and without the phase shift pi between the peaks, etc. If the potential profile is shallow, the solitons belong to the semi-infinite gap beneath the band structure of the linear KP model, while finite gaps between the Bloch bands remain empty.

Spontaneous symmetry breaking and switching in planar nonlinear optical antiwaveguides.

We consider guided light beams in a nonlinear planar structure described by the nonlinear Schrodinger equation with a symmetric potential hill. Such an "antiwaveguide" (AWG) structure induces a transition from symmetric to asymmetric modes via a transcritical pitchfork bifurcation, provided that the beam's power exceeds a certain critical value. It is shown analytically that the asymmetric modes always satisfy the Vakhitov-Kolokolov (necessary) stability criterion; nevertheless, the application of a general Jones' theorem shows that the AWG modes are always unstable.