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. To realize the actual character of the instability, we perform direct numerical simulations, which reveal that a deflecting instability, which drives the asymmetric beam into the cladding without giving rise to fanning or stripping of the beam, sets in after a propagation distance of approximately 16 transverse widths of the AWG's core. The symmetry-breaking bifurcation, in combination with the deflecting instability, may be used to design an all-optical switch. The switching can easily be controlled by means of a symmetry-breaking "hot spot" that acts upon an initial symmetric beam launched with a power exceeding the bifurcation value.