Analytical stability analysis of dark and bright self guided waves

We present an analytical stability analysis on dark (black and gray) self-guided waves and the fundamental state of the bright self-guided waves with nonzero intensity background trapped in a thin self-defocusing nonlinear film bounded by an infinite self- defocusing medium of different nonlinearity. It is found that the gray self-guided wave and the fundamental state of the bright self-guided waves with nonzero intensity background are stable to both symmetric and asymmetric perturbations, whereas the black self-guided wave is stable to symmetric perturbation but unstable to asymmetric perturbation (in contrast to the corresponding one in a uniform self-defocusing medium). For the nonlinear waveguides with the linear refractive index n_c, in the cladding smaller than that n_f the film the instability of the black self-guided waves is shown to result from the presence of the complex growth rate, while the instability for that trapped in a hollow waveguide (n_cc>n_f) may arise from the presence of either real or complex growth rate, depending on the waveguide parameters.