Analytical stable Gaussian soliton supported by a parity-time-symmetric potential with power-law nonlinearity

We address the existence and stability of spatial localized modes supported by a parity-time-symmetric complex potential in the presence of power-law nonlinearity. The analytical expressions of the localized modes, which are Gaussian in nature, are obtained in both (1+1) and (2+1) dimensions. A linear stability analysis corroborated by the direct numerical simulations reveals that these analytical localized modes can propagate stably for a wide range of the potential parameters and for various order nonlinearities. Some dynamical characteristics of these solutions, such as the power and the transverse power-flow density, are also examined.Comment: Nonlinear Dynamics (2014

Nonlinear localized modes in PT-symmetric optical media with competing gain and loss

The existence and stability of the nonlinear spatial localized modes are investigated in parity-time symmetric optical media characterized by a generic complex hyperbolic refractive index distribution with competing gain and loss profile. The exact analytical expressions of the localized modes are found for all values of the competing parameter and in the presence of both the self-focusing and self-defocusing Kerr nonlinearity. The effect of competing gain/loss profile on the stability structure of these localized modes are discussed with the help of linear stability analysis followed by the direct numerical simulation of the governing equation. The spatial localized modes in two-dimensional geometry as well as the transverse power-flow density associated with these localized modes are also examined.Comment: Final versio

Waveguides with Absorbing Boundaries: Nonlinearity Controlled by an Exceptional Point and Solitons

We reveal the existence of continuous families of guided single-mode solitons in planar waveguides with weakly nonlinear active core and absorbing boundaries. Stable propagation of TE and TM-polarized solitons is accompanied by attenuation of all other modes, i.e. the waveguide features properties of conservative and dissipative systems. If the linear spectrum of the waveguide possesses exceptional points, which occurs in the case of TM-polarization, an originally focusing (defocusing) material nonlinearity may become effectively defocusing (focusing). This occurs due to the geometric phase of the carried eigenmode when the surface impedance encircles the exceptional point. In its turn the change of the effective nonlinearity ensures the existence of dark (bright) solitons in spite of focusing (defocusing) Kerr nonlinearity of the core. The existence of an exceptional point can also result in anomalous enhancement of the effective nonlinearity. In terms of practical applications the nonlinearity of the reported waveguide can be manipulated by controlling the properties of the absorbing cladding.Comment: Published versio

Supersymmetry generated one-way invisible PT-symmetric optical crystals

We use supersymmetry transformations to design transparent and one-way reflectionless (thus unidirectionally invisible) complex crystals with balanced gain and loss profiles. The scattering coefficients are investigated using the transfer matrix approach. It is shown that the amount of reflection from the left can be made arbitrarily close to zero whereas the reflection from the right is enhanced arbitrarily (or vice versa).Comment: Final versio

Effect of Position-dependent Mass on Dynamical Breaking of Type B and Type X_2 N-fold Supersymmetry

We investigate effect of position-dependent mass profiles on dynamical breaking of N-fold supersymmetry in several type B and type X_2 models. We find that N-fold supersymmetry in rational potentials in the constant-mass background are steady against the variation of mass profiles. On the other hand, some physically relevant mass profiles can change the pattern of dynamical N-fold supersymmetry breaking in trigonometric, hyperbolic, and exponential potentials of both type B and type X_2. The latter results open the possibility of detecting experimentally phase transition of N-fold as well as ordinary supersymmetry at a realistic energy scale.Comment: 24 pages, no figures, to appear in Journal of Physics