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

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

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

Dirac electron in graphene under supersymmetry generated magnetic fields

We use supersymmetry transformations to obtain new one parameter family of inhomogeneous magnetic fields $\mathbf{B} = \widetilde{\mathcal{B}}(x,\lambda) \hat{e}_z$ for which the massless Dirac electron possesses exact solution. The inhomogeneity appearing in $\widetilde{\mathcal{B}}(x,\lambda)$ can be controlled by the parameter $\lambda$. The obtained magnetic fields are interpreted as deformed variants of some physically attainable well known magnetic fields. A particular example, when a constant magnetic field is deformed, is considered to show that equidistant Landau levels exist even in the presence of an infinite number of specially designed inhomogeneous magnetic fields

Coherent-perfect-absorber and laser for bound states in a continuum

It is shown that two fundamentally different phenomena, the bound states in continuum and the spectral singularity (or time-reversed spectral singularity), can occur simultaneously. This can be achieved, in particular, in a rectangular core dielectric waveguide with embedded active (or absorbing) layer. In such a system a two-dimensional bound state in a continuum is created in the plane of a waveguide cross section and it is emitted or absorbed along the waveguide core. The idea can be used for experimental implementation of a laser or a coherent-perfect-absorber for photonic bound state that resides in a continuous spectrum