42 research outputs found
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
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
Topological directed amplification
A phenomenon of topological directed amplification of certain initial
perturbations is revealed theoretically to emerge in a class of asymptotically
stable skin-effect lattices described by nonnormal Toeplitz operators
with positive ``numerical ordinate" . Nonnormal temporal
evolution, even in the presence of global dissipation, is shown to manifest a
counterintuitive transient phase of edge-state amplification -- a behavior,
drastically different from the asymptote, that spectral analysis of fails
to directly reveal. A consistent description of the effect is provided by the
general tool of ``pseudospectrum", and a quantitative estimation of the maximum
power amplification is provided by the {\it Kreiss constant}. A recipe to
determine an optimal initial condition that will attain maximum amplification
power is given by singular value decomposition of the propagator . It is further predicted that the interplay between nonnormality and
nonlinearity in a skin-effect laser array can facilitate narrow-emission
spectra with scalable stable-output power
Modes and exceptional points in waveguides with impedance boundary conditions
A planar waveguide with impedance boundary, composed of non-perfect metallic
plates, and with passive or active dielectric filling is considered. We show
the possibility of selective mode guiding and amplification when homogeneous
pump is added to the dielectric, and analyze differences in TE and TM mode
propagation. Such a non-conservative system is also shown to feature
exceptional points, for specific and experimentally tunable parameters, which
are described for a particular case of transparent dielectric.Comment: Optics Letters (2016
Dirac electron in graphene under supersymmetry generated magnetic fields
We use supersymmetry transformations to obtain new one parameter family of
inhomogeneous magnetic fields for which the massless Dirac electron possesses exact solution. The
inhomogeneity appearing in can be
controlled by the parameter . 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
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