288 research outputs found
All-optical diode action with Thue-Morse quasiperiodic photonic crystals
We theoretically investigate the possibility of realizing a nonlinear
all-optical diode by using the unique features of quasiperiodic 1D photonic
crystals. The interplay between the intrinsic spatial asymmetry in odd-order
Thue-Morse lattices and Kerr nonlinearity, combined with the unconventional
field localization properties of this class of quasiperiodic sequences, gives
rise to sharp resonances that can be used to give a polarization-insensitive,
nonreciprocal propagation with a contrast close to unity for low optical
intensities.Comment: submitted to JAP. Scale of Fig. 4 correcte
Constructing new nonlinear evolution equations with supersymmetry
The factorisation method commonly used in linear supersymmetric quantum
mechanics is extended, such that it can be applied to nonlinear quantum
mechanical systems. The new method is distinguishable from the linear
formalism, as the superpotential is forced to become eigenfunction-dependent.
An example solution is given for the nonlinear Schroedinger equation and its
supersymmetric partner equation. This method allows new nonlinear evolution
equations to be constructed from the solutions of known nonlinear equations,
and has the potential to be a useful tool for mathematicians and physicists
working in the field of nonlinear systems, allowing the discovery of previously
unknown `dualities' amongst soliton solutions and their respective equations.Comment: Some minor imprecisions were corrected, new figures, improved
discussion of Lax pairs for the scale-free equatio
Resonant self-pulsations in coupled nonlinear microcavities
A novel point of view on the phenomenon of self-pulsations is presented,
which shows that they are a balanced state formed by two counteracting
processes: beating of modes and bistable switching. A structure based on two
coupled nonlinear microcavities provides a generic example of system with
enhanced ability to this phenomenon. The specific design of such structure in
the form of multilayered media is proposed, and the coupled mode theory is
applied to describe its dynamical properties. It is emphasized that the
frequency of self-pulsations is related to the frequency splitting between
resonant modes and can be adjusted over a broad range.Comment: 5 pages, 4 figure
Complex Berry phase instability in PT-symmetric coupled waveguides
We show that the analogue of the geometric phase for non-Hermitian coupled
waveguides with PT-symmetry and at least one periodically varying parameter can
be purely imaginary, and will consequently result in the manifestation of an
instability in the system. The instability peaks seen in the spectrum of the
system's eigenstates after evolution along the waveguides can be directly
mapped to the spectrum of the derivative of the geometric function. The
instabilities are magnified as the exceptional point of the system is
approached, and non-adiabatic effects begin to appear. As the system cannot
evolve adiabatically in the vicinity of the exceptional point, PT-symmetry will
be observed breaking earlier than theoretically predicted
The multi-resonant Lugiato-Lefever model
We introduce a new model describing multiple resonances in Kerr optical
cavities. It perfectly agrees quantitatively with the Ikeda map and predicts
complex phenomena such as super cavity solitons and coexistence of multiple
nonlinear states
Suppression and splitting of modulational instability sidebands in periodically tapered optical fibers due to fourth-order dispersion
We study the modulational instability induced by periodic variations of
group-velocity dispersion in the proximity of the zero dispersion point.
Multiple instability peaks originating from parametric resonance coexist with
the conventional modulation instability due to fourth order dispersion, which
in turn is suppressed by the oscillations of dispersion. Moreover isolated
unstable regions appear in the space of parameters due to imperfect phase
matching. This confirms the dramatic effect of periodic tapering in the control
and shaping of MI sidebands in optical fibers
Giant asymmetric self-phase modulation in superconductor thin films
Self-phase modulation (SPM) of light pulses is found to occur strongly, at
low incident intensities, in the coupling of light with superconductors. We
develop a theory from a synthesis of the time-dependent Ginzburg-Landau (TDGL)
equation and basic electrodynamics which shows the strongly non-linear phase
accumulated in the interaction. Unusually, the SPM of the pulse in this system
is found to be highly asymmetric, producing a strongly redshifted spectrum when
interacting with a superconducting thin film, and it develops in just a few
nanometers of propagation. In this paper we present theoretical results and
simulations in the THz regime, for both hyperbolic secant and
supergaussian-shaped pulses
Linear and nonlinear photonic Jackiw-Rebbi states in waveguide arrays
We study analytically and numerically the optical analogue of the
Jackiw-Rebbi states in quantum field theory. These solutions exist at the
interface of two binary waveguide arrays which are described by two Dirac
equations with opposite sign masses. We show that these special states are
topologically robust not only in the linear regime, but also in nonlinear
regimes (with both focusing and de-focusing nonlinearity). We also reveal that
one can generate the Jackiw-Rebbi states starting from Dirac solitons.Comment: 4 pages, 3 figure
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