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

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

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

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

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

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