Controlling the path of discretized light in waveguide lattices

A general method for flexible control of the path of discretized light beams in homogeneous waveguide lattices, based on longitudinal modulation of the coupling constant, is theoretically proposed. As compared to beam steering and refraction achievable in graded-index waveguide arrays, the proposed approach enables to synthesize rather arbitrary target paths

Multistable Pulse-like Solutions in a Parametrically Driven Ginzburg-Landau Equation

It is well known that pulse-like solutions of the cubic complex Ginzburg-Landau equation are unstable but can be stabilised by the addition of quintic terms. In this paper we explore an alternative mechanism where the role of the stabilising agent is played by the parametric driver. Our analysis is based on the numerical continuation of solutions in one of the parameters of the Ginzburg-Landau equation (the diffusion coefficient $c$), starting from the nonlinear Schr\"odinger limit (for which $c=0$). The continuation generates, recursively, a sequence of coexisting stable solutions with increasing number of humps. The sequence "converges" to a long pulse which can be interpreted as a bound state of two fronts with opposite polarities.Comment: 13 pages, 6 figures; to appear in PR

SL(2,R) model with two Hamiltonian constraints

We describe a simple dynamical model characterized by the presence of two noncommuting Hamiltonian constraints. This feature mimics the constraint structure of general relativity, where there is one Hamiltonian constraint associated with each space point. We solve the classical and quantum dynamics of the model, which turns out to be governed by an SL(2,R) gauge symmetry, local in time. In classical theory, we solve the equations of motion, find a SO(2,2) algebra of Dirac observables, find the gauge transformations for the Lagrangian and canonical variables and for the Lagrange multipliers. In quantum theory, we find the physical states, the quantum observables, and the physical inner product, which is determined by the reality conditions. In addition, we construct the classical and quantum evolving constants of the system. The model illustrates how to describe physical gauge-invariant relative evolution when coordinate time evolution is a gauge.Comment: 9 pages, 1 figure, revised version, to appear in Phys. Rev.

On the generation and the nonlinear dynamics of X-waves of the Schroedinger equation

The generation of finite energy packets of X-waves is analysed in normally dispersive cubic media by using an X-wave expansion. The 3D nonlinear Schroedinger model is reduced to a 1D equation with anomalous dispersion. Pulse splitting and beam replenishment as observed in experiments with water and Kerr media are explained in terms of a higher order breathing soliton. The results presented also hold in periodic media and Bose-condensed gases.Comment: 18 pages, 6 figures, corrected version to be published in Physical Review

Non-Markovian Decay and Lasing Condition in an Optical Microcavity Coupled to a Structured Reservoir

The decay dynamics of the classical electromagnetic field in a leaky optical resonator supporting a single mode coupled to a structured continuum of modes (reservoir) is theoretically investigated, and the issue of threshold condition for lasing in presence of an inverted medium is comprehensively addressed. Specific analytical results are given for a single-mode microcavity resonantly coupled to a coupled resonator optical waveguide (CROW), which supports a band of continuous modes acting as decay channels. For weak coupling, the usual exponential Weisskopf-Wigner (Markovian) decay of the field in the bare resonator is found, and the threshold for lasing increases linearly with the coupling strength. As the coupling between the microcavity and the structured reservoir increases, the field decay in the passive cavity shows non exponential features, and correspondingly the threshold for lasing ceases to increase, reaching a maximum and then starting to decrease as the coupling strength is further increased. A singular behavior for the "laser phase transition", which is a clear signature of strong non-Markovian dynamics, is found at critical values of the coupling between the microcavity and the reservoir.Comment: to appear in Phys. Rev. A (December 2006 issue

A Vibrational Circular Dichroism Approach To The Determination Of The Absolute Configuration Of Flexible And Transparent Molecules: Fluorenone Ketals Of 1,N-Diols

The infrared absorption (IR) and vibrational circular dichroism (VCD) spectra for five ketal molecules, three of which obtained from 1,2-diols and two from 1,3-diols, were recorded in the mid-IR region. The spectra have been satisfactorily reproduced by DFT calculations, even with not too large wavefunction basis sets, especially due to the low number of conformers to be considered. The mobility of some moieties provides a recognizable signature. A characteristic couplet of VCD bands attributed to normal modes involving the methine and a phenyl ring bonded to the stereogenic carbon atom is evidenced for two ketals of the series as a signature of the absolute configuration; due comparison with existing literature is made. A relation is discussed of the present VCD data with the literature VCD data of simple alcohols and diols

Loschmidt echo and fidelity decay near an exceptional point

Non-Hermitian classical and open quantum systems near an exceptional point (EP) are known to undergo strong deviations in their dynamical behavior under small perturbations or slow cycling of parameters as compared to Hermitian systems. Such a strong sensitivity is at the heart of many interesting phenomena and applications, such as the asymmetric breakdown of the adiabatic theorem, enhanced sensing, non-Hermitian dynamical quantum phase transitions and photonic catastrophe. Like for Hermitian systems, the sensitivity to perturbations on the dynamical evolution can be captured by Loschmidt echo and fidelity after imperfect time reversal or quench dynamics. Here we disclose a rather counterintuitive phenomenon in certain non-Hermitian systems near an EP, namely the deceleration (rather than acceleration) of the fidelity decay and improved Loschmidt echo as compared to their Hermitian counterparts, despite large (non-perturbative) deformation of the energy spectrum introduced by the perturbations. This behavior is illustrated by considering the fidelity decay and Loschmidt echo for the single-particle hopping dynamics on a tight-binding lattice under an imaginary gauge field.Comment: 11 pages, 6 figures, to appear in Annalen der Physi

Photonic realization of the relativistic Kronig-Penney model and relativistic Tamm surface states

Photonic analogues of the relativistic Kronig-Penney model and of relativistic surface Tamm states are proposed for light propagation in fibre Bragg gratings (FBGs) with phase defects. A periodic sequence of phase slips in the FBG realizes the relativistic Kronig-Penney model, the band structure of which being mapped into the spectral response of the FBG. For the semi-infinite FBG Tamm surface states can appear and can be visualized as narrow resonance peaks in the transmission spectrum of the grating

Dynamic facial expressions of emotions are discriminated at birth

The ability to discriminate between different facial expressions is fundamental since the first stages of postnatal life. The aim of this study is to investigate whether 2-days-old newborns are capable to discriminate facial expressions of emotions as they naturally take place in everyday interactions, that is in motion. When two dynamic displays depicting a happy and a disgusted facial expression were simultaneously presented (i.e., visual preference paradigm), newborns did not manifest any visual preference (Experiment 1). Nonetheless, after being habituated to a happy or disgusted dynamic emotional expression (i.e., habituation paradigm), newborns successfully discriminated between the two (Experiment 2). These results indicate that at birth newborns are sensitive to dynamic faces expressing emotions