2,198 research outputs found
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 ), starting from the
nonlinear Schr\"odinger limit (for which ). 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
Coupled-mode theory for photonic band-gap inhibition of spatial instabilities
We study the inhibition of pattern formation in nonlinear optical systems using intracavity photonic crystals. We consider mean-field models for singly and doubly degenerate optical parametric oscillators. Analytical expressions for the new (higher) modulational thresholds and the size of the "band gap" as a function of the system and photonic crystal parameters are obtained via a coupled-mode theory. Then, by means of a nonlinear analysis, we derive amplitude equations for the unstable modes and find the stationary solutions above threshold. The form of the unstable mode is different in the lower and upper parts of the band gap. In each part there is bistability between two spatially shifted patterns. In large systems stable wall defects between the two solutions are formed and we provide analytical expressions for their shape. The analytical results are favorably compared with results obtained from the full system equations. Inhibition of pattern formation can be used to spatially control signal generation in the transverse plane
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