1,408 research outputs found
Stability of the self-phase-locked pump-enhanced singly resonant parametric oscillator
Steady-state and dynamics of the self-phase-locked (3\omega ==> 2\omega,
\omega) subharmonic optical parametric oscillator are analyzed in the
pump-and-signal resonant configuration, using an approximate analytical model
and a full propagation model. The upper branch solutions are found always
stable, regardless of the degree of pump enhancement. The domain of existence
of stationary states is found to critically depend on the phase-mismatch of the
competing second-harmonic process.Comment: LateX2e/RevteX4, 4 pages, 5 figures. Submitted to Phys. Rev. A
(accepted on Jan. 17, 2003
Optical Zener-Bloch oscillations in binary waveguide arrays
Zener tunneling in a binary array of coupled optical waveguides with
transverse index gradient is shown to produce a sequence of regular or
irregular beam splitting and beam recombination events superimposed to Bloch
oscillations. These periodic or aperiodic Zener-Bloch oscillations provide a
clear and visualizable signature in an optical system of coherent multiband
dynamics encountered in solid-state or matter-wave system
Discrete diffraction and shape-invariant beams in optical waveguide arrays
General properties of linear propagation of discretized light in homogeneous
and curved waveguide arrays are comprehensively investigated and compared to
those of paraxial diffraction in continuous media. In particular, general laws
describing beam spreading, beam decay and discrete far-field patterns in
homogeneous arrays are derived using the method of moments and the steepest
descend method. In curved arrays, the method of moments is extended to describe
evolution of global beam parameters. A family of beams which propagate in
curved arrays maintaining their functional shape -referred to as discrete
Bessel beams- is also introduced. Propagation of discrete Bessel beams in
waveguide arrays is simply described by the evolution of a complex
parameter similar to the complex parameter used for Gaussian beams in
continuous lensguide media. A few applications of the parameter formalism
are discussed, including beam collimation and polygonal optical Bloch
oscillations. \Comment: 14 pages, 5 figure
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
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
Polarization coupling and pattern selection in a type-II optical parametric oscillator
We study the role of a direct intracavity polarization coupling in the
dynamics of transverse pattern formation in type-II optical parametric
oscillators. Transverse intensity patterns are predicted from a stability
analysis, numerically observed, and described in terms of amplitude equations.
Standing wave intensity patterns for the two polarization components of the
field arise from the nonlinear competition between two concentric rings of
unstable modes in the far field. Close to threshold a wavelength is selected
leading to standing waves with the same wavelength for the two polarization
components. Far from threshold the competition stabilizes patterns in which two
different wavelengths coexist.Comment: 14 figure
Ray splitting in paraxial optical cavities
We present a numerical investigation of the ray dynamics in a paraxial
optical cavity when a ray splitting mechanism is present. The cavity is a
conventional two-mirror stable resonator and the ray splitting is achieved by
inserting an optical beam splitter perpendicular to the cavity axis. We show
that depending on the position of the beam splitter the optical resonator can
become unstable and the ray dynamics displays a positive Lyapunov exponent.Comment: 13 pages, 7 figures, 1 tabl
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
The Rest-Frame Instant Form of Relativistic Perfect Fluids and of Non-Dissipative Elastic Materials
For perfect fluids with equation of state , Brown gave an
action principle depending only on their Lagrange coordinates
without Clebsch potentials. After a reformulation on arbitrary spacelike
hypersurfaces in Minkowski spacetime, the Wigner-covariant rest-frame instant
form of these perfect fluids is given. Their Hamiltonian invariant mass can be
given in closed form for the dust and the photon gas. The action for the
coupling to tetrad gravity is given. Dixon's multipoles for the perfect fluids
are studied on the rest-frame Wigner hyperplane. It is also shown that the same
formalism can be applied to non-dissipative relativistic elastic materials
described in terms of Lagrangian coordinates.Comment: revtex file, 70 page
Analysis technique for exceptional points in open quantum systems and QPT analogy for the appearance of irreversibility
We propose an analysis technique for the exceptional points (EPs) occurring
in the discrete spectrum of open quantum systems (OQS), using a semi-infinite
chain coupled to an endpoint impurity as a prototype. We outline our method to
locate the EPs in OQS, further obtaining an eigenvalue expansion in the
vicinity of the EPs that gives rise to characteristic exponents. We also report
the precise number of EPs occurring in an OQS with a continuum described by a
quadratic dispersion curve. In particular, the number of EPs occurring in a
bare discrete Hamiltonian of dimension is given by ; if this discrete Hamiltonian is then coupled to continuum
(or continua) to form an OQS, the interaction with the continuum generally
produces an enlarged discrete solution space that includes a greater number of
EPs, specifically , in which
is the number of (non-degenerate) continua to which the discrete sector is
attached. Finally, we offer a heuristic quantum phase transition analogy for
the emergence of the resonance (giving rise to irreversibility via exponential
decay) in which the decay width plays the role of the order parameter; the
associated critical exponent is then determined by the above eigenvalue
expansion.Comment: 16 pages, 7 figure
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