588 research outputs found
Delayed feedback control of self-mobile cavity solitons
Control of the motion of cavity solitons is one the central problems in
nonlinear optical pattern formation. We report on the impact of the phase of
the time-delayed optical feedback and carrier lifetime on the self-mobility of
localized structures of light in broad area semiconductor cavities. We show
both analytically and numerically that the feedback phase strongly affects the
drift instability threshold as well as the velocity of cavity soliton motion
above this threshold. In addition we demonstrate that non-instantaneous carrier
response in the semiconductor medium is responsible for the increase in
critical feedback rate corresponding to the drift instability
Possible quantum kinematics. II. Non-minimal case
The quantum analogs of the N-dimensional Cayley-Klein spaces with different
combinations of quantum and Cayley-Klein structures are described for
non-minimal multipliers, which include the first and the second powers of
contraction parameters in the transformation of deformation parameter. The
noncommutative analogs of (N-1)-dimensional constant curvature spaces are
introduced. Part of these spaces for N=5 are interpreted as the noncommutative
analogs of (1+3) space-time models. As a result the wide variety of the quantum
deformations of realistic kinematics are suggested.Comment: 13 pages, no figure
Temporal solitons in an optically injected Kerr cavity with two spectral filters
We investigate theoretically the dynamical behavior of an optically injected Kerr cavity where the chromatic dispersion is induced by propagation of light through two Lorentzian spectral filters with different widths and central frequencies. We show that this setup can be modeled by a second order delay differential equation that can be considered as a generalization of the Ikeda map with included spectral filtering, dispersion, and coherent injection terms. We demonstrate that this equation can exhibit modulational instability and bright localized structures formation in the anomalous dispersion regime
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Dynamics of an inhomogeneously broadened passively mode-locked laser
We study theoretically the effect of inhomogeneous broadening of the
gain and absorption lines on the dynamics of a passively mode-locked laser.
We demonstrate numerically using travelling wave equations the formation of a
Lamb-dip instability and suppression of Q-switching in a laser with large
inhomogeneous broadening. We derive simplified delay-differential equation
model for a mode-locked laser with inhomogeneously broadened gain and
absorption lines and perform numerical bifurcation analysis of this model
Dynamics of an inhomogeneously broadened passively mode-locked laser
We study theoretically the effect of inhomogeneous broadening of the gain and absorption lines on the dynamics of a passively mode-locked laser. We demonstrate numerically using travelling wave equations the formation of a Lamb-dip instability and suppression of Q-switching in a laser with large inhomogeneous broadening. We derive simplified delay-differential equation model for a mode-locked laser with inhomogeneously broadened gain and absorption lines and perform numerical bifurcation analysis of this model
Numerical methods for solving a hereditary equation of hyperbolic type
A family of grid methods is constructed for the numerical solution of a wave equation with delay of general form; the methods are based on the idea of separating the current state and the history function. A theorem on the order of convergence of the methods is obtained by means of embedding into a general difference scheme with aftereffect. Results of calculating test examples with constant and variable delays are presented. © 2013 Pleiades Publishing, Ltd
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