11 research outputs found
Universal fractal structures in the weak interaction of solitary waves in generalized nonlinear Schr\"{o}dinger equations
Weak interactions of solitary waves in the generalized nonlinear
Schr\"{o}dinger equations are studied. It is first shown that these
interactions exhibit similar fractal dependence on initial conditions for
different nonlinearities. Then by using the Karpman-Solov'ev method, a
universal system of dynamical equations is derived for the velocities,
amplitudes, positions and phases of interacting solitary waves. These dynamical
equations contain a single parameter, which accounts for the different forms of
nonlinearity. When this parameter is zero, these dynamical equations are
integrable, and the exact analytical solutions are derived. When this parameter
is non-zero, the dynamical equations exhibit fractal structures which match
those in the original wave equations both qualitatively and quantitatively.
Thus the universal nature of fractal structures in the weak interaction of
solitary waves is analytically established. The origin of these fractal
structures is also explored. It is shown that these structures bifurcate from
the initial conditions where the solutions of the integrable dynamical
equations develop finite-time singularities. Based on this observation, an
analytical criterion for the existence and locations of fractal structures is
obtained. Lastly, these analytical results are applied to the generalized
nonlinear Schr\"{o}dinger equations with various nonlinearities such as the
saturable nonlinearity, and predictions on their weak interactions of solitary
waves are made.Comment: 22pages, 15 figure
Bistability and instability of dark-antidark solitons in the cubic-quintic nonlinear Schroedinger equation
We characterize the full family of soliton solutions sitting over a
background plane wave and ruled by the cubic-quintic nonlinear Schroedinger
equation in the regime where a quintic focusing term represents a saturation of
the cubic defocusing nonlinearity. We discuss existence and properties of
solitons in terms of catastrophe theory and fully characterize bistability and
instabilities of the dark-antidark pairs, revealing new mechanisms of decay of
antidark solitons.Comment: 8 pages, 10 figures, accepted in PR
Bright and dark solitons in the systems with strong light-matter coupling: exact solutions and numerical simulations
We theoretically study bright and dark solitons in an experimentally relevant
hybrid system characterized by strong light-matter coupling. We find that the
corresponding two-component model supports a variety of coexisting moving
solitons including bright solitons on zero and nonzero background, dark-gray
and gray-gray dark solitons. The solutions are found in the analytical form by
reducing the two-component problem to a single stationary equation with
cubic-quintic nonlinearity. All found solutions coexist under the same set of
the model parameters, but, in a properly defined linear limit, approach
different branches of the polariton dispersion relation for linear waves.
Bright solitons with zero background feature an oscillatory-instability
threshold which can be associated with a resonance between the edges of the
continuous spectrum branches. `Half-topological' dark-gray and nontopological
gray-gray solitons are stable in wide parametric ranges below the modulational
instability threshold, while bright solitons on the constant-amplitude pedestal
are unstable.Comment: 11 pages, 11 figures; accepted for Phys. Rev.
A route to high peak power and energy scaling in the mid-IR chirped-pulse oscillator-amplifier laser systems
The paper introduces a new route towards the ultrafast high laser peak power
and energy scaling in a hybrid mid-IR chirped pulse oscillator-amplifier
(CPO-CPA) system, without sacrificing neither the pulse duration nor energy.
The method is based on using a CPO as a seed source allowing the beneficial
implementation of a dissipative soliton (DS) energy scaling approach, coupled
with a universal CPA technique. The key is avoiding a destructive nonlinearity
in the final stages of an amplifier and compressor elements by using a chirped
high-fidelity pulse from CPO. Our main intention is to realize this approach in
a Cr2+:ZnS-based CPO as a source of energy-scalable DSs with well-controllable
phase characteristics for a single-pass Cr2+:ZnS amplifier. A qualitative
comparison of experimental and theoretical results provides a road map for the
development and energy scaling of the hybrid CPO-CPA laser systems, without
compromising pulse duration. The suggested technique opens up a route towards
extremely intense ultra-short pulses and frequency combs from the multi-pass
CPO-CPA laser systems that are particularly interesting for real-life
applications in the mid-IR spectral range from 1 to 20 um.Comment: 16 pages, 14 figure
High-Energy Passive Mode-Locking of Fiber Lasers
Mode-locking refers to the generation of ultrashort optical pulses in laser systems. A comprehensive study of achieving high-energy pulses in a ring cavity fiber laser that is passively mode-locked by a series of waveplates and a polarizer is presented in this paper. Specifically, it is shown that the multipulsing instability can be circumvented in favor of bifurcating to higher-energy single pulses by appropriately adjusting the group velocity dispersion in the fiber and the waveplate/polarizer settings in the saturable absorber. The findings may be used as practical guidelines for designing high-power lasers since the theoretical model relates directly to the experimental settings
Free-carrier-driven Kerr frequency comb in optical microcavities: Steady state, bistability, self-pulsation, and modulation instability
Continuous-wave pumped optical microresonators have been vastly exploited to generate a frequency comb (FC) utilizing the Kerr nonlinearity. Most of the nonlinear materials used to build photonic platforms exhibit nonlinear losses such as multiphoton absorption, free-carrier absorption, and free-carrier dispersion which can strongly affect their nonlinear performances. In this work, we model the Kerr FC based on a modified Lugiato-Lefever equation (LLE) along with the rate equation and develop analytical formulations to make a quick estimation of the steady state, bistability, self-pulsation, and modulation instability (MI) gain and bandwidth in the presence of nonlinear losses. The analytical model is valid over a broad wavelength range as it includes the effects of all nonlinear losses. Higher-order (>3)characteristic polynomials of intracavity power describing the steady-state homogeneous solution of the modified LLE are discussed in detail. We derive the generalized analytical expressions for the threshold (normalized) pump detuning that initiates the optical bistability when nonlinear losses are present. Free-carrier dispersion-led nonlinear cavity detuning is observed through the reverse Kerr tilt of the resonant peaks. We further deduce the expressions of the threshold pump intensity and the range of possible cavity detuning for the initiation of the MI considering the presence of nonlinear losses. The proposed model will be helpful in explaining several numerical and experimental results which have been previously reported and thereby will be able to provide a better understanding of the comb dynamics