Related papers: A delay differential eqution NOLM-NALM mode-locked…
This paper examines the problem of stabilizing linear distributed delay systems with nonlinear distributed delay kernels and dissipativity constraints. Specifically, the nonlinear distributed kernel includes functions such as polynomials,…
In this paper we study well-posedness and asymptotic stability for a class of nonlinear second-order evolution equations with intermittent delay damping. More precisely, a delay feedback and an undelayed one act alternately in time. We show…
This note is concerned with stability analysis of integral delay systems with multiple delays. To study this problem, the well-known Jensen inequality is generalized to the case of multiple terms by introducing an individual slack weighting…
Bound states of solitons (molecules) occur in various settings, playing an important role in the operation of fiber lasers, optical emulations, encoding, and communications. Soliton interactions are generally related to breathing dynamics…
Much recent progress has been achieved for stabilization of linear and nonlinear systems with input delays that are long and dependent on either time or the plant state---provided the dependence is known. In this paper we consider the delay…
Detailed experimental and theoretical investigations on two coupled fiber lasers, each with many longitudinal modes, reveal that the behavior of the longitudinal modes depends on both the coupling strength as well as the detuning between…
Linear scalar differential equations with distributed delays appear in the study of the local stability of nonlinear differential equations with feedback, which are common in biology and physics. Negative feedback loops tend to promote…
The problem considered in the paper is exponential stability of linear equations and global attractivity of nonlinear non-autonomous equations which include a non-delay term and one or more delayed terms. First, we demonstrate that…
This paper is devoted to the investigation of the nonnegative solutions and the stability and asymptotic properties of the solutions of fractional differential dynamic systems involving delayed dynamics with point delays. The obtained…
We review the conventional phase-locking technique in the long-term stabilization of the mode-locked fiber laser and investigate the phase noise limitation of the conventional technique. To break the limitation, we propose an improved…
In this paper, we present a novel stochastic and spatially lumped multi-mode model to describe the nonlinear dynamics of actively Q-switched lasers and random perturbations due to amplified spontaneous emission. This model will serve as a…
We present a complete numerical analysis and simulation of the full spatio-temporal dynamics of Kerr-lens mode-locking (KLM) in a laser on all time-scales. The KLM dynamics, which is the workhorse mechanism for generating ultrashort pulses,…
We report on the first solid-state dual-comb mode-locked laser simultaneously operating in different dispersion regimes. Due to the intrinsic polarization-multiplexing in a birefringent Yb:Ca$_3$NbGa$_3$Si$_2$O$_{14}$ (Yb:CNGS) gain medium,…
For a nonlinear equation with several variable delays $$ \dot{x}(t)=\sum_{k=1}^m f_k(t, x(h_1(t)),\dots,x(h_l(t)))-g(t,x(t)), $$ where the functions $f_k$ increase in some variables and decrease in the others, we obtain conditions when a…
Phase-locked laser arrays have been extensively investigated in terms of their stability and nonlinear dynamics. Specifically, enhancing the phase-locking stability allows laser arrays to generate high-power and steerable coherent optical…
The ability to control the laser modes within a subwavelength resonator is of key relevance in modern optoelectronics. This work deals with the theoretical research on optical properties of a PT--symmetric nano--scaled dimer formed by two…
We theoretically study chaos synchronization of two lasers which are delay-coupled via an active or a passive relay. While the lasers are synchronized, their dynamics is identical to a single laser with delayed feedback for a passive relay…
We consider the phase stability of a local oscillator (or laser) locked to a cavity QED system comprised of atoms with an ultra-narrow optical transition. The atoms are cooled to millikelvin temperatures and then released into the optical…
In this paper, we prove a theorem of linearized asymptotic stability for fractional differential equations with a time delay. More precisely, using the method of linearization of a nonlinear equation along an orbit (Lyapunov's first…
We present a flexible all-polarization-maintaining (PM) mode-locked ytterbium (Yb):fiber laser based on a nonlinear amplifying loop mirror (NALM). In addition to providing detailed design considerations, we discuss the different operation…