Related papers: A delay differential eqution NOLM-NALM mode-locked…
The dynamics of a semiconductor-laser array whose individual elements are coupled in a global way through an external mirror is numerically analysed. A coherent in-phase solution is seen to be preferred by the system at intermediate values…
Despite the wide applications for high-repetition-rate mode-locked fiber lasers, challenges persist in shortening the cavity length and coupling the fiber collimators for most existing techniques. Here, we introduce a novel collimator…
We analyse the effect of optical feedback on the dynamics of external-cavity mode-locked semiconductor lasers operated in the long cavity regime. Depending on the ratio between the cavity round-trip time and the feedback delay, we show…
We study the problem of modeling a non-linear dynamical system when given a time series by deriving equations directly from the data. Despite the fact that time series data are given as input, models for dynamics and estimation algorithms…
The primary objective of this paper is to establish a generalized framework for pulse-shaping on the delay-Doppler plane. To this end, we classify delay-Doppler pulse-shaping techniques into two types, namely, circular and linear…
This paper addresses the qualitative theory of mixed-order positive linear coupled systems with bounded or unbounded delays. First, we introduce a general result on the existence and uniqueness of solutions to mixed-order linear coupled…
We present the first experimental confirmation of the so-called "self-phaselocked delay interferometry". This laser frequency stabilization technique consists basically in comparing the prompt laser signal with a delayed version of itself…
We show the standard two-level continuous-time model of loss-modulated CO$_2$ lasers to display the same regular network of self-similar stability islands known so far to be typically present only in discrete-time models based on mappings.…
Hybrid numerical-experimental testing is a standard approach for complex dynamical structures that are, on the one hand, not easy to model due to complexity and parameter uncertainty and, on the other hand, too expensive for full-scale…
In this paper, we consider an equivariant Hopf bifurcation of relative periodic solutions from relative equilibria in systems of functional differential equations respecting $\Gamma \times S^1$-spatial symmetries. The existence of branches…
New methods are developed for the stabilization of a linear system with general time-varying distributed delays existing at the system's states, inputs and outputs. In contrast to most existing literature where the function of time-varying…
We investigate the polarization modulation properties of a variable-delay polarization modulator (VPM). The VPM modulates polarization via a variable separation between a polarizing grid and a parallel mirror. We find that in the limit…
Periodic patterns in dynamical behaviours of biological models described by simple form differential delay equations are studied. Mathematical models are given by a class of scalar delay differential equations with a multiplicative time…
We review our recent work leading to steady-state solutions of the semiclassical (Maxwell-Bloch) equations of a laser. These are coupled non-linear partial differential equations in space and time which have previously been solved either by…
Mode-locking is a process in which different modes of an optical resonator establish, through nonlinear interactions, stable synchronization. This self-organization underlies light sources that enable many modern scientific applications,…
The solvability of a delay differential equation arising in the construction of quadratic cost functionals, i.e. Lyapunov functionals, for a linear time-delay system with a constant and a distributed delay is investigated. We present a…
We present a scheme to phase-lock a 240 mW, 852 nm distributed Bragg reflector (DBR) laser to a fixed-frequency narrow-linewidth laser with a rapidly tunable frequency offset near 9 GHz. The phase-lock is accomplished by electronic feedback…
We study a variant of the Fisher-KPP equation with nonlocal dispersal. Using the theory of large deviations, we show the emergence of a "Bramson-like" logarithmic delay for the linearised equation with step-like initial data. We conclude…
We report on an environmentally stable, all-PM-fibre, Er-doped, mode-locked laser with a central wavelength of 1550 nm. Significantly, the laser possesses large net-normal dispersion such that its dynamics are comparable to that of an…
We consider a delay differential equation that occurs in the study of chronic myelogenous leukemia. After shortly reminding some previous results concerning the stability of equilibrium solutions, we concentrate on the study of stability of…