Turn-on-time statistics of modulated lasers subjected to resonant weak optical feedback

We present analytical calculations of the turn-on-time probability distribution of intensity-modulated lasers under resonant weak optical feedback. Under resonant conditions, the external cavity round-trip time is taken to be equal to the modulation period. The probability distribution of the solitary laser results are modified to give reduced values of the mean turn-on-time and its variance. Numerical simulations have been carried out showing good agreement with the analytical results.

Numerical simulation of gel electrophoresis of DNA knots in weak and strong electric fields.

Gel electrophoresis allows one to separate knotted DNA (nicked circular) of equal length according to the knot type. At low electric fields, complex knots, being more compact, drift faster than simpler knots. Recent experiments have shown that the drift velocity dependence on the knot type is inverted when changing from low to high electric fields. We present a computer simulation on a lattice of a closed, knotted, charged DNA chain drifting in an external electric field in a topologically restricted medium. Using a Monte Carlo algorithm, the dependence of the electrophoretic migration of the DNA molecules on the knot type and on the electric field intensity is investigated. The results are in qualitative and quantitative agreement with electrophoretic experiments done under conditions of low and high electric fields.

Nonlinear relaxation time and the detection of weak signals

Laser systems can be used to detect very weak optical signals. The physical mechanism is the dynamical process of the relaxation of a laser from an unstable state to a steady stable state. We present an analysis of this process based on the study of the nonlinear relaxation time. Our analytical results are compared with numerical integration of the stochastic differential equations that model this process.