John N. Elgin

Semiclassical formalism for the treatment of three-level systems

Abstract A generalised semiclassical formalism is developed for the treatment of resonant coherent interactions in three-level systems. The equations of motion for the system are derived in the form of a torque equation, and two constants of the motion are identified.

Soliton propagation in an optical fiber with third-order dispersion

A simple model is described that correctly explains numerically observed resonance features on the soliton spectrum when the perturbative effects of third-order dispersion are present.

Inverse scattering theory with stochastic initial potentials

Abstract Most applications of inverse scattering theory assume that the initial potential is a well-defined quantity. In applications to fibre optical systems, this is not necessarily the case, since the input pulse produced by a laser may not be spectrally pure and hence can have stochastic properties. We consider here the effect on the scattering data when the phase of the initial pulse varies randomly.

Spectral modulation and the growth of resonant modes associated with periodically amplified solitons.

A first-order spectral perturbation theory of resonant modes that evolve with periodically amplified optical fiber solitons is presented. In contrast with the modulational instability, these modes exhibit a linear growth in amplitude with respect to propagation and have a tuning characteristic that follows an inverse square-root dependence on the amplification period. Numerical results based on a complete solution of the nonlinear Schrödinger equation are also presented that confirm and quantify this behavior.

Saturation effects in transient stimulated Raman scattering

The evolution of the Stokes pulse generated by transient stimulated Raman scattering is considered for the case of ultrashort incident pulses. A model is proposed which allows for the effects of either depletion of the laser pump pulse or saturation of the non-linear medium.

Stability of travelling pulse solutions to a laser equation

Abstract The stability of travelling pulse solutions to a partial differential equation modelling a laser system is determined through a simple robust part-numerical method not previously applied to such a system. The agreement with the results of a full blown numerical simulation is complete for all the cases examined.

A method of suppressing velocity spreads of an electron beam in combined helical wiggler and axial guide magnetic field

Abstract A new method is proposed to suppress the velocity spreads of the electron beam by employing a tapered, reversed axial guide magnetic field. Three-dimensional analysis and nonlinear simulation show that this method can substantially suppress both transverse and longitudinal velocity spreads and evidently weaken the divergence in the configuration space of the electron beam. Compared to a positive guide field and uniformly reversed guide field, this method could be expected to enhance the gain and efficiency of a free-electron laser/maser.

A Shilnikov-type analysis in a system with symmetry

Abstract We perform a Shilnikov-type analysis for heteroclinic orbits of a symmetric system, which differs from the usual case in that it involves a symmetry, and there is more than one connecting orbit at the critical parameter value.

Asymptotic analysis of the Michelson system

We consider the dynamical system xttt = c2−½x2−xt for the parameter c close to zero. We perform a multiple timescale analysis to provide analytic forms for all bounded solutions of the formal normal form in the phase space, in a neighbourhood of the origin (x,c) = (0, 0). These take the form of Jacobi elliptic functions describing periodic and quasi-periodic solutions, and hyperbolic functions that describe heteroclinic connections. A comparison between these approximate analytical results and numerical simulations of the unperturbed system shows excellent correspondence.

Application of Kolmogorov entropy to the self-amplified spontaneous emission free-electron lasers

Based on the numerical simulation of Kolmogorov entropy, the dynamic behavior is investigated for the relativistic electrons injected into the wiggler in a self-amplified spontaneous emission free-electron laser system. Results show an interesting phenomenon that the self-fields of the electron beam have an effect of stabilizing the electron’s dynamic behavior. It is found that the adiabatic magnetic field of one-dimensional wiggler has trivial influence to the dynamic stability, although it is helpful to the electrons to enter the cavity smoothly. Moreover, the laser field deteriorates the stability of the electron’s dynamic behavior as it grows exponentially and becomes very strong in the rear range.