Dan Anderson

Wave-breaking-free pulses in nonlinear-optical fibers

A qualitative as well as quantitative investigation is made of the conditions for avoiding wave breaking during pulse propagation in optical fibers. In particular, it is shown that pulses having a parabolic intensity variation are approximate wave-breaking-free solutions of the nonlinear Schrodinger equation in the high-intensity limit. A simple expression for the compression factor of a fiber-grating compressor based on parabolic pulses is also derived.

Wave breaking in nonlinear-optical fibers

An analytical investigation is made of the interplay between dispersion and nonlinearity in the creation of wave breaking in optical fibers. Wave breaking is found to involve two independent processes: (a) overtaking of different parts of the pulse and (b) nonlinear generation of new frequencies during overtaking. Analytical predictions for the distance of wave breaking are obtained and found to be in good agreement with numerical results.

Variational approach to nonlinear self-focusing of Gaussian laser beams

The problem of nonlinear self‐focusing of Gaussian laser beams is reformulated in terms of a variational principle. By means of approximating Gaussian functions, expressions are obtained for the equilibrium radii and nonlinear frequency shifts of stationary self‐trapped laser beams. The nonsteady propagation is given an illuminating form in terms of a potential function description. The analysis confirms the recent results obtained by moment theory as opposed to those based on paraxial ray approximations.

Variational approach to collapse of optical pulses

Optical pulses, which propagate under the combined effects of nonlinearity, dispersion, and diffraction, may collapse in space and time. The standard method for analyzing these collapses is the aberrationless paraxial ray approximation. This method is known to give a quantitatively correct, although not particularly accurate, picture of most properties of the pulse dynamics. However, it is found that the predictions for some of the important pulse parameters are qualitatively wrong and could lead to incorrect conclusions. An alternative variational approach is suggested that remedies these deficiencies and gives results in good agreement with numerical results.

Statistical effects in the multistream model for quantum plasmas

A statistical multistream description of quantum plasmas is formulated, using the Wigner-Poisson system as dynamical equations. A linear stability analysis of this system is carried out, and it is shown that a Landau-like damping of plane wave perturbations occurs due to the broadening of the background Wigner function that arises as a consequence of statistical variations of the wave function phase. The Landau-like damping is shown to suppress instabilities of the one- and two-stream type.

Modulational instability of coherent optical-fiber transmission signals

We point out the importance of the modulational instability as a possible limiting factor for coherent optical-fiber transmission.

Soliton Perturbations: A Variational Principle for the Soliton Parameters

A variational perturbation method is developed to study the evolution of a single soliton in the presence of small perturbations. Adiabatic evolution equations for the parameters of the soliton are derived to first order in the perturbation without employing methods or results from the inverse scattering theory. The analysis accounts for the effects of shape modifications in the form of a dress or tail of the soliton. The method is applied to the perturbed Korteweg-deVries, modified Korteweg-deVries, nonlinear Schrodinger and sine-Gordon equations and the results are compared with those obtained from other approaches.

Asymptotic propagation properties of pulses in a soliton-based optical-fiber communication system

An analytical investigation is made of the asymptotic propagation properties of pulses evolving from nonsoliton initial conditions in an optical-fiber communication system. Explicit analytical results are obtained for the characteristic parameters of the asymptotically emerging soliton as well as of the accompanying decaying nonsoliton part. The importance of the dispersively decaying part of the pulse for a soliton-based optical-fiber communication system is especially emphasized.

Bandwidth limits due to mutual pulse interaction in optical soliton communication systems.

Mutual interaction between soliton pulses may severely limit the maximum bit rate of a soliton-based optical communication system. We present explicit analytical results for soliton separation as a function of propagation distance in the presence of mutual pulse interaction. In particular, we find that soliton coalescence can be avoided by proper phase shifting of consecutive pulses and that a phase shift of π/2 minimizes the initial mutual interaction.

Multipactor in rectangular waveguides

Multipactor inside a rectangular waveguide is studied using both an analytical approach and numerical simulations. Particular attention is given to an analysis of the role of such effects as the velocity spread of secondary emitted electrons and the action of the rf magnetic field on the electron motion. Conventional resonance theory is shown to give correct predictions for the multipactor threshold in cases where the height of the waveguide is very small and first order resonance multipactor dominates. In cases of higher order resonances, an accurate prediction of the multipactor threshold requires that the spread of the normal component of the electron emission velocity is taken into account. Furthermore, the spread of the tangential component of the electron emission velocity and the action of the rf magnetic field are shown to be very important when the waveguide height exceeds a certain critical value, which depends on the waveguide width. A new theory is developed for predicting the multipactor thre...