Trapping Electromagnetic Solitons in Cylinders

Electromagnetic waves, in vacuum or dielectrics, can be confined in unbounded cylinders in such a way that they turn around the main axis. For particular choices of the cylinder's section, interesting stationary configurations may be assumed. By refining some results obtained in previous papers, additional more complex situations are examined here. For such peculiar guided waves an explicit expression is given in terms of Bessel's functions. Possible applications are in the development of whispering gallery resonators.Comment: 8 pages, 5 figure

Computational aspects of pseudospectral Laguerre approximations

Pseudospectral approximations in unbounded domains by Laguerre polynomials lead to ill-conditioned algorithms. Introduced are a scaling function and appropriate numerical procedures in order to limit these unpleasant phenomena

Numerical Simulation of Electromagnetic Solitons and their Interaction with Matter

A suitable correction of the Maxwell model brings to an enlargement of the space of solutions, allowing for the existence of solitons in vacuum. We review the basic achievements of the theory and discuss some approximation results based on an explicit finite-difference technique. The experiments in two dimensions simulate travelling solitary electromagnetic waves, and show their interaction with conductive walls. In particular, the classical dispersion, exhibited by the passage of a photon through a small aperture, is examined.Comment: 17 pages, 9 figure