Basic physics of laser propagation in hollow waveguides

The basic theory of laser propagation in hollow waveguides is considered in the context of laser-plasma physics. The physical model of waves reflecting between the guide walls is used to show that there is a discrete series of modes, and to give the mode dispersion relation and losses in terms of a given reflectivity. The mathematical connection between this model and the solution of Maxwell's equations for lossless propagation in a cylinder is given. Thus the solutions for low loss propagation for any given reflectivity can be obtained, provided it is close to 1. Results are given using Fresnel reflectivity for perfect dielectric and finite conductivity waveguides. The relationship of the breakdown intensity in dielectric waveguides to known breakdown intensities is also derived. The practical implications for the guiding of intense laser pulses and the limitations of the model are discussed. The theory is shown to explain, at least qualitatively, a number of previous experimental results.