Laser propagation in cylindrical waveguides

Laser propagation in cylindrical waveguides is studied theoretically, assuming that the guide medium and the internal medium have permittivities and identical permeabilities that are uniform in space and time and independent of the fields. Approximate solutions to the cylindrical dispersion relation are found and compared with numerical solutions. For high refractive indices and small radii the modes are transverse electric and transverse magnetic, as in the loss-less case. As the refractive index is lowered or the radius increased the lower-order modes become hybrid electric and hybrid magnetic, and the lower-order transverse magnetic modes are modified. The higher-order modes, in any waveguide, are always transverse. The transition to hybrid modes is marked by the disappearance of the fundamental electric mode and the appearance of an additional magnetic mode. This mode and the losses of the magnetic modes adjacent to it are only adequately described by numerical solutions. The losses of the transverse modes are accurately reproduced by a simple model based on a mean reflectivity