The electromagnetic field of a guided Gaussian beam

An electromagnetic wave traveling along a dielectric slab between two parallel, plane conductors is analyzed for a special case that is particularly relevant to guided laser beams employed in integrated optics. The beam is assumed to have an approximate gaussian field dependence along the y-direction, defined to be transverse to the direction of propagation and to the normal to the conductor planes. Approximate expressions for the field in a well collimated beam are derived. Asymptotic approximations, valid far away from the focus of a beam that is not necessarily well collimated, are also derived. It is found that the TE and TM guided gaussian beams are not linearly polarized. This is unlike the case for the usual waveguide modes whose fields are constant along the y direction. It is also found that the guided gaussian beam must have a focus and that the divergence from focus is more rapid than for a similar gaussian beam in free space.