Excitation and power of the unbound modes within a circular dielectric waveguide

A complete orthonormal set of unbound spectral modes is presented for the ideal circular dielectric cylinder. The excitation of these modes under illumination by (i) a finite section of a plane wave obliquely incident on the cylinder and (ii) a quasi-monochromatic incoherent source is determined. Numerical results are given illustrating the rate of leakage of the power of the radiation field from the rod, and its dependence on certain parameters of the rod and of the illuminating field. The practical limitations of this exact formulation are discussed. It is also shown that the intensity distribution produced by diffraction at a circular aperture is very similar to that of the radiation field when the difference in dielectric constant between the cylinder and its surround is small.