An electromagnetic boundary value problem for a radiating dielectric cylinder with reflectors at both ends

A boundary value problem is solved for the time-variable homogeneous Maxwell equations describing electromagnetic radiation from a dielectric cylinder with mirrors on the face planes. The problem is reduced to the Fredholm integral equation of the second kind, allowing an approximate analytical solution. The problem in question has eigensolutions describing field distribution as well as eigenvalues corresponding to radiation frequencies (optical in this case). Attention is given to the cases of large and small jumps of the refractive index on the interface of the cylinder with the ambient medium, and to the case when permittivity is dependent on cylinder radius.