Summary: A time-domain technique is presented for computing the internal electromagnetic field within a one-dimensional medium characterized by spatially varying conductivity and permittivity profiles. A Green’s operator is defined which maps the incident fields on either side of the medium to the field at an arbitrary observation point. This operator is shown to be a matrix of integral operators with kernels satisfying known partial differential equations and various other initial and boundary identities. A scheme for numerically calculating these kernels is presented along with a few examples of the calculations. Moreover, consideration of the boundary values of the Green’s operator reveals a novel way for computing the reflection and transmission operators for the medium. Finally, a Green’s function approach to internal fields in the presence of a phase velocity mismatch at one of the boundaries of the medium is outlined in an appendix.