Transfer matrix of a Dirac-like singularity of the dielectric permittivity

We derive the general expression, for TE-polarization, of the transfer matrix associated to a Dirac-like singularity of the dielectric permittivity. We show that this approach is successful in modeling quantum wells, as well as localized loss centers used for the ''modal sculpturing'' in semiconductor lasers, Its range of validity includes any discontinuity of finite length as long as its actual extension remains much inferior to the optical wavelength.