Reflection of short pulses in linear optics

Two methods of calculating the reflected wave generated by a short optical pulse falling on a linear dielectric medium are given. As examples the cases of an input sech pulse modulating a resonant carrier wave and an input delta function are calculated. At atomic densities greater than about 10 18 atoms cm -3 an appreciable amount of the energy of the sech pulse is reflected. It is suggested that any nonlinear theory which ignores reflection may break down at these densities.