Absorption and stimulated emission by a thin slab obeying the Lorentz oscillator model

Abstract

In his celebrated 1916–17 papers in which he proposed the A and B coefficients for the spontaneous and stimulated emission of energy quanta from excited atoms, Einstein conjectured that stimulated emission involves the release of individual quanta (later dubbed “photons”) along the direction of an incident photon with the same energy, momentum, phase, and polarization state as that of the incident photon. According to classical electrodynamics, of course, an oscillating dipole must radiate an azimuthally symmetric electromagnetic field around its axis of oscillation. Nevertheless, Einstein suggested that the release of stored energy from excited atoms in the form of discrete quanta (photons) must be directional, and that, in the case of stimulated emission, the direction of the emitted photon must coincide with that of the incident photon. The goal of the present paper is to show that some of the prominent features of absorption and stimulated emission emerge from Maxwellian electrodynamics in conjunction with the simple mass-and-spring model of an atom known as the Lorentz oscillator model.