Throughout this monograph the effect of radiation upon a quantum system has been presented as an interaction between an atomic moment (usually the electric dipole moment) and a pulse of nearly periodic electromagnetic radiation, typically the electric field of that radiation. The strength of the interaction of such a field with an individual atom or molecule is typically parametrized by the field intensity (or radiation irradiance) and a transition moment (or oscillator strength). When the atoms form macroscopic aggregates, through which the laser radiation must pass, the laser-induced alteration of atomic states produces new fields that subtract from or add to the original field [Sho90, Chap. 12]. As a result, pulses propagating through matter become altered. The pulse amplitude will, at first, decrease as energy is absorbed by the atoms, but more dramatic effects can occur that drastically alter the shape of the pulse as it travels through greater thicknesses of matter [Sho90, Chap. 9]. Furthermore, new frequencies may be generated – the phenomena of nonlinear optics [Rei84; Gae06; Boy08].

Prior to the advent of laser radiation there was little interest in short pulses, and the equations describing radiation dealt with the flow of energy through matter that could absorb or divert the radiation, embodied in the theory of radiative transfer [Cha60; Tuc75; Ryb85; Car07]. Such descriptions characterized the radiation–matter interaction by a static complex-valued index of refraction, whose imaginary part produced absorption while the real (dispersive) part altered the propagation velocity [Bre32; Mea60; Bor99].