From prehistoric times has come recognition that sunlight and firelight provide warmth, and that such illumination casts shadows. Expressed in more contemporary terms one would say that light travels in rays, and that this radiation has the potential to provide heat energy to absorbing material. From the time of Newton it has been known that light sources emit radiation comprising a distribution of colors. During the nineteenth century it was recognized that radiation had characteristics of transverse waves (with wavelength associated to color) but until the late twentieth century, when lasers became laboratory tools, it was hardly necessary to delve into the equations of electromagnetic theory to treat such experiments as were then possible; interest lay primarily with thermodynamic considerations of energy flow or with measurements of the dark or bright lines seen in the distribution of light that, after passing through a slit, was dispersed by a prism or grating into constituent colors. Although laser light sources are essential for the types of atomic excitation considered in this monograph, the legacy from thermal radiation still influences many interpretations of the interaction between radiation and matter, and it is therefore useful to summarize some of those concepts.

The mathematics needed for describing laser radiation, or polarized light in general, has much in common with the mathematics of quantum theory discussed starting in Sec. 3.5 and specialized to two-level atoms in Sec. 5.6. In both cases one deals with two complex-valued functions – independent electric field amplitudes or probability amplitudes – whose absolute squares are measurable.