In 1963, then, it seemed entirely reasonable that a quantum theory of optical processes  -  light-fields, their propagation, and their interactions with sources and detectors  -  should appear under the title : On the quantum theory of optical coherence.  In essence what R. J. Glauber did in two epic papers published in March and September of 1963 was to show that if you replaced the variables in the coherence theory by suitable operators, then the various coherence functions could be associated with quantum operators and their eigenvalues and eigenfunctions.

When you do that, something very remarkable emerges from the theory.  Usually in quantum mechanics we work with operators which have real eigenvalues, and we say that the real eigenvalues constitute a catalogue of the results you could get in measurements of the corresponding variables, and then there are rules for calculating the relative probabilities of these various possible results.

Now, in quantum optics the electric field in a light-beam is represented by two sets of operators.  One of these sets is associated with the possibility of the radiation field's increasing its intensity by hw or nhw, as the result of the emission of radiation by the source.  The other set of terms is associated with the possibility of the absorption of energy from the light-beam by a detector.  The eigenvalues of this set of terms turn out not to be real numbers; they include complex functions of position and time which describe travelling waves such as satisfy Maxwell's equations.  So, the complete quantum theory of optical fields contains among the eigenvalues of the electric field operator all the classical waves that describe the phenomena of optics.  These waves are not approximations to some subtler truth : they are precise, valid solutions of correctly formulated problems in quantum optics.

Quantum optical theory developed dramatically.  Willis Lamb, the eponym of the ‘Lamb shift’, was one of those who in the 1950s demonstrated by impeccable theoretical arguments that the ‘optical maser’ (or laser) wouldn't work.  When it did, Lamb was so mortified that he devoted most of his efforts over the next 10 years to working out, in detail, why it does work, and how it works.  It's "a difficult problem in the non-equilibrium statistical mechanics of an open system" - but thanks to Lamb we probably have a better theory of the laser than we did of the thermionic valve triode oscillator!

Because quantum optics, unlike classical physical optics, deals with the interaction of light with its sources and detectors, as well as its propagation, it can treat the non-linear interactions of light with matter, so we have a theory, of non-linear optics.  The vibrational energy of the material the light is passing through can be included in the theory in a way very similar to the e-m energy of the light field so the theory could be extended to treat, e.g., parametric processes and Raman lasers.  And from the work on non-linear optics in the 1970s has come the excitement of optical bistability, and the prospect of the optical computer.