Theory of the spectrum of the quantised light field

L. P. Sieg

Alan V. Durrant

An approach to the quantum theory of light is described using absorber theory and source field theory. It is assumed that all optical fields have atomic sources, and that the so-called free field is a source field of the surrounding absorbing material of the universe. The field operators are defined to be functions of the atomic operators and act on the states of the atomic sources. The source field of a completely enclosing perfect absorber is found to be mathematically equivalent to the quantised free field of conventional theory, but the physical basis of the theory is different.

J N Elgin, G.H.C. New, J. M. Catherall

The analysis of two-photon resonant third-harmonic generation is generalised to include, in particular, the effects of imperfect index matching and two-photon tuning. Furthermore, whereas previously the authors considered only the temporal properties of the generated harmonic signal, here is spectral characteristics are also considered. The authors comment on a discrepancy between the predictions of semiclassical and quantised field formalisms. In the semiclassical analysis, it is shown that for large energy input pulses the harmonic spectrum is double peaked even near exact resonance and that this structure can be interpreted in terms of transitions between sets of doublet states of the Autler-Townes (1955) type. In a quantised field formalism, however, the picture is radically altered near exact resonance where a three-peaked spectrum is predicted.

L. P. Sieg

L. P. Sieg

Robert G. Bennett, Thomas M. Barlow, Almut Beige

The notion that the electromagnetic field is quantised is usually inferred from observations such as the photoelectric effect and the black-body spectrum. However accounts of the quantisation of this field are usually mathematically motivated and begin by introducing a vector potential, followed by the imposition of a gauge that allows the manipulation of the solutions of Maxwell's equations into a form that is amenable for the machinery of canonical quantisation. By contrast, here we quantise the electromagnetic field in a less mathematically and more physically-motivated way. Starting from a direct description of what one sees in experiments, we show that the usual expressions of the electric and magnetic field observables follow from Heisenberg's equation of motion. In our treatment, there is no need to invoke the vector potential in a specific gauge and we avoid the commonly-used notion of a fictitious cavity that applies boundary conditions to the field.