Spectra of Radiating Systems

Abstract

We have already noted that a possible way of measuring fluctuations of the field amplitudes is to detect the intensity of the radiation field emitted by an ensemble of atoms. More useful is the power spectrum , which is attributed to fluctuations of the field amplitudes and gives variations in the field intensity as a function of frequency. As demonstrated in the previous chapter, the calculation of the power spectrum requires the knowledge of the normally-ordered two-time correlation function of the electric field amplitudes evaluated at the position of a detector. In this chapter, we shall take a closer look at the relation of the spectrum to the correlation functions of the source variables and undertake a more detailed discussion of the calculation of the spectrum of radiation field emitted from the atoms. We shall be dealing entirely with power spectra of stationary and quasistationary fields, i.e., fields whose properties are independent of the origin of time. Under this condition, all the two-time correlation functions will involve components that depend on the time arguments only through their difference. Also, we shall follow the definition (1.70) of the power spectrum, which employs a simplified physical model of the detection process. In this model, the radiation field is measured with an ideal Fabry−Perot interferometer of bandwidth $\varGamma \rightarrow 0$, and its spectral range much larger than the width of the frequency spectrum of the measured field. The results presented here, however, can be easily extended to include finite bandwidth effects of the interferometer.