text: The study of correlation functions is critical to the study of quantum optics as the Fourier transform of the correlation function is the energy spectral density. Thus the two-time correlation function is a useful tool in the calculation of the energy spectrum for a given system. We take the parameter  to be the difference between the two times in which the function is calculated. While correlation functions can more easily be described using limits of the strength of the field and limits placed on the time of the system, they can be found more generally as well. For resonance fluorescence, the most important correlation functions are
  where
  Two-time correlation functions are generally shown to be independent of , and instead rely on  as . These functions can be used to find the spectral density  by computing the transform
  where K is a constant. The spectral density can be viewed as the rate of photon emission of photons of frequency  at the given time , which is useful in determining the power output of a system at a given time.
  The correlation function associated with the spectral density of resonance fluorescence is reliant on the electric field. Thus once the constant K has been determined, the result is equivalent to
  This is related to the intensity by 
  In the weak field limit when  the power spectrum can be determined to be
  In the strong field limit, the power spectrum is slight more complicated and found to be
  From these two functions it is easy to see that in the weak field limit a single peak appears at  in the spectral density due to the delta function, while in the strong field limit a Mollow triplet forms  with sideband peaks at , and appropriate peak width of  for the central peak and  for the sideband peaks.