  We present a novel frequency-filtering method for measuring and calculating
frequency-filtered photon-correlations. This novel method is a cavity-based
system we call the multi-mode array filter, which consists of an array of
tunable single-mode cavities that are equally spaced in frequency. By
introducing a mode-dependent phase modulation, we produce a near rectangular
frequency response, allowing us to increase the filter bandwidth -- and thus
the temporal response -- without sacrificing frequency isolation. We model the
frequency filtering using a cascaded quantum open systems approach which
completely neglects any back-action of the filter onto the source system. This
allows us to derive a closed set of operator moment equations for source and
filter system operators, thus providing an extremely efficient method to
calculate frequency-filtered first- and second-order correlation functions. We
demonstrate this novel filtering method by applying it to a resonantly driven
two-level atom. We present examples of frequency-filtered power spectra to
demonstrate the improved frequency isolation of the multi-mode array filter
over the single-mode filter. We then present results for the single-mode and
multi-mode-array filtered second-order auto- and cross-correlation functions.
These are compared against expressions derived in the secular approximation.
The improved frequency isolation of the multi-mode array filter allows us to
investigate new regimes of frequency-filtered photon correlations, such as
two-photon leapfrog processes, and the effect of vanishing bandwidth on
filtered auto-correlation functions.
