Increased time resolution with multiphoton interference beating

I investigate a variation of Hong–Ou–Mandel interference where two interference filters with different central frequencies are placed in the two output-ports of a beam splitter. Taking photons as wavepackets in the time domain, we get a general analytic formula for the probability that N photons emerge in each output-port after interference. The probability is shown to oscillate as a cosine function modulated by a dip and the oscillation period is inversely proportional to N which indicates a better time resolution with multiphoton beating.