Impulse response of grating-coupled waveguide filters by optical path integration in the time domain

Optical path integration in the time domain is presented as a method of finding the impulse response of dispersive, multiple-scattering systems. Using the particular example of a grating-coupled waveguide filter, we first show how a perturbation solution may be found to the inverse Fourier transform of the governing coupled-mode equations. An interpretation of the successive terms in the solution is then given in terms of path integrals. Finally, we show how analytic approximations to the published (but so far unexplained) impulse responses of such devices are obtained.