Microring resonators side coupled to signal waveguides provide compact
, narrow band, and large free spectral range optical channel dropping
filters, Higher order filters with improved passband characteristics a
nd larger out-of-band signal rejection are realized through the coupli
ng of multiple rings, The analysis of these devices is approached by t
he novel method of coupling of modes in time. The response of filters
comprised of an arbitrarily large number of resonators may be written
down by inspection, as a continued fraction, This approach simplifies
both the analysis and filter synthesis aspects of these devices.