A general planar waveguide autoregressive optical filter

A general architecture for an autoregressive (AR) planar waveguide optical filter is demonstrated for the first time, Its advantages are a flatter passband, sharper rolloff and better rejection in the stopband compared to finite impulse response (FIR) filters with the same number of stages. The architecture can be extended to an arbitrary number of stages. A modified Levinson algorithm is derived for filter synthesis and analysis which includes waveguide loss and phase errors between stages, The filter analysis algorithm allows the filter's coupling ratios and phase errors for each stage to be determined from the filter's spectral response, When combined with a postfabrication tuning process, this analysis method provides feedback for optimizing the response. Autoregressive lattice filters mere designed and fabricated using Ge-doped silica waveguides. Measurements are reported which demonstrate the synthesis and analysis algorithms. The impact of fabrication tolerances on filter synthesis and of measurement uncertainties on filter analysis are investigated.