Bandwidth of forward and backward coupling directional couplers

This paper deals with the filter properties of directional couplers. Formulas are derived for the bandwidth in wavelength units of couplers consisting of two waveguides that exchange their power either in the direction of the incident wave (forward couplers) or in the opposite direction (backward couplers). Backward couplers require the presence of a diffraction grating on one or both waveguides but they can achieve very much smaller bandwidth than forward couplers and hence are useful for constructing narrow-band optical wavelength filters.