Rational design of an integrated directional coupler for wideband operation

We consider a design procedure for directional couplers for which the coupling length is approximately wavelength-independent over a wide bandwidth. We show analytically that two coupled planar waveguides exhibit a maximum in the coupling strength, which ensures both wideband transmission and minimal device footprint. This acts as a starting point for mapping out the relevant part of phase space. This analysis is then generalized to the fully three-dimensional geometry of rib waveguides using an effective medium approximation. This forms an excellent starting point for fully numerical calculations and leads to designs with unprecedented bandwidths and compactness.