Bending of a planar lightwave circuit 2 × 2 coupler to desensitize it to wavelength, polarization, and fabrication changes

We present a planar lightwave circuit curved 2 × 2 coupler. Its splitting ratio has a low sensitivity to wavelength, polarization, and fabrication yet is low loss and compact. We present simple formulae for its design. We demonstrate a 50/50 version in silica-on-silicon waveguides. Finally, we discuss an uncertainty principle for general 2 x 2 couplers.