Design procedures for passive planar coupled waveguide devices

Many useful optical systems make use of coupled waveguides configured in nonplanar arrangements. This paper deals with the emulation of such systems in planar waveguide arrangements, so that otherwise nonplanar systems can be implemented as compact, integrated optics chips. As an example, design procedures are presented for a wholly planar 3×3 coupler to emulate the symmetric 3×3 fibre coupler; the first procedure is readily implemented yet holds only for weakly coupled guides, whereas the second is unwieldy but can accommodate arbitrarily strongly coupled guides. This discussion leads to general remarks about passive planar coupled waveguide devices and it is proven that, in theory, any lossless nonplanar coupled waveguide device´s behaviour can be emulated by a wholly planar coupled waveguide device. Lastly, using these ideas, implementations of planar emulations of the symmetric 4×4 and 5×5, fibre couplers are presented