Supermodes of grating-coupled multimode waveguides and application to mode conversion between copropagating modes mediated by backward Bragg scattering

An analysis of multimode waveguides where several modes are coupled via quasiperiodic perturbations is presented. The supermodes (or eigenmodes) of the structure are derived and orthonormality considerations are discussed. In addition, a new type of mode converter between copropagating modes is proposed, where mode conversion is mediated by a backward propagating mode. Adiabatic and nonadiabatic coupling coefficients are considered and the supermode formalism is used to conveniently describe the mode of operation of the device.