Vector coupled-mode theory of dielectric waveguides

A consistent derivation of a system of vector coupled-mode (VCM) equations for parallel dielectric waveguides is presented and compared with earlier versions of the improved coupled-mode theory (ICMT). As a validity test, it is shown that the effectively scalar transverse electric and transverse magnetic (TM) coupled-mode (CM) equations are direct limits of our full VCM formulation. In particular, our formulation does not lead to the fundamental error found with earlier coupled-mode theories (CMTs) in a case of TM fields. Functional equations of our VCMT are consistent with Maxwell´s equations and lead to higher precision. They can be applied to complicated arrays of strongly coupled parallel dielectric waveguides with true vectorial behavior.