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We present an extension of the canonical coupled mode theory ofelectromagnetic waves to the case of pulses and spatio-temporal perturbationsin complex media. Unlike previous attempts to derive such a model, our approachinvolves no approximation, and does not impose any restriction on thespatio-temporal profile. Moreover, the effect of modal dispersion on modeevolution and on the coupling to other modes is fully taken into account. Thus,our approach can yield any required accuracy by retaining as many terms in theexpansion as needed. It also avoids various artifacts of previous derivationsby introducing the correct form of the solution. We then provide what is, tothe best of our knowledge, the first ever validation of the coupled modeequations with exact numerical simulations, and demonstrate the wide range ofpossibilities enabled by spatio-temporal perturbations of pulses, includingpulse shortening or broadening or more complex shaping. Our formulation isvalid across the electromagnetic spectrum, and can be applied directly also toother wave systems.

physical review. b./physical review. b

Coupled-mode theory for electromagnetic pulse propagation in dispersive  media undergoing a spatio-temporal perturbation - exact derivation, numerical  validation and peculiar wave mixing