Revisiting Temporal Coupled-Mode Theory in Ultrafast Physics: An Ab-initio Approach

We employ an ab initio Maxwellian approach using quasinormal-mode theory to derive an "exact" Maxwell evolution (EME) equation for resonator dynamics. The new differential equation bears resemblance to the classical one found in coupled-mode-theory (CMT); however, it introduces novel terms embodying distinct physics, suggesting that the CMT predictions could be faulted by dedicated experiments. The new equation is anticipated to be applicable to all electromagnetic resonator geometries, and the theoretical approach we have taken can be extended to other wave physics.