Universal coupled-mode theory formulation of quasi-normal modes in a 1D photonic crystal

In terms of coupled-mode theory, only two real-valued normalized parameters are needed for describing the spectral properties of any 1D photonic crystal of finite size made of lossless materials: detuning ( δL ) with respect to the Bragg condition and coupling strength ( κL ). As far as its quasi-normal mode (QNM) spectrum is concerned, the usual “complex frequency” concept can be replaced by an effective “complex detuning” ( δL + i αL ), thus establishing a formal connection with the modal cartography, in the ( κL , αL ) plane, of purely index-coupled distributed-feedback lasers of normalized gain αL .