Coupling coefficients of coupled laser cavities

We discuss certain properties of the coupling coefficients for a specific model consisting of two coupled resonant cavities separated by a lossy coupling gap. The coupling coefficients are here defined in the framework of time-dependent coupled-cavity theory-not as end-fire power coupling between traveling waves of two adjacent waveguides. In particular, we explore the validity of a heuristic formula for the coupling coefficients proposed in an earlier publication. It turns out that, in this example, the heuristic formula is directly applicable only if the coupling gap is lossless and off-resonance, but it becomes inapplicable if the lossless gap approaches resonance. The heuristic formula remains useful, but requires a correction if the coupling gap is lossy. The phase angle of the complex coupling coefficient is found to be linearly dependent on the width of the coupling gap, assuming the value 0 (to within multiples of 2π) for an off-resonant gap and the value of for a resonant gap. It is not the purpose of this letter to explore properties of c³lasers or to specify their optimum operating conditions. Only the validity of the approximate coupling function is to be investigated.