Kramers-Kronig self-phasing effect in passive beam combining resonators

Passive phase adjustment via Kramers-Kronig (K-K) phase in coherent beam combining is reviewed and assessed. While recent experiments and modeling show that K-K does not improve the average output power when it is the only passive phasing mechanism in a resonator, K-K does improve the combining efficiency in the presence of other effects such as wavelength tuning, Kerr nonlinearity, and regenerative phase. For a two-laser array, an improvement in output power can be achieved by K-K alone if the constant of proportionality α between the gain and the K-K phase is very large (e.g., α = 100 rad/Neper), but this is unlikely to be practical in available materials, and does not appear to scale with array size.