The optical extinction theorem due to P. P. Ewald, C. W. Oseen and C. G. Darwin is used completely to describe the action of a dielectric slab as a Fabry-Perot interferometer. The analysis is very comparable to that given by Born and Wolf. It is then shown that by generalising the optical extinction theorem to the nonlinear regime essentially the same Fabry-Perot cavity action is regained but in this case the refractive index and hence the cavity tuning depends on the input intensity. This way a multistable output/input relation is derived. It is shown further how the extinction theorem will also handle the problem of 'standing waves' in the cavity. The possibility of optical turbulence in a Fabry-Perot cavity is briefly mentioned.
R. K. Bullough,
S. S. Hassan,
"Optical Extinction Theorem In The Nonlinear Theory Of Optical Multistability", Proc. SPIE 0369, Max Born Centenary Conf, (16 June 1983); doi: 10.1117/12.934377; https://doi.org/10.1117/12.934377