Refractive Fabry-Perot bistability with linear absorption: Theory of operation and cavity optimization

We present a theory of optical bistability for a Fabry-Perot cavity containing a medium with nonlinear refraction but linear absorption with only plane-wave and slowly varying envelope approximations. An analytic expression for the critical intensity I
c
for the onset of bistability is derived and used to compare cavity designs. It is shown that 1) the important material parameter for minimum I
c
is the ratio
n_{2}/\alpha 2
) the limit to I
c
is set by limitations on finesse due to inhomogeneities rather than the absorption itself, and 3) the cavity design which gives lowest I
c
for a given finesse is that for which the mirror transmissivity equals the absorption per pass; at high finesse this design leads to a total peak cavity transmission of 1/4 when mirror reflectivities are equal.