Power saturation effects in thick single-element optical limiters

Optical limiters relying on nonlinear absorption or nonlinear refraction are most effective against an incoming laser beam when the active material is thicker than one Rayleigh length. We have found that a variety of thick optical limiter configurations can be modelled by integrating the formulae for optical transmission by thin media, and that the results are exact to the first order in power or irradiance. The limiter behaviour saturates as the optical power increases. For the case of thick irradiance-dependent absorbers and an incident Gaussian beam model, we have also found that the predictions of a simple saturation formula for the optical transmittance agree well with the transmittance values computed using a numerical technique. Under certain conditions this saturation formula is also suitable for describing the transmission of nonlinear refractors, thereby providing a straight-forward technique for modelling limiters over a broad parameter range.