Optical extinction theorem theory of optical multi-stability bifurcations and turbulence in the Fabry-Perot interferometer

Abstract

We have reported two different aspects of this work already [1,2]. Nevertheless as the point of view is unconventional we review it here strictly within the context of the theory of optical bistability and optical multistability. We are concerned to connect the envelope Maxwel1-Bloch equations with optical bistability (multistability) in a Fabry-Perot (FP) cavity in a rigorous and potentially quantitative way. One problem in this connection is an adequate statement about standing waves. We present methods which derive the standing wave equations of motion completely as a part of a comprehensive non-linear refractive index theory of multistabi1ity inside the FP cavity. The theory is a c-number one — but a comparable quantum theory seems possible. A key feature of the argument is generalisation of the famous 'optical extinction theorem' [1,2,3] to this non-linear regime. In practice it means we do not invoke any boundary conditions at the surfaces of the FP cavity — only conditions at infinity — and this offers advantages for the quantitative description as we show.