General treatment of optical forces and potentials in mechanically variable photonic systems.

We present an analytical formalism for the treatment of the forces and potentials induced by light in mechanically variable photonic systems (or optomechanically variable systems) consisting of linear media. Through energy and photon-number conservation, we show that knowledge of the phase and the amplitude response of an optomechanically variable system, and its dependence on the mechanical coordinate of interest, is sufficient to compute the forces produced by light. This formalism not only offers a simple analytical alternative to computationally intensive Maxwell stress-tensor methods, but also greatly simplifies the analysis of mechanically variable photonic systems driven by multiple external laser sources. Furthermore, we show, through this formalism, that a scalar optical potential can be derived in terms of the phase and amplitude response of an arbitrary optomechanically variable one-port system and in generalized optomechanically variable multi-port systems, provided that their optical response is variable through a single mechanical degree of freedom. With these simplifications, well-established theories of optical filter synthesis could be extended to allow for the synthesis of complex optical force and potential profiles, independent of the construction of the underlying device or its field distribution.