Engineering optical forces in waveguides and cavities based on optical response

Abstract

We present a new treatment of optical forces, revealing that the forces in virtually all optomechanically variable systems can be computed exactly and simply from only the optical phase and amplitude response of the system. This treatment, termed the response theory of optical forces (or RTOF), provides conceptual clarity to the essential physics of optomechanical systems, which computationally intensive Maxwell stress-tensor analyses leave obscured, enabling the construction simple models with which optical forces and trapping potentials can be synthesized based on the optical response of optomechanical systems. A theory of optical forces, based on the optical response of systems, is advantageous since the phase and amplitude response of virtually any optomechanical system (involving waveguides, ring resonators or photonic crystals) can be derived, with relative ease, through well-established analytical theories. In contrast, conventional Maxwell stress tensor methods require the computation of complex 3-dimensional electromagnetic field distributions; making a theory for the synthesis of optical forces exceedingly difficult. Through numerous examples, we illustrate that the optical forces generated in complex waveguide and microcavity systems can be computed exactly through use of analytical scattering-matrix methods. When compared with Maxwell stress-tensor methods of force computation, perfect agreement is found.