The coupling of macroscopic objects via the optical near-field can generate strong attractive and repulsive forces. Here, I explore the static and dynamic optomechanical interactions that take place in a geometry consisting of a silicon nanomembrane patterned with a square-lattice photonic crystal suspended above a silicon-on-insulator substrate. This geometry supports a hybridized optical mode formed by the coupling of eigenmodes of the membrane and the silicon substrate layer. This system is capable of generating nanometer-scale deflections at low optical powers for membrane-substrate gaps of less than 200 nm due to the presence of an optical cavity created by the photonic crystal that enhances both the optical force and a force that arises from photo-thermal-mechanical properties of the system. Feedback between Brownian motion of the membrane and the optical and photo-thermal forces lead to dynamic interactions that perturb the mechanical frequency and linewidth in a process known as ``back-action.'' The static and dynamic properties of this system are responsible for optical bistability, mechanical cooling and regenerative oscillations under different initial conditions. Furthermore, solid objects separated by a small distance experience the Casimir force, which results from quantum fluctuations of the electromagnetic field (i.e. virtual photons).The Casimir force supplies a strong nonlinear perturbation to membrane motion when the membrane-substrate separation is less than 150 nm. Taken together, the unique properties of this system makes it an intriguing candidate for transduction, accelerometry, and sensing applications.
