Boundary condition for the optical force density

The optical force density as a function of position and time provides fundamental information to model local and, through integration, macroscopic kinetic motion of condensed matter. Here, the boundary condition associated with the optical force density is developed and investigated using an expression stemming from the work of Einstein and Laub, and in conjunction with Maxwell's equations to describe the electromagnetic fields. Consequently, a constraint is formed that allows a unique relationship between the total force and the force density, one that is achieved by virtue of the conservation principles for physical materials and described by locally homogenized constitutive parameters. Further insight can be garnered from new experimental studies, as summarized. The mathematical steps presented form a basis for modeling various optomechanical phenomena, including optical forces in and on solid-state systems such as membranes, beams, cantilevers, and waveguides, and can be interpreted in terms of a suite of related theoretical work. This specification of the force density boundary condition is relevant for basic scientific fields including those involved with various quantum cooling issues, molecular optomechanics, photochemistry, and biophysics (including mechanotransduction). The technologies impacted encompass integrated optomechanics (silicon photonics, where new optical device concepts can be enabled), communication systems (in which optical forces could supplant electronic switching), remote control and actuation, propulsion, sensing, and navigation.