  Recent experimental developments showed that the use of the radiation
pressure, induced by a continuous laser wave, to control fluid-fluid interface
deformations at the microscale, represents a very promising alternative to
electric or magnetic actuation. In this article, we solve numerically the
dynamics and steady state of the fluid interface under the effects of buoyancy,
capillarity, optical radiation pressure and viscous stress. A precise
quantitative validation is shown by comparison with experimental data. New
results due to the nonlinear dependence of the optical pressure on the angle of
incidence are presented, showing different morphologies of the deformed
interface going from needle-like to finger-like shapes, depending on the
refractive index contrast. In the transient regime, we show that the viscosity
ratio influences the time taken for the deformation to reach steady state.
