Optical Trapping and the Photorefractive Effect

Abstract

The photorefractive rate equations[1], now 30 years old, have been integral in supporting the growth of the field of photorefractive nonlinear optics. They have been used to model the strength and response time of the phase gratings responsible for nonlinear effects such as optical phase conjugation, image processing, and spatial solitons. Over time, several researchers in the photorefractive field have begun to display an interest in another optically mediated effect: optical tweezers. It is maybe not such a coincidence that Arthur Ashkin, one of the founders of the field of photorefractive nonlinear optics [2] also helped to found the field of optical tweezers [3]. Both of these effects are mediated by photoinduced motion of small particles: the first by charge migration induced by spatial gradients in the optical intensity, the second by forces induced by spatial gradients of optical intensity. Although optical tweezers is usually thought of in terms of manipulation of microscopic particles such as silica or polystyrene microspheres and biological microorganisms and cells, it can also be thought of as a nonlinear optical effect. Many of the methods of measuring forces on trapped particles rely on measurement of the distance of the trapped particle from the axis of the trapping beam. Commonly, this is done by using a split photodiode to monitor the deviation of the trapping light after passage through the trapped microsphere acting as a ball lens forced off the optical axis. It can be thought of as a case of light interacting with light via a medium with a nonlinear optical effect. Where does this nonlinearity come from? After all, neither the trapped microsphere, nor the surrounding fluid medium have any appreciable nonlinearity by themselves. It is the combination of the two components that results in the nonlinearity. The sphere reacts nonlinearly to light in the fluid medium. In a sense, this is closely related to the electrostrictive effect responsible for Brillouin scattering. In that case, electrostrictive forces resulting from a spatially varying optical field compresses the medium into regions of high intensity. If the spatial field variation is due to an optical interference pattern from two intersecting laser beams, the result is a phase grating that constitutes a real time hologram coupling one beam into the other. It is the origin of Brillouin enhanced four wave mixing and stimulated Brillouin scattering.