Using a multipole formulation to analytically understand optical micromanipulation

The power of optical micromanipulation is repeatedly demonstrated in laboratory everyday. Micro or nano particles are observed to move in intense laser fields due to optical forces. Since its conception four decades ago, optical micromanipulation has developed into a well established yet rapidly expanding experimental field. Applications can be found in very diverse areas, including physics, chemistry, and biology, or in other areas that small particles play a role. Nevertheless, its theoretical development is lagging significantly behind. Although in recent years, there appears to be more numerical simulations emerging, they do not always provide the needed insights. We believe that developing analytical models and applying them to study optical micromanipulation is of crucial importance, and this can deepen our understanding of the phenomena.

Despite a few pieces of excellent work, successful cases of interpreting an experiment using analytical models are rare. To our knowledge, the only exceptions are for Rayleigh particles where one can write down the explicit expression of the optical force using only the incident field (scattered field is not needed). Nonetheless, a great majority of optical micromanipulations involves Mie particle whose size is comparable with the wavelength. Consequently, a successful analytical theory in the Mie regime is strongly sought for. This requires one to write down a corresponding analytical expression for the optical force. This is provided by a recent development, where we derived an analytical multipolar force expression up to electric octopole order. This expression is the first analytical optical force expression that goes beyond the Rayleigh regime and extends into the Mie regime. Given the incident field profile, the analytical expression allows us to evaluate the optical forces analytically without the need of solving the scattering problem.

In this proposed research, we shall analytically and numerically separate the scattering force, absorption force, and gradient force. These forces are associated with very different physical processes and their physics are also very different. Once it is done, we will apply the newly obtained formula to analyze the numerical and experimental results for the distribution of small particles under laser illumination. Finally, we shall investigate the organization of a large number of particles under intense laser illumination, where a small optically bound cluster seems to prefer a different phase compare to a large cluster.

Our work will advance the understanding of optical micromanipulation in the Mie regime, thus it may open up new possibilities and applications.