Optical force calculations in arbitrary beams by use of the vector addition theorem

Abstract

We derive and apply formulas that employ the vector-wave addition theorem and rotation matrices for quantitative calculations of both radial and axial optical forces exerted on particles trapped in arbitrarily shaped tweezer beams. For the tightly focused beams encountered in optical tweezers, we shall highlight the importance of formulating the optical forces and beam symmetries in terms of the irradiance and total beam power. A major interest of the addition theorem treatment of optical forces is that it opens up the possibility of modeling a wide variety of beam shapes while automatically ensuring that the beams satisfy the Maxwell equations. In some of the first numerical applications of our method, we shall illustrate that resonance effects play an important role in the axial trapping position of particles comparable in size with the wavelength of the trapping beam.