Quantitative study of conservative gradient force and non-conservative scattering force exerted on a spherical particle in optical tweezers

We rigorously calculate the conservative gradient force (GF) and the non-conservative scattering force (SF) associated with the optical tweezers (the single beam optical trap). A wide range of parameters are considered, with particle size ranging from the Rayleigh to Mie regime (radius ∼3 µm), dielectric constant ranging from metallic (large and negative) to high dielectrics (large and positive), numerical aperture (NA) ranging from 0.5 to 1.33, and different polarizations. The trap depth associated with GF can reach 123 and 168 kT per mW for a 0.5 µm-radius polystyrene particle illuminated by a 1064 nm Gaussian beam with NA = 0.9 and 1.3, respectively. This indicates that unless at a low beam power or with a small NA, the Brownian fluctuations do not play a role in the stability. The transverse GF orthogonal to beam propagation always dominates over the transverse SF. While the longitudinal SF can be larger than the longitudinal GF when the scattering is strong, the NA is small, or when absorption is present, optical trapping under these conditions is difficult. Generally speaking, absorption reduces GF and enhances SF, while increasing a dielectric constant enhances GF slightly but boosts SF significantly owing to stronger scattering. These results verify previous experimental observations and explain why optical tweezers are so robust across such a wide range of conditions. Our quantitative calculations will also provide a guide to future studies.