  We demonstrate photophoretic force-based optical trapping of multiple
absorbing particles in air by loosely focusing a Gaussian beam with a series of
convex lenses of different focal lengths, and investigate the dependence of the
number of trapped particles and their sizes on the focal length. We observe the
formation of particle chains at a particular focal length, and measure the
dynamic range of optical trapping for each lens system. We then develop a
numerical simulation to explain the observed dynamic range of trapping by
estimating the temperature distribution across a particle surface, and
determining the photophoretic force. Our simulation results are in reasonable
agreement with experimental results. Interestingly, we also observe that the
average size of trapped particles reduces as we increase the lens focal
lengths, which suggests that intensity gradients may somehow be involved in the
mechanism of photophoretic trapping.
