Simultaneous measurement of mass and rotation of trapped absorbing particles in air

We trap absorbing micro-particles in air by photophoretic forces generated using a single loosely focused Gaussian trapping beam. We measure a component of the radial Brownian motion of a trapped particle cluster and determine the power spectral density, mean squared displacement, and normalized position and velocity autocorrelation functions in order to characterize the photophoretic body force in a quantitative fashion for the first time. The trapped particles also undergo spontaneous rotation due to the action of this force. This is evident from the spectral density that displays clear peaks at the rotation and the particles' inertial resonance frequencies. We fit the spectral density to the well-known analytical function derived from the Langevin equation, measure the resonance and rotation frequencies and determine values for particle mass that we verify at different trapping laser powers with reasonable accuracy.