Optical trapping of airborne particles is emerging as an essential tool in applications ranging from online characterization of living cells and aerosols to particle transport and delivery. However, existing optical trapping techniques using a single laser beam can trap only transparent particles (via the radiative pressure force) or absorbing particles (via the photophoretic force), but not particles of either type-limiting the utility of trapping-enabled aerosol characterization techniques. Here, we present the first optical trapping technique capable of trapping both transparent and absorbing particles with arbitrary morphology using a single shaped laser beam. Such a general-purpose optical trapping mechanism could enable new applications such as trapping-enabled aerosol characterization with high specificity.