Toward steering a jet of particles into an x-ray beam with optically induced forces

Optical trapping of light-absorbing particles in a gaseous environment is governed by a laser-induced photophoretic force, which can be orders of magnitude stronger than the force of radiation pressure induced by the same light intensity. In spite of many experimental studies, the exact theoretical background underlying the photophoretic force and the prediction of its influence on the particle motion is still in its infancy. Here, we report the results of a quantitative analysis of the photophoretic force and the stiffness of trapping achieved by levitating graphite and carbon-coated glass shells of calibrated sizes in an upright diverging hollow-core vortex beam, which we refer to as an 'optical funnel'. The measurements of forces were conducted in air at various gas pressures in the range from 5 mbar to 2 bar. The results of these measurements lay the foundation for developing a touch-free optical system for precisely positioning sub-micrometer bioparticles at the focal spot of an x-ray free electron laser, which would significantly enhance the efficiency of studying nanoscale morphology of proteins and biomolecules in femtosecond coherent diffractive imaging experiments.