Collisionless Boltzmann equation with an external periodic traveling force: Analytical solution and application to molecular optics

We present an analytical solution to the collisionless Boltzmann equation for describing the distribution function of molecular ensembles subject to an external periodic traveling force of pulsed optical fields. We apply our solution to study a pulsed standing wave mirror for neutral molecules, recently proposed [P. Ryytty et al., Phys. Rev. Lett. 84, 5074 (2000)]. Using our analytical solution we study the effects of the anharmonicity of optical potential on the reflectivity of the molecular mirror and the corresponding optimal pulse duration. We demonstrate that the reflectivity of the molecular mirror can be significantly improved by optimizing the pulse duration of the external optical fields when taking into account the anharmonicity of molecular motion.