Simulation of emission frequencies from angle-dependent partial frequency redistributions

Simple and efficient algorithms that will generate an emission frequency from an 'angle-dependent' partial frequency redistribution (PFR) are derived by applying basic probability rules. A general formula is developed from an arbitrary redistribution, and explicit formulas are then obtained for three angle-dependent PFR funtions: pure Doppler, Doppler with natural broadening, and collision damping with complete redistribution in the atom's rest frame. Both isotropic and dipole phase functions are considered for each case. It is found that an 'angle-dependent' redistribution is actually simpler to simulate than an 'angle-averaged' redistribution. In order to facilitate Monte Carlo simulation using the angle-dependent algorithms, angle transformations are developed to relate the incoming and outgoing photon paths with respect to a set of fixed coordinates. It is noted that the same algorithms can also be employed to simulate frequencies for 'angle-averaged' PFRs.