Generic formulation of a generalized Lorenz-Mie theory for pulsed laser illumination

Abstract

During the two last decades, a vigorous effort has been devoted to the study of interactions between arbitrary shaped beams (for continuous waves) and particles. When the particle under study allows one to solve the scattering problem by relying on the separability of variables, we say that the associated theory is a generalized Lorenz-Mie theory (GLMT). At the present time, GLMTs are available for the following kinds of particles: homogeneous spheres, multilayered spheres, ellipsoids, infinitely long cylinders (with circular or elliptical cross-sections), spheres with one arbitrarily located spherical inclusion, and aggregates. Such theories are relevant to the field of optical particle characterization in two-phase flows (phase-Doppler systems, rainbow refractometry, shadow Doppler techniques, for instance).

The aforementioned GLMTs are extensions of simpler theories when particles are illuminated by continuous plane waves. Another line of extension is derived by considering the case of illumination by pulses (single pulses or train of pulses), viewed as continuous arbitrary shaped beams modulated by a pulse envelope.

Nowadays, pulsed laser beams have become of common use, with a growing interest for the generation and applications of femtosecond pulses. In particular, pulsed lasers may activate many interesting nonlinear phenomena in microcavities, such as: stimulated Raman scattering, stimulated Brillouin scattering, third-order sum generation or lasing. They open the way for new optical particle characterization techniques, for instance: measurements of chemical species concentration in droplets.

It is therefore desirable to possess a GLMT for the case of particles illuminated by laser pulses, with arbitrary spatial supports. Such a GLMT will be presented in this paper. This GLMT is said to be generic. The word “generic” means that the theory is presented under a form allowing one to consider arbitrary scattering particles.