Measurements of Beam Shape Coefficients in Generalized Lorenz‐Mie Theory and the Density‐Matrix Approach. Part 1: Measurements

Abstract

Up to now, beam shape coefficients, gn or gnm, encoding an illuminating beam in generalized Lorenz‐Mie theory have been derived from a priori theoretical electromagnetic descriptions. It is shown that, from intensity measurements in the laboratory, one can measure so‐called density matrices associated with the beam shape coefficients. In the case of axisymmetric beams, when the beam is encoded by a set of special beam shape coefficients, gn, one has to consider one matrix, Inm. In the general case, i.e. when the beam is encoded by a double set of coefficients, gn,TMm, gn,TEn, one can measure three 4D matrices, Mnpmq, Enpmq, Cnpmq. Measuring such matrices from an actual beam in a laboratory and using them in the density matrix approach to the generalized Lorenz‐Mie theory would allow a better characterization of the scattering phenomena occurring when a scatter center is illuminated by an arbitrary‐shaped beam, therefore opening up new opportunities for refined particle characterization.