Energy Redistribution Signatures in Transmission Microscopy of Rayleigh- and Mie-particles

The transmission characteristics of a spherical (possibly multilayered) particle of arbitrary size under focused illumination are discussed within the generalized Lorenz-Mie theory. Expressions generalizing the total extinction and scattering cross-sections to their fractional counterparts are presented which allow for a convenient modeling of transmission signals, both on-axis and off-axis. The strong dependence of the signal on the collection angle and the complex polarizability are readily included in this minimal, yet accurate model. The precise signature of the energy redistribution and absorption are found for particles of arbitrary complex-valued polarizability. For perfect dielectrics, a transition from sensitive extinction to insensitive scattering signals is observed and quantified for apertures including angles larger than twice the beam's angle of divergence. Implications for positioning, temperature control, spectroscopy and optimized extinction measurements are discussed.
Comment: 15 pages, 9 figures