Generalization of the optical theorem for light scattering from a particle at a planar interface.

Journal of the Optical Society of America. A, Optics, image science, and vision

PubMedID: 24323012

Small A, Fung J, Manoharan VN. Generalization of the optical theorem for light scattering from a particle at a planar interface. J Opt Soc Am A Opt Image Sci Vis. 2013;30(12):2519-25.
The optical theorem provides a powerful tool for calculating the extinction cross section of a particle from a solution to Maxwell's equations, relating the cross section to the scattering amplitude in the forward direction. The theorem has been generalized by a number of other workers to consider a particle near an interface between media with different refractive indices. Here we present a derivation of the generalized optical theorem that is valid for a particle embedded in the interface, as well as an incident beam undergoing total internal reflection. We also obtain an additional useful physical result: we show that the far-field scattered field must be zero in the direction parallel to the interface. Our results enable the verification of computations of scattering by particles embedded in interfaces and may be relevant to experiments on colloidal particles at fluid interfaces.