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.
© 2013 Optical Society of America
Original Manuscript: August 14, 2013
Revised Manuscript: October 17, 2013
Manuscript Accepted: October 17, 2013
Published: November 12, 2013
Vol. 9, Iss. 2 Virtual Journal for Biomedical Optics
Alex Small, Jerome Fung, and Vinothan N. Manoharan, "Generalization of the optical theorem for light scattering from a particle at a planar interface," J. Opt. Soc. Am. A 30, 2519-2525 (2013)