Generalization of the optical theorem for monochromatic electromagnetic beams of arbitrary wavefront in cylindrical coordinates

- The optical theorem is generalized for the case of beams in cylindrical coordinates.
- Expressions for the extinction, absorption and scattering cross-sections are derived.
- Further expressions are obtained based on the resonance scattering theory formalism.
- Examples for scalar plane waves and 2D quasi-Gaussian focused beams are considered.
- The case of a circular (absorptive) cylinder is chosen to illustrate the examples.

The optical theorem constitutes of the fundamental theorems in optical, acoustical, quantum, and gravitational wave scattering, which relates the extinction cross-section to the forward scattering complex amplitude function of plane waves. In this analysis, a generalized formalism is presented for beams of arbitrary character in cylindrical coordinates without restriction to the plane wave case of the angles of incidence and scattering. Based on the partial-wave series expansion method of cylindrical multipole, analytical expressions for the extinction, absorption, scattering cross-sections and efficiency factors are derived for an object of arbitrary shape. An “interference scattering” term arises in the cross-section (or efficiency), which describes the mutual interference between the diffracted or specularly reflected waves. Examples for plane waves and 2D scalar quasi-Gaussian focused beams are also considered, which illustrate the theory. The generalized optical theorem in cylindrical coordinates can be applied to evaluate the extinction efficiency from any object of arbitrary geometry placed on or off the axis of the incident beam. Applications in the context of wave scattering theory by a single particle or multiple particles would benefit from the results of the present study, in addition to other phenomena such as the radiation force and torque.