Radiation force and torque on an elliptical cylinder illuminated by a TE-polarized non-paraxial focused Gaussian light sheet with arbitrary incidence.

Abstract

Predicting and computing the optical radiation force and torque experienced by an elliptical cylinder illuminated by a structured finite light-sheet beam in two dimensions (2D) remains a challenge from the standpoint of light-matter interactions in electromagnetic (EM) optics, tweezers, laser trapping, and scattering theory. In this work, the partial-wave series expansion method in cylindrical coordinates (which utilizes standard Bessel and Hankel wave functions) is proposed, verified, and validated. Exact expressions for the longitudinal and transverse radiation force components (per length) as well as the axial radiation torque component (per length) are derived analytically without any approximations. The example of a TE-polarized non-paraxial focused Gaussian light sheet illuminating a perfect electrically conducting (PEC) elliptical cylinder is considered. The scattering coefficients of the elliptical cylinder are determined by imposing the Neumann boundary condition and numerically solving a linear system of equations by matrix inversion. The structural functions are determined using a single numerical angular integration procedure to enforce the orthogonality and thus validity of the solution, making the proposed method semi-analytical. Calculations are performed for the non-dimensional longitudinal and transverse radiation force efficiencies (or functions) as well as the axial radiation torque efficiency. Emphases are given to varying the ellipticity of the cylindrical particle, its non-dimensional size, the non-paraxial beam waist (i.e., focusing), and the angle of incidence in the polar plane. Suitable convergence plots confirm the validity of the partial-wave series method to evaluate accurately the radiation force and torque with no limitation to a particular frequency range or particle size. The results are mostly relevant in understanding the fundamentals of the optical/EM radiation force and torque theories for structured focused light sheets and related applications dealing with the interactions of EM waves with elongated tubular particles with elliptical surfaces in particle manipulation and other areas. The analogy with the acoustical counterpart is also noted, which shows the universal character of the radiation force and torque phenomena.