Dynamic oscillatory powers, cross sections, and energy efficiencies in coherent optical heterodyning

In a recent analysis [J. Quant. Spectrosc. Radiat. Transfer250, 106994 (2020)JQSRAE0022-407310.1016/j.jqsrt.2020.106994], the emergence of a dynamic oscillatory radiation force in coherent optical/electromagnetic (EM) heterodyning has been demonstrated for TM- and TE-polarized amplitude-modulated (AM) plane waves interacting with a lossless dielectric circular cylinder. A dynamic oscillatory component of the EM radiation force emerged at the beat frequency of two interfering fully correlated wave fields driven at slightly different frequencies. This work extends the scope of that analysis to examine the oscillatory behavior of energy-related physical observables from the standpoint of energy conservation applied to scattering. Partial-wave series for the oscillatory scattering, extinction and absorption powers, cross sections, and energy efficiencies are derived in cylindrical coordinates for a circular homogeneous cylinder material using the short-term time averaging (STTA) procedure and Poynting's theorem. AM plane progressive waves incident upon a lossless dielectric cylinder with arbitrary radius are considered. Numerical computations of the oscillatory scattering and extinction energy efficiencies illustrate the theory. A criterion based on computing and quantifying accurately the percentage (or relative) error between the dynamic (oscillatory) extinction and scattering efficiencies is developed and numerically evaluated. This benchmark tool provides physical validation and verification of the results from the standpoint of energy conservation. The results show that the percent (relative) error increases at the resonances of the dielectric cylinder as its refractive index increases. Far from the resonances, the oscillatory component of the STTA remains appropriate because the percent (relative) error does not exceed 0.05%, provided the beating difference frequency is much smaller than that of the primary waves. The case of an absorptive dielectric cylinder is also illustrated and discussed. The present analysis is of fundamental importance in order to validate dynamic radiation force computational results from the standpoint of energy conservation in the development, design, and optimization of oscillatory optical heterodyne tweezers and tractor beams in related applications in particle manipulation.