Discrete superposition of equal-frequency Bessel beams: Time-average forces exerted on dielectric and magnetodielectric Rayleigh particles

We demonstrate the ability of scalar frozen waves - wave fields constructed from suitable superpositions of equal-frequency and arbitrary-order Bessel beams - to trap and manipulate both low- and high-index dielectric and magnetodielectric Rayleigh particles. Explicit analytical expressions are derived for the optical forces based on a dipole approximation and taking into account magnetic polarizabilities. Two examples of frozen waves are numerically investigated, revealing that it is indeed possible to optically trap such particles at multiple transverse planes and at specific radial positions. Our results suggest that such optical wave fields may serve as laser beams in optical trapping, atom guiding, optical bistouries and so on.