Pushing and Pulling Ponderomotive Forces in Wavepackets and Beat Waves

TL;DR

The paper investigates how ponderomotive forces govern the time-averaged motion of small particles in 1D propagating wave packets, including forward and backward phase/group-velocity configurations. By applying perturbative averaging to simple and composite particles (dumbbell, permanent dipole, induced dipole) and analyzing beat-wave fields, it derives explicit expressions for the ponderomotive force and identifies regimes of pushing, pulling, and trapping. It demonstrates a conserved energy-momentum relation $\mathcal{P}/\mathcal{W}=s$ for composite particles and shows how beat waves can realize controlled transport, including backward-pulling scenarios and a super-wavepacket approach for adiabatic manipulation. The results offer design principles for optical/acoustic tractor beams, particle sorting, and dynamic transport using pulsed wavefields, with potential applications across nano- to micro-scale particle manipulation.

Abstract

We consider ponderomotive forces acting on small particles in propagating wave packets (pulses). Specifically, we analyze simple point particles as well as composite dipole and dumbbell particles in the fields of forward-propagating (parallel phase and group velocities) and backward-propagating (antiparallel phase and group velocities) wave packets. Depending on the characteristics of the wave packet, particles may be pushed away from the wave source or pulled toward it. We also examine particle dynamics in the field of a beat wave generated by two forward-propagating waves with slightly different frequencies. Such a beat wave can emulate a periodic sequence of either forward- or backward-propagating pulses. In particular, this provides a simple mechanism for realizing pulling forces as employed in optical and acoustic `tractor beams'.

Figures (10)

• Figure 1: Longitudinal shift of the particle under the action of the pulses with different relations $\eta_g= v_g/v_{\rm ph}$ between the wave phase, $v_{\rm ph}$, and group, $v_g$, velocities. Thin oscillating lines -- solution of Eq. (\ref{['eq2']}), thick smooth lines -- solution of Eq. (\ref{['eq4']}). (a)-- the phase and group velocities are co-directed, $s=1$. (b)-- the phase and group velocities are anti-parallel, $s=-1$.
• Figure 2: Composite particle. Two sub-particles of: (a) -- equal (dumbbell, $\sigma=1$), (b) -- opposite (dipole, $\sigma=-1$) "charges" are connected by the massless rod of length $d$. (c) -- induced dipole (polarizable) particle, whose dipole moment (the rod length) is proportional to the applied field.
• Figure 3: Evolution of the dumbbell center of mass (a), the rotation angle (b), and frequency $\nu=d\varphi/d\tau$ under the action of the backward wave ($s=-1$) pulse. Parameters of the pulse are: $a_0=0.05$, $\eta_g=0.75$. The dumbbell rod length $d=0.1$. Gray lines -- solutions of complete equation Eq. (\ref{['eq_cm']}) and (\ref{['angle']}); red lines -- solutions of time-averaged equations Eq. (\ref{['eq4']}) and (\ref{['eq_phi']}); shaded area -- pulse shape. Time is normalized to the pulse duration $\tau_p=\theta_0/\eta_g$.
• Figure 4: The angular oscillations of 50 dipoles, whose initial rotation angles $\varphi(0)$ are randomly distributed over the interval $(0,\pi)$. (a) -- $a_0=0.002$; (b) -- $a_0=0.02$; (c) -- $a_0=0.03$. The oscillation frequency increases with increased wave amplitude, while the oscillation amplitude remains practically unchanged.
• Figure 5: The relation between the energy and the momentum of composite particles after the pulse passage. Open circles, open squares, and stars mark results related to the parameter $\eta_g$ values 0.5, 1.0, and 2.0, respectively.