Non-conservative Optical Forces Research Articles

One-way optomechanical interaction between nanoparticles

Within a closed system, physical interactions are reciprocal. However, the effective interaction between two entities of an open system may not obey reciprocity. Here, we describe a non-reciprocal interaction between nanoparticles which is one-way, almost insensitive to the interparticle distance, and scalable to many particles. The interaction we propose is based on the non-conservative optical forces between two nanoparticles with highly directional scattering patterns. However, we elucidate that scattering patterns can in general be very misleading about the interparticle forces. We introduce zeroth- and first-order non-reciprocity factors to precisely quantify the merits of any optomechanical interaction between nanoparticles. Our proposed one-way interaction could constitute an important step in the realization of mesoscopic heat pumps and refrigerators, the study of non-equilibrium systems, and the simulation of non-Hermitian quantum models.

Tailoring the gradient and scattering forces for longitudinal sorting of generic-size chiral particles.

Based on the concepts of conservative and non-conservative optical forces (COF and NCOF), we analyze the physical mechanism of longitudinal chirality sorting along the direction of light propagation in some simple optical fields. It is demonstrated, both numerically and analytically for particle of arbitrary size, that the sorting relies solely on the NCOF, which switches its direction when particle chirality is reversed. For particles larger than half of the optical wavelength λ, the NCOF far surpasses its counterpart COF, enabling the longitudinal chirality sorting. When the particle is much smaller than λ, however, the COF outweighs the NCOF, destroying the sorting mechanism. A scenario is thus proposed that totally eliminates the COF while leaving the sorting NCOF unchanged, extending the applicability of longitudinal chirality sorting to small particles.

Coherent oscillations of a levitated birefringent microsphere in vacuum driven by nonconservative rotation-translation coupling.

We demonstrate an effect whereby stochastic, thermal fluctuations combine with nonconservative optical forces to break detailed balance and produce increasingly coherent, apparently deterministic motion for a vacuum-trapped particle. The particle is birefringent and held in a linearly polarized Gaussian optical trap. It undergoes oscillations that grow rapidly in amplitude as the air pressure is reduced, seemingly in contradiction to the equipartition of energy. This behavior is reproduced in direct simulations and captured in a simplified analytical model, showing that the underlying mechanism involves nonsymmetric coupling between rotational and translational degrees of freedom. When parametrically driven, these self-sustained oscillators exhibit an ultranarrow linewidth of 2.2 μHz and an ultrahigh mechanical quality factor in excess of 2 × 108 at room temperature. Last, nonequilibrium motion is seen to be a generic feature of optical vacuum traps, arising for any system with symmetry lower than that of a perfect isotropic microsphere in a Gaussian trap.

The zoo of nonconservative optical forces

Optical forces are usually described as conservative ones originating from intensity gradients in optical tweezers. However, the fundamental optical action on matter is nonconservative. In contrast to gradient forces, the spectrum of action of nonconservative forces is much wider: they can propel, pull, rotate objects or move objects along complicated trajectories. Different manifestations of nonconservative optical forces will be reviewed and their dependence on the specific spatial properties of optical fields will be discussed. New developments relevant to the nonconservative optical forces such as negative forces (tractor beams) and transversal forces will also be discussed.

Negative Nonconservative Forces: Optical “Tractor Beams” for Arbitrary Objects

Based on the conservation of linear momentum on scattering from arbitrary objects, we demonstrate the generation of nonconservative optical forces that act in a direction opposite to the propagation of the incident beam. The concept can be applied to tailor the force fields produced on nonabsorbing bodies regardless of their sizes and shapes.

Response theory of optical forces in two-port photonics systems: a simplified framework for examining conservative and non-conservative forces

We extend the response theory of optical forces to general electromagnetic systems which can be treated as multi-port systems with multiple mechanical degrees of freedom. We demonstrate a fundamental link between the scattering properties of an optical system to its ability to produce conservative or non-conservative optical forces. Through the exploration of two nontrivial two-port systems, including an analytical Fabry-Perot interferometer and a more complex particle-in-a-waveguide structure, we show perfect agreement between the response theory and numerical first-principle calculations. We show that new insights into the origins of optical forces from the response theory provide clear means of understanding conservative and non-conservative forces in a regime where traditional gradient force picture fails.

Reverse optical forces in negative index dielectric waveguide arrays

Nonconservative optical forces acting on dipolar particles are considered in longitudinally invariant optical fields. We demonstrate that the orientation of these forces is strictly dictated by the propagation vector associated with such field configurations. As a direct consequence of this, it is impossible to achieve a reversal of optical forces in homogeneous media. We show instead that translation invariant optical tractor fields can in fact be generated in the negative index environment produced in a special class of fully dielectric waveguide arrays.

Brownian vortexes

Mechanical equilibrium at zero temperature does not necessarily imply thermodynamic equilibrium at finite temperature for a particle confined by a static but nonconservative force field. Instead, the diffusing particle can enter into a steady state characterized by toroidal circulation in the probability flux, which we call a Brownian vortex. The circulatory bias in the particle's thermally driven trajectory is not simply a deterministic response to the solenoidal component of the force but rather reflects interplay between advection and diffusion in which thermal fluctuations extract work from the nonconservative force field. As an example of this previously unrecognized class of stochastic heat engines, we consider a colloidal sphere diffusing in a conventional optical tweezer. We demonstrate both theoretically and experimentally that nonconservative optical forces bias the particle's fluctuations into toroidal vortexes whose circulation can reverse direction with temperature or laser power.

Influence of Nonconservative Optical Forces on the Dynamics of Optically Trapped Colloidal Spheres: The Fountain of Probability

We demonstrate both experimentally and theoretically that a colloidal sphere trapped in a static optical tweezer does not come to equilibrium, but rather reaches a steady state in which its probability flux traces out a toroidal vortex. This nonequilibrium behavior can be ascribed to a subtle bias of thermal fluctuations by nonconservative optical forces. The circulating sphere therefore acts as a Brownian motor. We briefly discuss ramifications of this effect for studies in which optical tweezers have been treated as potential energy wells.

An efficient method for the creation of tunable optical line traps via control of gradient and scattering forces

Interparticle interaction energies and other useful physical characteristics can be extracted from the statistical properties of the motion of particles confined by an optical line trap. In practice, however, the potential energy landscape, U(x), imposed by the line provides an extra, and in general unknown, influence on particle dynamics. We describe a new class of line traps in which both the optical gradient and scattering forces acting on a trapped particle are designed to be linear functions of the line coordinate and in which their magnitude can be counterbalanced to yield a flat U(x). These traps are formed using approximate solutions to general relations concerning non-conservative optical forces that have been the subject of recent investigations [Y. Roichman, B. Sun, Y. Roichman, J. Amato-Grill, and D. G. Grier, Phys. Rev. Lett. 100, 013602-4 (2008).]. We implement the lines using holographic optical trapping and measure the forces acting on silica microspheres, demonstrating the tunability of the confining potential energy landscape. Furthermore, we show that our approach efficiently directs available laser power to the trap, in contrast to other methods.