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Optics Letters

Dynamics of microparticles trapped in a perfect vortex beam

Mingzhou Chen, Michaël Mazilu, Yoshihiko Arita, Ewan M. Wright, Kishan Dholakia

Published Nov 14, 2013• 368 citations
Publisher

Abstract

We analyze microparticle dynamics within a "perfect" vortex beam. In contrast to other vortex fields, for any given integer value of the topological charge, a "perfect" vortex beam has the same annular intensity profile with fixed radius of peak intensity. For a given topological charge, the field possesses a well-defined orbital angular momentum density at each point in space, invariant with respect to azimuthal position. We experimentally create a perfect vortex and correct the field in situ, to trap and set in motion trapped microscopic particles. For a given topological charge, a single trapped particle exhibits the same local angular velocity moving in such a field independent of its azimuthal position. We also investigate particle dynamics in "perfect" vortex beams of fractional topological charge. This light field may be applied for novel studies in optical trapping of particles, atoms, and quantum gases.

DOI
10.1364/ol.38.004919

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We analyze microparticle dynamics within a "perfect" vortex beam. In contrast to other vortex fields, for any given integer value of the topological charge, a "perfect" vortex beam has the same annular intensity profile with fixed radius of peak intensity. For a given topological charge, the field possesses a well-defined orbital angular momentum density at each point in space, invariant with respect to azimuthal position. We experimentally create a perfect vortex and correct the field in situ, to trap and set in motion trapped microscopic particles. For a given topological charge, a single trapped particle exhibits the same local angular velocity moving in such a field independent of its azimuthal position. We also investigate particle dynamics in "perfect" vortex beams of fractional topological charge. This light field may be applied for novel studies in optical trapping of particles, atoms, and quantum gases.
Vortex beams with different topological charge usually have different profiles and radii of peak intensity. This introduces a degree of complexity the fair study of the nature of optical OAM (orbital angular momentum). To avoid this, we introduced a new approach by creating a perfect vortex beam using an annular illuminating beam with a fixed intensity profile on an SLM that imposes a chosen topological charge. The radial intensity profile of such an experimentally created perfect vortex beam is independent to any given integer value of its topological charge. The well-defined OAM density in such a perfect vortex beam is probed by trapping microscope particles. The rotation rate of a trapped necklace of particles is measured for both integer and non-integer topological charge. Experimental results agree with the theoretical prediction. With the flexibility of our approach, local OAM density can be corrected in situ to overcome the problem of trapping the particle in the intensity hotspots. The correction of local OAM density in the perfect vortex beam therefore enables a single trapped particle to move along the vortex ring at a constant angular velocity that is independent of the azimuthal position. Due to its particular nature, the perfect vortex beam may be applied to other studies in optical trapping of particles, atoms or quantum gases.
We demonstrate the transfer of orbital angular momentum to optically levitated microparticles in vacuum [1]. We prepare two-dimensional and three-dimensional optical potentials. In the former case the microparticle is placed within a Laguerre-Gaussian beam and orbits the annular beam profile with increasing angular velocity as the air drag coefficient is reduced. We explore the particle dynamics as a function of the topological charge of the levitating beam. Our results reveal that there is a fundamental limit to the orbital angular momentum that may be transferred to a trapped particle, dependent upon the beam parameters and inertial forces present. This effect was predicted theoretically [2] and can be understood considering the underlying dynamics arising from the link between the magnitude of the azimuthal index and the beam radius [3]. Whilst a Laguerre-Gaussian beam scales in size with azimuthal index `, recently we have created a “perfect” vortex beam whose radial intensity profile and radius are both independent of topological charge [4, 5]. As the Fourier transform of a perfect vortex yields a Bessel beam. Imaging a perfect vortex, with its subsequent propagation thus realises a complex three dimensional optical field. In this scenario we load individual silica microparticles into this field and observe their trajectories. The optical gradient and scattering forces interplay with the inertial and gravitational forces acting on the trapped particle, including the rotational degrees of freedom. As a result the trapped microparticle exhibits a complex three dimensional motion that includes a periodic orbital motion between the Bessel and the perfect vortex beam. We are able to determine the three dimensional optical potential in situ by tracking the particle. This first demonstration of trapping microparticles within a complex three dimensional optical potential in vacuum opens up new possibilities for fundamental studies of many-body dynamics, mesoscopic entanglement [6, 7], and optical binding [8, 9].
We demonstrate the transfer of orbital angular momentum (OAM) to optically levitated microparticles in vacuum. We create two-dimensional (2D) and three-dimensional (3D) optical potentials possessing OAM. In the former case the microparticle is placed within a Laguerre-Gaussian (LG) beam and orbits the annular beam profile with increasing angular velocity as the air drag coefficient is reduced. Our results reveal that there is a fundamental limit to the OAM that may be transferred to a trapped particle, dependent upon the beam parameters and inertial forces present. Whilst a LG beam scales in size with azimuthal index, recently we have created a “perfect vortex” beam whose radial intensity profile and radius are both independent of topological charge. As the Fourier transform of a “perfect vortex” yields a Bessel beam, imaging a “perfect vortex”, with its subsequent propagation thus realises a complex three-dimensional optical field. In this scenario we load individual silica microparticles into this field where the optical gradient and scattering forces interplay with the inertial and gravitational forces acting on the trapped particle. As a result the trapped microparticle exhibits a complex three-dimensional motion that includes a periodic orbital motion between the Bessel and the “perfect vortex” beam. We are able to determine the three dimensional optical potential in situ by tracking the particle. This first demonstration of trapping microparticles within a complex 3D optical potential in vacuum opens up new possibilities for fundamental studies of many-body dynamics, mesoscopic entanglement, and optical binding.
The design and implementation of a multiplexed spiral phase mask in an experimental optical tweezer setup are presented. This diffractive optical element allows the generation of multiple concentric vortex beams with independent topological charges. The generalization of the phase mask for multiple concentric vortices is also shown. The design for a phase mask of two multiplexed vortices with different topological charges is developed. We experimentally show the transfer of angular momentum to the optically trapped microparticles by enabling orbiting dynamics around the optical axis independently within each vortex. The angular velocity of the confined particles versus the optical power in the focal region is also discussed for different combinations of topological charges.
We discuss a simple method to generate a configurable annular vortex beam (AVB) with the maximum possible peak intensity, employing a phase hologram whose transmittance is the phase of a Bessel beam. Due to its maximum intensity, the AVB provides the optimal density of the orbital angular moment. Another attribute of the generated AVB is the relatively high invariance of the intensity profile when the topological charge is changed. We demonstrate the advantages and flexibility of these AVBs for optical trapping applications.