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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Micromanipulation with Bessel beams: studies of angular momentum and reconstruction

David McGloin, Veneranda G. Garces, Kishan Dholakia

Published Oct 18, 2004• 0 citations
Publisher

Abstract

Bessel beams have a number of properties that make them useful for optical manipulation. These include a central core which does not diffract over a characteristic distance, the reconstruction of the cross sectional intensity around obstacles and the ability of the beams to possess orbital angular momentum. Here we examine the utility of the Bessel beam to quantitatively examine the transfer of spin and orbital angular momentum to particle trapped away from the beam axis. We show the simultaneous transfer of orbital and spin angular momentum to an off-axis particle. We experimentally study how both the spin and orbital angular momentum of light behaves upon passage through microscopic optically trapped particles. Particles trapped with Gaussian and, separately, Bessel light beams in two spatially distinct sample chambers are studied with trapped objects in the first chamber acting as distorting obstacles. We examine the differences between Bessel beams and Gaussian beams in such experiments. We also show how the Bessel beam can be used to simultaneously trap particles that can be as much as 1cm away from each other. We discuss applications of these results and suggest other topics where the Bessel beam may be of use.

DOI
10.1117/12.556319

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Bessel beams have a number of properties that make them useful for optical manipulation. These include a central core which does not diffract over a characteristic distance, the reconstruction of the cross sectional intensity around obstacles and the ability of the beams to possess orbital angular momentum. Here we examine the utility of the Bessel beam to quantitatively examine the transfer of spin and orbital angular momentum to particle trapped away from the beam axis. We show the simultaneous transfer of orbital and spin angular momentum to an off-axis particle. We experimentally study how both the spin and orbital angular momentum of light behaves upon passage through microscopic optically trapped particles. Particles trapped with Gaussian and, separately, Bessel light beams in two spatially distinct sample chambers are studied with trapped objects in the first chamber acting as distorting obstacles. We examine the differences between Bessel beams and Gaussian beams in such experiments. We also show how the Bessel beam can be used to simultaneously trap particles that can be as much as 1cm away from each other. We discuss applications of these results and suggest other topics where the Bessel beam may be of use.
This thesis describes the experimental and theoretical work that investigated the transfer of orbital angular momentum from light to matter. This was achieved by combining two established areas of laser physics which were "optical tweezers" and Laguerre-Gaussian laser modes. The optical tweezers are essentially a tightly focussed laser beam from a high numerical aperture microscope objective lens, which traps particles in three dimensions just below the beam focus. By incorporating a Laguerre- Gaussian laser mode into the tweezers system, the trapping efficiency was doubled. These improved optical tweezers have been successfully demonstrated both theoretically and experimentally. In addition to the spin angular momentum which is associated with the polarisation state, the Laguerre-Gaussian laser modes also possess orbital angular momentum. The "optical spanners" utilised this property by transferring orbital angular momentum from the laser beam to the trapped particle, causing it to rotate whilst being held in the optical trap. This effect was theoretically modelled and experimentally observed. Using the optical spanners, the spin angular momentum of the laser was used to directly cancel the orbital angular momentum in the beam, which was observed as a cessation in rotation of the trapped particle. This demonstrated the mechanical equivalence of the spin and orbital components of angular momentum in a light beam, and gave experimental evidence for the well defined nature of the orbital angular momentum present in Laguerre-Gaussian laser modes.
The orbital angular momentum density of Bessel beams is calculated explicitly within a rigorous vectorial treatment. This allows us to investigate some aspects that have not been analysed previously, such as the angular momentum content of azimuthally and radially polarized beams. Furthermore, we demonstrate experimentally the mechanical transfer of orbital angular momentum to trapped particles in optical tweezers using a high-order Bessel beam. We set transparent particles of known dimensions into rotation, where the sense of rotation can be reversed by changing the sign of the singularity. Quantitative results are obtained for rotation rates. This paper's animations are available from the Multimedia Enhancements page.
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.
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].
Optical vortices became a hot topic since almost two decades ago, when it was recognized that Laguerre-Gaussian laser modes carry orbital angular momentum [Allen et al. Phys Rev A 45, 8185 (1992)] related with a screw phase dislocation, and different from the spin angular momentum associated to circular polarization. In 1995, this dynamical quantity was transferred to matter in an optical micromanipulation system for the first time [H. He, et al., Phys. Rev. Lett. 75, 826 (1995)], and since then, a number of studies on angular momentum of light have unveiled different interesting aspects on the subject. However, there are still open questions, which have arisen together with the generation of novel light beams, such as vector vortices, for instance. In contrast with scalar vortices, with usual polarization states (linear, circular, elliptical), the orientation and magnitude of the electric field of vector vortices (solutions of the vector wave equation) is a function of space and time. In this work, we present an experimental study of the local angular momentum density of a Bessel vector vortex of first order by means of an optical trap. For this purpose, we used different probe particles in order to sense the local contribution to the optical angular momentum in each region of the beam. But optical fields are not the only wave fields that may exhibit phase dislocations or singularities. There are close analogies between light and sound fields that can be exploited in order to get a better understanding of common phenomena and study new aspects in both branches of physics. Here we also present the first experimental demonstration and theoretical analysis of acoustical vortices in free field, with similar properties to those of the optical vortices, including the angular momentum that can be transferred to matter. The corresponding analogies and differences with the optical case turn out to be very enlightening for the understanding of the phenomenon of angular momentum in wave fields.