Singular optical beams have been studied for many years after the pioneering work where the wave function of the laser radiation is presented as a steady-state solution of the wave equation for a harmonic oscillator. A major step in understanding the nature of singular beams has been made by introducing the concept of the angular momentum of light and analyzing local energy transfer in a vortex beam. It is now well accepted that the orbital angular momentum of light is an intrinsic feature of the optical vortex. However, the orbital angular momentum was always analyzed for travelling modes and the important issue of the orbital angular momentum associated with standing waves still remains open. The main motivation of our work is to reveal the structure of the orbital angular momentum in a standing wave formed by the counter-propagating optical vortices and study its suitability for an optical trapping and guiding. In this work we show that a superposition of two (or more) vortex beams generates a field structure which has a form of a standing wave in both the radial and longitudinal directions, but it is rotating simultaneously along the tangential direction. We demonstrate that then field of this optical vortex structure could be used as an optical trap and simultaneously transfer the angular momentum of the electromagnetic wave to an object inside the area of vortex localisation. We believe this study provides a basis for developing a novel concept of three-dimensional optical traps where vortices could be created in a local volume by a direct transfer of the angular orbital momentum of the electromagnetic wave to trapped objects.
Singular optical beams have been studied for many years after the pioneering work where the wave function of the laser radiation is presented as a steady-state solution of the wave equation for a harmonic oscillator. A major step in understanding the nature of singular beams has been made by introducing the concept of the angular momentum of light and analyzing local energy transfer in a vortex beam. It is now well accepted that the orbital angular momentum of light is an intrinsic feature of the optical vortex. However, the orbital angular momentum was always analyzed for travelling modes and the important issue of the orbital angular momentum associated with standing waves still remains open. The main motivation of our work is to reveal the structure of the orbital angular momentum in a standing wave formed by the counter-propagating optical vortices and study its suitability for an optical trapping and guiding. In this work we show that a superposition of two (or more) vortex beams generates a field structure which has a form of a standing wave in both the radial and longitudinal directions, but it is rotating simultaneously along the tangential direction. We demonstrate that then field of this optical vortex structure could be used as an optical trap and simultaneously transfer the angular momentum of the electromagnetic wave to an object inside the area of vortex localisation. We believe this study provides a basis for developing a novel concept of three-dimensional optical traps where vortices could be created in a local volume by a direct transfer of the angular orbital momentum of the electromagnetic wave to trapped objects.
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.
Photons carry one unit of angular momentum associated with their spin~\cite{Beth1936}. Structured vortex beams carry additional orbital angular momentum which can also be transferred to matter~\cite{Allen1992}. This extra twist has been used for example to drive motion of microscopic particles in optical tweezers as well as to create vortices in degenerate quantum gases~\cite{He1995,Andersen2006}. Here we demonstrate the transfer of optical orbital angular momentum from the transverse spatial structure of the beam to the internal (electronic) degrees of freedom of an atom. Probing a quadrupole transition of a single trapped 40Ca+ ion localized at the center of the vortex, we observe strongly modified selection rules, accounting for both the photon spin and the vorticity of the field. In particular, we show that an atom can absorb two quanta of angular momentum from a single photon even when rotational symmetry is conserved. In contrast to previous findings~\cite{Araoka2005,Loeffler2011a,Mathevet2013}, our experiment allows for conditions where the vorticity of the laser beam determines the optical excitation, contributing to the long-standing discussion on whether the orbital angular momentum of photons can be transferred to atomic internal degrees of freedom~\cite{VanEnk1994,Babiker2002,Jauregui2004, Schmiegelow2012, Mondal2014, Scholz-Marggraf2014} and paves the way for its use to tailor light-matter interactions.
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.
Photons can carry angular momentum, not only due to their spin, but also due to their spatial structure. This extra twist has been used, for example, to drive circular motion of microscopic particles in optical tweezers as well as to create vortices in quantum gases. Here we excite an atomic transition with a vortex laser beam and demonstrate the transfer of optical orbital angular momentum to the valence electron of a single trapped ion. We observe strongly modified selection rules showing that an atom can absorb two quanta of angular momentum from a single photon: one from the spin and another from the spatial structure of the beam. Furthermore, we show that parasitic ac-Stark shifts from off-resonant transitions are suppressed in the dark centre of vortex beams. These results show how light's spatial structure can determine the characteristics of light-matter interaction and pave the way for its application and observation in other systems.
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.