L. Allen

Astigmatic laser mode converters and transfer of orbital angular momentum

Abstract We present the design of a mode converter which transforms a Hermite-gaussian mode of arbitrarily high order to a Laguerre-gaussian mode and vice versa. The converter consists of two cylindrical lenses and is based on appropriate use of the Gouy phase. We demonstrate mode conversion experimentally and consider where the concomitant transfer of orbital angular momentum is localized.

THE ORBITAL ANGULAR MOMENTUM OF LIGHT

Publisher Summary This chapter discusses the orbital angular momentum of light, outlines the theoretical basis for the orbital angular momentum of beams within the paraxial approximation, and indicates the unapproximated theory, based on the full set of Maxwell equations. The chapter discusses the problems associated with the separation and identification of spin and orbital contributions to the angular momentum properties of a field, the properties of Laguerre–Gaussian beams, which are physically realizable in the laboratory, and the ways in which the beams may be generated. It reviews the phenomenological behavior of beams possessing orbital angular momentum and their interaction with matter in bulk. The chapter also describes the measurement of the rotational Doppler shift, which arises when beams possessing orbital and spin angular momenta are rotated. The dipole-interaction of atoms with the orbital angular momentum of light beams is considered. The roles of spin and orbital angular momentum are also compared and contrasted.

Orbital angular momentum and nonparaxial light beams

Abstract The simple relationship between total angular momentum and energy and the seemingly natural separation of the angular momentum into spin and orbital components in the paraxial approximation, are investigated for a general nonparaxial form of monochromatic beam with near cylindrical symmetry.

An experiment to observe the intensity and phase structure of Laguerre–Gaussian laser modes

We outline an easily reproduced experiment that allows the student to investigate the intensity and phase structure of transverse laser modes. In addition to discussing the usual Hermite–Gaussian laser modes we detail how Laguerre–Gaussian laser modes can be obtained by the direct conversion of the Hermite–Gaussian output. A Mach–Zehnder interferometer allows the phase structure of the Laguerre–Gaussian modes to be compared with the phase structure of a plane wave with the same frequency. The resulting interference patterns clearly illustrate the azimuthal phase dependence of the Laguerre–Gaussian modes, which is the origin of the orbital angular momentum associated with each of them.

AZIMUTHAL DOPPLER SHIFT IN LIGHT BEAMS WITH ORBITAL ANGULAR MOMENTUM

Abstract We show that an atom moving in a light beam with orbital angular momentum experiences an azimuthal shift in the resonant frequency in addition to the usual axial Doppler and recoil shifts. For a Laguerre-Gaussian beam characterised by an orbital angular momentum quantum number l , the shift is lV φ / r where r is the radial atomic position and V φ the azimuthal component of velocity. The predicted shift could play a significant role in interactions between atoms and standing light fields in cooling experiments as well as in ion traps.

Introduction to the atoms and angular momentum of light special issue

A very brief comment concerning the literature relating to the angular momentum of light is followed by a precis of a review article on the orbital angular momentum of light published in 1999. An outline is then given of the key developments since 1999 in the study of the angular momentum of light and of the related topic of optical vortices.

Radiation forces on a two-level atom in a σ+ − σ− configuration of Laguerre-Gaussian beams

Abstract We investigate the radiation forces associated with the J = 0 → J = 1 transition of a two-level atom in a laser configuration of two counter-propagating Laguerre-Gaussian (LG) beams with opposite circular polarisations. It is shown that, in addition to the usual dissipative and dipole forces, the atom experiences a torque about the beam axis. The latter arises from the orbital angular momentum properties of the Laguerre-Gaussian beams. The atom experiences either a static torque or a purely velocity-dependent torque, depending on the relative signs of the orbital angular momenta of the two LG beams. The trajectories of the atom are calculated in each case by solving the optical Bloch equations together with the classical equation of motion for the atom.

Doppler cooling of ion cyclotron motion in counter-propagating Laguerre-Gaussian beams

Abstract We demonstrate theoretically that ions moving in the field of two axial counter-propagating Laguerre-Gaussian (LG) light modes and a constant axial magnetic field, exhibit novel cooling effects. When the beams have orbital angular momentum l of the same sign we find that in addition to an axial force similar to the conventional plane wave Doppler cooling force, there is a velocity-independent quantised torque about the common beam axis which significantly influences the subsequent motion of the ion. The new effects are illustrated for the cooling of 24 Mg + ions in the presence of an axial magnetic field.

Optical Molasses and the Orbital Angular Momentum of Light

Recent work has shownl,2 that the near-resonance interaction of atoms with a Laguerre-Gaussian (LG) beam provides new effects associated with the orbital angular momentum properties of the light3. In particular such atoms are subject to a torque about the beam axis and an additional non-axial Doppler shift. It has been suggested1,2 that these mechanisms may have some useful consequences in the field of cooling and trapping of atoms and ions. We have therefore considered the dissipative force on a two-level atom due to two counter-propagating LG beams 1 and 2.

Orbital Angular Momentum Effects of Light on Atoms; A Density-Matrix Theory

It has been shown1 that Laguerre-Gaussian light beams possess quantised orbital angular momentum, lℏ. A quantum calculation of the interaction of such beams with a free atom has shown that both the internal and gross motions of the atom are affected. The internal motion manifests itself as an additional shift in the resonance, called the Azimuthal Doppler shift2, while the atom also experiences a quantised torque about the axis of the beam3.