Alison M. Yao

Orbital angular momentum: origins, behavior and applications

As they travel through space, some light beams rotate. Such light beams have angular momentum. There are two particularly important ways in which a light beam can rotate: if every polarization vector rotates, the light has spin; if the phase structure rotates, the light has orbital angular momentum (OAM), which can be many times greater than the spin. Only in the past 20 years has it been realized that beams carrying OAM, which have an optical vortex along the axis, can be easily made in the laboratory. These light beams are able to spin microscopic objects, give rise to rotational frequency shifts, create new forms of imaging systems, and behave within nonlinear material to give new insights into quantum optics.

Quantum correlations in optical angle-orbital angular momentum variables

Entanglement in a Twist The strong correlations observed in quantum mechanically entangled particles, such as photons, offer potential for secure communication and quantum information processing. Leach et al. (p. 662) now show such strong quantum correlations between the complementary variables—angular position and orbital angular momentum—of two photons created during the parametric down-conversion process in a nonlinear crystal. This demonstration of entanglement in an angular basis establishes that angles are genuine quantum observables and can therefore be considered a resource for quantum information processing, capable of secure, high-dimension, key distribution. Strong quantum correlations are induced between the angular position and angular momentum of two photons. Entanglement of the properties of two separated particles constitutes a fundamental signature of quantum mechanics and is a key resource for quantum information science. We demonstrate strong Einstein, Podolsky, and Rosen correlations between the angular position and orbital angular momentum of two photons created by the nonlinear optical process of spontaneous parametric down-conversion. The discrete nature of orbital angular momentum and the continuous but periodic nature of angular position give rise to a special sort of entanglement between these two variables. The resulting correlations are found to be an order of magnitude stronger than those allowed by the uncertainty principle for independent (nonentangled) particles. Our results suggest that angular position and orbital angular momentum may find important applications in quantum information science.

Microrheology with optical tweezers

Microrheology is the study of the flow of materials over small scales. It is of particular interest to those involved with investigations of fluid properties within Lab-on-a-Chip structures or within other micron-scale environments. The article briefly reviews existing active and passive methods used in the study of fluids. It then explores in greater detail the use of optical tweezers as an emerging method to investigate rheological phenomena, including, for example, viscosity and viscoelasticity, as well as the related topic of flow. The article also describes, briefly, potential future applications of this topic, in the fields of biological measurement, in general, and Lab-on-a-Chip, in particular.

Discriminatory optical force for chiral molecules

We suggest that the force F exerted upon a chiral molecule by light assumes the form under appropriate circumstances, where a and b pertain to the molecule whilst w and h are the local densities of electric energy and helicity in the optical field; the gradients of these quantities thus governing the molecules centre-of-mass motion. Whereas a is identical for the mirror-image forms or enantiomers of the molecule, b has opposite signs; the associated contribution to F therefore pointing in opposite directions. A simple optical field is presented for which vanishes but does not, so that F is absolutely discriminatory. We then present two potential applications: a Stern–Gerlach-type deflector capable of spatially separating the enantiomers of a chiral molecule and a diffraction grating to which chiral molecules alone are sensitive; the resulting diffraction patterns thus encoding information about their chiral geometry.

Measuring storage and loss moduli using optical tweezers: Broadband microrheology

We present an experimental procedure to perform broadband microrheological measurements with optical tweezers. A generalized Langevin equation is adopted to relate the time-dependent trajectory of a particle in an imposed flow to the frequency-dependent moduli of the complex fluid. This procedure allows us to measure the material linear viscoelastic properties across the widest frequency range achievable with optical tweezers.

Full characterization of the quantum spiral bandwidth of entangled biphotons

Spontaneous parametric down-conversion has been shown to be a reliable source of entangled photons. Among the wide range of properties shown to be entangled, it is the orbital angular momentum that is the focus of our study. We investigate, in particular, the bi-photon state generated using a Gaussian pump beam. We derive an expression for the simultaneous correlations in the orbital angular momentum, l, and radial momentum, p, of the down-converted Laguerre-Gaussian beams. Our result allows us, for example, to calculate the spiral bandwidth with no restriction on the geometry of the beams: l, p, and the beam widths are all free parameters. Moreover, we show that, with the usual paraxial and collinear approximations, a fully analytic expression for the correlations can be derived.

Multipoint viscosity measurements in microfluidic channels using optical tweezers

We demonstrate the technique of multipoint viscosity measurements incorporating the accurate calibration of micron sized particles. We describe the use of a high-speed camera to measure the residual motion of particles trapped in holographic optical tweezers, enabling us to calculate the fluid viscosity at multiple points across the field-of-view of the microscope within a microfluidic system.

On the natures of the spin and orbital parts of optical angular momentum

The modern field of optical angular momentum began with the realisation by Allen et al in 1992 that, in addition to the spin associated with polarisation, light beams with helical phase fronts carry orbital angular momentum. There has been much confusion and debate, however, surrounding the intricacies of the field and, in particular, the separation of the angular momentum into its spin and orbital parts. Here we take the opportunity to state the current position as we understand it, which we present as six perspectives: (i) we start with a reprise of the 1992 paper in which it was pointed out that the Laguerre–Gaussian modes, familiar from laser physics, carry orbital angular momentum. (ii) The total angular momentum may be separated into spin and orbital parts, but neither alone is a true angular momentum. (iii) The spin and orbital parts, although not themselves true angular momenta, are distinct and physically meaningful, as has been demonstrated clearly in a range of experiments. (iv) The orbital part of the angular momentum in the direction of propagation of a beam is not simply the azimuthal component of the linear momentum. (v) The component of spin in the direction of propagation is not the helicity, although these are related quantities. (vi) Finally, the spin and orbital parts of the angular momentum correspond to distinct symmetries of the free electromagnetic field and hence are separately conserved quantities.

Diffraction Gratings for Chiral Molecules and Their Applications

We suggest the use of certain readily producible types of light to exert a force that points in opposite directions for the enantiomers of a chiral molecule and propose multiple devices based upon this novel manifestation of optical activity: in particular, our discriminatory chiral diffraction grating; a device that could be employed, for example, to measure the enantiomeric excess of a sample of chiral molecules simply and to high precision. Our work is relevant for many types of molecules and our proposed devices may be realizable using currently existing technology.

Angular momentum decomposition of entangled photons with an arbitrary pump

We calculate the biphoton state generated by spontaneous parametric down-conversion in a thin crystal and under collinear phase matching conditions using a pump consisting of any superposition of Laguerre-Gauss modes. The result has no restrictions on the angular or radial momenta or, in particular, on the width of the pump, signal and idler modes. We demonstrate the strong effect of the ratio of the pump width to the signal/idler widths on the composition of the down-converted entangled fields. The knowledge of this ratio is shown to be essential for calculating the maximally entangled states that can be produced using pumps with a complex spatial profile.