Eric Yao

Observation of the vortex structure of a non-integer vortex beam

An optical beam with an eil phase structure carries an orbital angular momentum of l per photon. For integer l values, the phase fronts of such beams form perfect helices with a single screw-phase dislocation, or vortex, on the beam axis. For non-integer l values, Berry (2004 J. Opt. A: Pure Appl. Opt. 6 259) predicts a complex-phase structure comprising many vortices at differing positions within the beam cross-section. Using a spatial light modulator we produce eil beams with varying l. We examine the phase structure of such beams after propagation through an interference-based phase-measurement technique. As predicted, we observe that for half-integer l values, a line of alternating charge vortices is formed near the radial dislocation.

Interactive application in holographic optical tweezers of a multi-plane Gerchberg-Saxton algorithm for three-dimensional light shaping.

Phase-hologram patterns that can shape the intensity distribution of a light beam in several planes simultaneously can be calculated with an iterative Gerchberg-Saxton algorithm [T. Haist et al., Opt. Commun. 140, 299 (1997)]. We apply this algorithm in holographic optical tweezers. This allows us to simultaneously trap several objects in individually controllable arbitrary 3-dimensional positions. We demonstrate the interactive use of our approach by trapping microscopic spheres and moving them into an arbitrary 3-dimensional configuration.

Uncertainty principle for angular position and angular momentum

The uncertainty principle places fundamental limits on the accuracy with which we are able to measure the values of different physical quantities (Heisenberg 1949 The Physical Principles of the Quantum Theory (New York: Dover); Robertson 1929 Phys. Rev. 34 127). This has profound effects not only on the microscopic but also on the macroscopic level of physical systems. The most familiar form of the uncertainty principle relates the uncertainties in position and linear momentum. Other manifestations include those relating uncertainty in energy to uncertainty in time duration, phase of an electromagnetic field to photon number and angular position to angular momentum (Vaccaro and Pegg 1990 J. Mod. Opt. 37 17; Barnett and Pegg 1990 Phys. Rev. A 41 3427). In this paper, we report the first observation of the last of these uncertainty relations and derive the associated states that satisfy the equality in the uncertainty relation. We confirm the form of these states by detailed measurement of the angular momentum of a light beam after passage through an appropriate angular aperture. The angular uncertainty principle applies to all physical systems and is particularly important for systems with cylindrical symmetry.

Fourier relationship between angular position and optical orbital angular momentum

We demonstrate the Fourier relationship between angular position and angular momentum for a light mode. In particular we measure the distribution of orbital angular momentum states of light that has passed through an aperture and verify that the orbital angular momentum distribution is given by the complex Fourier-transform of the aperture function. We use spatial light modulators, configured as diffractive optical components, to define the initial orbital angular momentum state of the beam, set the defining aperture, and measure the angular momentum spread of the resulting beam. These measurements clearly confirm the Fourier relationship between angular momentum and angular position, even at light intensities corresponding to the single photon level.

Simplified measurement of the orbital angular momentum of single photons

Abstract We describe a simplification of a recent approach for sorting photons according to their orbital angular momentum (OAM) [Leach et al., Phys. Rev. Lett. 88 (2002) 257901]. The original cascade of Mach–Zehnder interferometers required optical elements that can increase the OAM per photon of any passing light by a fixed amount, which in practice introduced loss. Our simplification, which we demonstrate experimentally, does not require these lossy elements but instead shifts the phase in one arm of each interferometer. We also point out that an earlier scheme for sorting Hermite–Gaussian (HG) modes [Xue et al., Opt. Lett. 26 (2001) 1746] could be modified to sort photons according to their OAM.

Observation of quantum entanglement using spatial light modulators

We use spatial light modulators to observe the quantum entanglement of down-converted photon pairs. Acting as diffractive optical elements within one of the beams, they can be reconfigured in real time to set the spatial profile of the measured mode. Such configurations are highly applicable to the measurement of orbital angular momentum states or other spatial modes, such as those associated with quantum imaging.

Simulation of superresolution holography for optical tweezers

Optical tweezers manipulate microscopic particles using foci of light beams. Their performance is therefore limited by diffraction. Using computer simulations of a model system, we investigate the application of superresolution holography for two-dimensional (2D) light shaping in optical tweezers, which can beat the diffraction limit. We use the direct-search and Gerchberg algorithms to shape the center of a light beam into one or two bright spots; we do not constrain the remainder of the beam. We demonstrate that superresolution algorithms can significantly improve the normalized stiffness of an optical trap and the minimum separation at which neighboring traps can be resolved. We also test if such algorithms can be used interactively, as is desirable in optical tweezers.

A spatial light phase modulator with an effective resolution of 4 mega-pixels

We report the design, construction and characterization of a 4 mega-pixel, optically-addressed, spatial light modulator (OSLM). The intensity distribution corresponding to a kinoform is displayed across two wide-screen liquid crystal on silicon displays, the images of which are combined and relayed to the address face of a 40 mm aperture OSLM. This spatially varying intensity profile is converted into a phase hologram on the readout side of the OSLM. When illuminated at 532 nm we measure a first-order diffraction efficiency of ≈50% at 400 line pairs and ≈20% at 900 line pairs. We show that aberration associated with the non-flatness of the device can be corrected within software by modification of the hologram.

Observation of Gouy-phase-induced transversal intensity changes in focused beams

We created superpositions of two different TEM modes in focused beams. Such modes show relative dephasing along the beam axis due to Gouys phase. This leads to interference effects and significant modifications of a beams transverse intensity distribution near the beam focus. We investigate the features of the resulting field profiles.

Three-dimensional structures in optical tweezers

We use holographic optical tweezers to trap multiple micron-sized objects and manipulate them in 3-dimensions. Trapping multiple objects allow us to create 3-dimensional structures, examples of which include; simple cubes which can be rotated or scaled, complex crystal structures like the diamond lattice or interactive 3-dimensional control of trapped particles anywhere in the sample volume.