Orbital angular momentum 25 years on [invited]

Twenty-five years ago Allen, Beijersbergen, Spreeuw, and Woerdman published their seminal paper establishing that light beams with helical phase-fronts carried an orbital angular momentum. Previously orbital angular momentum had been associated only with high-order atomic/molecular transitions and hence considered to be a rare occurrence. The realization that every photon in a laser beam could carry an orbital angular momentum that was in excess of the angular momentum associated with photon spin has led both to new understandings of optical effects and various applications. These applications range from optical manipulation, imaging and quantum optics, to optical communications. This brief review will examine some of the research in the field to date and consider what future directions might hold

An introduction to ghost imaging: quantum and classical

Ghost imaging has been a subject of interest to the quantum optics community for the past 20 years. Initially seen as manifestation of quantum spookiness, it is now recognized as being implementable in both single- and many-photon number regimes. Beyond its scientific curiosity, it is now feeding novel imaging modalities potentially offering performance attributes that traditional approaches cannot match

On the dragging of light by a rotating medium

When light is passing through a rotating medium the optical polarization is rotated. Recently, it has been reasoned that this rotation applies also to the transmitted image. We examine these two phenomena by extending an analysis of Player (Player 1976 Proc. R. Soc. A 349, 441-445) to general electromagnetic fields. We find that in this more general case, the wave equation inside the rotating medium has to be amended by a term which is connected to the orbital angular momentum (OAM) of the light. We show that optical spin and OAM account for the rotation of the polarization and the rotation of the transmitted image, respectively

Optical orbital angular momentum

We present a brief introduction to the orbital angular momentum of light, the subject of our theme issue and, in particular, to the developments in the 13 years following the founding paper by Allen et al. (Allen et al. 1992 Phys. Rev. A 45, 8185 (doi:10.1103/PhysRevA.45.8185)). The papers by our invited authors serve to bring the field up to date and suggest where developments may take us next

Comparing the information capacity of entangled Laguerre-Gaussian and Hermite-Gaussian modal sets in a finite-aperture system

Using a spontaneous parametric down-conversion process to create entangled spatial states, we compare the information capacity associated with measurements in the Hermite–Gaussian and Laguerre–Gaussian modal basis in an optical system of finite aperture. We show that the cross-talk imposed by the aperture restriction degrades the information capacity. However, the Laguerre–Gaussian mode measurements show greater resilience to cross talk than the Hermite–Gaussian, suggesting that the Laguerre–Gaussian modal set may still offer real-world advantages over other modal sets

Fast Compressive 3D Single-pixel Imaging

In this work, we demonstrate a modified photometric stereo system with perfect pixel registration, capable of reconstructing continuous real-time 3D video at ~8 Hz for 64 x 64 image resolution by employing evolutionary compressed sensing

Generation of Caustics and Spatial Rogue Waves from Nonlinear Instability

Caustics are natural phenomena in which nature concentrates the energy of waves. Although, they are known mostly in optics, caustics are intrinsic to all wave phenomena. For example, studies show that fluctuations in the profile of an ocean floor can generate random caustics and focus the energy of tsunami waves. Caustics share many similarities to rogue waves, as they both exhibit heavy-tailed distribution, i.e. an overpopulation of large events. Linear Schr\"odinger-type equations are usually used to explain the wave dynamics of caustics. However, in that the wave amplitude increases dramatically in caustics, nonlinearity is inevitable in many systems. In this Letter, we investigate the effect of nonlinearity on the formation of optical caustics. We show experimentally that, in contrast to linear systems, even small phase fluctuations can generate strong caustics upon nonlinear propagation. We simulated our experiment based on the nonlinear Schr\"odinger equation (NLSE) with Kerr-type nonlinearity, which describes the wave dynamics not only in optics, but also in some other physical systems such as oceans. Therefore, our results may also aid our understanding of ocean phenomena.Comment: 5 pages, 4 figure

DMD-based software-configurable spatially-offset Raman spectroscopy for spectral depth-profiling of optically turbid samples

Spectral depth-profiling of optically turbid samples is of high interest to a broad range of applications. We present a method for measuring spatially-offset Raman spectroscopy (SORS) over a range of length scales by incorporating a digital micro-mirror device (DMD) into a sample-conjugate plane in the detection optical path. The DMD can be arbitrarily programmed to collect/reject light at spatial positions in the 2D sample-conjugate plane, allowing spatially offset Raman measurements. We demonstrate several detection geometries, including annular and simultaneous multi-offset modalities, for both macro- and micro-SORS measurements, all on the same instrument. Compared to other SORS modalities, DMD-based SORS provides more flexibility with only minimal additional experimental complexity for subsurface Raman collection

Image reconstruction from photon sparse data

We report an algorithm for reconstructing images when the average number of photons recorded per pixel is of order unity, i.e. photon-sparse data. The image optimisation algorithm minimises a cost function incorporating both a Poissonian log-likelihood term based on the deviation of the reconstructed image from the measured data and a regularization-term based upon the sum of the moduli of the second spatial derivatives of the reconstructed image pixel intensities. The balance between these two terms is set by a bootstrapping technique where the target value of the log-likelihood term is deduced from a smoothed version of the original data. When compared to the original data, the processed images exhibit lower residuals with respect to the true object. We use photon-sparse data from two different experimental systems, one system based on a single-photon, avalanche photo-diode array and the other system on a time-gated, intensified camera. However, this same processing technique could most likely be applied to any low photon-number image irrespective of how the data is collected

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.Comment: 4 pages, 4 figure