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

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

Optical Rogue Waves in Vortex Turbulence

We present a spatio-temporal mechanism for producing 2D optical rogue waves in the presence of a turbulent state with creation, interaction and annihilation of optical vortices. Spatially periodic structures with bound phase lose stability to phase unbound turbulent states in complex Ginzburg- Landau and Swift-Hohenberg models with external driving. When the pumping is high and the external driving is low, synchronized oscillations are unstable and lead to spatio-temporal turbulence with high excursions in amplitude. Nonlinear amplification leads to rogue waves close to turbulent optical vortices, where the amplitude tends to zero, and to probability distribution functions with long tails typical of extreme optical events.Comment: 5 pages, 7 figure

Chirality and the angular momentum of light

Chirality is exhibited by objects that cannot be rotated into their mirror images. It is far from obvious that this has anything to do with the angular momentum of light, which owes its existence to rotational symmetries. There is nevertheless a subtle connection between chirality and the angular momentum of light. We demonstrate this connection and, in particular, its significance in the context of chiral light–matter interactions

Scattering of light with angular momentum from an array of particles

Understanding the scattering properties of various media is of critical importance in many applications, from secure high-bandwidth communications to extracting information about biological and mineral particles dissolved in sea water. In this paper we demonstrate how beams carrying orbital angular momentum can be used to detect the presence of symmetric or chiral subsets of particles in disordered media. Using a generalized Mie theory, we calculate analytical expressions for quasimonochromatic structured light scattered by dilute distributions of micro- and nanoparticles. These allow us to determine the angular momentum of the scattered field as a function of the angular momentum of the incident beam and of the spatial distributions of scattering particles. Our numerical results show that we can distinguish structured from random distributions of particles, even when the number density of ordered particles is a few percent of the total istribution. We also find that the signal-to-noise ratio, in the forward direction, is equivalent for all orders of the Laguerre-Gaussian modes in relatively dense (but still dilute) distributions of particles smaller than the beam waist and the Rayleigh range of the beam

Measuring storage and loss moduli using optical tweezers: broadband microrheology

We present an experimental procedure to perform broadband microrheological measurements with optical tweezers. A generalised 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.Comment: 5 pages, 3 figure

Strong chiral optical force for small chiral molecules based on electric-dipole interactions, inspired by the asymmetrical hydrozoan Velella velella\textit{Velella velella}

Drawing inspiration from a remarkable chiral force found in nature, we show that a static electric field combined with an optical lin$\perp$lin polarization standing wave can exert a chiral optical force on a small chiral molecule that is several orders of magnitude stronger than other chiral optical forces proposed to date, being based on leading electric-dipole interactions rather than relying on weak magnetic-dipole and electric-quadrupole interactions. Our chiral optical force applies to most small chiral molecules, including isotopically chiral molecules, and does not require a specific energy-level structure. Potential applications range from chiral molecular matter-wave interferometry for precision metrology and tests of fundamental physics to the resolution of enantiomers for use in chemistry and biology

Optomechanical transport of cold atoms induced by structured light

Optomechanical pattern forming instabilities in a cloud of cold atoms lead to self-organized spatial structures of light and atoms. Here, we consider the optomechanical self-structuring of a cold atomic cloud in the presence of a phase structured input field, carrying orbital angular momentum. For a planar ring cavity setup, a model of coupled cavity field and atomic density equations describes a wide range of drifting modulation instabilities in the transverse plane. This leads to the formation of rotating self-organized rings of light-atom lattices. Using linear stability analysis and numerical simulations of the coupled atomic and optical dynamics, we demonstrate the presence of macroscopic atomic transport corresponding to the pattern rotation, induced by the structured pump phase profile

Control of polarization rotation in nonlinear propagation of fully-structured light

Knowing, and controlling, the spatial polarization distribution of a beam is of importance in applications such as optical tweezing, imaging, material processing and communications. Here we show how the polarization distribution is affected by both linear and nonlinear (self-focussing) propagation. We derive an analytical ex- pression for the polarization rotation of fully-structured light (FSL) beams during linear propagation and show that the observed rotation is due entirely to the difference in Gouy phase between the two eigenmodes comprising the FSL beams, in excellent agreement with numerical simulations. We also explore the effect of cross-phase modulation due to self-focusing (Kerr) nonlinearity and show that polarization rotation can be controlled by changing the eigenmodes of the superposition, and physical parameters such as the beam size, the amount of Kerr nonlinearity and the input power. Finally, we show that by biasing cylindrical vector (CV) beams to have elliptical polarization, we can vary the polarization state from radial through spiral to azimuthal using nonlinear propagation