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Preparation, control, and measurement of optical vortices are increasingly important, as they play essential roles in both fundamental science and optical technology applications. Spatial light modulation is the main approach behind the control strategies, although there are limitations concerning the controllable wavelength. It is therefore crucial to develop approaches that expand the spectral range of light modulation. Here, we demonstrate the modulation of light by light in nonlinear optical interactions to demonstrate the identification of the topological charge of optical vortices. A triangular-lattice pattern is observed in light beams resulting from the spatial cross modulation between an optical vortex and a triangular shaped beam undergoing parametric interaction. Both up- and downconversion processes are investigated, and the far-field image of the converted beam exhibits a triangular lattice. The number of sites and the lattice orientation are determined by the topological charge of the vortex beam. In the downconversion process, the lattice orientation can also be affected by phase conjugation. The observed cross modulation works for a large variety of spatial field structures. Our results show that modulation of light by light can be used at wavelengths for which solid-state devices are not yet available.

We report on an experiment that investigates the spatial mode conversion in the process of parametric down-conversion seeded by a light beam in a superposition of orbital angular momentum modes. This process is interpreted in terms of a geometric representation of first-order spatial modes in a Poincar\'e sphere, providing an intuitive image of the phase conjugation and the topological charge conservation. We also make a comparison with the analogous phenomenon for optical parametric oscillators., Comment: 5 pages, 6 figures

A vector vortex beam presents local polarization states that are spatially modulated in the plane transverse to propagation. By employing a two-crystal-sandwich source allowing for nonlinear interactions between input fields of any polarization, we analyze experimentally the process of stimulated parametric down-conversion and observe unique effects when the pump and seed fields are vector vortex beams. We reconstruct the transverse polarization pattern of the generated idler beam by Stokes polarimetry. The experimental results obtained are in good qualitative agreement with theory and exhibit manifold polarization transverse distributions for different combinations of pump and seed vector vortex beams, which may find applications in both classical and quantum optics.

The orbital angular momentum conservation of light reveals different diffraction patterns univocally dependent on the topological charge of the incident light beam when passing through a triangular aperture. It is demonstrated that these patterns, which are accessed by observing the far-field measurement of the diffracted light, can also be obtained using few photon sources. In order to explain the observed patterns, we introduce an analogy of this optical phenomenon with the study of diffraction for the characterization of the crystal structure of solids. We demonstrate that the finite pattern can be associated with the reciprocal lattice obtained from the direct lattice generated by the primitive vectors composing any two of the sides of the equilateral triangular slit responsible for the diffraction. Using the relation that exists between the direct and reciprocal lattices, we provide a conclusive explanation as to why the diffraction pattern of the main maxima is finite. This can shed a new light on the investigation of crystallographic systems.

Optical modes possessing orbital angular momentum constitute a very useful platform for experimental studies on the quantum limits of Thermodynamics. Here, we present experimental results for entangled photon pairs subjected to thin turbulence simulated with spatial light modulators and interpret them in the context of the generalized Jarzysnki's fluctuation relation. By holographic measurement of the orbital angular momentum, we obtain the work distribution produced by the turbulence for single and double-sided turbulence channels. The use of the Klyshko's advanced wave picture allows us to interpret the experimental scheme as two-way processes in a fully quantum picture., Comment: 10 pages, 11 figures, two new appendices

We introduce a simple method to characterize the topological charge associated with the orbital angular momentum of a m-order elliptic light beam. This method consists in the observation of the far field pattern of the beam carrying orbital angular momentum, diffracted from a triangular aperture. We show numerically and experimentally, for Mathieu, Ince–Gaussian, and vortex Hermite–Gaussian beams, that only isosceles triangular apertures allow us to determine in a precise and direct way, the magnitude m of the order and the number and sign of unitary topological charges of isolated vortices inside the core of these beams.

Vector vortex beams have played a fundamental role in the better understanding of coherence and polarization. They are described by spatially inhomogeneous polarization states, which present a rich optical mode structure that has attracted much attention for applications in optical communications, imaging, spectroscopy and metrology. However, this complex mode structure can be quite detrimental when propagation effects such as turbulence and birefringence perturb the beam. Optical phase conjugation has been proposed as a method to recover an optical beam from perturbations. Here we demonstrate full phase conjugation of vector vortex beams using three-wave mixing. Our scheme exploits a fast non-linear process that can be conveniently controlled via the pump beam. Our results pave the way for sophisticated, practical applications of vector beams., 7 pages, 8 figures

It is well established in the theory of quantum computation that the controlled-NOT (CNOT) gate is a fundamental element in the construction of a quantum computer. Here, we propose and experimentally demonstrate within a classical light framework that a Mach–Zehnder interferometer composed of polarized beam splitters and a pentaprism in the place of one of the mirrors works as a linear optical quantum CNOT gate. To perform the information processing, the polarization and orbital angular momentum of light act as the control and target qubits, respectively. The readout process is simple, requiring only a linear polarizer and a triangular diffractive aperture prior to detection. The viability and stability of our experiment suggest that the present proposal is a valuable candidate for future implementations in optical quantum computation protocols.

The advanced-wave picture is "... an intuitive treatment of two-photon correlation with the help of the concept of an effective field acting upon one of the two detectors and formed by parametric conversion of the advanced wave emitted by the second detector ..." [A. V. Belinskii and D. N. Klyshko, JETP 78, 259 (1994)]. This quote from Belinskii and Klyshko nicely describes the concept of the advanced-wave picture; an intuitive tool for designing and predicting results from coincidence-based two-photon experiments. Up to now, the advanced-wave picture has been considered primarily for the case of an ideal plane-wave pump beam and only for design purposes. Here we study the advanced wave picture for a structured pump beam and in the context of stimulated emission provoked by an auxiliary input laser beam. This suggests stimulated parametric down-conversion as a useful experimental tool for testing the experimental sets designed with the advanced-wave picture. We present experimental results demonstrating the strategy of designing the experiment with advanced-wave picture and testing with stimulated emission., 11 pages, 10 figures

Taking into account relaxing Kerr nonlinearity and walk-off effects, the conditions and gain spectra of cross-phase modulation-induced modulational instability (XPM-MI) of two incoherently copropagating optical waves of different frequencies and same polarization are investigated. We devote particular attention to the mixed case in which one pulse propagates under the normal group-velocity dispersion (GVD) regime, while the second one is under an anomalous GVD regime. We unveil that in the limit of an instantaneuous nonlinear response, the typical frequency with maximum gain converges to a finite value in the mixed GDV regime, while it continuously grows with the group-velocity mismatch in the normal GVD regime. As a result, the maximum gain typically decreases with the group-velocity mismatch in the mixed regime, contrasting with the opposite trend in the normal GVD regime. Further, we show that besides the mode having maximum gain at a frequency decaying with $1/{\ensuremath{\tau}}^{1/3}$ in the slow response limit, there is a second mode having maximum gain with a distinct scaling behavior ${\mathrm{\ensuremath{\Omega}}}_{\text{max}}\ensuremath{\propto}1/\ensuremath{\tau}$ in the absence of group-velocity mismatch. The associated maximum gains scale, respectively, as $1/{\ensuremath{\tau}}^{2/3}$ and $1/\ensuremath{\tau}$, thus signaling the corresponding quadratic and linear dispersion relation of these modes in the low-frequency limit. A detailed analysis of the influence of the nonlinear response time and group-velocity dispersion on the MI gain spectrum is also provided.

We show that the orbital angular momentum can be used to unveil lattice properties hidden in diffraction patterns of a simple triangular aperture. Depending on the orbital angular momentum of the incident beam, the far field diffraction pattern reveals a truncated optical lattice associated with the illuminated aperture. This effect can be used to measure the topological charge of light beams.

We investigate theoretically and experimentally the decomposition of high-order Bessel beams in terms of a new family of nondiffracting beams, referred as Hermite-Bessel beams, which are solutions of the Helmholtz equation in Cartesian coordinates. Based on this decomposition we develop a geometrical representation of first-order Bessel beams, equivalent to the Poincare sphere for the polarization states of light and implement an unitary transformation within our geometrical representation using linear optical elements.

We demonstrate that the reciprocal lattice in the Fraunhofer diffraction pattern of single photons with orbital angular momentum passing through an equilateral triangular slit provides quantitative information of the total amount of orbital angular momentum.

In this Letter we numerically and experimentally demonstrated that a lattice with an optical vortex distributed over the entire lattice can be generated in the Fourier space using three higher-order Laguerre-Gauss beams placed at the vertices of an equilateral triangle in real space. In this scheme the optical vortice's lattice presents a topological defect in its central region. Probing the net topological charge of the whole lattice, we found that it corresponds to the topological charge associated with the orbital angular momentum of each beam in real space.

We report on the theoretical and experimental demonstration of a geometrical representation for nondiffracting beams with orbital angular momentum. This representation is a SU(2) structure equivalent to the Poincare sphere for the polarization states of light, which describes the different states of light beams possessing orbital angular momentum in terms of nondiffracting beams. We have also investigated unitary transformations within our geometrical representation using linear optical elements, equivalent to a polarization state rotation on the Poincare sphere. A new class of nondiffracting beams is also suggested.

Based on the decomposition of high-order Bessel beams we demonstrated a class of beams which are solution of the exact Helmholtz equation in Cartesian coordinates. Our results suggest a new class of nondiffracting beams.