Enrique J. Galvez

Poincaré-beam patterns produced by nonseparable superpositions of Laguerre-Gauss and polarization modes of light

We present a study of Poincaré-beam polarization patterns produced by collinear superposition of two Laguerre-Gauss spatial modes in orthogonal polarization eigenstates (circular or linear). We explore theoretically and experimentally the combinations that are possible. We find that the resulting patterns can be explained in terms of mappings of points on the Poincaré sphere onto points in the transverse plane of the beam mode. The modes that we produced yielded many types of polarization singularities.

Propagation dynamics of optical vortices due to Gouy phase

We study the propagation of off-axis vortices in a paraxial beam formed by two collinear Laguerre-Gauss beams. We show that the vortices move about the beam axis as the light propagates resulting in a rotation of the beams transverse profile. This rotation is explained by the Gouy phase acquired by the component beams. Experimental measurements of the angular position of the vortices are in good agreement with a two-mode theory.

Interference with correlated photons: Five quantum mechanics experiments for undergraduates

We describe five quantum mechanics experiments that have been designed for an undergraduate setting. The experiments use correlated photons produced by parametric down conversion to generate interference patterns in interferometers. The photons are counted individually. The experimental results illustrate the consequences of multiple paths, indistinguishability, and entanglement. We analyze the results quantitatively using plane-wave probability amplitudes combined according to Feynman’s rules, the state-vector formalism, and amplitude packets. The apparatus fits on a 2′×4′ optical breadboard.We describe five quantum mechanics experiments that have been designed for an undergraduate setting. The experiments use correlated photons produced by parametric down conversion to generate interference patterns in interferometers. The photons are counted individually. The experimental results illustrate the consequences of multiple paths, indistinguishability, and entanglement. We analyze the results quantitatively using plane-wave probability amplitudes combined according to Feynman’s rules, the state-vector formalism, and amplitude packets. The apparatus fits on a 2′×4′ optical breadboard.

Photon quantum mechanics and beam splitters

We are developing materials for classroom teaching about the quantum behavior of photons in beam splitters as part of a project to create five experiments that use correlated photons to exhibit nonclassical quantum effects vividly and directly. Pedagogical support of student understanding of these experiments requires modification of the usual quantum mechanics course in ways that are illustrated by the treatment of the beam splitter presented here.

Generation of isolated asymmetric umbilics in light's polarization

Polarization-singularity C-points, a form of line singularities, are the vectorial counterparts of the optical vortices of spatial modes and fundamental optical features of polarization-spatial modes. Their generation in tailored beams has been limited to lemon and star C-points that contain symmetric dislocations in state-of-polarization patterns. In this article we present the theory and laboratory measurements of two complementary methods to generate isolated asymmetric C-points in tailored beams, of which symmetric lemons and stars are limiting cases; and we report on the generation of monstars, an asymmetric C-point with characteristics of both lemons and stars.

What’s Going On Here?

From earliest times humans have speculated about the nature of matter. The Greeks with their characteristic genius developed a highly systematic set of ideas about matter. They called these ideas “physics,” but physics in the modern sense of the word comes into being only in the seventeenth century.

Composite optical vortices formed by collinear Laguerre-Gauss beams

We study the optical fields that are produced when two Laguerre Gauss beams, each carrying an optical vortex, are superimposed collinearly. We find that the resulting beam contains new vortices. The number of vortices and their location depends on the charge of the vortices of the component beams and the relative intensity of the two beams. Our presentation focuses on the cases where the component Laguerre-Gauss beams are of order one and two.

Gaussian beams in the optics course

We introduce the physics of high-order Gaussian beams to the treatment of Gaussian beams in the undergraduate optics course. Of particular interest are Laguerre-Gauss beams, which provide the basis for discussing the new and increasingly important concept of the orbital angular momentum of light. We also describe laboratory exercises that complement the class material.

Imaging optical singularities: Understanding the duality of C-points and optical vortices

We image optical singularities by exploiting the connection between scalar and vector fields. We examine the sensitivity of optical vortices to perturbations and suggest a method of study via imaging polarimetry of the optical field. This is possible by converting optical vortices to polarization-singularity C-points. We present the deliberate creation of C-points using a superposition of two circularly polarized beams of opposite helicity, with a phase vortex in one and a planar wavefront in the other. We present a theoretical analysis and measurements of the transformation of C-points from lemon to star, going through the monstar stage. We do this by varying the phase gradient of the optical vortex.

Interferometric measurement of the helical mode of a single photon

We present measurements of the helical mode of single photons and do so by sending heralded photons through a Mach–Zehnder interferometer that prepares the light in a helical mode with topological charge one, and interferes it with itself in the fundamental non-helical mode. Masks placed after the interferometer were used to diagnose the amplitude and phase of the mode of the light. Auxiliary measurements verified that the light was in a non-classical state. The results are in good agreement with theory. The experiments demonstrate in a direct way that single photons carry the entire spatial helical-mode information.