In this work we provide a practical formulation to evaluate both, dynamical an geometrical phases, for any
polarization state entering an optical system characterized by a Jones matrix. By employing an automated
and robust interferometric experiment, we observe characteristic behaviors depending on whether the system
is homogeneous, with orthogonal eigenpolarizations, or inhomogeneous, with nonorthogonal eigenpolarizations.
The results apply either for classical or quantum states of light and can be used for the design of Pancharatnam-
Berry phase optical elements.
The design, fabrication and characterization of space-variant Pancharatnam-Berry phase optical elements is presented for the terahertz regime (THz). These PBOEs are made out of polystyrene and were fabricated by commercially available three-dimensional printers, providing a simple and inexpensive solution for the generation of THz vector beams. The polarization structure was characterized by using a THz time-domain imaging system. These devices can find applications in future THz technologies and provide new tools for the study of polarization morphologies
The commutation between the Helmholtz equation and the derivative operator allows us to generate novel nondiffracting beams. We apply a general differential operator to Bessel beams and study the resulting phase structure and orbital angular momentum (OAM). We find the parameters that preserve the OAM of the seed beam and show how to produce and control shape preserving vortex arrays. In analogy to the Poincaré sphere, our approach is used to develop an operator sphere connecting higher-order Bessel beams.
We study the energy ow pattern in the superposition of two off-axis optical vortices with orthogonal polarization states. This system presents a rich structure of polarization singularities, which allows us to study the transverse spin and orbital angular momentum of different polarization morphologies, which includes C points (stars, lemons and monstars) and L lines. We perform numerical simulations of the optical forces acting on submicron particles and show interesting configurations. We provide the set of control parameters to unambiguously distinguish between the spin and orbital ow contributions.
Quantum Optical Coherence Tomography can achieve a greater image resolution compared to its classical counterpart, due to the entanglement of the photon pairs. Following the idea that higher the number of entangled photons, higher the resolution, we study the physical underpinnings that appear when using photon triplets. Unlike the usual Hong-Ou-Mandel interferometer used for QOCT, a much simpler implementation in the form of a Michelson interferometer is used in this work. We find that axial resolution can be improved by a factor of four. Additionally, we provide the numerical method to reconstruct the image given the triple coincidence rate.
We study both theoretically and experimentally the cross-correlation function of single-ringed Laguerre-Gaussian (LG) beams, which allows us to determinate the topological charge of the beam by performing power measure-ments only. We employ a superposition of two exact copies of the original LG beam whose centroids are displaced from each other. The behaviour of the auto-correlation is studied as a function of the displacement between these two copies of the beam for different topological charges. Our results indicate that the auto-correlation is described by a polynomial function of the displacement parameter, and the number of zeros of this polynomial maintains a one to one correspondence with the topological charge. A detailed description of the experiment to perform these measurements is also provided, our experimental findings are in excellent agreement with the theory. This technique offers an alternative for measuring the content of orbital angular momentum in a beam without the need of a camera.
An alternative method to experimentally measure the topological charge of a vortex beam is presented. The method is based on the number of polarization singularities arising in the superposition of two off-axis Laguerre-Gauss beams having orthogonal polarizations. The experimental setup consists of a modified Mach-Zehnder interferometer which provides control over the polarization structure by allowing us to introduce lateral displace ments as well as relative phase variations between the two arms of the interferometer. A comparison between theoretical and experimental results is done with very good agreement. This method offers an alternative for measuring orbital angular momentum content in a beam without the need of interfering with a reference plane wave. The dynamics of polarization singularities are also studied experimentally.
We study the propagating and shaping characteristics of the novel one-dimensional Cartesian Parabolic-Gaussian
beams. The transverse profile is described by the parabolic cylinder functions and are apodized by a Gaussian
envelope. Their physical properties are studied in detail by finding the 2n-order intensity moments of the beam.
Propagation through complex ABCD optical systems, normalization factor, beam width, the quality M2 factor
and its kurtosis parameter are derived. We discuss its behavior for different beam parameters and the relation
between them. The Cartesian Parabolic-Gaussian beams carry finite power and form a biorthogonal set of
solutions of the paraxial wave equation in Cartesian coordinates.
We study the propagating and shaping characteristics of the novel Whittaker-Gaussian beams (WGB). The transverse profile is described by the Whittaker functions. Their physical characteristics are studied in detail by finding the 2n-order intensity moments of the beam. Propagation through complex ABCD optical systems, normalization factor, beamwidth, the quality M2 factor and its kurtosis parameter are derived. We discuss its behavior for different beam parameters and the relation between them. The WGBs carry finite power and form a biorthogonal set of solutions of the paraxial wave equation (PWE) in circular cylindrical coordinates.
We present results describing the behavior of optically trapped airborne particles, both solid and liquid. Using back focal
plane interferometry we measure characteristic power spectra describing the position fluctuations within the trap. We
show it is easy to transfer between an over and under damped regime by either varying the trapping power or the
distance into the medium the beam is focused. The results assist in the understanding of airborne tweezers and it is hoped
having under damped systems could lead to exploring analogies in many areas of fundamental physics.