An unsettled discussion on the bounds of the geometric phase motivates us to explore its differences with the propagation phase. We prepare an experiment that allows us to modify both phases in the same setup and record the effect this has on white light interference fringes. Our results show clear differences between the phases where the propagation phase moves the white light interference pattern as a whole but the geometric phase does not. We present the addition of the geometric phase as we stack two retarders and compare it to the addition of the propagation phase obtained when stacking two glass windows.
We present a summarized and simplified introduction to our wave description of geometric phase. We start by discussing the addition of cosine waves of different amplitudes and a phase between them, from which immediately arises the geometric phase in 1D. We then expand on the analysis to the 2D case using the orthogonal components of a polarized light wave. We then show a graphic visualization that facilitates the analysis of geometric phase and use it to quantify the geometric phase obtained by passing different states of polarization through a quarter wave plate.
Wave branching occurs during propagation in a gently disordered medium. It appears in many different physical situations involving diverse length scales: from electron waves refracted in semiconductors to ocean waves deflected by surface eddies. Very recently, this phenomenon has been observed in light by studying the propagation of laser beams in soap films, opening an exciting field of research where the entire machinery of structured light can be brought to bear. Here, we develop computational tools to simulate and characterize the branched flow of light propagating through two-dimensional inhomogeneous media. We present the effects of varying the correlation length of the scattering medium, the influence of shaping the input beam, and the statistical features depicting the branching of light.
This work, based on classical light, was in uenced by quantum applications, where comparison of quantum states is an important issue. Laguerre-Gaussian modes were used to encode and compare two independent signals. Polarization controlled SWAP gate exchanges information between two strings of data, therefore preventing them from the leakage. Comparison is done with kHz frequency, achieved by the Digital Micromirror Device. Detected power, being a single value, represents an overlap of both signals. Presented system is capable to perform direct error analysis together with a normalization procedure, which overcomes the necessity of data post-processing and largely reduces time required for such comparison. We present a calibration procedure, which uses the glass sample to determine the performance of the experimental setup.
In a typical interferometric experiment, the overlap between the reference and probe beams produces an intensity pattern composed of fringes. This fringe pattern contains information regarding the interaction of the probe beam with the sample. If the probe beam passes through a polarizing system, it acquires both a dynamic and geometric phase. The former related to the optical pathlength, whereas the latter related to changes in the state of polarization. As a consequence, the fringe pattern suffers a lateral spatial shift and, mainly due to the geometric phase, change its visibility. In this work, we derive simple expressions relating the fringe visibility with the geometric phase and retardance introduced by the polarizing optical system, in terms of the input polarization state. By doing so, we extract the eigenvectors and eigenvalues of the Jones matrix that characterizes the sample. Therefore, our results enable the implementation of a fringe polarimetry technique, i.e., we can infer the polarization properties of the test sample through visibility measurements.
In this manuscript, a simple and low-cost method for phase-shifting interferometry by the rotation of a polarizer is presented. The principle of the proposal relies on the polarization aberration introduced by a cube beam-splitter due to its geometry, to the angular dependence with the coating and to the polarization angle of the input beam. The interferometric setup performs as a two-window common-path interferometer in which the added phase-shifting is achieved by simply rotating a polarizer at the interferometer output. The viability of the proposal is sustained with experimental results in which the phase-shift value and the resulting wavefront are calculated with Farrel’s technique and the Three-step PSI algorithm respectively.
We implement laboratory activities for the construction of key concepts in quantum optics based on experimentation and discussion. These activities were realized in the Quantum Optics Laboratory at Tecnologico de Monterrey with a multidisciplinary group of undergraduate students. We focus on experiments that involve understanding the concept of a photon, such as single photon interference, correlated photons, and entangle- ment. As an indicator of acquired learning, we design a questionnaire with conceptual questions. This initiative seeks to stimulate the development of multidisciplinary projects in quantum optics taking as a starting point the understanding of basic concepts.
We study the effects of the optical forces acting on nanoparticles when they are illuminated with structured light. We developed a computational toolbox that calculates optical forces. The results allow us to obtain the trajectory described by the particles depending on their initial conditions and physical properties. As an example, we generate structured light beams by superimposing optical vortices. The resulting beam generates gradient, scattering and curl forces. We show the dynamics of dielectric and metallic nanoparticles. This work may stimulate further research on controlling nanometer-size particles using light beams with space-variant polarization.
We present a polarimetry method based on measurement of the geometric phase. We implement a dual-path Mach-Zehnder interferometer to measure the geometric phase introduced by polarization optics composed of retarders. The method can be used either to determine a polarization state of light or to measure the Jones matrix of retarders and polarization 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
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.
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.
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.
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.
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