Complex vector light fields have become a topic of late due to their exotic features, such as their non-homogeneous transverse polarisation distributions and the non-separable coupling between their spatial and polarisation degrees of freedom. In general, vector beams propagate in free space along straight lines, being the Airy-vector vortex beams the only known exception. Here, we introduce a new family of vector beams that exhibit properties that have not been observed before, such as their ability to freely accelerate along parabolic trajectories. We anticipate that these novel vector beams might find applications in fields such as optical manipulation, microscopy, laser material processing, among others.
It is well known that entanglement is invariant to local unitary transformations, this implies the degree of entanglement or non-separability remains constant during free-space propagation, which is true for both quantum and classically-entangled modes. Here we demonstrate an exception to this rule using a carefully engineered vectorial light field, and study its non-separability dynamics upon free-space propagation. We show that the local non-separability between the spatial and polarisation degrees of freedom dramatically decays to zero, while preserving the purity of the state and hence the global non-separability. We show this by numerical simulations and corroborate it experimentally. Our results evince novel properties of classically-entangled modes, point to the need for new measures of non-separability for such vectorial fields, while paving the way to novel applications for customised structured light.
In this work, we present a strategy for the modal decomposition of a partially coherent Ince-Gaussian (PCIG) beam. It is shown that the beam can be represented as a suitable superposition of spatially coherent modes. As soon as the beam's spatial coherence decreases, its modal content reveals the existence of transverse coherent higher order modes, with the same ellipticity. We study the dependence of the modal decomposition in terms of the ellipticity and transverse coherence length.
We present an experimental scheme to calculate the inner product of two arbitrary scalar optical fields. The scheme is based on using an interferometer to generate superpositions of the optical fields with a relative phase difference between the two fields. The intensity observed permits the calculation of the inner product using numerical integration. The experimental results obtained for the inner product of a few common optical fields are presented along with comparison with simulations.
We introduce and generate the partially coherent non{canonical vortex beams and study their characteristics. The characterization of these fields by means of its intensity is difficult due to the random fluctuations in space and time of partially coherent fields, but it is demonstrated that the cross{correlation function provides information of the composition, spatial coherence structure and singularities of the non{canonical vortex beams. Our approach is based on experimental measurements and numerical simulations of these beams, which show excellent agreement.
We present an experimental setup to generate partially coherent Ince-Gaussian beams. The partially coherent field is constructed using a rotating ground glass disk to reduce the spatial coherence of a laser source and digital holograms. Our results show that the cross correlation function of these beams inherit properties of their spatial structure. The experimental cross correlation function is measured by means of a well known wavefront folding interferometer, which allows us to characterize the properties of the beam. The comparison between theoretical and experimental results yields excellent agreement.
We study the spatial coherence properties of partially coherent vortex beams. The mathematical model employed for the generation and control of the spatially partially coherent beam is based on a statistical model, in which the field is constructed from the incoherent superposition of an ensemble of individual vortices carrying topological charges of different values and handedness. Results show that if the ensemble from which the partially coherent vortex is generated consists of a mixed composition of individual vortices it is not always possible to determine its topological charge unambiguously.
Optical vector beams arise from point to point spatial variations of the electric component of an electromagnetic field over the transverse plane. In this work, we present a novel experimental technique to generate arbitrary vec- tor beams, and provide sufficient evidence to validate their state of polarization. This technique takes advantage of the capability of a Spatial Light Modulator to simultaneously generate two components of an electromagnetic field by halving the screen of the device and subsequently recombining them in a Sagnac interferometer. Our experimental results show the versatility and robustness of this technique for the generation of vector beams.
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.
Combining the multiple degrees of freedom of photons has become topical in quantum communication and information
processes. This provides advantages such as increasing the amount of information that is be packed into
a photon or probing the wave-particle nature of light through path-polarisation entanglement. Here we present
two experiments that show the advantages of using hybrid entanglement between orbital angular moment (OAM)
and polarisation. Firstly, we present results where high dimensional quantum key distribution is demonstrated
with spatial modes that have non-separable polarisation-OAM DOF called vector modes. Secondly, we show
that through OAM-polarisation entanglement, the traditional which-way experiment can be performed without
using the traditional physical path interference approach.
High-dimensional encoding using higher degrees of freedom has become topical in quantum communication protocols. When taking advantage of entanglement correlations, the state space can be made even larger. Here, we exploit the entanglement between two dimensional space and polarization qubits, to realize a four-dimensional quantum key distribution protocol. This is achieved by using entangled states as a basis, analogous to the Bell basis, rather than typically encoding information on individual qubits. The encoding and decoding in the required complementary bases is achieved by manipulating the Pancharatnam-Berry phase with a single optical element: a q-plate. Our scheme shows a transmission fidelity of 0.98 and secret key rate of 0.9 bits per photon. While the use of only static elements is preferable, we show that the low secret key rate is a consequence of the filter based detection of the modes, rather than our choice of encoding modes.
A means to digitally generate a partially coherent beam with orbital angular momentum is presented. Our approach is based on encoding the randomness of broadband light passing through a spiral phase plate in a spatial light modulator. We illustrate the technique by generating partially coherent beams with orbital angular momentum content and different coherence lengths, with no moving optical elements. We study the cross correlation spectra which yields to good agreement with theory.
In this work we revisit Young's experiment and show how it can be done with digital holography. We study different properties of light and show that depending on how light interferes, fringe patterns in other observables arise. We explain this conceptually and demonstrate how this can be implemented experimentally. We aid the reader with a tutorial-like approach and provide the necessary tools to easily perform the experiments.
We study the realization of quantum algorithms using classical optical elements and a coherent laser source. The encoded qubits are present in form of path qubits, polarization and orbital angular momentum. In particular, we propose an implementation for the Deutsch Algorithm in a Sagnac interferometer and the Deutsch-Jozsa Algorithm in a ring cavity.
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.
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.
The intensity distributions of self-focusing dual Airy beams are studied analytically by means of their statistical moments. Closed form expressions are derived that allow the determination of the focal shift through two different criteria; the first one is based on the second moment of the intensity whereas the second takes advantage of the beams symmetry to employ encircled-power calculations for defining the focus. Our results confirm the existence of a focal shift as expected, and show an effective quadratic dependence on the truncation parameter of the Airy beams.
A means to measure orbital angular momentum in a partially coherent beam is demonstrated by using a wavefront
folding interferometer. This interferometer allows us to study the cross correlation function of a partially coherent
vortex beam. It is shown that the cross correlation function possesses ring dislocations which are related to the
topological charge of the partially coherent vortex, exhibiting a one to one correspondence between the number of
rings and the value of the topological charge, thus providing a direct measure of the orbital angular momentum.
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.
The generation of intra-cavity superpositions of Bessel-Gauss beams in an axicon resonator is studied numerically
by means of a genetic algorithm. The coherent superposition of low order modes is induced by introducing crossed
wires within the simulated cavity. Two different strategies are shown to be equivalent for the generation of the
same superposition of two Bessel-Gauss beams with opposite azimuthal orders. In the first strategy the angle
between a pair of cross-wires is varied for mode selection, the second consists on introducing a number of crosswires
at equally spaced angles in which the number of wires corresponds exactly to the order of the superposed
modes. Our results suggest a direct method for generating experimentally a coherent mode superposition of
Bessel-Gauss beams using an axicon-based Bessel-Gauss resonator. These beams are relevant in areas such as
optical trapping and micromanipulatio
The phenomena of focal shift is studied in vector Parabolic-Gauss beams. Two different criteria are employed
to define the actual focus of the beam, one makes use of the energy of the beam enclosed in a circular area
of radius r, oriented along the propagation axis, and the second criteria computes the second order moment of
the intensity distribution with respect to the radial coordinate. The focal shift is confirmed for these type of
beams, and its dependence on beam parameters such as the
Gaussian-Fresnel number and their polarization is discussed.
We study the three dimensional distributioin of vector Mathieu-Gauss (vMG) beams near the focus of a non-aperturing
thin lens. These beams constitute a family of solutions to the vectorial wave equation in the paraxial
approximation. We adopt an energy criterion for defining the width of the beam as well as the focal plane. It is
observed in our analysis that the focal plane does not coincide with the geometric focus, but it is slightly shifted
towards the lens. The dependence of the focal shift on the different parameters of the vMG beams is discussed
for beams with different polarizations.
The vector Mathieu-Gauss beams of integer order are examined as the solutions of the vector paraxial wave equation in elliptical coordinates. The propagation of the vector components and the three-dimensional intensity distribution of focused vector Mathieu-Gauss beams are analyzed for a variety of polarizations. Conditions in which the linearly polarized Mathieu-Gauss beams can be approximated by the scalar solutions of the paraxial wave equation are also discussed.
We present a detailed study of the unstable Bessel resonator. The cavity of this laser consists of a reflective axicon and a convex spherical output coupler. A matrix method analysis for the bare resonator is employed to extract the eigenmodes and eigenvalues of the cavity, which allows us to obtain the fundamental and higher-order modes. Diffractive losses and relative phase shift behavior, in terms of both the varying radius of curvature of the output coupler and the cavity length, are studied with the matrix method and the Fox-Li algorithm. Direct comparison of the transverse mode profiles with a similar resonator employing a concave output coupler is performed, showing excellent agreement for large values of the radius of curvature. We also considered the effects of varying the aperture of the output coupler and the wedge angle of the axicon on the transverse mode profiles and diffractive losses.
An image processing algorithm, mainly based on morphological enhancement and segmentation, is developed and applied to optical microscope images of transverse cuts of fabric filaments, to retrieve useful shape characteristics. Adaptive filtering and non-linear fitting algorithms are also applied. Computer generated noisy images are used to estimate the algorithm accuracy with excellent results. This algorithm is a significant improvement over the current human-based inspection method for filament shape analysis, and its development and application will improve quality control in textile industry. The complete procedure is outlined in the present work, showing relevant results and pointing out pertinent restrictions.
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