Low-cost printed holography for the generation of structured light.

Recently, the study of structured light fields has attracted great interest, which includes their generation and characterization techniques, as well as their application. Most of these techniques rely on the use of expensive devices, such as liquid crystal spatial light modulators or digital micromirror devices that also require specialized knowledge and software. In this work, we present a scheme for producing low-cost amplitude holograms for the generation of structured light fields. We demonstrate the feasibility of this technique by creating a variety of paraxial modes, such as the well-known Laguerre-Gaussian and Hermite-Gaussian beams. We also demonstrate the potential of our technique in solving the phase retrieval problem to generate 2D and 3D holographic images of objects. Finally, we compare our proposal with the typical generation techniques using digital micromirror devices. Our proposal will pave the path for the generation of structured light beams in more affordable ways for the application in undergrad laboratories.

Partially coherent Ince-Gaussian beams.

We report on the study and generation of Ince-Gaussian beams in the spatially partially coherent regime. The inherent random fluctuations both in time and space of these partially coherent fields make their characterization difficult. Our results show that the cross-correlation function (CCF) provides insight into the composition of the Ince-Gaussian beam, as well as into its spatial coherence structure and singularities. Our experimental findings are in very good agreement with the numerical simulations, particularly revealing a rich structure of nodal lines in the CCF.

Morphological transformation of generalized spirally polarized beams by anisotropic media and its experimental characterization.

We present a generalization of the known spirally polarized beams (SPBs) which we will call generalized spirally polarized beams (GSPBs). We characterize in detail both theoretically and experimentally the streamline morphologies of the GSPBs and their transformation by arbitrary polarization optical systems described by complex Jones matrices. We find that the description of the passage of GSPBs through a polarization system is equivalent to the stability theory of autonomous systems of ordinary differential equations. While the streamlines of the GSPB exhibit a spiral geometry, the streamlines of the output field may exhibit spirals, saddles, nodes, ellipses, and stars as well. Using a novel experimental technique based on a Sagnac interferometer, we have been able to generate in the laboratory each one of the different cases of GSPBs and record their corresponding characteristic streamline morphologies.

Accessible quantitative phase imaging in confocal microscopy with sinusoidal-phase synthetic optical holography.

We present a technically simple implementation of quantitative phase imaging in confocal microscopy based on synthetic optical holography with sinusoidal-phase reference waves. Using a Mirau interference objective and low-amplitude vertical sample vibration with a piezo-controlled stage, we record synthetic holograms on commercial confocal microscopes (Nikon, model: A1R; Zeiss: model: LSM-880), from which quantitative phase images are reconstructed. We demonstrate our technique by stain-free imaging of cervical (HeLa) and ovarian (ES-2) cancer cells and stem cell (mHAT9a) samples. Our technique has the potential to extend fluorescence imaging applications in confocal microscopy by providing label-free cell finding, monitoring cell morphology, as well as non-perturbing long-time observation of live cells based on quantitative phase contrast.

Geometric phase morphology of Jones matrices.

We demonstrate an innovative technique based on the Pancharatnam-Berry phase that can be used to determine whether an optical system characterized by a Jones matrix is homogeneous or inhomogeneous, containing orthogonal or nonorthogonal eigenpolarizations, respectively. Homogeneous systems have a symmetric geometric phase morphology showing line dislocations and sets of polarization states with an equal geometric phase. In contrast, the morphology of inhomogeneous systems exhibits phase singularities, where the Pancharatnam-Berry phase is undetermined. The results show an alternative to extract polarization properties such as diattenuation and retardance, and can be used to study the transformation of space-variant polarized beams.

On-demand tailored vector beams.

We introduce an effective optical system to produce optical beams with arbitrary, inhomogeneous polarization states. Using our system, we are capable of generating vector beams with discretionarily chosen transverse complex fields in a straightforward way. We generate several different instances of well-known vector beams and the less common spirally polarized vector beams, as well as a full Poincaré beam. We visually show the continual transition between azimuthally and radially polarized beams via a collection of spirally polarized beams. We experimentally determine the polarization states of the generated beams and quantitatively assess the performance of our system. We find that the measured polarization distributions accurately coincide with the intended input polarization distributions.

Digital generation of partially coherent vortex beams.

We present an experimental technique to generate partially coherent vortex beams with an arbitrary azimuthal index using only a spatial light modulator. Our approach is based on digitally simulating the intrinsic randomness of broadband light passing through a spiral phase plate. We illustrate the versatility of the technique by generating partially coherent beams with different coherence lengths and orbital angular momentum content, without any moving optical device. Consequently, we study its cross-correlation function in a wavefront folding interferometer. The comparison with theoretical predictions yields excellent agreement.

Orbital angular momentum of optical vortices from power measurements and the cross-correlation function.

We show that the complex-amplitude cross-correlation function between two beams can be obtained by the global Stokes parameters. We apply this approach to determine the topological charge of a Laguerre-Gaussian (LG) beam by performing power measurements only. Additionally, we study the connection of the cross-correlation function with the degree of polarization for nonuniformly polarized beams, and we obtain closed-form expressions of the cross correlation for LG vector modes and the generalized full Poincaré beams.

Quasi-one-dimensional optical lattices for soliton manipulation.

Based on angular spectrum engineering, we report the generation of optical lattices whose two-dimensional transverse nondiffracting pattern can be reduced to a quasi-one-dimensional intensity structure formed by either a single or multiple parallel channels. Remarkably, many features for each channel such as its maximum intensity, modulation, width, or separation among channels, can be controlled and modified in order to meet the requirements of particular applications. In particular, we demonstrate that these lattices can provide useful schemes for soliton routing and steering. We demonstrate the existence domain of ground-state solitons for the single quasi-one-dimensional lattice, and we show that these nondiffracting beams allow "push and pull" dynamics among the neighbor solitons propagated along the nondiffracting channels generated.

Focal shift in vector Mathieu-Gauss beams.

The three dimensional distribution of focused vector Mathieu-Gauss beams (vMG) is studied in the vicinity of the geometrical focus of an unapertured thin lens. We adopt two different intensity based criteria for defining the actual focus. Our analysis confirms the existence of a focal shift towards the lens for this type of beams. The dependence of the focal shift on the different parameters of the beams is discussed in detail. Beams with different states of polarization are studied as well, and it is shown that the focal shift is independent of the polarization.

A deterministic detector for vector vortex states.

Encoding information in high-dimensional degrees of freedom of photons has led to new avenues in various quantum protocols such as communication and information processing. Yet to fully benefit from the increase in dimension requires a deterministic detection system, e.g., to reduce dimension dependent photon loss in quantum key distribution. Recently, there has been a growing interest in using vector vortex modes, spatial modes of light with entangled degrees of freedom, as a basis for encoding information. However, there is at present no method to detect these non-separable states in a deterministic manner, negating the benefit of the larger state space. Here we present a method to deterministically detect single photon states in a four dimensional space spanned by vector vortex modes with entangled polarisation and orbital angular momentum degrees of freedom. We demonstrate our detection system with vector vortex modes from the |[Formula: see text]| = 1 and |[Formula: see text]| = 10 subspaces using classical and weak coherent states and find excellent detection fidelities for both pure and superposition vector states. This work opens the possibility to increase the dimensionality of the state-space used for encoding information while maintaining deterministic detection and will be invaluable for long distance classical and quantum communication.

Propagation of generalized vector Helmholtz-Gauss beams through paraxial optical systems.

We introduce the generalized vector Helmholtz-Gauss (gVHzG) beams that constitute a general family of localized beam solutions of the Maxwell equations in the paraxial domain. The propagation of the electromagnetic components through axisymmetric ABCD optical systems is expressed elegantly in a coordinate-free and closed-form expression that is fully characterized by the transformation of two independent complex beam parameters. The transverse mathematical structure of the gVHzG beams is form-invariant under paraxial transformations. Any paraxial beam with the same waist size and transverse spatial frequency can be expressed as a superposition of gVHzG beams with the appropriate weight factors. This formalism can be straightforwardly applied to propagate vector Bessel-Gauss, Mathieu-Gauss, and Parabolic-Gauss beams, among others.

Optical rankine vortex and anomalous circulation of light.

Rankine vortex characteristics of a partially coherent optical vortex are explored using classical and physical optics. Unlike a perfectly coherent vortex mode, the circulation is not quantized. Excess circulation is predicted owing to the wave nature of composite vortex fields. Based on these findings, we propose a vortex stellar interferometer.

Comment on "Eigenfields and output beams of an unstable Bessel-Gauss resonator".

We comment on a recent paper by D. Ling et al. [Appl. Opt. 45, 4102 (2006)]. In that paper, the authors adopted the entire matrix formalism that we established in a previous work [J. Opt. Soc. Am. A 22, 1909 (2005)] for finding the eigenmodes of an unstable Bessel resonator. Nevertheless, the results are inaccurate mainly because (a) it was overlooked that light crosses through the axicon twice in a complete round trip and (b) the numerical method used to evaluate the diffraction integral equations cannot resolve the eigenvalues and eigenfields for the given resonator configuration.

Analysis of eigenfields in the axicon-based Bessel-Gauss resonator by the transfer-matrix method: comment.

Numerical calculations recently published [J. Opt. Soc. Am. A23, 912 (2006)] on the eigenmodes in axicon-based Bessel-Gauss resonators revealed significant inconsistencies regarding the modal patterns, the mode losses, the mode ordering by loss, and the intracavity field distributions. We show that the results are inaccurate mainly because (a) it was overlooked in the derivation of the matrix equations that light crosses twice through the axicon in a complete round-trip and (b) the numerical method used to evaluate the diffraction integral equations cannot resolve the eigenvalues and eigenfields for the given resonator configuration.

Theory of the unstable Bessel resonator.

A rigorous analysis of the unstable Bessel resonator with convex output coupler is presented. The Huygens-Fresnel self-consistency equation is solved to extract the first eigenmodes and eigenvalues of the cavity, taking into account the finite apertures of the mirrors. Attention was directed to the dependence of the output transverse profiles; the losses; and the modal-frequency changes on the curvature of the output coupler, the cavity length, and the angle of the axicon. Our analysis revealed that while the stable Bessel resonator retains a Gaussian radial modulation on the Bessel rings, the unstable configuration exhibits a more uniform amplitude modulation that produces output profiles more similar to ideal Bessel beams. The unstable cavity also possesses higher-mode discrimination in favor of the fundamental mode than does the stable configuration.