Polarization basis for vortex beams

Tight-focusing parabolic reflector schemes for petawatt lasers

A comparative study of three different tight-focusing schemes for high-power lasers is performed numerically. Using the Stratton-Chu formulation, the electromagnetic field in the vicinity of the focus is evaluated for a short-pulse laser beam incident upon an on-axis high numerical aperture parabola (HNAP), an off-axis parabola (OAP), and a transmission parabola (TP). Linearly- and radially-polarized incident beams are considered. It is demonstrated that while all the focusing configurations yield intensities above 10²³ W/cm² for a 1 PW incident beam, the nature of the focused field can be drastically modified. In particular, it is shown that the TP, with its focal point behind the parabola, actually converts an incoming linearly-polarized beam into an m = 2 vector beam. The strengths and weaknesses of each configuration are discussed in the context of future laser-matter interaction experiments. Finally, a generalization of NA calculations up to 4π-illumination is proposed through the solid angle formulation, providing a universal way to compare light cones from any kind of optics.

Taming Friedrich-Wintgen Interference in a Resonant Metasurface: Vortex Laser Emitting at an On-Demand Tilted Angle

Friedrich-Wintgen (FW) interference is an atypical coupling mechanism that grants loss exchange between leaky resonances in non-Hermitian classical and quantum systems. Intriguingly, such a mechanism makes destructive interference possible for scenarios in which a radiating wave becomes a bound state in the continuum (BIC) by giving away all of its losses. Here we propose and demonstrate experimentally an original concept to tailor FW-BICs with polarization singularity at on-demand wavevectors in an optical metasurface. As a proof-of-concept, using hybrid organic-inorganic halide perovskite as an active material, we empower this novel polarization singularity to obtain lasing emission, exhibiting both highly directional emission at oblique angles and a polarization vortex in momentum space. Our results pave the way to steerable coherent emission with a tailored polarization pattern for applications in optical communication/manipulation in free space, high-resolution imaging/focusing, and data storage.

Production of orbital angular momentum states of optical vortex beams using a vortex half-wave retarder with double-pass configuration

Higher orders of orbital angular momentum states (OAMs) of light have been produced with a double-pass configuration through a zero-order vortex half-wave retarder (VHWR). This double-pass technique can reduce the number of VHWR plates used, thus reducing costs. The OAM states of the vortex beams are identified by the near-field Talbot effect. Polarization dependence of the vortex states can also be demonstrated with this VHWR using Talbot effect. Without using the Talbot patterns, this effect of the polarization on the vortex beam can not be recognized. A theoretical validation has also been provided to complement the experimental results. Our study gives an improved understanding of this approach to use a VHWR plate.

Depolarization of Vector Light Beams on Propagation in Free Space

Nonparaxial propagation of the vector vortex light beams in free space was investigated theoretically. Propagation-induced polarization changes in vector light beams with different spatial intensity distributions were analyzed. It is shown that the hybrid vector Bessel modes with polarization-OAM (orbital angular momentum) entanglement are the exact solutions of the vector Helmholtz equation. Decomposition of arbitrary vector beams in the initial plane z = 0 into these polarization-invariant beams with phase and polarization singularities was used to analyze the evolution of the polarization of light within the framework of the 2 × 2 coherency matrix formalism. It is shown that the 2D degree of polarization decreases with distance if the incident vector beam is not the modal solution. The close relationship of the degree of polarization with the quantum-mechanical purity parameter is emphasized.

Mueller Matrix Polarimetry with Invariant Polarization Pattern Beams

A wide class of nonuniformly totally polarized beams that preserve their transverse polarization pattern during paraxial propagation was studied. Beams of this type are of interest, in particular, in polarimetric techniques that use a single input beam for the determination of the Mueller matrix of a homogeneous sample. In these cases, in fact, it is possible to test the sample response to several polarization states at once. The propagation invariance of the transverse polarization pattern is an interesting feature for beams used in these techniques, because the polarization state of the output beam can be detected at any transverse plane after the sample, without the use of any imaging/magnifying optical system. Furthermore, exploiting the great variety of the beams of this class, the ones that better fit specific experimental constrains can be chosen. In particular, the class also includes beams that present all possible polarization states across their transverse section (the full Poincaré beams (FPB)). The use of the latter has recently been proposed to increase the accuracy of the recovered Mueller matrix elements. Examples of FPBs with propagation-invariant polarization profiles and its use in polarimetry are discussed in detail. The requirement of invariance of the polarization pattern can be limited to the propagation in the far field. In such a case, less restrictive conditions are derived, and a wider class of beams is found.

All-dielectric metasurface with multi-function in the near-infrared band

This paper presents an approach to design the all-dielectric metasurface with multi-function in the near-infrared range of 1.5-1.6 µm. Based on the geometric phase principle, the all-dielectric metasurface is composed of the Si nanopillar and the SiO₂ substrate as an emitter unit distributed in a 21×21 array. Under the incidence of the circularly polarized light at 1550 nm, the metasurface works as a vortex-beam generator with high performance which generates the vortex beam with topological charges of ±1, and the mode purity of the vortex beam is 90.66%. Under the incidence of the linearly polarized light at 1550 nm, the metasurface also works as the azimuthally/radially polarized beam generator with high performance, and the purities of the azimuthally and the radially polarized beams are 92.52% and 91.02%, respectively. Moreover, the metasurface generates different output spots under the different incident lights which can be applied to optical encryption, and the metasurface with the phase gradient also can be used as the dual-channel encoder/decoder in optical communication. The simulated results are in good agreement with the theoretical derivation. The designed metasurface may become a potential candidate as a multi-function photon device in the integrated optical system in the future.

Synthesis and characterization of non-uniformly totally polarized light beams: tutorial

Polarization of a light beam is traditionally studied under the hypothesis that the state of polarization is uniform across the transverse section of the beam. In such a case, if the paraxial approximation is also assumed, the propagation of the beam reduces to a scalar problem. Over the last few decades, light beams with spatially variant states of polarization have attracted great attention, due mainly to their potential use in applications such as optical trapping, laser machining, nanoscale imaging, polarimetry, etc. In this tutorial, an introductory treatment of non-uniformly totally polarized beams is given. Besides a brief review of some useful parameters for characterizing the polarization distribution of such beams across transverse planes, from both local and global points of view, several methods for generating them are described. It is expected that this tutorial will serve newcomers as a starting point for further studies on the subject.

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.

Analyzing characteristics of spiral vector beams generated by mixing of orthogonal LP11 modes in a few-mode optical fiber

We have demonstrated a method for the generation of spiral vector beams using a few-mode optical fiber. The beams are generated due to the combination of orthogonal linearly polarized modes with a tilted polarization vector in the few-mode optical fiber. The excitation of these modes is controlled by the incident state of polarization and coupling conditions at the input end of the fiber. The beams with clockwise and counterclockwise nature of spiral polarization are generated, and switching between them is demonstrated. The obtained results emphasize the strong dependency of polarization of generated spiral vector beams and other orthogonal linearly polarized modes on the input state of polarization. The simulated results of mode mixing are verified experimentally with good agreement.

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.

Optical rotation of a uniformly, linearly polarized Bessel-like beam in free space

We report on the observation of a light beam in air whose polarization state is uniform and linear at the transverse region where the intensity is high and rotates uniformly with propagation distance. The beam is obtained by interference of two circularly polarized Bessel beams of opposite helicities and very similar, but not equal, cone angles. The measured rotation rate is in agreement with that expected from theory.

Tailored optical vector fields for ultrashort-pulse laser induced complex surface plasmon structuring

Precise tailoring of optical vector beams is demonstrated, shaping their focal electric fields and used to create complex laser micro-patterning on a metal surface. A Spatial Light Modulator (SLM) and a micro-structured S-waveplate were integrated with a picosecond laser system and employed to structure the vector fields into radial and azimuthal polarizations with and without a vortex phase wavefront as well as superposition states. Imprinting Laser Induced Periodic Surface Structures (LIPSS) elucidates the detailed vector fields around the focal region. In addition to clear azimuthal and radial plasmon surface structures, unique, variable logarithmic spiral micro-structures with a pitch Λ ∼1μm, not observed previously, were imprinted on the surface, confirming unambiguously the complex 2D focal electric fields. We show clearly also how the Orbital Angular Momentum(OAM) associated with a helical wavefront induces rotation of vector fields along the optic axis of a focusing lens and confirmed by the observed surface micro-structures.

Maxwell-Gaussian beams with cylindrical polarization

It is common practice to work in the approximation that beam-like radiation fields are polarized transverse to the propagation axis. However, even in the paraxial approximation, this fails to correctly describe beam polarization and propagation characteristics. We present here the paraxial Maxwell's equations for beams having cylindrical polarization, which describe the full vector structure of these beams in the paraxial regime. The effect that these relations have on the polarization and propagation of cylindrically polarized Laguerre-Gauss and Bessel-Gauss beams is subsequently explored.

Topological phase structure of vector vortex beams

The topological phase acquired by vector vortex optical beams is investigated. Under local unitary operations on their polarization and transverse degrees of freedom, the vector vortices can only acquire discrete geometric phase values, 0 or π, associated with closed paths belonging to different homotopy classes on the SO(3) manifold. These discrete values are demonstrated through interferometric measurements, and the spin-orbit mode separability is associated to the visibility of the interference patterns. The local unitary operations performed on the vector vortices involved both polarization and transverse mode transformations with birefringent wave plates and astigmatic mode converters. The experimental results agree with our theoretical simulations and generalize our previous results obtained with polarization transformations only.

Polarization changes at Lyot depolarizer output for different types of input beams

Lyot depolarizers are optical devices made of birefringent materials used for producing unpolarized beams from totally polarized incident light. The depolarization is produced for polychromatic input beams due to the different phase introduced by the Lyot depolarizer for each wavelength. The effect of this device on other types of incident fields is investigated. In particular two cases are analyzed: (i) monochromatic and nonuniformly polarized incident beams and (ii) incident light synthesized by superposition of two monochromatic orthogonally polarized beams with different wavelengths. In the last case, it is theoretically and experimentally shown that the Lyot depolarizer increases the degree of polarization instead of depolarizes.

Generation of spirally polarized propagation-invariant beam using fiber microaxicon

We present here a fiber microaxicon (MA)based method to generate spirally polarized propagation-invariant optical beam. MA chemically etched in the tip of a two-mode fiber efficiently converts the generic cylindrically polarized vortex fiber mode into a spirally polarized propagation-invariant (Bessel-type) beam via radial dependence of polarization rotation angle. The combined roles of helico-conical phase and nonparaxial propagation in the generation and characteristics of the output beam from the fiber MA are discussed.

Higher-order Poincaré sphere, stokes parameters, and the angular momentum of light

A higher-order Poincaré sphere and Stokes parameter representation of the higher-order states of polarization of vector vortex beams that includes radial and azimuthal polarized cylindrical vector beams is presented. The higher-order Poincaré sphere is constructed by naturally extending the Jones vector basis of plane wave polarization in terms of optical spin angular momentum to the total optical angular momentum that includes higher dimensional orbital angular momentum. The salient properties of this representation are illustrated by its ability to describe the higher-order modes of optical fiber waveguides, more exotic vector beams, and a higher-order Pancharatnam-Berry geometric phase.

Vectorial structure of far field of cylindrically polarized beams diffracted at a circular aperture

Based on the vector angular spectrum representation and the method of stationary phase, the analytical vectorial structure of the cylindrically polarized Laguerre-Gaussian beam diffracted at a circular aperture is derived in the far field, which provides an approach to further comprehend the vectorial properties of the apertured cylindrically polarized beams. The radially polarized, azimuthally polarized, and unapertured cases can be viewed as the special cases of our general result. The analyses show that the far-field energy flux distributions of the entire beam, the TE term, and the TM term depend on the beam order, the ratio of the waist width to the wavelength, the truncation parameter, and the angle between the electric field vector and the radial direction.

Spatially engineered polarization states and optical vortices in uniaxial crystals

We describe how the propagation of light through uniaxial crystals can be used as a versatile tool towards the spatial engineering of polarization and phase, thereby providing an all-optical technique for vectorial and scalar singular beam shaping in optics. Besides the prominent role played by the linear birefringence, the influence of circular birefringence (the optical activity) is discussed as well and both the monochromatic and polychromatic singular beam shaping strategies are addressed. Under cylindrically symmetric light-matter interaction, the radially, azimuthally, and spirally polarized eigen-modes for the light field are revealed to be of a fundamental interest to describe the physical mechanisms at work when dealing with scalar and vectorial optical singularities. In addition, we also report on nontrivial effects arising from cylindrical symmetry breaking, e.g. tilting the incident beam with respect to the crystal optical axis.

Nonparaxial analyses of radially polarized beams diffracted at a circular aperture

On the basis of the vectorial Rayleigh diffraction integral, the analytical expressions for the electromagnetic fields of the radially polarized beams diffracted at a circular aperture are derived, which helps us investigate the propagation properties of the apertured radially polarized beams in the nonparaxial and paraxial regimes. The unapertured and paraxial cases can be viewed as the special cases of the general result obtained in this paper. The analyses indicate that the nonparaxiality of the apertured radially polarized beams depends on the ratio of the waist width to the wavelength and the truncation parameter. In addition, the truncation parameter and the beam order have a great impact on the beam diffraction effect and the beam evolution behavior.

Partially correlated sources with complete polarization

We show that the correlation matrix of any electromagnetic planar source endowed with complete polarization must be of a universal form, no matter how the field components are correlated across the source plane. Such form entails that both the realizability conditions and the search of vector modes of the source reduce to scalar problems. We shall also briefly dwell on how propagation affects the polarization properties of the field and, in particular, we discuss cases in which propagated light remains completely polarized.

Nonparaxial fields with maximum joint spatial-directional localization. II. Vectorial case

The monochromatic nonparaxial vector fields that achieve a minimum spatial spread for a given directional spread are found. The derivation of these fields is analogous to the one presented in part I of this series for the case of scalar fields. This derivation is based on a variational treatment and multipolar expansion. The resulting lower bounds for the spreads of vector fields turn out to be considerably more restrictive than for scalar fields.

Highly focused spirally polarized beams

The features of spirally polarized light beams focused by high-numerical-aperture systems are investigated in the nonparaxial regime by means of Debye theory with a multipole expansion technique. General expressions of the expanding coefficients are given, as well as the electric field distributions across the focal plane. Numerical examples are presented for the case of spirally polarized beams of the donut type. Comparisons with recent experimental results are also shown.

Nonparaxial propagation of spirally polarized optical beams

The free-propagation features of light beams whose transverse electric field lines are logarithmic spirals (namely, spirally polarized beams) are investigated in both the paraxial and the nonparaxial regime. The complete propagated electric field is considered, and some general properties are obtained regardless of the specific transverse distribution. Simple and significant analytical results are obtained when the transverse intensity profile is chosen as that pertinent to an axially symmetric Laguerre-Gaussian beam of order 1 (namely, spirally polarized donut beams). In particular, it is found that for such beams, the propagated longitudinal electric field can be expressed as a simple superposition of elegant Laguerre-Gaussian beams. Numerical results are presented for different values of the beam parameters and are compared with recently obtained experimental results.

Polarization singularities in optical lattices

Polarization singularities are shown to be unavoidable features of three-dimensional optical lattices. These singularities take the form of lines of circular polarization, C lines, and lines of linear polarization, L lines. The polarization figures surrounding a C line (L line) rotate about the line with winding number +/-1/2 (+/-1). C and L lines permeate the lattice, meander throughout the unit cell, and form closed loops. Surprisingly, every point in a linearly polarized optical lattice is found to be a singularity about which the surrounding polarization vectors rotate with an integer winding number.

General vectorial decomposition of electromagnetic fields with application to propagation-invariant and rotating fields

A novel decomposition of the transversal part of the electric field vector of a general non-paraxial electromagnetic field is presented, which is an extension of the radial/aximuthal decomposition and is known as gammazeta decomposition. Purely gamma and zeta polarized fields are examined and the decomposition is applied to propagation-invariant, rotating, and self-imaging electromagnetic fields. An experimental example on the effect of state of polarization in the propagation characteristics of the field: its is shown that a simple modification of the polarization conditions of the angular spectrum converts a self-imaging field into a propagation-invariant field.