Polarization tailored novel vector beams based on conical refraction

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.

Conical refraction mode of an optical resonator

The fundamental mode of a conical refraction resonator, i.e., an optical cavity where light experiences conical refraction (CR) from a biaxial crystal, is experimentally demonstrated in the plano-concave cavity configuration. We have discovered that the fundamental CR mode is characterized by the polarization and intensity structures of CR beams between the plane mirror and CR crystal, and it resembles the fundamental Gaussian mode with homogeneous polarization between the crystal and concave mirror. We theoretically explained this fundamental CR mode using the dual cone model and symmetry of the CR phenomenon and confirmed this explanation by numerical simulations.

Formation of hybrid higher-order cylindrical vector beams using binary multi-sector phase plates

Nowadays, the well-known cylindrical vector beams (CVBs) – the axially symmetric beam solution to the full-vector electromagnetic wave equation – are widely used for advanced laser material processing, optical manipulation and communication and have a great interest for data storage. Higher-order CVBs with polarisation order greater than one and superpositions of CVBs of various orders (hybrid CVBs) are especially of interest because of their great potential in contemporary optics. We performed a theoretical analysis of the transformation of first-order CVBs (radially and azimuthally polarised beams) into hybrid higher-order ones using phase elements with complex transmission functions in the form of the cosine or sine functions of the azimuthal angle. Binary multi-sector phase plates approximating such transmission functions were fabricated and experimentally investigated. The influence of the number of sectors and a height difference between neighbouring sectors, as well as the energy contribution of the different components in the generated hybrid higher-order CVBs were discussed in the context of polarisation transformation and vector optical field transformation in the focal region. The possibility of polarisation transformation, even in the case of weak focusing, is also demonstrated. The simple structure of the profile of such plates, their high diffraction efficiency and high damage threshold, as well as the easy-to-implement polarisation transformation principle provide advanced opportunities for high-efficient, quickly-switchable dynamic control of the generation of structured laser beams.

Classical and quantum analysis of propagation invariant vector flat-top beams

Laser beams with a near uniform intensity profile, such as flat-top and super-Gaussian beams, have found many applications, particularly in laser materials processing. Unfortunately such beams are not eigenmodes of free-space and, thus, alter their intensity profile during propagation. This may be overcome by creating vector flat-top beams. Here, we exploit the polarization dependent efficiency of spatial light modulators to create a vector flat-top beam that maintains its intensity profile and vector nature during propagation. We apply a holistic classical and quantum toolkit to analyze the dynamics of the vector state during propagation and demonstrate the versatility of these beams in an optical trapping and tweezing application. Our simple generation approach and holistic analysis toolbox will appeal to an audience who wish to employ these beams in a variety of applications.

Generation of the periodically polarized structured light beams

We report a kind of structured light beam with periodical polarization and phase singularities. It is generated from a setup consisting of conical refraction transformation and 4f-system. By this setup, the periodical structures are produced without any change of intensity distributions. We analyze both theoretically and experimentally the polarization and phase structures of the periodically structured light beam. The dependence of period is demonstrated on the length of crystal and the focal length. It is shown that the polarization of the input beam can be used to control the polarization and phase structures of the output beam.

Extreme Ultraviolet Fractional Orbital Angular Momentum Beams from High Harmonic Generation

We investigate theoretically the generation of extreme-ultraviolet (EUV) beams carrying fractional orbital angular momentum. To this end, we drive high-order harmonic generation with infrared conical refraction (CR) beams. We show that the high-order harmonic beams emitted in the EUV/soft x-ray regime preserve the characteristic signatures of the driving beam, namely ringlike transverse intensity profile and CR-like polarization distribution. As a result, through orbital and spin angular momentum conservation, harmonic beams are emitted with fractional orbital angular momentum, and they can be synthesized into structured attosecond helical beams –or “structured attosecond light springs”– with rotating linear polarization along the azimuth. Our proposal overcomes the state of the art limitations for the generation of light beams far from the visible domain carrying non-integer orbital angular momentum and could be applied in fields such as diffraction imaging, EUV lithography, particle trapping, and super-resolution imaging.

Achromatization of conical diffraction: application to the generation of a polychromatic optical vortex

Vortex beams are plagued by the intrinsic chromaticity of the physical phenomenon used to generate them. To the authors' best knowledge, attempts to generate them in a broad spectral range remain quite scarce and limited in their results. Crystal optics and especially conical diffraction (CD) (or refraction) intrinsically create achromatic vortices. The vortex is created by a wavelength-independent topological charge, embedded directly in the Fresnel equations. However, for biaxial crystals of low crystallographic symmetry, which includes all crystals used practically for CD, the dispersion of the binormal axis creates a chromaticity effect. In this Letter, we propose a new way to compensate this dispersion of the binormal axis of a biaxial crystal in order to generate white-light vortex beams by CD in a 250 nm spectral range, covering almost all the visible range. The advantages of the ability to use CD in a wide spectral range vastly exceed the sole generation of vortex beams.

Interferometric characterization of the structured polarized light beam produced by the conical refraction phenomenon

The interest on the conical refraction (CR) phenomenon in biaxial crystals has revived in the last years due to its prospective for generating structured polarized light beams, i.e. vector beams. While the intensity and the polarization structure of the CR beams are well known, an accurate experimental study of their phase structure has not been yet carried out. We investigate the phase structure of the CR rings by means of a Mach-Zehnder interferometer while applying the phase-shifting interferometric technique to measure the phase at the focal plane. In general the two beams interfering correspond to different states of polarization (SOP) which locally vary. To distinguish if there is an additional phase added to the geometrical one we have derived the appropriate theoretical expressions using the Jones matrix formalism. We demonstrate that the phase of the CR rings is equivalent to that one introduced by an azimuthally segmented polarizer with CR-like polarization distribution. Additionally, we obtain direct evidence that the Poggendorff dark ring is an annular singularity, with a π phase change between the inner and outer bright rings.

Visualizing polarization singularities in Bessel-Poincaré beams

We demonstrate that an annulus of light whose polarization is linear at each point, but the plane of polarization gradually rotates by π radians can be used to generate Bessel-Poincaré beams. In any transverse plane this beam exhibits concentric rings of polarization singularities in the form of L-lines, where the polarization is purely linear. Although the L-lines are invisible in terms of light intensity variations, we present a simple way to visualize them as dark rings around a sharp peak of intensity in the beam center. To do this we use a segmented polarizer whose transmission axes are oriented differently in each segment. The radius of the first L-line is always smaller than the radius of the central disk of the zero-order Bessel beam that would be produced if the annulus were homogeneously polarized and had no phase circulation along it.

Transformation of vector beams with radial and azimuthal polarizations in biaxial crystals

We present both experimentally and theoretically the transformation of radially and azimuthally polarized vector beams when they propagate through a biaxial crystal and are transformed by the conical refraction phenomenon. We show that, at the focal plane, the transverse pattern is formed by a ring-like light structure with an azimuthal node, this node being found at diametrically opposite points of the ring for radial/azimuthal polarizations. We also prove that the state of polarization of the transformed beams is conical refraction-like, i.e., that every two diametrically opposite points of the light ring are linearly orthogonally polarized.

On the dual-cone nature of the conical refraction phenomenon

In conical refraction (CR), a focused Gaussian input beam passing through a biaxial crystal and parallel to one of the optic axes is transformed into a pair of concentric bright rings split by a dark (Poggendorff) ring at the focal plane. Here, we show the generation of a CR transverse pattern that does not present the Poggendorff fine splitting at the focal plane, i.e., it forms a single light ring. This light ring is generated from a nonhomogeneously polarized input light beam obtained by using a spatially inhomogeneous polarizer that mimics the characteristic CR polarization distribution. This polarizer allows modulating the relative intensity between the two CR light cones in accordance with the recently proposed dual-cone model of the CR phenomenon. We show that the absence of interfering rings at the focal plane is caused by the selection of one of the two CR cones.