Generation of Laguerre-Gaussian LGp0 beams using binary phase diffractive optical elements

Dual projectile beams

Accelerating beams, of which the Airy beam is an important representative, are characterized by intensity maxima that propagate along curved trajectories. In this work we present a simple approach to directly generate accelerating beams with controllable trajectories by means of binary phase structures that consist of only a π phase step modulation in comparison to previous studies where two-dimensional cubic phase modulations for example are required, and which have practical limitations due to their challenging fabrication with phase plates or diffractive optical elements (DOEs), or the spatially extended system needed for their generation at the Fourier plane. In our approach, two intensity maxima are formed that propagate along root parabolic trajectories in contrast to Airy and higher order caustic beams that propagate along a parabolic curve, hence we call these beams Dual Projectile Beams (DPBs). By tailoring a step or slit phase patterns with additional Fresnel lenses, we either generate hollow-core or abruptly focusing beams and control their curvatures. Moreover, using DPBs as a simpler complement to complex structured light fields, we demonstrate their versatility at the example of their interaction with nonlinear matter, namely the formation of a spatial soliton in a photorefractive material. We show that the formed solitary state propagates almost unchanged for a distance of several Rayleigh lengths. This light matter interaction can be regarded as a light beam deceleration. The simplicity of this approach makes these beams suitable for integrated optics and high-power laser applications using DOEs or meta-surfaces.

Coupling light to higher order transverse modes of a near-concentric optical cavity

Optical cavities in the near-concentric regime have near-degenerate transverse modes; the tight focusing transverse modes in this regime enable strong coupling with atoms. These features provide an interesting platform to explore multi-mode interaction between atoms and light. Here, we use a spatial light modulator (SLM) to shape the phase of an incoming light beam to match several Laguerre-Gaussian (LG) modes of a near-concentric optical cavity. We demonstrate coupling efficiency close to the theoretical prediction for single LG modes and well-defined combinations of them, limited mainly by imperfections in the cavity alignment.

Elegant Gaussian beams: nondiffracting nature and self-healing property

Alongside the well-known solutions of standard beams, elegant Gaussian beams (eGBs) have been presented as alternative solutions to the paraxial wave equation. In this work, we show that the eGBs in cartesian (elegant Hermite-Gauss) and cylindrical (elegant Laguerre-Gauss) coordinates are asymptotically equivalent to pseudo-nondiffracting beams (pNDBs) in the same coordinates (cosine-Gauss and Bessel-Gauss, respectively). A theoretical comparison of their intensity distributions at different planes without and with obstruction is given, allowing to revisit and discuss the diffraction-free nature and self-healing property. The obtained results demonstrate that both families of beams are indistinguishable and have similar propagation features, which means that the eGBs class can be used as an alternative to pNDBs.

Far-field modeling of obstructed Laguerre-Gauss beams

It was shown in the paper Opt. Lett.40, 3739 (2015)OPLEDP0146-959210.1364/OL.40.003739 that Laguerre-Gauss beams (LGB_n) of order n and Bessel beams (BB) are asymptotically equivalent for n≫1. Here we demonstrate that an LGB_n and a BB are equivalent just in the inner multiring parts of the two beams. However, the outer multiring parts are completely different, and this leads us to apply a truncation on the two beams to make them indistinguishable. Since the LGB_n could be approximated by a BB only in the inner multiring part, we suggest another beam that could replace its outer multiring part. By considering the LGB_n as a sum of n rings having different radii and widths, we model the LGB_n outer multiring part by a sum of what we call in this paper "ring shifted-Gaussian beams." The peer-to-peer comparison of the LGB_n with the two cited beams allowed us to provide a new analytical description of the obstructed LGB_n far field. These results will be very useful to study many aspects related to the LGB_n diffraction by apertures and stops. As an example, we show at the end of this paper how the self-healing ability of an obstructed LGB_n could be studied analytically.

Self-written waveguides in photopolymer

Self-written waveguide (SWW) trajectories fabricated inside a dry photopolymer bulk material, acrylamide/polyvinyl alcohol (AA/PVA), are studied. Their production using both Gaussian and Laguerre-Gauss exposing (writing) light beams, output from optical fibers, is explored. The formation of the primary and secondary eyes is also discussed. Furthermore, the interactions that take place when two counterpropagating beams pass through the photopolymer material (both Gaussian and Laguerre-Gauss) are examined. In all cases experimental and theoretical results are presented. Good agreement between the predictions of the proposed model and experimental observations are demonstrated.

Design of binary phase filters for depth-of-focus extension via binarization of axisymmetric aberrations

We present a novel design approach for a binary phase mask with depth-of-focus (DoF) extension ability. Our method considers that the binarized version of an axisymmetric continuous phase pupil generates twin-intensity profiles that are symmetric with respect to the focal plane, each of which resembles the focal behavior of its continuous original. The DoF extension is realized by repositioning and coherently summing the twin foci to achieve an elongated focus along the axial direction. The shift of the two foci towards the focal plane can be handled by superimposing the defocus term in the continuous pupil function. We demonstrate our proposed design approach for two representative axisymmetric aberration functions, i.e., defocused phase axicon and spherical aberration. The manipulation of topological parameters in the phase axicon and spherical aberration, along with the defocus strength, enables the multiple binary phase-filter designs of DoF extension of 3.2-7.1 fold with a phase axicon and 2.8-14.8 fold with a spherical aberration, compared to the case with a clear aperture.