Search Results (14)

Exploding or concentrating beams, vortex beams, and cylindrical vector beams have a precisely shaped transversal amplitude profile such that they produce a continuously concentrating and intensifying focal spot upon focusing as the lens aperture is opened. This effect is the physical manifestation of the mathematical fact that Fresnel diffraction integral predicts an infinite intensity at the focus when the aperture effects are ignored. Here, using a full electromagnetic, nonparaxial focusing model, we show that the singularity in exploding cylindrical vector beams is an artifact of the paraxial approximation. Nevertheless, the exploding or concentrating effect, alien to any other light beam with finite power, keeps going up to unit numerical aperture, equivalent to infinite aperture radius. This unique feature enables a dynamic control of the focal intensity and spot size down to the sub-wavelength scale using a single light beam, imitating similar control when focusing an ideal plane wave, but requiring a finite amount of power. Full article

Toroidal vortices, as intriguing topological structures, play a fundamental role across a wide range of physical fields. In this study, we theoretically propose a family of structured optical toroidal vortices as generalized forms of toroidal vortices in paraxial continuous wave beams. These structured optical toroidal vortices exhibit unique rotational symmetry while preserving the topological properties of standard toroidal vortices. The three-dimensional topological structures demonstrate l-fold rotational symmetry, which is closely related to the topological charges. Structured toroidal vortices introduce additional topological invariants within the toroidal light field. These topological light fields hold significant potential applications in the synthesis of complex topological structure and optical information encoding. Full article

For the most popular method of scan formation in Optical Coherence Tomography (OCT) based on plane-parallel scanning of the illuminating beam, we present a compact but rigorous K-space description in which the spectral representation is used to describe both the axial and lateral structure of the illuminating/received OCT signals. Along with the majority of descriptions of OCT-image formation, the discussed approach relies on the basic principle of OCT operation, in which ballistic backscattering of the illuminating light is assumed. This single-scattering assumption is the main limitation, whereas in other aspects, the presented approach is rather general. In particular, it is applicable to arbitrary beam shapes without the need for paraxial approximation or the assumption of Gaussian beams. The main result of this study is the use of the proposed K-space description to analytically derive a filtering function that allows one to digitally transform the initial 3D set of complex-valued OCT data into a desired (target) dataset of a rather general form. An essential feature of the proposed filtering procedures is the utilization of both phase and amplitude transformations, unlike conventionally discussed phase-only transformations. To illustrate the efficiency and generality of the proposed filtering function, the latter is applied to the mutual transformation of non-Gaussian beams and to the digital elimination of arbitrary aberrations at the illuminating/receiving aperture. As another example, in addition to the conventionally discussed digital refocusing enabling depth-independent lateral resolution the same as in the physical focus, we use the derived filtering function to perform digital “super-refocusing.” The latter does not yet overcome the diffraction limit but readily enables lateral resolution several times better than in the initial physical focus. Full article

Paraxial beam modes, which propagate in space and focus without changing their transverse intensity pattern, are of great value for multiplexing transmitted data in optical communications, both in waveguides and in free space. The best-known paraxial modes are the Hermite-Gaussian and Laguerre-Gaussian beams. Here, we derive explicit analytical expressions for Ince-Gaussian (IG) beams for several first values of the indices p = 3, 4, 5, and 6. In total, we obtain expressions for the amplitudes of 24 IG beams. These formulae are written as superpositions of the Laguerre-Gaussian (LG) or Hermite-Gaussian (HG) beams, with the superposition coefficients explicitly depending on the ellipticity parameter. Due to simultaneous representation of the IG modes via the LG and HG modes, it is easy to obtain the IG modes in the limiting cases wherein the ellipticity parameter is zero or approaches infinity. The explicit dependence of the obtained expressions for the IG modes on the ellipticity parameter makes it possible to change the intensity pattern at the beam cross-section by continuously varying the parameter values. For the first time, the intensity distributions of the IG beams are obtained for negative values of the ellipticity parameter. The obtained expressions could facilitate a theoretical analysis of properties of the IG modes and could find practical applications in the numerical simulation or generation of such beams with a liquid-crystal spatial light modulator. Full article

Elements of micromachines can be driven by light, including structured light with phase and/or polarization singularities. We investigate here a paraxial vector Gaussian beam with an infinite number of polarization singularities residing evenly on a straight line. The intensity distribution is derived analytically and the polarization singularities are shown to exist only in the initial plane and in the far field. The azimuthal angle of the polarization singularities is shown to increase in the far field by π/2. We obtain the longitudinal component of the spin angular momentum (SAM) density and show that it is independent of the azimuthal angle of the polarization singularities. Upon propagation in free space, an infinite number of C-points is generated, where polarization is circular. We show that the SAM density distribution has a shape of four spots, two with left and two with right elliptic polarization. The distance to the transverse plane with the maximal SAM density decreases with decreasing distance between the polarization singularities in the initial plane. Generating such alternating areas with positive and negative SAM density, despite linear polarization in the initial plane, manifests the optical spin Hall effect. Application areas of the obtained results include designing micromachines with optically driven elements. Full article

Elements of micromachines can be driven by light, including structured light with phase and/or polarization singularities. We investigate a paraxial vectorial Gaussian beam with multiple polarization singularities residing on a circle. Such a beam is a superposition of a cylindrically polarized Laguerre–Gaussian beam with a linearly polarized Gaussian beam. We demonstrate that, despite linear polarization in the initial plane, on propagation in space, alternating areas are generated with a spin angular momentum (SAM) density of opposite sign, that manifest about the spin Hall effect. We derive that in each transverse plane, maximal SAM magnitude is on a certain-radius circle. We obtain an approximate expression for the distance to the transverse plane with the maximal SAM density. Besides, we define the singularities circle radius, for which the achievable SAM density is maximal. It turns out that in this case the energies of the Laguerre–Gaussian and of the Gaussian beams are equal. We obtain an expression for the orbital angular momentum density and find that it is equal to the SAM density, multiplied by −m/2 with m being the order of the Laguerre–Gaussian beam, equal to the number of the polarization singularities. We consider an analogy with plane waves and find that the spin Hall affect arises due to the different divergence between the linearly polarized Gaussian beam and cylindrically polarized Laguerre–Gaussian beam. Application areas of the obtained results are designing micromachines with optically driven elements. Full article

The microlens array (MLA) system can aid in realizing fast beam deflection owing to the lateral displacement between arrays. The MLA system has the advantages of miniaturization and good functionality. However, during system operation, crosstalk beams are generated between each microlens array unit, introducing additional stray light, thus affecting the imaging contrast of the system. Therefore, this study uses the matrix operation method to trace the paraxial ray to trace the optical system and analyzes the generation mechanism of crosstalk stray light in the MLA system. Furthermore, this study proposes a crosstalk suppression method based on a stop array to reasonably suppress stray light. Finally, an example of an infrared array scanning infrared optical system is considered so as to verify the correctness and feasibility of the proposed crosstalk stray light suppression method. Therefore, this paper introduces the stray light suppression principle to guide the optical design process of the system, providing a theoretical basis for the design and analysis of the microlens array scanning and search system. Full article

Free-electron lasers (FELs) are the most advanced class of light-sources, by virtue of their unique capability to lase high-brightness pulses characterized by wavelengths spanning the extreme-ultraviolet, the soft and hard X-ray spectral domains, as well as by temporal lengths lying in the femtosecond (fs) timescale. The next step to push the current standards in ultrafast X-ray science is strongly linked to the possibility of engineering and exploiting time-resolved experiments exclusively for FELs pulses, ideally having different colors tunable at specific electronic resonance of the chemical elements. At the seeded FERMI FEL (Trieste, Italy) this goal is committed to the optical device known as AC/DC, which stands for the auto correlator/delay creator. AC/DC is designed to double the incoming FEL pulse splitting the photon beam by inserting a grazing incidence flat mirror, thus preserving the spectral and temporal properties, and further delaying one of these two pulses in time. It can independently tune the FEL pulses fluence on the two optical paths by means of solid-state filters, too. Here, we present a detailed description about this optical device. Strong emphasis is dedicated to the AC/DC opto-mechanical design and to the laser-based feedback systems implemented to compensate for any mismatch affecting the FEL optical trajectory, ascribable to both mechanical imperfections and paraxial errors rising during a temporal delay scan. Full article

We studied paraxial light beams, obtained by a continuous superposition of off-axis Gaussian beams with their phases chosen so that the whole superposition is invariant to free-space propagation, i.e., does not change its transverse intensity shape. Solving a system of five nonlinear equations for such superpositions, we obtained an analytical expression for a propagation-invariant off-axis elliptic Gaussian beam. For such an elliptic beam, an analytical expression was derived for the orbital angular momentum, which was shown to consist of two terms. The first one is intrinsic and describes the momentum with respect to the beam center and is shown to grow with the beam ellipticity. The second term depends parabolically on the distance between the beam center and the optical axis (similar to the Steiner theorem in mechanics). It is shown that the ellipse orientation in the transverse plane does not affect the normalized orbital angular momentum. Such elliptic beams can be used in wireless optical communications, since their superpositions do not interfere in space, if they do not interfere in the initial plane. Full article

Spin-orbital interaction of light attracts much attention in nanophotonics opening new horizons for modern optical systems and devices. The photonic spin Hall effect or Imbert-Fedorov shift takes a special place among the variety of spin-orbital interaction phenomena. It exhibits as a polarization-dependent transverse light shift usually observed in specular scattering of light at interfaces with anisotropic materials. Nevertheless, the effect of the polarization mixing caused by anisotropy on the Imbert-Fedorov shift is commonly underestimated. In this work, we demonstrate that polarization mixing contribution cannot be ignored for a broad range of optical systems. In particular, we show the dominant influence of the mixing term over the standard one for the polarized optical beam incident at a quarter-wave plate within the paraxial approximation. Moreover, our study reveals a novel contribution with extraordinary polarization dependence not observable within the simplified approach. We believe that these results advance the understanding of photonic spin Hall effect and open new opportunities for spin-dependent optical phenomena. Full article

Usual Gaussian beams are particular scalar solutions to the paraxial Helmholtz equation, which neglect the vector nature of light. In order to overcome this inconvenience, Simon et al. (J. Opt. Soc. Am. A 1986, 3, 536–540) found a paraxial solution to Maxwell’s equation in vacuum, which includes polarization in a natural way, though still preserving the spatial Gaussianity of the beams. In this regard, it seems that these solutions, known as Gauss-Maxwell beams, are particularly appropriate and a natural tool in optical problems dealing with Gaussian beams acted or manipulated by polarizers. In this work, inspired in the Bohmian picture of quantum mechanics, a hydrodynamic-type extension of such a formulation is provided and discussed, complementing the notion of electromagnetic field with that of (electromagnetic) flow or streamline. In this regard, the method proposed has the advantage that the rays obtained from it render a bona fide description of the spatial distribution of electromagnetic energy, since they are in compliance with the local space changes undergone by the time-averaged Poynting vector. This feature confers the approach a potential interest in the analysis and description of single-photon experiments, because of the direct connection between these rays and the average flow exhibited by swarms of identical photons (regardless of the particular motion, if any, that these entities might have), at least in the case of Gaussian input beams. In order to illustrate the approach, here it is applied to two common scenarios, namely the diffraction undergone by a single Gauss-Maxwell beam and the interference produced by a coherent superposition of two of such beams. Full article

Multiple laser beams and single-mode optical fibers output can be approximated by assuming that the emitted light has a symmetrical Gaussian intensity profile, which corresponds to the transverse electromagnetic mode (TEM₀₀), which is designated as a Gaussian beam. Current free-accessible design tools are limited to the spatial analysis of the beams, in general, and to the intensity, in particular, and to the graphical visualization in 2D with very limited options. In this work, a novel a computer-aided laser-fiber output beam TEM₀₀ designer, CATEM00, is presented based on the 3D representations typically provided by camera beam profilers, and on the fundamentals of the wave theory of light, including diverse flexibility capabilities for graphical manipulation and parameter comprehension both in terms of spatial behavior and in angular confinement. It must be highlighted that not only is the spatial limitation design of light impact relevant in TEM₀₀ applications but, also, the angle with which the light reaches the target. Hence, the availability of capabilities of phase design in TEM₀₀ following the paraxial limitations is highly convenient. Results and discussion in terms of intensity, power, divergence and wave fronts are presented considering a set of study cases, showing its coherence with Gaussian beam theory. Full article

Concerted rotations of a self-focused varied line-space diffraction grating about its groove axis and surface normal define a new geometric class of monochromator. Defocusing is canceled, while the scanned wavelength is reinforced at fixed conjugate distances and horizontal deviation angle. This enables high spectral resolution over a wide band, and is of particular advantage at grazing reflection angles. A new, rigorous light-path formulation employs non-paraxial reference points to isolate the lateral ray aberrations, with those of power-sum ≤ 3 explicitly expanded for a plane grating. Each of these 14 Fermat equations agrees precisely with the value extracted from numerical raytrace simulations. An example soft X-ray design (6° deviation angle and 2 × 4 mrad aperture) attains a resolving power > 25,000 over a three octave scan range. The proposed rotation scheme is not limited to plane surfaces or monochromators, providing a new degree of freedom in optical design. Grating rotation about its third (meridional) axis may be employed to cancel vertical deflection of the diffracted beam while maintaining the above aberration correction. This enables a simpler (pure rotary) motion for the exit slit and a fixed beam direction both horizontally and vertically. Full article

Recently we introduced the class of highly localized wavepackets (HLWs) as a generalization of optical Bessel-like needle beams. Here we report on the progress in this field. In contrast to pulsed Bessel beams and Airy beams, ultrashort-pulsed HLWs propagate with high stability in both spatial and temporal domain, are nearly paraxial (supercollimated), have fringe-less spatial profiles and thus represent the best possible approximation to linear “light bullets”. Like Bessel beams and Airy beams, HLWs show self-reconstructing behavior. Adaptive HLWs can be shaped by ultraflat three-dimensional phase profiles (generalized axicons) which are programmed via calibrated grayscale maps of liquid-crystal-on-silicon spatial light modulators (LCoS-SLMs). Light bullets of even higher complexity can either be freely formed from quasi-continuous phase maps or discretely composed from addressable arrays of identical nondiffracting beams. The characterization of few-cycle light bullets requires spatially resolved measuring techniques. In our experiments, wavefront, pulse and phase were detected with a Shack-Hartmann wavefront sensor, 2D-autocorrelation and spectral phase interferometry for direct electric-field reconstruction (SPIDER). The combination of the unique propagation properties of light bullets with the flexibility of adaptive optics opens new prospects for applications of structured light like optical tweezers, microscopy, data transfer and storage, laser fusion, plasmon control or nonlinear spectroscopy. Full article