Complete spatial characterization of a pulsed doughnut-type beam by use of spherical optics and a cylindrical lens

Nonlinear post-compression of a hybrid vortex mode in a gas-filled capillary

We demonstrate nonlinear temporal compression of a vortex beam by propagation in a gas-filled capillary. Starting from an ytterbium-based laser delivering 700 μJ 640 fs pulses at a 100 kHz repetition rate, the vortex beam is generated using a spiral phase plate and coupled to a capillary where it excites a set of four modes that have an overlap integral of 97% with a Laguerre-Gauss LG10 mode. Nonlinear propagation of this hybrid, orbital angular momentum (OAM)-carrying mode results in temporal compression down to 74 fs at the output. Beam and pulse characterizations are carried out to determine the spatial profile and temporal duration of compressed pulses. This result in multimode nonlinear optics paves the way towards the generation of OAM-carrying few-cycle pulses, isolated attosecond XUV pulses, and tunable UV pulses through resonant dispersive wave emission.

Transmission of an optical vortex beam in antiresonant fibers generated in an all-fiber system

We report an experimental study on transmission of orbital angular momentum mode in antiresonant fibers generated with a dedicated all-fiber optical vortex phase mask. The vortex generator can convert Gaussian beam into vortex beams with topological charge l = 1. Generated vortex beam is directly butt-coupled into the antiresonant fiber and propagates over distance of 150 cm. The stability and sensitivity of the transmitted vortex beam on the external perturbations including bending, axial stress, and twisting is investigated. We demonstrate distortion-free vortex propagation for the axial stress force below 0.677 N, a bend radius greater than 10 cm.

Influence of Spatio-Temporal Couplings on Focused Optical Vortices

Ultra-intense laser pulses with helical phases are of interest in laser-driven charged particle acceleration and related experiments with extreme light. However, such optical vortices can be affected by the presence of residual spatial-temporal couplings. Their field distributions after propagating in free-space and in the focal plane of an ideal focusing mirror were assessed through numerical modeling, based on the Gaussian decomposition method for a 25 fs pulse with a Supergaussian spatial profile. The wash-out of the central hole in the doughnut-shaped profile in the focal plane corresponds to the rotation of the phase discontinuity.

Superposition of two fractional optical vortices and the orbital angular momentum measurement by a deep-learning method

We propose a single diffractive optical element called the composite fractional spiral zone plates to generate superimposed fractional optical vortices. Such an element is composed of two fractional spiral zone plates (FSZPs) through logical AND operation, and the produced beam carries superimposed fractional orbital angular momentum (OAM) states. By controlling the topological charge of the superimposed FSZPs, denoted by l₁ and l₂, one can flexibly obtain the desired superimposed fractional OAM modes of the generated beam. Especially, a deep-learning model with a densely connected convolutional neural network architecture is utilized to accurately predict the superimposed fractional OAM states of SFOVs. The average recovery rate of the superimposed fractional OAM states based on the training model is over 99%, and the average error is as small as 0.02. This work may pave the way for wide-ranging applications such as smart OAM communication, particle transmission, and even quantum entanglement.

Modern Types of Axicons: New Functions and Applications

Axicon is a versatile optical element for forming a zero-order Bessel beam, including high-power laser radiation schemes. Nevertheless, it has drawbacks such as the produced beam's parameters being dependent on a particular element, the output beam's intensity distribution being dependent on the quality of element manufacturing, and uneven axial intensity distribution. To address these issues, extensive research has been undertaken to develop nondiffracting beams using a variety of advanced techniques. We looked at four different and special approaches for creating nondiffracting beams in this article. Diffractive axicons, meta-axicons-flat optics, spatial light modulators, and photonic integrated circuit-based axicons are among these approaches. Lately, there has been noteworthy curiosity in reducing the thickness and weight of axicons by exploiting diffraction. Meta-axicons, which are ultrathin flat optical elements made up of metasurfaces built up of arrays of subwavelength optical antennas, are one way to address such needs. In addition, when compared to their traditional refractive and diffractive equivalents, meta-axicons have a number of distinguishing advantages, including aberration correction, active tunability, and semi-transparency. This paper is not intended to be a critique of any method. We have outlined the most recent advancements in this field and let readers determine which approach best meets their needs based on the ease of fabrication and utilization. Moreover, one section is devoted to applications of axicons utilized as sensors of optical properties of devices and elements as well as singular beams states and wavefront features.

Spectral control of the orbital angular momentum of a laser beam based on 3D properties of spiral phase plates fabricated for an infrared wavelength

This paper examines the spectral properties of a spiral phase plate (SPP) generating orbital angular momentum (OAM) beams. A simple method is proposed for calculating the resulting OAM by measuring only two maximum expansion coefficients. A comparative numerical simulation of the proposed and traditional methods is performed. An SPP is fabricated for generation of an OAM with integer values at infrared and visible wavelengths. Qualitative experimental studies of the changes in a generated OAM with a change in the operating wavelength are performed using the spatial filtering method. The experimental results are found to agree with the results of numerical simulation. Beams with integer and fractional OAM values are obtained experimentally by changing the wavelength.

Measuring laser beam quality, wavefronts, and lens aberrations using ptychography

We report on an approach for quantitative characterization of laser beam quality, wavefronts, and lens aberrations using ptychography with a near-infrared supercontinuum laser. Ptychography is shown to offer a powerful alternative for both beam propagation ratio M² and wavefront measurements compared with existing techniques. In addition, ptychography is used to recover the transmission function of a microlens array for aberration analysis. The results demonstrate ptychography's flexibility in wavefront metrology and optical shop testing.

Astigmatic transforms of an optical vortex for measurement of its topological charge

We obtain analytical expressions for the complex amplitudes of optical vortices deformed by astigmatic transforms, i.e., passed either through a cylindrical lens or through an inclined spherical lens. We also obtain similar analytical expressions describing propagation of an optical vortex generated when a Gaussian beam illuminates an inclined spiral phase plate (SPP) or when an elliptic Gaussian beam illuminates a SPP (not inclined). All these optical vortices with a topological charge (TC) n are described by the n-th order Hermite polynomial with a complex argument. It is shown that the argument is real only on a straight line in the transverse plane of the laser beam. There are n intensity nulls on this line. The treated here astigmatic transforms are used to determine the integer TC of optical vortices. We conduct a comparative experimental study of different astigmatic transforms and we show that the transform with a cylindrical lens is the best for determining the TC. Unlike other similar works, in this study we achieve transformation of n-degenerate intensity null of an optical vortex with the TC n=100 into n isolated first-order intensity nulls.

Simultaneous control of orbital angular momentum and beam profile in two-mode polarization-maintaining fiber

We report simultaneous control of the orbital angular momentum (OAM) and beam profile of vortex beams generated in two-mode polarization-maintaining optical fiber. Two higher-order eigenmodes of the fiber are combined to form optical vortices. Reduced coherence between the fiber modes decreases the mode purity. Varying the coherence of the fiber modes changes the average OAM while maintaining a constant annular intensity profile. Additionally, a donut mode has been shown to be insensitive to bends and twists in the fiber.

Quantitative measurement of the orbital angular momentum of light with a single, stationary lens

We show that the average orbital angular momentum (OAM) of twisted light can be measured simply and robustly with a single stationary cylindrical lens and a camera. Theoretical motivation is provided, along with self-consistent optical modeling and experimental results. In contrast to qualitative interference techniques for measuring OAM, we quantitatively measure non-integer average OAM in mode superpositions.

Continuously tunable orbital angular momentum generation using a polarization-maintaining fiber

We demonstrate the generation of orbital angular momentum (OAM) in a two-mode polarization-maintaining (PM) optical fiber. We combine two linearly polarized modes of PM fiber to generate linearly polarized optical vortex beams with OAM. The average OAM can be finely varied by changing the phase between modes. We have quantitatively measured the resulting OAM to vary between ±1ℏ per photon while varying the relative phase between the LP_11e- and LP_11o-like fiber modes. The modal purity is 97%.

Measurement of the M² beam propagation factor using a focus-tunable liquid lens

We demonstrate motion-free beam quality M² measurements of stigmatic, simple astigmatic, and general astigmatic (twisted) beams using only a focus-tunable liquid lens and a CCD camera. We extend the variable-focus technique to the characterization of general astigmatic beams by measuring the 10 second-order moments of the power density distribution for the twisted beam produced by passage through multimode optical fiber. Our method measures the same M² values as the traditional variable-distance method for a wide range of laser beam sources, including nearly TEM(00) (M²≈1) and general astigmatic multimode beams (M²≈8). The method is simple and compact, with no moving parts or complex apparatus and measurement precision comparable to the standard variable-distance method.

Determination of topological charges of polychromatic optical vortices

We introduce a simple, single beam method for determination of the topological charge of polychromatic optical vortices. It is based on astigmatic transformation of singular optical beams, where the intensity pattern of a vortex beam acquires a form of dark stripes in the focal plane of a cylindrical lens. The number of the dark stripes is equal to the modulus of the vortex topological charge, while the stripe tilt indicates the charge sign. We demonstrate experimentally the effectiveness of this technique by revealing complex topological structure of polychromatic singular beams.

Propagation analysis of the Laguerre-Gaussian beam with astigmatism

The entire range of transformations that a Laguerre-Gaussian (LG) beam with astigmatism can go through in free space is clarified. The transformations are governed by the relative phase between the astigmatic Hermite-Gaussian components. Formulas describing the behavior of this relative phase are obtained and used to classify and map the transformation patterns to initial beam parameters. The difference between an LG beam and a phase singular beam generated by a hologram under astigmatic conditions is also investigated.

Moments of the Wigner distribution of rotationally symmetric partially coherent light

The Wigner distribution of rotationally symmetric partially coherent light is considered, and the constraints for its moments are derived. Although all odd-order moments vanish, these constraints lead to a drastic reduction in the number of parameters that we need to describe all even-order moments: whereas in general we have (N + 1)(N + 2)(N + 3)/6 different moments of order N, this number reduces to (1 + N/2)2 in the case of rotational symmetry. A way to measure the moments as intensity moments in the output planes of (generally anamorphic) fractional Fourier-transform systems is presented.

Wigner distribution moments in fractional Fourier transform systems

It is shown how all global Wigner distribution moments of arbitrary order in the output plane of a (generally anamorphic) two-dimensional fractional Fourier transform system can be expressed in terms of the moments in the input plane. Since Wigner distribution moments are identical to derivatives of the ambiguity function at the origin, a similar relation holds for these derivatives. The general input-output relationship is then broken down into a number of rotation-type input-output relationships between certain combinations of moments. It is shown how the Wigner distribution moments (or ambiguity function derivatives) can be measured as intensity moments in the output planes of a set of appropriate fractional Fourier transform systems and thus be derived from the corresponding fractional power spectra. The minimum number of (anamorphic) fractional power spectra that are needed for the determination of these moments is derived. As an important by-product we get a number of moment combinations that are invariant under (anamorphic) fractional Fourier transformation.