Upper Bound to the Orbital Angular Momentum Carried by an Ultrashort Pulse

Generation and applications of x-ray and extreme ultraviolet beams carrying orbital angular momentum

In addition to spin angular momentum, light can carry orbital angular momentum. The orbital angular momentum degree of freedom in the extreme ultraviolet and x-ray regimes enables fundamental studies of light-matter interactions and new methods to study materials. Advances in x-ray optics, as well as undulator radiation and high harmonic generation techniques, lead to the creation of beams with non-trivial phase structure, such as a helical phase structure, creating new possibilities for the use of extreme ultraviolet and x-ray photons with orbital angular momentum in probing complex electronic structures in matter. In this article, we review the generation and applications of orbital angular momentum beams in the x-ray and extreme ultraviolet regime. We discuss several recent works that exploit the orbital angular momentum degree of freedom and showcase the potential advantages of using these beams.

Few-cycle optical vortices for strong-field physics

We report on the generation of optical vortices with few-cycle pulse durations, 500μJ per pulse, at a repetition rate of 1 kHz. To do so, a 25 fs laser beam at 800 nm is shaped with a helical phase and coupled into a hollow-core fiber filled with argon gas, in which it undergoes self-phase modulation. Then, 5.5 fs long pulses are measured at the output of the fiber using a dispersion-scan setup. To retrieve the spectrally resolved spatial profile and orbital angular momentum (OAM) content of the pulse, we introduce a method based on spatially resolved Fourier-transform spectroscopy. We find that the input OAM is transferred to all frequency components of the post-compressed pulse. The combination of these two information shows that we obtain few-cycle, high-intensity vortex beams with a well-defined OAM, and sufficient energy to drive strong-field processes.

Generalized binary spiral zone plates with a single focus obtained by feedforward neural network

Traditional spiral zone plates (SZPs) have been widely used to generate optical vortices, but this structure suffers from multiple focuses. To eliminate high-order foci, the current method is to design a binary structure that has a sinusoidal transmittance function along the radial direction. With the rapid development of artificial neural networks, they can provide alternative methods to design novel SZPs with a single focus. In this paper, we first propose the concept of generalized binary spiral zone plates (GBSZPs), and train a feedforward neural network (FNN) to obtain the mapping relationship between the relative intensity of each focus and the structural parameters of GBSZPs. Then the structural parameters of GBSZPs with a single focus were predicted by the trained FNN. It is found by simulations and experiments that the intensities of high-order foci can be as low as 0.2% of the required first order. By analyzing the radial transmittance function, it is found that this structure has a different distribution function from the previous radial sinusoidal function, which reveals that the imperfect radial sinusoidal form also can guide the design of binary zone plates to eliminate high-order foci diffraction. These findings are expected to direct new avenue towards improving the performance of optical image processing and quantum computation.

Generation of spatiotemporal optical vortices in ultrashort laser pulses using rotationally interleaved multispirals

Ultrashort optical vortex pulses carrying spatiotemporal orbital angular momentum (OAM) have inspired versatile applications such as the micromachining of integrated quantum chips and discoveries such as optical toroidal structures and OAM-carrying X-waves. Generating high-quality ultrashort vortices with controllable topological charges remains a crucial issue. Thus, we propose a rotationally interleaved multispiral to generate such vortices. A multispiral comprises multiple identical spirals rotated around the center in the equal-azimuthal interval and interleaved in equal-radius increments; this structure overcomes the previous structural asymmetry of the single spiral and improves the vortex quality. Accordingly, we conducted theoretical analyses, numerical simulations, and experimental investigations that demonstrated the feasibility of multispirals in generating the ultrashort vortices with symmetric distributions and flexibly controlling the topological charges. The proposed study is significant for broader applications involving ultrashort vortices and extensive investigations in related areas such as research on electron vortices, plasmonic vortices, and other matter vortices.

Space-time wave packets localized in all dimensions

Optical wave packets that are localized in space and time, but nevertheless overcome diffraction and travel rigidly in free space, are a long sought-after field structure with applications ranging from microscopy and remote sensing, to nonlinear and quantum optics. However, synthesizing such wave packets requires introducing non-differentiable angular dispersion with high spectral precision in two transverse dimensions, a capability that has eluded optics to date. Here, we describe an experimental strategy capable of sculpting the spatio-temporal spectrum of a generic pulsed beam by introducing arbitrary radial chirp via two-dimensional conformal coordinate transformations of the spectrally resolved field. This procedure yields propagation-invariant ‘space-time’ wave packets localized in all dimensions, with tunable group velocity in the range from 0.7c to 1.8c in free space, and endowed with prescribed orbital angular momentum. By providing unprecedented flexibility in sculpting the three-dimensional structure of pulsed optical fields, our experimental strategy promises to be a versatile platform for the emerging enterprise of space-time optics.

Propagation-invariant wave packets confined in space and time can be useful for optical sensing, imaging, and nonlinear and quantum optics. Here the authors demonstrate control over the angular dispersion of optical wave packets in two-transverse dimensions to synthesize space-time wave packets localized in all dimensions.

Time-varying orbital angular momentum in tight focusing of ultrafast pulses

The orbital angular momentum (OAM) of light has important applications in a variety of fields, including optical communication, quantum information, super-resolution microscopic imaging, particle trapping, and others. However, the temporal properties of OAM in ultrafast pulses and in the evolution process of spin-orbit coupling has yet to be revealed. In this work, we theoretically studied the spatiotemporal property of time-varying OAM in the tightly focused field of ultrafast light pulses. The focusing of an incident light pulse composed of two time-delayed femtosecond sub-pulses with the same OAM but orthogonal spin states is investigated, and the ultrafast dynamicsa time delay of OAM variation during the focusing process driven by the spin-orbit coupling is visualized. Temporal properties of three typical examples, including formation, increase, and transformation of topological charge are investigated to reveal the non-uniform evolutions of phase singularities, local topological charges, self-torques, and time-varying OAM per photon. This work could deepen the understanding of spin-orbit coupling in time domain and promote many promising applications such as ultrafast OAM modulation, laser micromachining, high harmonic generation, and manipulation of molecules and nanostructures.

Local OAM manipulation of a terahertz wave from the air filament by chirping the few-cycle vortex pump laser

We propose a scheme to manipulate the local orbital angular momentum (OAM) of the ultra-broadband (0.1-30 THz) terahertz (THz) waves from the laser-induced short air filament via chirping the few-cycle vortex laser pump. The simulation results show that either the THz vortex pulses with linear azimuth-dependent phases or the THz angular accelerating vortex beams (AAVBs) with nonlinear azimuth-dependent phases can be produced by tuning the chirp parameter of the pump. Thus, the dominant physical mechanism for THz generation can be determined. The THz temporal and transverse spatial distributions can be also controlled by the chirp parameter. Furthermore, their local OAM density distributions present very complex structures because most of the modulated azimuthal intensity and the corresponding local angular helicity distributions are not able to cancel out completely. Via analyzing the simulated THz results at the different pump intensities, we classify the initial pump intensity into three cases. For the low intensity case, the Kerr effect comes into prominence, so the generated THz radiation shall be vortex pulses. While for the high intensity case, the leading plasma effect dominates. In contrast, when the pump intensity is at the medium level, the Kerr nonlinearity and the plasma effect may be comparable and competitive. Basically, THz AAVBs are generated for both high and medium intensity cases. Our study will provide the possibility for studying the optically induced rotation technology more intuitively from the perspective of angular momentum transfer.

Simulation of near-diffraction- and near-dispersion-free OAM pulses with controllable group velocity by combining multiple frequencies, each carrying a Bessel mode

Optical pulses carrying orbital angular momentum (OAM) have recently gained interest. In general, it might be beneficial to simultaneously achieve: (i) minimum diffraction, (ii) minimum dispersion, and (iii) controllable group velocity. Here, we explore via simulation the generation of near-diffraction-free and near-dispersion-free OAM pulses with arbitrary group velocities by coherently combining multiple frequencies. Each frequency carries a specific Bessel mode with the same topological charge (ℓ) but different k_r (spatial frequency) values based on space-time correlations. Moreover, we also find that (i) both positive and negative group velocities could be achieved and continuously controlled from the subluminal to superluminal values and (ii) when the ℓ is varied from 0 to 10, the simulated value of the group velocity remains the same. However, as the ℓ value increases, the pulse duration becomes longer for a given number of frequency lines.

Angular momentum of the vortex ultrashort pulsed beam with a smaller beam waist

The angular momentum (AM) of light has important implications for many fields of optics research, such as optics communication, quantum information and laser-scan microscopy. Thus, in this paper, we intend to investigate the average AM of the vortex ultrashort pulsed beam (VUPB), which is generated and widely applied in the field of high-intensity and ultrafast regimes. According to the vector potential, we firstly derive the electromagnetic field of the VUPB, then analyze the spatial intensity, the phase profile and the polarization state of the beam. We explore that the total AM per photon of VUPB is not n ℏ value when the beam waist w₀ is of wavelength or sub-wavelength order, since the polarization of VUPB is changed from linear to circular polarization with the decrease of beam waist, which introduces the conversion of the orbital AM to the spin AM. Moreover, based on the conservation of the total AM, the minimum waist of VUPB can be obtained, which is dependent on the pulse duration time α and topological charge n. Finally, the average AM of the fractional VUPB expressed by the superposition of the integer VUPB with different weights, is analyzed, which is not equal to the AM of fractional CW beam μ - sin (2μπ)/2π (μ is the fractional topological charge), but is associated with the beam waist w₀ and α. Therefore, we think that the AM of VUPB can be controlled by adjusting the α and w₀.

Transient-grating single-shot supercontinuum spectral interferometry (TG-SSSI)

We present a technique for the single-shot measurement of the spatiotemporal (1D space+time) amplitude and phase of an ultrashort laser pulse. The method, transient grating single-shot supercontinuum spectral interferometry (TG-SSSI), is demonstrated by the space-time imaging of short pulses carrying spatiotemporal optical vortices. TG-SSSI is well suited for characterizing ultrashort laser pulses that contain singularities associated with spin/orbital angular momentum or polarization.

Ultrashort Vortex Pulses with Controlled Spectral Gouy Rotation

Recently, the spatio-spectral propagation dynamic of ultrashort-pulsed vortex beams was demonstrated by 2D mapping of spectral moments. The rotation of characteristic anomalies, so-called “spectral eyes”, was explained by wavelength-dependent Gouy phase shift. Controlling of this spectral rotation is essential for specific applications, e.g., communication and processing. Here, we report on advanced concepts for spectral rotational control and related first-proof-of-principle experiments. The speed of rotation of spectral eyes during propagation is shown to be essentially determined by angular and spectral parameters. The performance of fixed diffractive optical elements (DOE) and programmable liquid-crystal-on silicon spatial light modulators (LCoS-SLMs) that act as spiral phase gratings (SPG) or spiral phase plates (SPP) is compared. The approach is extended to radially chirped SPGs inducing axially variable angular velocity. The generation of time-dependent orbital angular momentum (self-torque) by superimposing multiple vortex pulses is proposed.

Effects of the Coupling between the Orbital Angular Momentum and the Temporal Degrees of Freedom in the Most Intense Ring of Ultrafast Vortices

It has recently been shown that the temporal and the orbital angular momentum (OAM) degrees of freedom in ultrafast (few-cycle) vortices are coupled. This coupling manifests itself with different effects in different parts of the vortex, as has been shown for the ring surrounding the vortex where the pulse energy is maximum, and also in the immediate vicinity of the vortex center. However, in many applications, the ring of maximum energy is not of primary interest, but the one where the peak intensity of the pulse is maximum, which is particularly true in nonlinear optics applications such as experiments with ultrafast vortices that excite high harmonics and attosecond pulses that also carry OAM. In this paper, the effects of the OAM-temporal coupling on the ring of maximum pulse peak intensity, which do not always coincide with the ring of maximum pulse energy, are described. We find that there is an upper limit to the magnitude of the topological charge that an ultrafast vortex with a prescribed pulse shape in its most intense ring can carry, and vice versa, a lower limit to the pulse duration in the most intense ring for a given magnitude of the topological charge. These limits imply that, with a given laser source spectrum, the duration of the synthesized ultrafast vortex increases with the magnitude of the topological charge. Explicit analytical expressions are given for the ultrafast vortices that contain these OAM-temporal couplings effects, which may be of interest in various applications, in particular in the study of their propagation and interaction with matter.

Fractional vortex ultrashort pulsed beams with modulating vortex strength

In most papers about the fractional vortex continuous beams (FVCBs), the relationship between the total vortex strength S_α and the propagation distance is not analyzed since the vortex structure is not stable in the near field. In this paper, we theoretically study the fractional vortex ultrashort pulsed beams (FVUPBs) possessing non-integer topological charges α at arbitrary plane and find that the vortex structure is propagation-distance-dependent. Both the intensity and phase distributions are calculated to analyze the vortex structure. To evaluate the propagation properties of FVUPBs, we focus on the total vortex strength (TVS) of FVUPBs to investigate the number of vortex, and demonstrate that the birth of a vortex is at α = m + ɛ, where m is an integer, ɛ is a changing fraction depending on the pulse durations, peak wavelengths and propagation distances. Furthermore, we discover that the FVUPBs carry decreasing TVS along the propagation axis in free space. This special vortex structure for FVUPBs appears due to the mixture weight of vortex pulsed beam with different integer topological charges (TCs) n. However, the total orbital angular momentum is invariant during propagation. The above phenomenon presented in our paper are totally particular and intriguing compared with the FVCBs.

Effects of orbital angular momentum on few-cycle and sub-cycle pulse shapes: coupling between the temporal and angular momentum degrees of freedom

We describe the effects of the coupling between the orbital angular momentum (OAM) and the temporal degrees of freedom in pulsed Laguerre-Gauss beams as a significant increase of the duration of few-cycle pulses when the OAM carried by the pulse is large, and as an enhancement to other previously known spatiotemporal couplings as radial red- and blue-shift of the mean frequency. In contrast to other detrimental, but retrievable, effects in the generation and propagation of ultrashort vortices such as spatial, group velocity, and topological charge dispersions, the OAM-temporal coupling effect is unavoidable and, therefore, has an impact on applications such as OAM-based optical communications, or on the generation of vortex-carrying attosecond pulses.