Harmonic Vortex Research Articles

Enhancement of second-order vortex harmonics in epsilon-near-zero materials

When a spatially-inhomogeneous vortex laser field irradiating an epsilon-near-zero (ENZ) material is theoretically investigated, second-order vortex harmonics occur due to the symmetry breaking from the field spatial-inhomogeneity. Their signal intensity is sensitive to three factors: the ENZ field enhancing ratio, the ENZ material thickness, and the field inhomogeneity degree. Their competition supports a high conversion efficiency of around 10−6 for second-order harmonics from the incident fundamental laser field under an optimum thickness of ENZ materials.

Spatial shaping of low- and high-order harmonics generated using vortex beams

We demonstrate the generation of the low- and high-order harmonic vortex beams from a single spiral phase plate illuminated by different laser wavelengths. The second harmonic (532 nm) originates from the application of the wavefront-structured 1064 nm femtosecond pulses with fractional orbital angular momentum (OAM) during propagation through a lithium triborate crystal, while the third harmonic (500 nm) originates from the application of the wavefront-structured near-IR (1500 nm) femtosecond pulses with integer OAM during propagation through a 150 μm thick fused silica plate. The topological charges (TCs) of the second and third harmonics are measured and compared. The increase in TC and the peculiarities in OAM variations during modification of the polarisation of the incident radiation are analysed and discussed. The two-colour-pump-driven second-harmonic vortex radiation interacted with an Ar gas jet to generate vortex harmonics up to the 14th order with double-lobe complex spatial profiles in the extreme ultraviolet region.

Vortex harmonic generation in indium tin oxide thin film irradiated by a two-color field.

When a two-color Laguerre-Gaussian laser beam propagates through an indium tin oxide (ITO) material, the spatial distributions of odd- and even-order vortex harmonics carrying orbital angular momentum (OAM) are studied. The origin of vortex harmonics can be directly clarified by investigating their dependence on the incident laser field amplitude and frequency. In addition, it is shown that the spectral intensities of vortex harmonics are sensitive to the epsilon-near-zero nonlinear enhancing effects and the thickness of ITO materials. Thus the vortex harmonics can be conveniently tunable, which provides a wider potential application in optical communications based on high-order OAM coherent vortex beams.

Optimization of extreme ultraviolet vortex beam based on high harmonic generation

In high harmonic generation (HHG), Laguerre–Gaussian (LG) beams are used to generate extreme ultraviolet (XUV) vortices with well-defined orbital angular momentum (OAM), which have potential applications in fields such as microscopy and spectroscopy. An experimental study on the HHG driven by vortex and Gaussian beams is conducted in this work. It is found that the intensity of vortex harmonics is positively correlated with the laser energy and gas pressure. The structure and intensity distribution of the vortex harmonics exhibit significant dependence on the relative position between the gas jet and the laser focus. The ring-like structures observed in the vortex harmonics, and the interference of quantum paths provide an explanation for the distinct structural characteristics. Moreover, by adjusting the relative position between the jet and laser focus, it is possible to discern the contributions from different quantum paths. The optimization of the HH vortex field is applicable to the XUV, which opens up a new way for exploiting the potential in optical spin or manipulating electrons by using the photon with tunable orbital angular momentum.

Phase-matching of high-order harmonic generation in the extreme ultraviolet region with orbital angular momentum.

High-order harmonics can generate vortex beams with orbital angular momentum (OAM) in the extreme ultraviolet region. However, experimental research on their phase-matching (PM) characteristics is limited. In this study, vortex high-order harmonic generation (HHG) in the extreme ultraviolet region was generated with Ar gas. Phase-matched HHG with OAM was obtained by optimizing the focus position, laser energy, and gas pressure. The dependence of the PM characteristics on these parameters was analyzed. In addition, we conducted an experimental analysis of the dimensional properties of vortex harmonics under PM conditions. This study is a contribution towards the intense vortex high-order harmonic light sources and their applications.

Structuring light beams via nonlinear diffraction in 3D nonlinear photonic crystal

We show that nonlinear diffraction in nonlinear photonic crystal offers a convenient way to generate structured light at new frequencies. To this end we fabricate a 3D nonlinear photonic crystal containing two layers of fork-shaped ferroelectric domain gratings. Illumination of the structure by a fundamental Gaussian beam leads to the generation of two co-propagating second harmonic vortices with opposite topological charges, whose subsequent interference forms Hermite–Gaussian (HG) beams in far field.

Highly Efficient 3D Nonlinear Photonic Crystals in Ferroelectrics

AbstractNonlinear photonic crystals (NPCs) with spatially modulated second‐order nonlinear coefficients are indispensable in nonlinear optics and modern photonics. To access full degrees of freedom in the generation and control of coherent light at new frequencies, three dimensional (3D) NPCs have been recently fabricated employing the femtosecond laser writing technique in ferroelectric crystals. However, the nonlinear interaction efficiencies in 3D NPCs so far are rather low, which has been a major barrier to further development. Here, fabrication challenges of large‐scale 3D NPCs have been overcome to realize more than four orders of magnitude efficiency improvement over previously reported crystals. With the generation of second harmonic vortex beam as an example, the measured conversion efficiencies as high as 2.9 × 10−6 W−1 (femtosecond pulse‐pumped) and 1.2 × 10−5 W−1 (continuous‐wave‐pumped) are comparable with those in 1D or 2D NPCs. A general approach of structural simplification to relax fabrication challenge of truly complex 3D structures without sacrificing the predesigned functions is also presented. This realization of efficient nonlinear interactions in 3D NPCs paves the way for their novel applications in nonlinear photonics and quantum optics including nonlinear orbital angular momentum multiplexing and high‐dimensional entangled source.

Highly efficient harmonic vortex generation from a laser irradiated hollow-cone target.

It has been recently reported that ultraviolet harmonic vortices can be produced when a high-power circular-polarized laser pulse travels through a micro-scale waveguide. However, the harmonic generation quenches typically after a few tens of microns of propagation, due to the buildup of electrostatic potential that suppresses the amplitude of the surface wave. Here we propose to use a hollow-cone channel to overcome this obstacle. When traveling in a cone target, the laser intensity at the entrance is relatively low to avoid extracting too many electrons, while the slow focusing by the cone channel subsequently counters the established electrostatic potential, allowing the surface wave to maintain a high amplitude for a much longer distance. According to three-dimensional particle-in-cell simulations, the harmonic vortices can be produced with very high efficiency >20%. The proposed scheme paves the way for the development of powerful optical vortices sources in the extreme ultraviolet regime-an area of significant fundamental and applied physics potential.

Enhancement and redshift of vortex harmonic radiation in epsilon-near-zero materials.

The harmonic radiation from a vortex laser field interacting with an epsilon-near-zero (ENZ) material is numerically investigated via solving the Maxwell-paradigmatic-Kerr equations. For a laser field of long duration, the harmonics up to the seventh-order can be generated with a low laser intensity (∼109 W/cm2). Moreover, the intensities of high order vortex harmonics at the ENZ frequency are higher than at other frequency points due to the ENZ field enhancement effects. Interestingly, for a laser field of short duration, the obvious frequency redshift occurs beyond enhancement in high order vortex harmonic radiation. The reason is that the strong change of the laser waveform propagating in the ENZ material and the non-constant field enhancement factor around the ENZ frequency. Because the topological number of harmonic radiation is linearly proportional to its harmonic order, the high order vortex harmonics with redshift still possess the exact harmonic orders indicated by the transverse electric field distribution of each harmonic.

Revisiting the photonic orbital Hall effect with the vortex mode decomposition

The photonic orbital Hall effect (POHE) refers to the vortex-dependent beam shifts, which is generally believed to result from the conversion of intrinsic orbital angular momentum (IOAM) to extrinsic orbital angular momentum (EOAM). However, the physical mechanism of the POHE, such as how the IOAM is converted to the EOAM, remains further elucidation. In this paper, we re-examine the POHE of a vortex beam with additional IOAM illuminating at an optically thin slab by means of vortex mode decomposition. By considering the competition and coupling between the radial and azimuthal vortex harmonics of the abnormal mode in the transmitted beam, it is found that the underlying mechanism of the POHE is in fact a spin-to-orbital angular momentum (OAM) conversion process. And the IOAM carried by the incident beam is directly superimposed on the OAM obtained during the conversion. Our findings not only offer an alternative perspective for understanding the POHE, but also exhibit application potential in orbit–orbit and spin–orbit optical components.

An exploration for making the laminar flow steady over a square cylinder with 45° incidence in the presence of a twin small rotating controller

The capability of a twin rotating controllers to suppress the harmonic force fluctuation on a square cylinder with 45° angle of incidence has been numerically investigated in the present study for a frequently studied laminar flow. A point by point searching strategy has been used to find the possible installing locations of the controllers performing complete suppression of the force fluctuation. All cases that suppressed the hydrodynamic force completely and/or semi-completely have been selected for further investigations. Obtained results show that only one installing location of the controllers is able to suppress the fluctuations of the hydrodynamic forces on the whole system completely. Of course, there is still a weak secondary harmonic vortex shedding downstream the whole of the system, which does not affect the made steady flow in the upstream and near-wake regions. Besides, the drag coefficients on the square cylinder and rotating controller decrease by 30.62% and 45.76%, respectively. Further investigation shows that the hydrodynamic forces on the square cylinder always fluctuate harmonically regardless of the controller location, and the harmonic frequency of the lift coefficient of the cylinder is the main frequency of the other periodic fluctuations in the flow field.

Experimental investigation of vortex shedding of an airfoil at post-stall incidences

The harmonic vortex shedding from airfoil happens in various incidences. It has noticeable effects on the structure design and aerodynamic performance. In this paper, wind tunnel tests were conducted on a stationary NACA4412 airfoil at angles of attack ranging from [Formula: see text] to [Formula: see text] and Re number between [Formula: see text] and [Formula: see text] to examine the vortex shedding frequency and Strouhal number. The wake dynamics at post-stall incidences were investigated by surface pressure, wake flow velocity measurement, and smoke flow visualization. Three phases of the wake dynamics were observed with increasing the incidences beyond the stall: (i) the tiny vortices are shed from the airfoil’s suction side with scattered frequencies, (ii) the shear layer is separated from the LE, rolls up over the airfoil’s suction side and forms the harmonic vortex street, and (iii) the separation point moves from the airfoil’s suction side to the pressure side and leads to the vortex shedding like the bluff bodies. Frequency analysis of aerodynamic loads shows that the flow field’s low-frequency feature has a substantial effect normal to the surface while the vortex street unsteadiness impacts both perpendicular and parallel to the surface. The base pressure coefficient increases suddenly by the vortex street onset in the region (ii) and reaches about 0.4. The universal Strouhal number of 0.18 that is independent of Reynolds number was captured for the angles of attack well beyond the stall. Flow visualization shows that the vortex street establishes longitudinally closer to the airfoil at lower freestream velocity compared to the upper one.

Optical vortex array generation of intense high-order harmonics

An ultra-short and ultra-intense optical vortex array (OVA) is generated when two intense counter-propagating Laguerre–Gaussian (LG) pulses with [Formula: see text]-polarization impinge on two solid thin targets. In this paper, we propose a method for generating an OVA of high intensity, short wavelength, and high-order mode. Three-dimensional (3D) particle-in-cell (PIC) simulation results demonstrated that the generated high-order vortex harmonics interfered with each other in the transmitted area. These interference patterns of the fundamental and high-order harmonics exhibit an OVA distribution. Furthermore, vortex oscillating mirror (VOM) and classic wave interference models are then used to explain the simulation results.

Novel ultrafast structured EUV/x-ray sources from nonlinear optics

Coherent extreme-ultraviolet (EUV)/x-ray laser sources, structured in their temporal/spectral, spatial and angular momentum properties are emerging as unique tools to probe the nanoworld. One of the key ingredients for the emergence of such sources is the extraordinary coherence in the up-conversion of infrared laser sources through the highly nonlinear process of high-order harmonic generation. In this contribution we will review the advances during the last decade that led to the generation of structured EUV/xray sources, such as circularly polarized attosecond pulses, harmonic vortices with time-varying orbital angular momentum, ultrafast vector and vector/vortex beams, tunable high-order harmonic combs or attosecond pulse trains with time-dependent polarization states. The use of such sources is being already applied to the investigation of chiral matter or magnetic materials. In the latter case, structured ultrafast sources are very promising to achieve a complete understanding of the electronic and spin interactions that govern sub-femtosecond magnetization dynamics.

Vortex mode decomposition of the topology-induced phase transitions in spin-orbit optics

The topology-induced phase transition (TPT) in spin-orbit optics refers to a process of topological transition from one kind of spin-orbit interaction (e.g., spin-controlled vortex generation) to another (e.g., photonic spin-Hall effect). However, it is not clear in the TPT how a light beam evolves from a vortex state with a topological charge of \ifmmode\pm\else\textpm\fi{}2 to nonvortex states with spin-Hall shifts. Here, we examine the orbital angular momentum content (vortex harmonics) of a typical TPT process, i.e., the spin-orbit interactions of a light beam transmitted through an optically thin slab, based on vortex mode decomposition. It is found that the two kinds of spin-orbit interactions and the intermediate states can be described in a unified framework by considering the superposition and competition of three vortex modes with topological charges of 2, 1, and 0 (or \ensuremath{-}2, \ensuremath{-}1, and 0). These findings provide an alternative perspective for understanding the two spin-orbit interactions of light in a unified form and can be extended to the TPT-like processes in other physical systems.

Wind-Induced Vibration Control of High-Rise Structures Using Compound Damping Cables

Based on the vibration reduction mechanism of compound damping cables, this study focuses on the wind-induced vibration control of high-rise structures with additional mass at the top. The differential equation of motion of the system under the action of the composite damping cable is established, and the analytical solution of the additional damping ratio of the structure is deduced, which is verified by model tests. The vibration response of the structure under the action of simple harmonic vortex excitation and randomly fluctuating wind loads is studied, and the effect of different viscous coefficients of the dampers in the composite damping cable and different installation heights of the damping cable on the vibration control is analyzed. The results show that a small vortex excitation force will cause large vibrations of low-dampened towering structures, and the structure will undergo buffeting under the action of wind load pulse force. The damping cable can greatly reduce the amplitude of structural vibration. The root means square of structural vibration displacement varies with damping. The viscosity coefficient of the device and the installation height of the main cable of the damping cable are greatly reduced.

Nonlinear beam shaping in periodical χ (2) fork gratings with structural defects

Nonlinear beam shaping provides an efficient way to control the phase and amplitude of optical waves while shifting their frequency. Periodical topological structures with a modulated second-order nonlinear optical coefficient (χ (2)) are commonly used to generate special optical beams at new frequencies, e.g. the second harmonic vortices. In this paper, we theoretically study the influence of structural imperfection on nonlinear beam shaping and demonstrate how to utilize these imperfections for second harmonic generation with controlled orbital angular momentums. The results indicate that the studied nonlinear beam-shaping process has excellent tolerance to structural defects, and introducing designed defects of different scales and shapes constitutes a flexible approach for controlling the orbital angular momentum of light at new frequencies. As a proof of concept example, the nested χ (2) structures are designed for generating optical vortices with predesigned topological charges along different directions. In addition, the performance of the nonlinear generation of vortex beams with a fundamental beam shifted from the center of the fork grating is also discussed. The study opens up new prospects for the optimization of nonlinear χ (2) structures for special beam generation at new frequencies.

Nonlinear Volume Holography: Nonlinear Volume Holography in 3D Nonlinear Photonic Crystals (Laser Photonics Rev. 14(11)/2020)

In article number 2000224 by Yan Sheng and co-workers, nonlinear volume holography is realized by 3D micro-engineering the second-order nonlinear coefficient of a ferroelectric crystal with femtosecond laser pulses. A proof-of-concept nonlinear reconstruction of second harmonic vortex beam is demonstrated. The 3D nonlinear volume holography provides a universal approach for efficient generation of coherent light at new frequencies with predesigned phase and amplitude structures.

Tuning the orbital angular momentum of high harmonics by manipulating the collinear photon channels in two-color high-harmonic generation

This work investigates the characteristics of collinear photon channels in the two-color vortex high-order harmonic generation, and proposes a method to generate the harmonic vortices with well-defined and tunable orbital angular momentum.

Large second-harmonic vortex beam generation with quasi-nonlinear spin–orbit interaction

A harmonic vortex beam is a typical vector beam with a helical wavefront at harmonic frequencies (e.g., second and third harmonics). It provides an additional degree of freedom beyond spin- and orbital-angular momentum, which may greatly increase the capacity for communicating and encoding information. However, conventional harmonic vortex beam generators suffer from complex designs and a low nonlinear conversion efficiency. Here, we propose and experimentally demonstrate the generation of a large second-harmonic (SH) vortex beam with quasi-nonlinear spin–orbit interaction (SOI). High-quality SH vortex beams with large topological charges up to 28 are realized experimentally. This indicated that the quasi-angular-momentum of a plasmonic spiral phase plate at the excitation wavelength (topological charge, q) could be imprinted on the harmonic signals from the attached WS2 monolayer. The generated harmonic vortex beam has a topological charge of ln=2nq (n is the harmonic order). The results may open new avenues for generating harmonic optical vortices for optical communications and enables novel multi-functional hybrid metasurface devices to manipulate harmonic beams.