We present the first experimental evidence, supported by theory and simulation, of spatiotemporal optical vortices (STOVs). Quantized STOVs are a fundamental element of the nonlinear collapse and subsequent propagation of short optical pulses in material media. A STOV consists of a ring-shaped null in the electromagnetic field about which the phase is spiral, forming a dynamic torus which is concentric with and tracks the propagating pulse. Depending on the sign of the material dispersion, the local electromagnetic energy flow is saddle or spiral about the STOV. STOVs are born and evolve conserving topological charge; they can be simultaneously created in pairs with opposite windings, or generated from a point null. Our results, here obtained for optical pulse collapse and filamentation in air, are generalizable to broad class of nonlinearly propagating waves.
Spatiotemporal optical vortices (STOVs) are a new type of intrinsic optical orbital angular momentum (OAM) structure in which the OAM vector is orthogonal to the propagation direction [Optica 6, 1547, (2019)] and the optical phase circulates in space-time. Here, we experimentally and theoretically demonstrate, for the first time, the generation of the second harmonic of a STOV-carrying pulse along with the conservation of STOV-based OAM. Our experiments verify that individual photons can have intrinsic orbital angular momentum perpendicular to their propagation direction.
Recently, a spatiotemporal optical vortex (STOV) with a transverse orbital angular momentum (OAM) has been generated from coherent ultrafast pulses using mode-locked lasers. In contrast, we demonstrate theoretically and experimentally that a STOV can be generated from a light source with partial temporal coherence with fluctuating temporal phase. By eliminating the need of mode-locked laser sources, the partially coherent STOV will serve as a convenient and cost-effective transverse OAM source.
As a new degree of freedom for optical manipulation, recently spatiotemporal optical vortices (STOVs) carrying transverse orbital angular momentums have been experimentally demonstrated with pulse shapers. Here a spatiotemporal differentiator is proposed to generate STOVs with transverse orbital angular momentum. In order to create phase singularity in the spatiotemporal domain, the spatiotemporal differentiator is designed by breaking spatial mirror symmetry. In contrast to pulse shapers, the device proposed here is a simple one-dimensional periodic nanostructure and thus it is much more comp…
Spatio-temporal optical vortices (STOVs) are a new type of optical orbital angular momentum (OAM) with optical phase circulation in space-time. In prior work [N. Jhajj et al., Phys. Rev X 6, 031037 (2016)], we demonstrated that a STOV is a universal structure emerging from the arrest of self-focusing collapse leading to nonlinear self-guiding in material media. Here, we demonstrate linear generation and propagation in free space of STOV-carrying pulses. Our measurements and simulations demonstrate STOV mediation of space-time energy flow within the pulse and conservation of OAM in space-time. …
In this study, we demonstrate the concept of combining optical combs with optical vortices for the first time. By combining the advantages of the both light sources, we realize an optical vortex comb technology for arbitrary spatiotemporal phase manipulation. This idea corresponds to simultaneous control of the longitudinal and transverse modes of light based on the high controllability of the optical comb. As a proof-of-concept experiment, we applied an optical vortex comb to the generation and rotational control of a ring-shaped optical lattice. Furthermore, to demonstrate the utility of thi…
Isolated attosecond spatio-temporal optical vortices: Interplay between the topological charge and orbital angular momentum scaling in high harmonic generation
Shenzhen University（深圳大学）；East China Normal University（华东师范大学）；University of Shanghai for Science and Technology（上海理工大学）；Northwestern Polytechnical University（西北工业大学）
The additional degree of freedom as introduced by the orbital angular momentum (OAM) of light has revolutionized the various technological applications. Optical pulses with OAM have applications in the generation of twisted attosecond pulses, ultrafast spectroscopy, telecommunication, high harmonic generation and in many other areas of physics as well. In this paper, we present a numerical investigation of the propagation dynamics of ultrashort Laguerre Gauss (LG) vortices using nonlinear envelope equation (NEE) in a dispersive and nonlinear medium. Asymmetric splitting of ultrashort LG vortic…
Using an example of a Raman active medium we describe how a common nonlinear process of four-wave mixing can be used to induce strong coupling between the spatial and temporal degrees of freedom in optical waves. This coupling produces several unexpected effects. Amongst those are cascaded excitation of multiply charged optical vortices, spatial focusing in a nonlinearly defocusing medium and generation of helically shaped spatio-temporal optical solitons.
Generation of few-cycle optical vortex pulses is challenging due to the large spectral bandwidths, as most vortex generation techniques are designed for monochromatic light. In this work, we use a spiral phase plate to generate few-cycle optical vortices from an ultrafast titanium:sapphire oscillator, and characterize them in the spatiotemporal domain using a recently introduced technique based on spatially resolved Fourier transform spectrometry. The performance of this simple approach to the generation of optical vortices is analyzed from a wavelength dependent perspective, as well as in the…
Optical parametric amplification of spatiotemporal optical vortices
Zhejiang Key Laboratory of 3D Micro/Nano Fabrication and Characterization, Department of Electronic and Information Engineering, School of Engineering, Westlake University（西湖大学工程学院电子信息工程系三维微纳加工与表征浙江省重点实验室）；School of Optical and Electronic Information and Wuhan National Laboratory for Optoelectronics, Huazhong University of Science and Technology（华中科技大学光学与电子信息学院/武汉光电国家研究中心）；Westlake-Kromoson Joint Laboratory of Light-Field Intelligence, School of Engineering, Westlake University（西湖大学工程学院光场智能西湖-科慕森联合实验室）
Vortex solitons (dark solitons) are described in self-defocusing Kerr media whose phase line singularity is not parallel to the propagation direction, but is perpendicular or tilted almost arbitrary angles, depending on the medium linear dispersion. These solitons broaden the so-called spatiotemporal optical vortices recently observed in experiments to the nonlinear realm, opening new perspectives in practical applications of optical vortices.
The orbital angular momentum (OAM) of light holds great promise for applications in optical communication, super-resolution imaging, and high-dimensional quantum computing. However, the spatio-temporal coherence of the light source has been essential for generating OAM beams, as incoherent ambient light would result in polychromatic and obscured OAM beams in the visible spectrum. Here, we extend the applications of OAM to ambient lighting conditions. By miniaturizing spiral phase plates and integrating them with structural color filters, we achieve spatio-temporal coherence using only an incoh…
Vortices are whirling disturbances commonly found in nature ranging from tremendously small scales in Bose-Einstein condensates to cosmologically colossal scales in spiral galaxies. An optical vortex, generally associated with a spiral phase, can carry orbital angular momentum (OAM). The optical OAM can either be in the longitudinal direction if the spiral phase twists in the spatial domain or in the transverse direction if the phase rotates in the spatiotemporal domain. In this article, we demonstrate the intersection of spatiotemporal vortices and spatial vortices in a wave packet. As a resu…
Knowledge of spatio-temporal couplings such as pulse-front tilt or curvature is important to determine the focused intensity of high-power lasers. Common techniques to diagnose these couplings are either qualitative or require hundreds of measurements. Here we present both a new algorithm for retrieving spatio-temporal couplings, as well as novel experimental implementations. Our method is based on the expression of the spatio-spectral phase in terms of a Zernike-Taylor basis, allowing us to directly quantify the coefficients for common spatio-temporal couplings. We take advantage of this meth…
Using SEA TADPOLE, we directly measure the spatio-temporal field of diffracting ultrashort pulses with femtosecond temporal and micrometer spatial resolutions. Using a circular aperture and an opaque disk, we observe boundary wave pulses including their superluminal speeds.
In any form of wave propagation, strong spatiotemporal coupling appears when non-elementary, three-dimensional wave-packets are composed by superimposing pure plane waves, or spontaneously generated by light-matter interaction and nonlinear processes. Ultrashort pulses with orbital angular momentum (OAM), or ultrashort vortices, furnish a critical paradigm in which the analysis of the spatiotemporal coupling in the form of temporal-OAM coupling can be carried out accurately by analytical tools. By generalizing and unifying previously reported results, we show that universal and spatially heter…
Spatiotemporal Optical Vortices From All-Dielectric Bilayer Metagratings
The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；University of Electronic Science and Technology of China（电子科技大学）；Chinese Academy of Sciences（中国科学院）；Wuhan University of Technology（武汉理工大学）
In structured light with controllable degrees of freedom (DoFs), the vortex beams carrying orbital angular momentum (OAM) give access to provide additional degrees of freedom for information transfer, and in classic field, the propagation invariant space time electromagnetic pulses are the possible approach to high dimensional states. This paper arose an idea that coupling the space polarization nonseparable states of vortex beams and space time nonseparable states of spatiotemporal pulse can generate numerous unique and beneficial effects. Here, we introduce an family of space time nonseparab…
Quadrature bases that incorporate spatio-temporal degrees of freedom are derived as eigenstates of momentum dependent quadrature operators. The resulting bases are shown to be orthogonal for both the particle-number and spatio-temporal degrees of freedom. Using functional integration, we also demonstrate the completeness of these quadrature bases.
A general analysis of undistorted propagation of localized wavepackets in photonic crystals based on a Wannier-function expansion technique is presented. Different kinds of propagating and stationary spatio-temporal localized waves are found from an asymptotic analysis of the Wannier function envelope equation.
Probing Internal Dynamics of Spatiotemporal Optical Vortex Strings: Spatiotemporal Attraction and Filament Stretching
Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences（中国科学院上海光学精密机械研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Tianjin University（天津大学）；Chongqing University of Technology（重庆理工大学）
We draw an intuitive picture of the spatio-temporal properties of the entangled state of twin photons, where they are described as classical wave-packets. This picture predicts a precise relation between their temporal and transverse spatial separations at the crystal output. The space-time coupling described by classical arguments turns out to determine in a precise way the spatio-temporal structure of the quantum entanglement, analysed by means of the biphotonic correlation and of the Schmidt dimensionality of the entanglement.
In $χ^{(2)}$ three-wave mixing, the noise-seeded spatio--temporal modulational instability has a dramatic impact on the spatial-soliton dynamics, leading to the counterintuitive observation of a soliton with no apparent participation of the high-frequency field in the process.
We present an experimental methodology to observe spatio-temporal second-order quantum coherence of surface plasmon polaritons which are emitted by nitrogen vacancy color centers attached at the apex of an optical tip. The approach relies on leakage radiation microscopy in the Fourier space and we use this approach to test wave-particle duality for surface plasmon polaritons.
