Spatio-temporal optical vortices: principles of description and basic properties
Aleksandr Bekshaev
备注：
34 pages, 9 figures. Initially, this was prepared as a sort of "auto-tutorial" for the author's personal use but, probably, may be interesting for other people. In the last version, the explicit formula of the Hermite-polynomial addition theorem and closed analytical expressions (64), (67) for the high-order STOV propagation are added
本汇编总结了时空光学涡旋（STOV）结构与性质所依据的主要物理基础。STOV描述与表征的一般方法基于标量近轴高斯波包模型。在此基础上，任意阶的STOV结构被视为时空厄米-高斯模式的叠加。该方法能够以显式且物理透明的方式系统表征STOV的主要性质。特别地，我们分析了STOV的振幅和相位分布、它们在自由传播和光学系统中的演化、内部能量流以及轨道角动量。讨论了STOV的拓扑决定的内在不对称性以及“能量中心”与“概率中心”之间的差异[Phys. Rev. A 107, L031501 (2023)]，并进行了定性解释。概述了STOV的产生和诊断方法，并简要描述了非高斯（贝塞尔型）STOV的主要性质。最后，考虑了全文所采用的标量高斯模型的局限性，并提出了可能的推广。整个介绍可作为STOV相关思想及其非凡性质的初步入门。
英文摘要：
This compilation represents a summary of the main physical foundations underlying the structure and properties of spatio-temporal optical vortices (STOV). The general approach to the STOV description and characterization is based on the model of scalar paraxial Gaussian wave packet. On this ground, the STOV structures of arbitrary orders are considered as superpositions of spatio-temporal Hermite-Gaussian modes. This approach enables a systematic characterization of the main STOV properties in an explicit and physically transparent form. In particular, we analyze the STOV amplitude and phase distributions, their evolution upon free propagation and in optical systems, internal energy flows and the orbital angular momentum. The topologically determined inherent asymmetry of the STOVs and the difference between the "energy center" and "probability center" [Phys. Rev. A 107, L031501 (2023)] are discussed and qualitatively interpreted. Methods for the STOV generation and diagnostics are outlined, and the main properties of non-Gaussian (Bessel-type) STOVs are briefly described. Finally, limitations of the scalar Gaussian model, accepted throughout the whole text, are considered, and possible generalizations are exposed. The whole presentation may be useful as initial introduction to the STOV-associated ideas and their extraordinary properties.
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…
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 conse…
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…
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 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…
We present a spatio-temporal mechanism for producing 2D optical rogue waves in the presence of a turbulent state with creation, interaction and annihilation of optical vortices. Spatially periodic structures with bound phase lose stability to phase unbound turbulent states in complex Ginzburg- Landau and Swift-Hohenberg models with external driving. When the pumping is high and the external driving is low, synchronized oscillations are unstable and lead to spatio-temporal turbulence with high excursions in amplitude. Nonlinear amplification leads to rogue waves close to turbulent optical vorti…
We introduce the basic elements of a spatio-angular theory of fluorescence microscopy, providing a unified framework for analyzing systems that image single fluorescent dipoles and ensembles of overlapping dipoles that label biological molecules. We model an aplanatic microscope imaging an ensemble of in-focus fluorescent dipoles as a linear Hilbert-space operator, and we show that the operator takes a particularly convenient form when expressed in a basis of complex exponentials and spherical harmonics$-$a form we call the dipole spatio-angular transfer function. We discuss the implications o…
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）
Spatiotemporal optical vortices (STOVs) carrying transverse orbital angular momentum (OAM) are of rapidly growing interest for the field of optics due to the new degree of freedom that can be exploited. In this paper, we propose cylindrical vector two dimensional STOVs (2D-STOVs) containing two orthogonal transverse OAMs in both x-t and y-t planes for the first time, and investigate the tightly focusing of such fields using the Richards-Wolf vectorial diffraction theory. Highly confined spatiotemporal wavepackets with polarization structure akin to toroidal topology is generated, whose spatiot…
Acoustic toroidal vortices with programmable links and knots
National Laboratory of Solid State Microstructures & School of Advanced Manufacturing Engineering, Nanjing University（南京大学固体微结构物理国家重点实验室与先进制造工程学院）；College of Engineering and Applied Sciences & Collaborative Innovation Center of Advanced Microstructures, Nanjing University（南京大学工程与应用科学学院与先进微结构协同创新中心）；Centre for Disruptive Photonic Technologies, School of Physical and Mathematical Sciences, Nanyang Technological University（南洋理工大学物理与数学学院破坏性光子技术中心）；School of Electrical and Electronic Engineering, Nanyang Technological University（南洋理工大学电气与电子工程学院）；Jiangsu Key Laboratory of Artificial Functional Materials & Jiangsu Physical Science Research Center, Nanjing University（南京大学江苏省人工功能材料重点实验室与江苏物理科学研究中心）
Single-shot 3D characterization the spatiotemporal optical vortex via a spatiotemporal wavefront sensor (STWFS)
Key Laboratory of High Power Laser and Physics, 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高功率激光物理重点实验室）；Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences（中国科学院大学材料科学与光电技术研究中心）；School of Physics, Xi'an Jiaotong University（西安交通大学物理学院）；College of Information Science and Technology, Donghua University（东华大学信息科学与技术学院）
