Vectorial nonlinear optics refers to the investigation of optical processes whose nonlinear polarization (NP) undergoes spin-orbit coupling (SOC) interactions where, in general, the driving light field or the new field generated by the interaction containing the SOC property. To contribute to fundamental knowledge in this domain, we examine the type-II second harmonic generation (SHG) induced by vectorial laser modes. First, we provide a general theory to analyze the vectorial SHG process. Second, by using two typical vector modes as examples, we show how the SOC of the pump field dictates nonlinear interaction. Finally, we corroborate our theoretical predictions through experiments to confirm the crucial role of the SOC in nonlinear interactions. These results enhance our fundamental understanding of SOC-mediated nonlinear optics and lay the foundation for further fundamental studies as well as possible applications.
We model second harmonic generation in subwavelength III-V-on-insulator waveguides. The large index contrast induces strong longitudinal electric field components that play an important role in the nonlinear conversion. We show that many different waveguide dimensions are suitable for efficient conversion of a fundamental quasi-TE pump mode around the 1550 nm telecommunication wavelength to a higher-order second harmonic mode.
Reducing the Carrier-Envelope-Phase-dependence of High-Harmonic-Generation by Vectorial-Time-Polarization-Gating
Raymond and Beverly Sackler Faculty of Exact Sciences, School of Chemistry, Tel Aviv University（特拉维夫大学理学院化学系）；Tel-Aviv University Center for Light-Matter-Interaction（特拉维夫大学光物质相互作用中心）
Adaptive optics normally concerns the feedback correction of phase aberrations. Such correction has been of benefit in various optical systems, with applications ranging in scale from astronomical telescopes to super-resolution microscopes. Here we extend this powerful tool into the vectorial domain, encompassing higher-dimensional feedback correction of both polarisation and phase. This technique is termed vectorial adaptive optics (V-AO). We show that V-AO can be implemented using sensor feedback, indirectly using sensorless AO, or in hybrid form combining aspects of both. We validate improv…
Nonlinear optical generation has been a well-established way to realize frequency conversion in nonlinear optics, whereas previous studies were just focusing on the scalar light fields. Here we report a concise yet efficient experiment to realize frequency conversion from vector fields to vector fields based on the vectorial nonlinear optical process, e.g., the second-harmonic generation. Our scheme is based on two cascading type-I phase-matching BBO crystals, whose fast axes are configured elaborately to be perpendicular to each other. Without loss of generality, we take the full Poincaré bea…
Diffractive optical elements (DOEs) are widely applied as compact solutions for desired light manipulations via wavefront shaping. Recent advanced chip applications further require their feature sizes to move down to the subwavelength, which inevitably brings forth vectorial effects of optical fields and makes the typical scalar-based theory invalid. However, simulating and optimizing their vectorial fields, which are associated with billions of adjustable parameters in the optical element, are difficult to do, because of the issues of numerical stability and the highly-demanding computational…
Optical intrinsic angular momentum can be regarded as derivation from spatial superposition of optical vector fields embodied by spinning or and spiraling the electric field vector. We employ vectorial formulation derivation to comprehensively study all angular momentum contents of optical vector fields in arbitrary superposition states, including the longitudinal and transverse, spin and orbital (SAM and OAM) components. As for the orthogonal superposition fields, there inherently exists spin-orbit shift from longitudinal SAM to OAM, and the whole local spin flow manifests local multiple fold…
Comprehending the unique characteristics of structured ultrafast optical pulses is essential to the physics, applications and instrumentations of ultrafast lasers. However, full-vectrorial characterizations of the pulses remain challenging because of their multiple degrees of freedom. In this work, we implement and demonstrate the vectorial interferometric polarimeter for electric-field reconstruction (VIPER) which, for the first time, is able to precisely determine the specific three-dimensional E-field at every spatial-temporal coordinate throughout the entire detection region. This metrolog…
Optical aberrations have been studied for centuries, placing fundamental limits on the achievable resolution in focusing and imaging. In the context of structured light, the spatial pattern is distorted in amplitude and phase, often arising from optical imperfections, element misalignment, or even from dynamic processes due to propagation through perturbing media such as living tissue, free-space, underwater and optical fibre. Here we show that the polarisation inhomogeneity that defines vectorial structured light is immune to all such perturbations, provided they are unitary. By way of exampl…
Integrating conventional optics into compact nanostructured surfaces is the goal of flat optics. Despite the enormous progress of this technology, there are still critical challenges for real world applications due to a limited efficiency in the visible, on average lower than $60\%$, which originates by absorption losses in wavelength thick ($\approx 500$nm) structures. Another issue is the realization of on-demand optical components for controlling vectorial light at visible frequencies simultaneously in both reflection and transmission, and with a predetermined wavefront shape. In this work,…
Vectorial structured light with spatially varying amplitude, phase, and polarization is reshaping many areas of modern optics, including nonlinear optics, as diverse parametric processes can be used to explore interactions between such complex vector fields, extending the frontiers of optics to new physical phenomena. However, the most basic nonlinear application, i.e., frequency conversion, still remains challenging for vectorial structured light since parametric processes are polarization dependent, leading to a change in the spatial topological structure of signals. In this work, to break t…
Nanometer-resolution 3D Tomographic and Vectorial Near-field Imaging in Dielectric Optical Resonators
State Key Laboratory of Surface Physics, Key Laboratory of Micro and Nano Photonic Structures (MOE), and Department of Physics, Fudan University（复旦大学表面物理国家重点实验室、微纳光子结构教育部重点实验室和物理系）；Shanghai Key Laboratory of Metasurfaces for Light Manipulation, Fudan University（复旦大学光调控超材料上海市重点实验室）
Graded index (GRIN) lenses are commonly used for compact imaging systems. It is not widely appreciated that the ion-exchange process that creates the rotationally symmetric GRIN lens index profile also causes a symmetric birefringence variation. This property is usually considered a nuisance, such that manufacturing processes are optimized to keep it to a minimum. Here, rather than avoiding this birefringence, we understand and harness it by using GRIN lenses in cascade with other optical components to enable extra functionality in commonplace GRIN lens systems. We show how birefringence in th…
Vectorial engineering of second-harmonic generation in silicon-based waveguides integrated with 2D materials
School of Engineering, Mackenzie Presbyterian University（麦肯锡长老会大学工程学院）；MackGraphe, Mackenzie Presbyterian Institute（麦肯锡长老会研究所 MackGraphe）；Brazilian Nanotechnology National Laboratory (LNNano), Brazilian Center for Research in Energy and Materials (CNPEM)（巴西国家纳米技术实验室（LNNano），巴西能源与材料研究中心（CNPEM））
An electrical pulse E(t) is completely defined by its time-dependent amplitude and polarisation direction. For optical pulses the manipulation and characterisation of the light polarisation state is fundamental due to its relevance in several scientific and technological fields. In this work we demonstrate the complete temporal reconstruction of the electric field of few-cycle pulses with a complex time-dependent polarisation. Our experimental approach is based on extreme ultraviolet interferometry with isolated attosecond pulses and on the demonstration that the motion of an attosecond electr…
Light is a union of electric and magnetic fields, and nowhere is their complex relationship more evident than in the near fields of nanophotonic structures. There, complicated electric and magnetic fields varying over subwavelength scales are generally present, leading to photonic phenomena such as extraordinary optical momentum, super-chiral fields, and a complex spatial evolution of optical singularities. An understanding of such phenomena requires nanoscale measurements of the complete optical field vector. However, while it was recently demonstrated that near-field scanning optical microsc…
Many polarisation techniques have been harnessed for decades in biological and clinical research, each based upon measurement of the vectorial properties of light or the vectorial transformations imposed on light by objects. Various advanced vector measurement/sensing techniques, physical interpretation methods, and approaches to analyse biomedically relevant information have been developed and harnessed. In this review, we focus mainly on summarizing methodologies and applications related to tissue polarimetry, with an emphasis on the adoption of the Stokes-Mueller formalism. Several recent b…
Near-field microscopy is widely used for characterizing electromagnetic fields at nanoscale, where nanoprobes afford the opportunity to extract subwavelength optical quantities, including the amplitude, phase, polarization and chirality. However, owing to the complexity of various nanoprobes, a general and intuitive theory is highly needed to assess the vectorial field response of the nanoprobes and interpret the mechanism of the probe-field interaction. Here, we develop a general imaging theory based on the reciprocity of electromagnetism and multipole expansion analysis. The proposed theory …
We study numerically and experimentally the impact of temporal randomness on the formation of analogue optical blast-waves in nonlinear fiber optics. The principle-of-operation is based on a two-components nonlinear interaction occurring between a partially coherent probe wave co-propagating in a normally dispersive optical fiber together with an orthogonally polarized intense short pulse. The cross-polarized interaction induces a dual phase-singularity in the probe profile which leads to the formation of two sharp fronts of opposite velocities. An optical blast-wave is then generated and lead…
We develop a full theoretical analysis of the nonlinear interactions of the two polarizations of a waveguide by means of a vectorial model of pulse propagation which applies to high index subwavelength waveguides. In such waveguides there is an anisotropy in the nonlinear behavior of the two polarizations that originates entirely from the waveguide structure, and leads to switching properties. We determine the stability properties of the steady state solutions by means of a Lagrangian formulation. We find all static solutions of the nonlinear system, including those that are periodic with resp…
Focused optical fields are key to a multitude of applications involving light-matter interactions, such as optical microscopy, single-molecule spectroscopy, optical tweezers, lithography, or quantum coherent control. A detailed vectorial characterization of the focused optical fields that includes a description beyond the paraxial approximation is key to optimize technological performance as well as for the design of meaningful experiments and interpret properly their results. Here, we present PyFocus, an open-source Python software package to perform fully vectorial calculations of focused el…
We experimentally demonstrate the emergence of a purely azimuthally polarized vectorial vortex beam with a phase singularity upon Brewster reflection of focused circularly polarized light from a dielectric substrate. The effect originates from the polarizing properties of the Fresnel reflection coefficients described in Brewster's law. An astonishing consequence of this effect is that the reflected field's Cartesian components acquire local phase singularities at Brewster's angle. Our observations are crucial for polarization microscopy and open new avenues for the generation of exotic states …
We employ structured light for the second-harmonic generation from subwavelength AlGaAs nanoparticles that support both electric and magnetic multipolar Mie resonances. The vectorial structure of the pump beam allows addressing selectively Mie-resonant modes and control the strength of the generated nonlinear fields. We observe experimentally the enhancement of the second-harmonic generation for the azimuthally polarized vector beams near magnetic dipole resonance, and match our observations with the numerical decomposion of the Mie-type multipoles for the fundamental and generated second-harm…
We consider how vectorial aspects (polarization) of light propagation can be implemented, and its origin, within a Feynman path integral approach. A key part of this scheme is in generalising the standard optical path length integral from a scalar to a matrix quantity. Reparametrization invariance along the rays allows a covariant formulation where propagation can take place along a general curve. A general gradient index background is used to demonstrate the scheme. This affords a description of classical imaging optics when the polarization aspects may be varying rapidly and cannot be neglec…
Vectorial field reconstruction without detecting the field
Institute for Applied Physics, Technical University of Darmstadt（达姆施塔特工业大学应用物理研究所）；ICFO–Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology（巴塞罗那科技研究院光子科学研究所）；Fraunhofer Institute for Applied Optics and Precision Engineering IOF（弗劳恩霍夫应用光学和精密工程研究所）
In-bulk processing of materials by laser radiation has largely evolved over the last decades and still opensup new scientific and industrial potentials. The development of any in-bulk processing application relieson the knowledge of laser propagation and especially the volumetric field distribution near the focus.Many commercial programs can simulate this, but, in order to adapt them, or to develop new methods,one usually needs to create a specific software. Besides, most of the time people also need to measurethe actual field distribution near the focus to evaluate their assumptions in the si…
Seeing full vectorial structures of light fields with a single-shot holographic multiplexed detector
School of Optoelectronic Engineering, Xidian University（西安电子科技大学光电工程学院）；Key Laboratory of Light Field Manipulation and System Integration Applications in Fujian Province, School of Physics and Information Engineering, Minnan Normal University（闽南师范大学物理与信息工程学院福建省光场调控与系统集成应用重点实验室）；School of physics, Xidian University（西安电子科技大学物理学院）；State Key Laboratory of Integrated Optoelectronics, College of Electronic Science and Engineering, Jilin University（吉林大学电子科学与工程学院集成光学国家重点实验室）
Multicomponent Bose-Einstein condensates, quantum Hall systems, and chiral magnetic materials display twists and knots in the continuous symmetries of their order parameter, known as Skyrmions. Originally discovered as solutions to the nonlinear sigma model in quantum field theory, these vectorial excitations are quantified by a topological winding number dictating their interactions and global properties of the host system. Here, we report the first experimental observation of a stable individual second order meron, and antimeron, appearing in an electromagnetic field. These complex textures …
Position measurement of a levitated particle with vectorial light
Pontifical Catholic University of Rio de Janeiro（里约热内卢天主教大学）；Universidade Federal do Rio de Janeiro（里约热内卢联邦大学）；Tecnológico de Monterrey（蒙特雷理工学院）；University of Southampton（南安普顿大学）
High-harmonic generation (HHG) in solids has been touted as a way to probe ultrafast dynamics and crystal symmetries in condensed matter systems. Here, we investigate the polarization properties of high-order harmonics generated in monolayer MoS$_2$, as a function of crystal orientation relative to the mid-infrared laser field polarization. At several different laser wavelengths we experimentally observe a prominent angular shift of the parallel-polarized odd harmonics for energies above approximately 3.5 eV, and our calculations indicate that this shift originates in subtle differences in the…
Optical properties of periodic arrays of nanoholes of a triangular shape with experimentally realizable parameters are examined in both linear and nonlinear regimes. Utilizing fully vectorial three-dimensional approach based on the nonlinear hydrodynamic Drude model describing metal coupled to Maxwells equations and Bloch equations for molecular emitters we analyze linear transmission, reflection, and nonlinear power spectra. Rigorous numerical calculations demonstrating second and third harmonic generation by the triangular hole arrays are performed. It is shown that both the Coulomb interact…
Type II second-harmonic generation was performed in a 15.8-mm-long KTiOPO4 micrometric ridge waveguide with an average transversal section of 38 micrometer^2. Theoretical predictions are compared with experiments. Strong agreements are obtained for both phase-matching wavelengths and second-harmonic intensity. This work opens wide perspectives for integrated parametric optics.
We report on the generation, and momentum space distribution of fluorescence emission from individual SiO2 microsphere on dye coated Au mirror. The molecular fluorescence emission mediated via whispering gallery modes of the sphere is studied using polarization resolved optical energy-momentum micro-spectroscopy. Our experiments reveal intensity dependence of split modes of the cavity as a function of in-plane wavevector and emission polarization in the far field. The exotic far-field distribution can be understood by sphere-image sphere model that further reveals the polarization dependence o…
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.
We investigate the process of the second harmonic generation by plasmonic nano-antennas that exhibit Fano-like resonances. A rigorous fully vectorial Maxwell-hydrodynamics approach is employed to directly calculate the second order susceptibilities as function of the pump frequency, considering a periodic array of nanodolmens comprised of three Au nanorods. The results of the numerical simulations demonstrate noticeable enhancement of the second harmonic efficiency by the antisymmetric mode. Additionally, a simple analytical model based on two coupled nonlinear oscillators is proposed. It is s…
Controlling the wavefront of an extreme ultraviolet (XUV) high-order harmonic beam during the generation process offers to focus the beam without resorting to any XUV optics. By characterizing the XUV intensity profile and wavefront, we quantitatively retrieve both the size and the position of the waist of each generated harmonics and show that optics-free focusing leads to focused XUV spot with micrometer size. We use this remarkable coherent effect to demonstrate efficient and adjustable spectral filtering of the XUV light, along with a strong rejection of the fundamental beam, without using…
