We present a detailed study of the fields and propagation characteristics around the focus of ultrashort radially-polarized laser beams (RPLBs) having low-order spatio-temporal couplings (STCs). The three STCs considered are the focusing of the different frequencies to different positions along the longitudinal coordinate, the focusing of the frequencies to different positions along one transverse coordinate, and the beam waist or Rayleigh range having a power-law frequency dependence. The STCs considered are deemed low-order because they are generally linear in frequency. The combination of a low-order vector beam, ultrashort pulse duration, and the three different STCs shows promise for exotic applications in dielectric or charged particle manipulation and potentially other strong-field phenomena. The STCs presented are all developed in a standard frequency-domain model where each case involves a different chromatic term. We present the results unique to the vector nature of the RPLBs and compare them to the linearly polarized cases, opening up opportunities for control of the electric field around the focus with the additional element of polarization.
We derive an asymptotically accurate formula for the beam waist of ultrashort, tightly-focused fundamental linearly-polarized, radially-polarized, and azimuthally-polarized modes in free space. We compute the exact beam waist via numerical cubature to ascertain the accuracy with which our formula approximates the exact beam waist over a broad range of parameters of practical interest. Based on this, we describe a method of choosing parameters in the model given the beam waist and pulse duration of a laser pulse.
Analytic expressions for the fields of a radially polarized, ultrashort and tightly focused laser pulse propagating in a linear-response plasma are derived and discussed. The fields are obtained from solving the inhomogenous wave equations for the vector and scalar potentials, linked by the Lorenz gauge, in a plasma background. First the scalar potential is eliminated using the gauge condition, then the vector potential is synthesized from Fourier components of an initial uniform distribution of wavenumbers, and the inverse Fourier transformation is carried out term-by-term in a truncated seri…
Exact closed-form solutions to Maxwell's equations are used to investigate electron acceleration driven by radially polarized laser beams in the nonparaxial and ultrashort pulse regime. Besides allowing for higher energy gains, such beams could generate synchronized counterpropagating electron bunches.
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.
We measure the detailed spatiotemporal profiles of femtosecond laser pulses in the infrared wavelength range λ=2.5-11μm, and the absolute nonlinear response of major air constituents (N2, O2, and Ar) over this range. The spatiotemporal measurements reveal wavelength-dependent pulse front tilt and temporal stretching in the infrared pulses.
Using SEA TADPOLE with micrometer-range spatial and femtosecond-range temporal resolution, we report the first direct spatiotemporal measurements of ultrashort Bessel-X pulses. We demonstrate their propagation invariance and superluminal velocity and verify our results with simulations
By using a reductive perturbation method, we derive from Maxwell-Bloch equations a cubic generalized Kadomtsev-Petviashvili equation for ultrashort spatiotemporal optical pulse propagation in cubic (Kerr-like) media without the use of the slowly varying envelope approximation. We calculate the collapse threshold for the propagation of few-cycle spatiotemporal pulses described by the generic cubic generalized Kadomtsev-Petviashvili equation by a direct numerical method and compare it to analytic results based on a rigorous virial theorem. Besides, typical evolution of the spectrum (integrated o…
Exact closed-form solutions to Maxwell's equations are used to investigate the acceleration of electrons in vacuum driven by ultrashort and nonparaxial radially polarized laser pulses. We show that the threshold power above which significant acceleration takes place is greatly reduced by using a tighter focus. Moreover, electrons accelerated by tightly focused single-cycle laser pulses may reach around 80% of the theoretical energy gain limit, about twice the value previously reported with few-cycle paraxial pulses. Our results demonstrate that the direct acceleration of electrons in vacuum is…
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…
Due to their broad spectral width, ultrashort lasers provide new possibilities to shape light beams and control their properties, in particular through the use of spatio-temporal couplings. In this context, we present a theoretical investigation of the linear propagation of ultrashort laser beams that combine temporal chirp and a standard aberration known as longitudinal chromatism. When such beams are focused in a vacuum, or in a linear medium, the interplay of these two effects can be exploited to set the velocity of the resulting intensity peak to arbitrary values within the Rayleigh length…
The investigation of spatio-temporal couplings (STCs) of broadband light beams is becoming a key topic for the optimization as well as applications of ultrashort laser systems. This calls for accurate measurements of STCs. Yet, it is only recently that such complete spatio-temporal or spatio-spectral characterization has become possible, and it has so far mostly been implemented at the output of the laser systems, where experiments take place. In this survey, we present for the first time STC measurements at different stages of a collection of high-power ultrashort laser systems, all based on …
We report on the morphological effects induced by the inhomogeneous absorption of cylindrically polarized femtosecond laser irradiation of silver (Ag) in sub-ablation conditions. A theoretical prediction of the role of surface plasmon excitation in the production of self-formed periodic ripples structures is evaluated. Furthermore, a combined hydrodynamical and thermoelastic model is presented to account for the influence of temperature-related lattice movements in laser beam conditions that are sufficient to produce material melting. The ability to control the size of the morphological change…
By using a powerful reductive perturbation technique, or a multiscale analysis, a generic Kadomtsev-Petviashvili evolution equation governing the propagation of femtosecond spatiotemporal optical solitons in quadratic nonlinear media beyond the slowly varying envelope approximation is put forward. Direct numerical simulations show the formation, from adequately chosen few-cycle input pulses, of both stable line solitons (in the case of a quadratic medium with normal dispersion) and of stable lumps (for a quadratic medium with anomalous dispersion). Besides, a typical example of the decay of th…
Focusing control of ultrashort pulsed beams is an important research topic, due to its impact to subsequent interaction with matter. In this work, we study the propagation near the focus of ultrashort laser pulses of ~25 fs duration under diffractive focusing. We perform the spatio-spectral and spatio-temporal measurements of their amplitude and phase, complemented by the corresponding simulations. With them, we demonstrate that pulse shaping allows modifying in a controlled way not only the spatio-temporal distribution of the light irradiance in the focal region, but also the way it propagate…
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…
Ultrashort laser pulses are described having chromatic astigmatism, where the astigmatic phase varies linearly with the offset from the central frequency. Such a spatio-temporal coupling not only induces interesting space-frequency and space-time effects, but it removes cylindrical symmetry. We analyze the quantitative effects on the spatio-temporal pulse structure on the collimated beam and as it propagates through a focus, with both the fundamental Gaussian beam and Laguerre-Gaussian beams. Chromatic astigmatism is a new type of spatio-temporal coupling towards arbitrary higher complexity be…
Fully analytic expressions, for the electric and magnetic fields of an ultrashort and tightly focused laser pulse of the radially polarized category, are presented to lowest order of approximation. The fields are derived from scalar and vector potentials, along the lines of our earlier work for a similar pulse of the linearly polarized variety. A systematic program is also described from which the fields may be obtained to any desired accuracy, analytically or numerically.
We develop a spatiotemporal mode decomposition technique to study the mode power distribution of ultrashort pulses emerging from long spans of graded-index multimode fiber, for different input laser conditions. We find that beam mode power content in the dispersive pulse propagation regime can be described by the Bose-Einstein law, as a result of the process of power diffusion from linear and nonlinear mode coupling among nondegenerate mode groups. In the soliton regime, the output mode power distribution approaches the Rayleigh-Jeans law
The temporal characterization of ultrafast laser pulses has become a cornerstone capability of ultrafast optics laboratories and is routine both for optimizing laser pulse duration and designing custom fields. Beyond pure temporal characterization, spatio-temporal characterization provides a more complete measurement of the spatially-varying temporal properties of a laser pulse. These so-called spatio-temporal couplings (STCs) are generally nonseparable chromatic aberrations that can be induced by very common optical elements -- for example diffraction gratings and thick lenses or prisms made …
Ultra-high intensity femtosecond lasers at focus are now routinely used for relativistic motion of charged particles with peak intensities over 10^18W/cm^2. Such high-field experiments are very sensitive to the value of the peak intensity. Therefore, precise knowledge of the pulse intensity is a key prerequisite for the correct interpretation of experimental data. Accurate measurement of energy, spectral and spatial profiles being well established, peak intensity evaluation then only requires the determination of the spatiotemporal Strehl ratio. Here I propose a new method based on a simple an…
We predict analytically and confirm with numerical simulations that inter-mode dispersion in nanowire waveguide arrays can be tailored through periodic waveguide bending, facilitating flexible spatio-temporal reshaping without break-up of femtosecond pulses. This approach allows simulta- neous and independent control of temporal dispersion and spatial diffraction that are often strongly connected in nanophotonic structures.
Surface plasmon polariton is collective oscillation of the free electrons at metal dielectric interface. As a wave phenomenon, surface plasmon polaritons can be focused using appropriate excitation geometry of metallic structures. We theoretically demonstrate the possibility of controlling nanoscale short pulse superfocusing based on the generation of radially polarized surface plasmon polariton mode of conical metallic tip. Numerical simulation for femtosecond pulse propagation along a silver nano-needle is discussed. The spatial distribution for a near field strongly depends on a linear chir…
Nonlinear propagation of signals in single-mode fiber is well understood, and is typically observed by measuring the temporal profile or optical spectrum of an emerging signal. In multimode fibers, the nonlinearity has both a spatial and a temporal element, and a complete investigation of the interactions between propagating modes requires resolving the output in both space and time. We report here spatiotemporal measurements of two nonlinear interacting LP$_{0m}$ modes of a step-index few-mode fiber (FMF). We describe a method to selectively excite two propagating modes through the use of a p…
We present a technique for the single-shot measurement of the space- and time-resolved spatiotemporal 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 (STOVs). TG-SSSI is well-suited for characterizing ultrashort laser pulses that contain singularities associated with spin/orbital angular momentum or polarization.
Spectral dispersion of ultrashort pulses allows simultaneous focusing of light in both space and time creating so-called spatio-temporal foci. Such space-time coupling may be combined with existing holographic techniques to give a further dimension of control when generating focal light fields. It is shown that a phase-only hologram placed in the pupil plane of an objective and illuminated by a spatially chirped ultrashort pulse can be used to generate three dimensional arrays of spatio-temporally focused spots. Exploiting the pulse front tilt generated at focus when applying simultaneous spat…
We shape fs optical pulses and deliver them in a single spatial mode to the input of a multimode fiber. The pulse is shaped in time such that at the output of the multimode fiber an ultrashort pulse appears at a predefined focus. Our result shows how to raster scan an ultrashort pulse at the output of a stiff piece of square-core step-index multimode fiber and in this way the potential for making a nonlinear fluorescent image of the scene behind the fiber, while the connection to the multimode fiber can be established via a thin and flexible single-mode fiber. The experimental results match ou…
The development of optical metrology suited to ultrafast lasers has played a key role in the progress of these light sources in the last few decades. Measurement techniques providing the complete $E$-field of ultrashort laser beams in both time and space are now being developed. Yet, they had so far not been applied to the most powerful ultrashort lasers, which reach the PetaWatt range by pushing the Chirped Pulse Amplification scheme to its present technical limits. This situation left doubts on their actual performance, and in particular on the peak intensity they can reach at focus. In this…
We introduce a new class of nondiffracting optical pulses possessing orbital angular momentum. By generalizing the X-waves solution of the Maxwell equation, we discover the coupling between angular momentum and the temporal degrees of freedom of ultra-short pulses. The spatial twist of propagation invariant light pulse turns out to be directly related to the number of optical cycles. Our results may trigger the development on novel multi-level classical and quantum transmission channels free of dispersion and diffraction, may also find application in the manipulation of nano-structured objects…
Acoustic signals generated by filamentation of ultrashort TW laser pulses in water are characterized experimentally. Measurements reveal a strong influence of input pulse duration on the shape and intensity of the acoustic wave. Numerical simulations of the laser pulse nonlinear propagation and the subsequent water hydrodynamics and acoustic wave generation show that the strong acoustic emission is related to the mechanism of superfilamention in water. The elongated shape of the plasma volume where energy is deposited drives the far-field profile of the acoustic signal, which takes the form of…
Tightly-focused, ultrashort radially-polarized laser beams have a large longitudinal field, which provides a strong motivation for direct particle acceleration and manipulation in vacuum. The broadband nature of these beams means that chromatic properties of propagation and focusing are important to consider. We show via single particle simulations that using the correct frequency-dependent beam parameters is imperative, especially as the pulse duration decreases to the few-cycle regime. The results with different spatio-spectral amplitude profiles show both a drastic increase or decrease of t…
The pronounced dependence of the nonlinear parameters of both dielectric and semiconductor materials on the wavelength, and the nonlinear interaction between the ultra-short laser pulse and the material requires precise control of the wavelength of the pulse, in addition to the precise control of the pulse energy, pulse duration and focusing optics. This becomes particularly important for fine sub-wavelength single pulse sub-surface processing. Based on two different numerical models and taking Si as example material, we investigate the spatio-temporal behavior of a pulse propagating through t…
We report with single particle simulations that longitudinal chromatism, a commonly occuring spatio-temporal coupling in ultrashort laser pulses, can have a significant influence in the longitudinal acceleration of electrons via high-power, tightly-focused radially polarized laser beams. This effect can be advantageous, and even more-so when combined with small values of temporal chirp. However, the effect can also be highly destructive when the magnitude and sign of the longitudinal chromatism is not ideal, even at very small magnitudes. This motivates the characterization and understanding o…
Femtosecond laser micromachining provides high precision and less thermal diffusion in surface structuring as a result of the ultrashort temporal duration and ultrahigh peak intensity of the femtosecond laser pulses. To increase the throughput of surface patterning, the focal spot size can be expanded with loose focusing, which, however, could lead to nonlinear self-focusing of the pulses when the pulses propagate in air. We solve the problem by use of spatiotemporally focused femtosecond laser pulses for ablation of metal surfaces, which gives rise to improved surface quality as compared with…
We propose a novel method to reconstruct the spatio-temporal amplitude and phase of the electric field of ultrashort laser pulses using spatially-resolved spectral interferometry. This method is based on a fiber-optic coupler interferometer that has certain advantages in comparison with standard interferometer systems, such as it being alignment-free and selection of the reference beam at a single point. Our technique, which we refer to as STARFISH, offers compactness and simplicity. We report its application to the experimental characterization of chirped pulses and to spatio-temporal reconst…
A photon is the single excitation of a particular spatiotemporal mode of the electromagnetic field. A precise knowledge of the mode structure is therefore essential for its processing and detection, as well as for applying generic quantum light states to novel technologies. Here we demonstrate an adaptive scheme for reconstructing the arbitrary amplitude and phase spectro-temporal profile of an ultrashort single-photon pulse. The method combines techniques from the fields of ultrafast coherent control and quantum optics to map the mode of a fragile quantum state onto that of an intense coheren…
We introduce an approach to implement full coherent control on nanometer length scales. It is based on spatio-temporal modulation of the surface plasmon polariton (SPP) fields at the thick edge of a nanowedge. The SPP wavepackets propagating toward the sharp edge of this nanowedge are compressed and adiabatically concentrated at a nanofocus, forming an ultrashort pulse of local fields. The one-dimensional spatial profile and temporal waveform of this pulse are completely coherently controlled.
Spatiotemporal nonlinear interactions in multimode fibers are of interest for beam shaping and frequency conversion by exploiting the nonlinear propagation of different pump regimes from quasi-continuous wave to ultrashort pulses centered around visible to infrared pump wavelengths. The nonlinear effects in multi-mode fibers depend strongly on the excitation condition, however relatively little work has been reported on this subject. Here, we present the first machine learning approach to learn and control the nonlinear frequency conversion inside multimode fibers by tailoring the excitation c…
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…
Coherent light beams composed of ultrashort pulses are now increasingly used in different fields of Science, from time-resolved spectroscopy to plasma physics. Under the effect of even simple optical components, the spatial properties of these beams can vary over the duration of the light pulse. In this letter, we show how such spatio-temporally coupled electromagnetic fields can be exploited to produce an attosecond lighthouse, i.e. a source emitting a collection of isolated attosecond pulses, propagating in angularly well-separated light beams. This very general effect not only opens the way…
Ponderomotive Achromat for Electron Optics: Radially Polarized Annular Focusing and a Round-Lens Corrector Regime
Sensing Technology Research Institute, National Institute of Advanced Industrial Science and Technology（产业技术综合研究所传感技术研究机构）；Institute of Multidisciplinary Research for Advanced Materials, Tohoku University（东北大学先进材料学综合研究机构）
We present a study of the propagation of three-dimensional (3D) bipolar electromagnetic ultrashort pulses in an inhomogeneous array of semiconductor carbon nanotubes (CNTs) in the presence of a control high-frequency (HF) electric field. The inhomogeneity is present in the form of a layer with an increased concentration of conduction electrons, which acts as a barrier for the propagation of ultrashort electromagnetic pulses through the CNT array. The dynamics of the pulse is described by a nonlinear equation for the vector potential of the electromagnetic field (it takes the form of a 3D gener…
Using the Jacobi Elliptic Functions, an analytical solution is developed for the nonlinear amplitude equation of Surface Plasmon Polaritons (SPPs) in a graphene-dielectric waveguide. It is shown that the field localization of SPPs coupled with TM polarized terahertz light can be enhanced if the nonlinearity is increased. On the side, a numerical solution based on Split Step Beam Propagation Method (SSBPM) suggests that spatial Modulation Instabilty (MI) can be dominant. Accordingly, larger nonlinearity leads to the generation of discrete plasmon solitons rather than the diffracted profile resu…
