Directly measuring the spatio-temporal electric field of focusing ultrashort pulses

Ultrabroadband flying-focus using an axiparabola-echelon pair

Flying-focus pulses promise to revolutionize laser-driven secondary sources by decoupling the trajectory of the peak intensity from the native group velocity of the medium over distances much longer than a Rayleigh range. Previous demonstrations of the flying focus have either produced an uncontrolled trajectory or a trajectory that is engineered using chromatic methods that limit the duration of the peak intensity to picosecond scales. Here we demonstrate a controllable ultrabroadband flying focus using a nearly achromatic axiparabola-echelon pair. Spectral interferometry using an ultrabroadband superluminescent diode was used to measure designed super- and subluminal flying-focus trajectories and the effective temporal pulse duration as inferred from the measured spectral phase. The measurements demonstrate that a nearly transform- and diffraction-limited moving focus can be created over a centimeter-scale-an extended focal region more than 50 Rayleigh ranges in length. This ultrabroadband flying-focus and the novel axiparabola-echelon configuration used to produce it are ideally suited for applications and scalable to >100 TW peak powers.

Spatiotemporal mode-locking and dissipative solitons in multimode fiber lasers

Multimode fiber (MMF) lasers are emerging as a remarkable testbed to study nonlinear spatiotemporal physics with potential applications spanning from high energy pulse generation, precision measurement to nonlinear microscopy. The underlying mechanism for the generation of ultrashort pulses, which can be understood as a spatiotempoal dissipative soliton (STDS), in the nonlinear multimode resonators is the spatiotemporal mode-locking (STML) with simultaneous synchronization of temporal and spatial modes. In this review, we first introduce the general principles of STML, with an emphasize on the STML dynamics with large intermode dispersion. Then, we present the recent progress of STML, including measurement techniques for STML, exotic nonlinear dynamics of STDS, and mode field engineering in MMF lasers. We conclude by outlining some perspectives that may advance STML in the near future.

Single-shot compressed optical field topography

Femtosecond lasers are powerful in studying matter's ultrafast dynamics within femtosecond to attosecond time scales. Drawing a three-dimensional (3D) topological map of the optical field of a femtosecond laser pulse including its spatiotemporal amplitude and phase distributions, allows one to predict and understand the underlying physics of light interaction with matter, whose spatially resolved transient dielectric function experiences ultrafast evolution. However, such a task is technically challenging for two reasons: first, one has to capture in single-shot and squeeze the 3D information of an optical field profile into a two-dimensional (2D) detector; second, typical detectors are only sensitive to intensity or amplitude information rather than phase. Here we have demonstrated compressed optical field topography (COFT) drawing a 3D map for an ultrafast optical field in single-shot, by combining the coded aperture snapshot spectral imaging (CASSI) technique with a global 3D phase retrieval procedure. COFT can, in single-shot, fully characterize the spatiotemporal coupling of a femtosecond laser pulse, and live stream the light-speed propagation of an air plasma ionization front, unveiling its potential applications in ultrafast sciences.

Single-shot spatiotemporal characterization of a multi-PW laser using a multispectral wavefront sensing method

The single-shot spatiotemporal characterization of an ultrahigh intensity laser pulse was performed using a multispectral wavefront sensor. For the measurement of the spatio-spectral electric field, a femtosecond laser pulse was spectrally modulated and separated by a Fabry-Perot etalon coupled with a grating pair, and its spatio-spectral electric field was measured with a wavefront sensor. The spatiotemporal electric field was reconstructed from the measured spatio-spectral electric field of a multi-PW laser pulse. We found that the spatiotemporal distortion could reduce the focused laser intensity by 15%, compared to the case of a diffraction-limited and transform-limited laser pulse.

Integrated pulse scope for tunable generation and intrinsic characterization of structured femtosecond laser

Numerous techniques have been demonstrated for effective generation of orbital angular momentum-carrying radiation, but intracavity generation of continuously tunable pulses in the femtosecond regime remains challenging. Even if such a creation was realized, the generated pulses-like all pulses in reality-are complex and transitory objects that can only be comprehensively characterized via multidimensional spaces. An integrated lasing system that generates pulses while simultaneously quantifies them can achieve adaptive pulse tailoring. Here, we report a femtosecond pulse scope that unifies vector vortex mode-locked lasing and vectorial quantification. With intracavity-controlled Pancharatnam-Berry phase modulation, continuous and ergodic generation of spirally polarized states along a broadband higher-order Poincaré sphere was realized. By intrinsically coupling a two-dimensional polarization-sensitive time-scanning interferometer to the laser, multidimensional spatiotemporal features of the pulse were further visualized. The proposed methodology paves the way for design optimization of ultrafast optics by integrating complex femtosecond pulse generation and structural customization, facilitating its applications in optical physics research and laser-based manufacturing.

Simulations of wavelength-multiplexed holography for single-shot spatiotemporal characterization of NIF's advanced radiographic capability (ARC) laser

We simulate the use of a newly developed single-shot wavelength-multiplexed holography-based diagnostic, STRIPED FISH, to fully characterize the as-delivered laser pulses of the National Ignition Facility's Advanced Radiographic Capability (NIF-ARC) laser. To that end, we have performed simulations of the NIF-ARC pulse incorporating (a) a time-integrated spatial-profile measurement and a complete temporal-intensity-and-phase measurement using a frequency resolved optical gating, but without any spatiotemporal pulse characterizations, and (b) simulated first-order spatiotemporal distortions, which could be measured on a single shot if a STRIPED FISH device were deployed.

Real-time multispeckle spectral-temporal measurement unveils the complexity of spatiotemporal solitons

The dynamics of three-dimensional (3D) dissipative solitons originated from spatiotemporal interactions share many common characteristics with other multi-dimensional phenomena. Unveiling the dynamics of 3D solitons thus permits new routes for tackling multidisciplinary nonlinear problems and exploiting their instabilities. However, this remains an open challenge, as they are multi-dimensional, stochastic and non-repeatable. Here, we report the real-time speckle-resolved spectral-temporal dynamics of a 3D soliton laser using a single-shot multispeckle spectral-temporal technology that leverages optical time division multiplexing and photonic time stretch. This technology enables the simultaneous observation on multiple speckle grains to provide long-lasting evolutionary dynamics on the planes of cavity time (t) - roundtrip and spectrum (λ) - roundtrip. Various non-repeatable speckly-diverse spectral-temporal dynamics are discovered in both the early and established stages of the 3D soliton formation.

Impact of frequency-dependent spherical aberration in the focusing of ultrashort pulses

In this paper, the temporal and spatial intensity pulse distributions are calculated around the focal region of an optical system using a combination of ray tracing and a wave propagation method. We analyze how to measure the width of the intensity pulse distributions to estimate pulse duration and spot size in order to study the impact of the variation of spherical aberration with frequency in a pulse on the intensity distributions. Two experimental techniques used in the laboratory are also modeled: the knife-edge test to measure spatial distribution and the intensity autocorrelation technique to measure the temporal distribution. We use two measuring criteria, the full-width half-maximum (FWHM) and standard deviation (σ), to compare the spatial and temporal intensity distributions of the calculated diffraction patterns and those obtained from the simulated experimental techniques. We show that the FWHM is not a good criterion, since it gives different results in the measured intensity distributions in time and space when they are measured directly from the theoretical modeling and when they are measured from the modeled experimental techniques used in the laboratory. The standard deviation, however, is a consistent criterion, giving the same results for the calculated intensity distributions and the modeled experiments.

Spatially truncated Gaussian pulsed beam and its application in modeling diffraction of ultrashort pulses from hard apertures

A new kind of pulsed beam, which we call a spatially truncated Gaussian pulsed beam, is defined to represent a Gaussian pulsed beam that is diffracted from a semi-infinite hard aperture. The analytical equations for the propagation of the spatially truncated Gaussian pulsed beam through a nonrotationally symmetric paraxial system with second-order dispersion is derived starting from the generalized spatiotemporal Huygens integral. The spatially truncated Gaussian pulsed beam is then combined with the conventional Gaussian pulsed beam decomposition method to enable the modeling of diffraction of a general ultrashort pulse from an arbitrarily shaped hard aperture. The accuracy of the analytical propagation equation derived for the propagation of the truncated Gaussian pulsed beam is evaluated by a numerical comparison with diffraction results obtained using the conventional pulse propagation method based on the Fourier transform algorithm. The application of the modified Gaussian pulsed beam decomposition method is demonstrated by propagating an ultrashort pulse after a circular aperture through a dispersive medium and a focusing aspherical lens with large chromatic aberration.

Complex spatiotemporal coupling distortion pre-compensation with double-compressors for an ultra-intense femtosecond laser

In an ultra-intense femtosecond chirped-pulse amplification laser, the imperfect diffraction wave-fronts of the second and the third gratings of the compressor, where spatio-spectral coupling exists, could introduce a complex spatiotemporal coupling distortion (STCD) and degrade the pulsed beam in both near- and far-fields. Here, we propose a method of double-compressors for pre-compensation. By inserting a scaled down compressor (small compressor) with a deformable retro-reflection mirror into the beam-line, the frequency-dependent wave-front distortion, i.e., the complex STCD, could be removed. We simulate the results in two different ultra-intense femtosecond lasers with 80 and 400 nm bandwidths for comparison, and near ideal focused peak intensities could be obtained in both cases. Meanwhile, the influences of several miss-matching effects, which might appear in engineering, are also analyzed and discussed for applications.

Arbitrarily distorted 2-dimensional pulse-front measurement and reliability analysis

A method of 2-dimensional (2-D) space-scanned (in the x-y plane) spatiotemporal double-slit interference is used to reconstruct the 2-D pulse-front (in the x-y-t domain) of a femtosecond pulsed beam. While comparing with recent other methods, the method possesses two advantages: no reference pulse/beam is required anymore, and an arbitrarily distorted pulse-front, not just pulse-front tilt and pulse-front curvature, could be detected. Meanwhile, the influence of different factors of unknown pulsed beams and optical elements on the measurement reliability is also analyzed for engineering applications.

A trillion frames per second: the techniques and applications of light-in-flight photography

Cameras capable of capturing videos at a trillion frames per second allow to freeze light in motion, a very counterintuitive capability when related to our everyday experience in which light appears to travel instantaneously. By combining this capability with computational imaging techniques, new imaging opportunities emerge such as 3D imaging of scenes that are hidden behind a corner, the study of relativistic distortion effects, imaging through diffusive media and imaging of ultrafast optical processes such as laser ablation, supercontinuum and plasma generation. We provide an overview of the main techniques that have been developed for ultra-high speed photography with a particular focus on 'light-in-flight' imaging, i.e. applications where the key element is the imaging of light itself at frame rates that allow to freeze its motion and therefore extract information that would otherwise be blurred out and lost.

Single-shot real-time detection technique for pulse-front tilt and curvature of femtosecond pulsed beams with multiple-slit spatiotemporal interferometry

Spatiotemporal coupling (STC) of femtosecond pulsed beams could significantly reduce the focal-spot intensity of ultra-intense lasers. We theoretically present a very simple method for single-shot real-time detecting pulse-front tilt, curvature, or tilt and curvature (PFT, PFC or PFT&PFC) by using multiple-slit spatiotemporal interferometry (MSTI). An unknown input pulsed beam is spatially cut by a high-density multiple-slit and changed into a series of spatially separated sub-pulses. By only measuring the spatial distribution of the interference pattern in the far-field, PFT, PFC, or PFT&PFC can be detected. Comparing with recent methods, no reference pulses or beams, no temporal or spatial scanning, and no temporal or spectral measurement is required. The single-shot and spatial-only measurement will greatly simplify the real-time detection of PFT and PFC.

Direct Writing with Tilted-Front Femtosecond Pulses

Shaping light fields in both space and time provides new degrees of freedom to manipulate light-matter interaction on the ultrafast timescale. Through this exploitation of the light field, a greater appreciation of spatio-temporal couplings in focusing has been gained, shedding light on previously unexplored parameters of the femtosecond light pulse, including pulse front tilt and wavefront rotation. Here, we directly investigate the effect of major spatio-temporal couplings on light-matter interaction and reveal unambiguously that in transparent media, pulse front tilt gives rise to the directional asymmetry of the ultrafast laser writing. We demonstrate that the laser pulse with a tilted intensity front deposits energy more efficiently when writing along the tilt than when writing against, producing either an isotropic damage-like or a birefringent nanograting structure. The directional asymmetry in the ultrafast laser writing is qualitatively described in terms of the interaction of a void trapped within the focal volume by the gradient force from the tilted intensity front and the thermocapillary force caused by the gradient of temperature. The observed instantaneous transition from the damage-like to nanograting modification after a finite writing length in a transparent dielectric is phenomenologically described in terms of the first-order phase transition.

Autocorrelation z-scan technique for measuring the spatial and temporal distribution of femtosecond pulses in the focal region of lenses

In this work we present an Autocorrelation z-scan technique to measure, simultaneously, the spatial and temporal distribution of femtosecond pulses near the focal region of lenses. A second-order collinear autocorrelator is implemented before the lens under test to estimate the pulse width. Signals are obtained by translating a Two Photon Absorption (TPA) sensor along the optical axis and by measuring the second-order autocorrelation trace at each position z. The DC signal, which is typically not considered important, is taken into account since we have found that this signal provides relevant information. Experimental results are presented for different lenses and input wavefronts.

Spatial-spectral characterization of focused spatially chirped broadband laser beams

Proper alignment is critical to obtain the desired performance from focused spatially chirped beams, for example in simultaneous spatial and temporal focusing (SSTF). We present a simple technique for inspecting the beam paths and focusing conditions for the spectral components of a broadband beam. We spectrally resolve the light transmitted past a knife edge as it was scanned across the beam at several axial positions. The measurement yields information about spot size, M2, and the propagation paths of different frequency components. We also present calculations to illustrate the effects of defocus aberration on SSTF beams.

Pulse front adaptive optics: a new method for control of ultrashort laser pulses

Ultrafast lasers enable a wide range of physics research and the manipulation of short pulses is a critical part of the ultrafast tool kit. Current methods of laser pulse shaping are usually considered separately in either the spatial or the temporal domain, but laser pulses are complex entities existing in four dimensions, so full freedom of manipulation requires advanced forms of spatiotemporal control. We demonstrate through a combination of adaptable diffractive and reflective optical elements - a liquid crystal spatial light modulator (SLM) and a deformable mirror (DM) - decoupled spatial control over the pulse front (temporal group delay) and phase front of an ultra-short pulse was enabled. Pulse front modulation was confirmed through autocorrelation measurements. This new adaptive optics technique, for the first time enabling in principle arbitrary shaping of the pulse front, promises to offer a further level of control for ultrafast lasers.

Spatiotemporal dynamics of multimode optical solitons

As optical fiber communications and fiber lasers approach fundamental limits there is considerable interest in multimode fibers. In nonlinear science, they represent an exciting environment for complex nonlinear waves. As in single-mode fiber, solitons may be particularly important. Multimode solitons consist of synchronized, non-dispersive pulses in multiple spatial modes, which interact via the Kerr nonlinearity of the fiber. They are expected to exhibit novel spatiotemporal characteristics, dynamics and, like single-mode solitons, may provide a convenient intuitive tool for understanding more complex nonlinear phenomena in multimode fibers. Here we explore experimentally and numerically basic properties and spatiotemporal behaviors of these solitons: their formation, fission, and Raman dynamics.

Spatiotemporal noise characterization for chirped-pulse amplification systems

Optical noise, the core of the pulse-contrast challenge for ultra-high peak power femtosecond lasers, exhibits spatiotemporal (ST) coupling induced by angular dispersion. Full characterization of such ST noise requires two-dimensional measurements in the ST domain. Thus far, all noise measurements have been made only in the temporal domain. Here we report the experimental characterization of the ST noise, which is made feasible by extending cross-correlation from the temporal domain to the ST domain. We experimentally demonstrate that the ST noise originates from the optical surface imperfections in the pulse stretcher/compressor and exhibits a linear ST coupling in the far-field plane. The contrast on the far-field axis, underestimated in the conventional measurements, is further improved by avoiding the far-field optics in the stretcher. These results enhance our understanding of the pulse contrast with respect to its ST-coupling nature and pave the way toward the design of high-contrast ultra-high peak power lasers.

High-field physics experiments are often plagued by noise in the driving laser, which remains poorly characterized. Ma et al. study the noise in a pulse stretcher and compressor system in the spatiotemporal domain and find that noise from the stretcher elements governs the pulse contrast at the laser focus.

Shaping and spatiotemporal characterization of sub-10-fs pulses focused by a high-NA objective

We describe a setup consisting of a 4f pulse shaper and a microscope with a high-NA objective lens and discuss the aspects most relevant for an undistorted spatiotemporal profile of the focused beam. We demonstrate shaper-assisted pulse compression in focus to a sub-10-fs duration using phase-resolved interferometric spectral modulation (PRISM). We introduce a nanostructure-based method for sub-diffraction spatiotemporal characterization of strongly focused pulses. The distortions caused by optical aberrations and space-time coupling from the shaper can be reduced by careful setup design and alignment to about 10 nm in space and 1 fs in time.

Simulated propagation of ultrashort pulses modulated by low-Fresnel-number lenses using truncated series expansions

Numerical simulation of the paraxial propagation of pulses modulated by lenses is demonstrated using the Laguerre-Gaussian (LG) series expansion method. This technique allows for relatively swift evaluation of the structures of several individual monochromatic fields transformed by arbitrary amplitude and phase modulating pupil functions, which can be superimposed via the inverse Fourier transform to determine the structure of a modulated pulse. The transformation of ultrashort pulses by spherical, diffractive, and conical lenses is simulated using this method, which is particularly effective with the use of vector and matrix techniques available in many popular numerical software packages. A description of the convergence of the LG series to the results of the conventional integral techniques is presented for a conical lens under illumination by a continuous wave from which a simple but robust criterion for axial accuracy in problems of circular symmetry is suggested.

Spatiotemporal characterization of ultrashort laser pulses using spatially resolved Fourier transform spectrometry

We present a method for characterizing ultrashort laser pulses in space and time, based on spatially resolved Fourier transform spectrometry. An unknown pulse is interfered with a delayed, spatially uniform reference on a CCD camera. The reference pulse is created by spatially filtering a portion of the unknown pulse. By scanning the delay between the two pulses, an interferogram is obtained at each pixel, allowing us to determine the spatially resolved phase difference between the unknown pulse and the reference pulse. High-resolution spatiotemporal characterization of an ultrashort pulse is demonstrated, and the sensitivity of the method to spatiotemporal coupling is shown for the case of a pulse with pulse front tilt.

A fundamental understanding of the dependence of the laser-induced breakdown spectroscopy (LIBS) signal strength on the complex focusing dynamics of femtosecond laser pulses on either side of the focus

We correlate the focusing dynamics of 50 femtosecond (fs) laser radiation as it interacts with a silicon sample to laser-induced breakdown spectroscopy (LIBS) signal strength. Presented are concentric ring-shaped variations in the electric field in the prefocus region due to lens aberrations and nonsymmetry between the prefocus and post-focus beam profile as a result of continuum generation, occurring around the focus. Experimental results show different signal trends for both atmospheric and vacuum conditions, attributed to the existence of a continuum for the former. Lens aberrations effects on the LIBS signal strength are investigated using a plano-convex spherical lens and an aspherized achromatic lens. High-resolution scanning electron micrographs of the silicon surface after ablation, along with theoretical simulations, reveal the electric field patterns near the focus. The research results contribute to fundamental understanding of the basic physics of ultrashort, femtosecond laser radiation interacting with materials.

Spatiotemporal characterization of few-cycle laser pulses

In this paper we apply a broadband fiber optic coupler interferometer to the measurement of few-cycle laser pulses. Sub-8-fs pulses delivered by an ultrafast oscillator were characterized spatiotemporally using STARFISH, which is based on spatially resolved spectral interferometry. The reference pulse was measured with the d-scan technique. The pulses were focused by an off-axis parabolic mirror and were characterized at different transverse planes along the focusing region. The evolution of the retrieved pulses is analyzed, exhibiting small variations in the temporal (and spectral) amplitude and phase during propagation. Finally, the peak irradiance evolution is estimated from the integration of the spatiotemporal intensity.

Accuracy measurements and improvement for complete characterization of optical pulses from nonlinear processes via multiple spectral-shearing interferometry

We demonstrate that multiple spectral-shearing interferometry increases the precision and accuracy of measurements of the spectral phase of a complex pulse (time-bandwidth product = 125) arising from self-phase modulation in a gas filled capillary. We verify that the measured interferometric phase is accurate to 0.1 rad across the full bandwidth by checking the consistency between the spectral phases of each individual shear measurement. The accuracy of extracting pulse parameters (group delay dispersion, pulse duration and peak intensity) for single shear measurements were verified to better than 10% by comparison with the multishear reconstruction. High order space-time coupling is quantified across a single transverse dimension, verifying the suitability of such pulses for use in strong field experiments.

Ultrasmall bullets of light--focusing few-cycle light pulses to the diffraction limit

We demonstrate an essentially dispersion-free and diffraction-limited focusing of few-cycle laser pulses through all-reflective microscope objectives. By transmitting 6-fs-pulses from a Ti:sapphire oscillator through an all-reflective 0.5 NA objective, we reach a focus with a beam diameter of 1.0 µm, preserving the time structure of the pulses. The temporal and spatial pulse profile is recorded simultaneously using a novel tip-enhanced electron emission autocorrelator, indicating a focal volume of these pulses of only 1.8 µm3. We anticipate that the demonstrated technique is of considerable interest for inducing and probing optical nonlinearities of individual nanostructures.

Measuring extremely complex pulses with time-bandwidth products exceeding 65,000 using multiple-delay crossed-beam spectral interferometry

We measure the complete electric field of extremely complex ultrafast waveforms using the simple linear-optical, interferometric pulse-measurement technique, MUD TADPOLE. The waveforms were measured with ~40 fs temporal resolution over a temporal range of ~3.5 ns and had time-bandwidth products exceeding 65,000. The approach is general and could allow the measurement of arbitrary optical waveforms.

Spatio-temporal characterization of ultrashort pulses diffracted by circularly symmetric hard-edge apertures: theory and experiment

We carry out a complete spatio-temporal characterization of the electric field of an ultrashort laser pulse after passing through a diffractive optical element composed of several binary amplitude concentric rings. Analytical expressions for the total diffraction field in the time and spectral domain are provided, using the Rayleigh-Sommerfeld formulation of the diffraction. These expressions are experimentally validated. The spatio-temporal amplitude and phase structure of the pulse are measured at different planes beyond the diffractive optical element using spatially-resolved spectral interferometry assisted by an optical fiber coupler (STARFISH). Our results allow corroborating theoretical predictions on the presence of multiple pulses or complex spectral distributions due to the diffraction-induced effects by the hard-edge ring apertures.

Basic diffraction phenomena in time domain

Using a recently developed technique (SEA TADPOLE) for easily measuring the complete spatiotemporal electric field of light pulses with micrometer spatial and femtosecond temporal resolution, we directly demonstrate the formation of theo-called boundary diffraction wave and Arago's spot after an aperture, as well as the superluminal propagation of the spot. Our spatiotemporally resolved measurements beautifully confirm the time-domain treatment of diffraction. Also they prove very useful for modern physical optics, especially in micro- and meso-optics, and also significantly aid in the understanding of diffraction phenomena in general.

Measuring temporally complex ultrashort pulses using multiple-delay crossed-beam spectral interferometry

We introduce a spectral-interferometry (SI) technique for measuring the complete intensity and phase of relatively long and very complex ultrashort pulses. Ordinarily, such a method would require a high-resolution spectrometer, but our method overcomes this need. It involves making multiple measurements using SI (in its SEA TADPOLE variation) at numerous delays, measuring many temporal pulselets within the pulse, and concatenating the resulting pulselets. Its spectral resolution is the inverse delay range--many times higher than that of the spectrometer used. Our simple proof-of-principle implementation of it provided 71 fs temporal resolution and a temporal range of 100 ps using a few-cm low-resolution spectrometer.

Spatiotemporal amplitude and phase retrieval of space-time coupled ultrashort pulses using the Shackled-FROG technique

We demonstrate the validity of the Shackled-frequency-resolved-optical-gating technique for the complete characterization, both in space and in time, of ultrashort optical pulses that present strong angular dispersion. Combining a simple imaging grating with a Hartmann-Shack sensor and standard frequency-resolved-optical-gating detection at a single spatial position, we are able to retrieve the full spatiotemporal structure of a tilted pulse.

Parametric spatio-temporal control of focusing laser pulses

Simultaneous spatial and temporal focusing pulses are created using parametric pulse shaping and characterized with scanning SEA TADPOLE. Multiple foci are created with optically-controlled longitudal and transverse spatial positions. The characterized foci are in agreement with the predictions of a Fourier optics model. The measurements reveal significant pulse front tilt resulting from the simultaneous spatial and temporal focusing optics.

Direct spatiotemporal measurements of accelerating ultrashort Bessel-type light bullets

We measure the spatiotemporal field of ultrashort pulses with complex spatiotemporal profiles using the linear-optical, interferometric pulse-measurement technique SEA TADPOLE. Accelerating and decelerating ultrashort, localized, nonspreading Bessel-X wavepackets were generated from a approximately 27 fs duration Ti:Sapphire oscillator pulse using a combination of an axicon and a convex or concave lens. The wavefields are measured with approximately 5 microm spatial and approximately 15 fs temporal resolutions. Our experimental results are in good agreement with theoretical calculations and numerical simulations.

Measuring the spatiotemporal field of ultrashort Bessel-X pulses

We present direct measurements of the spatiotemporal electric field of an ultrashort Bessel-X pulse generated using a conical lens (axicon). These measurements were made using the linear-optical interferometric technique SEA TADPOLE, which has micrometer spatial resolution and femtosecond temporal resolution. From our measurements, both the superluminal velocity of the Bessel pulse and the propagation invariance of the central spot are apparent. We verified our measurements with simulations.

Spatiotemporal amplitude and phase retrieval of Bessel-X pulses using a Hartmann-Shack sensor

We propose a new experimental technique, which allows for a complete characterization of ultrashort optical pulses both in space and in time. Combining the well-known Frequency-Resolved-Optical-Gating technique for the retrieval of the temporal profile of the pulse with a measurement of the near-field made with an Hartmann-Shack sensor, we are able to retrieve the spatiotemporal amplitude and phase profile of a Bessel-X pulse. By following the pulse evolution along the propagation direction we highlight the superluminal propagation of the pulse peak.

Complete retrieval of the field of ultrashort optical pulses using the angle-frequency spectrum

We propose an experimental technique that allows for a complete characterization of the amplitude and phase of optical pulses in space and time. By the combination of a spatially resolved spectral measurement in the near and far fields and a frequency-resolved optical gating measurement, the electric field of the pulse is obtained through a fast, error-reduction algorithm.

Measuring the spatiotemporal electric field of tightly focused ultrashort pulses with sub-micron spatial resolution

We demonstrate a powerful and practical spectral interferometer with near-field scanning microscopy (NSOM) probes for measuring the spatiotemporal electric field of tightly focused ultrashort pulses with high spatial and spectral resolution. Our measurements involved numerical apertures as high as 0.44 and yielded the spatiotemporal field at and around the foci produced by two microscope objectives and several different lenses. For the first time, we measure the spatiotemporal field of the Bessel-like X-shaped pulse caused by spherical aberrations and a "fore-runner pulse" due to chromatic aberrations. We observed spatial features smaller than 1 microm and verified these results with non-paraxial simulations.