Single-shot spectral interferometry with chirped pulses

Single-shot observation of nonlinear pulse splitting in a Kerr medium

We report single-shot, time-resolved observation of self-steepening and temporal splitting of near-infrared, 50 fs, micro-joule pulses propagating nonlinearly in flint (SF11) glass. A coherent, smooth-profiled, 60-nm-bandwidth probe pulse that propagated obliquely to the main pulse through the Kerr medium recorded a time sequence of longitudinal projections of the main pulse's induced refractive index profile in the form of a phase-shift "streak," in which frequency-domain interferometry recovered with ∼10 fs temporal resolution. A three-dimensional simulation based on a unidirectional pulse propagation equation reproduced observed pulse profiles.

Temporal resolution of ultrafast compressive imaging using a single-chirped optical probe

Ultrafast compressive imaging captures three-dimensional spatiotemporal information of transient events in a single shot. When a single-chirped optical probe is applied, the temporal information is obtained from the probe modulated in amplitude or phase using a direct frequency-time mapping method. Here, we extend the analysis of the temporal resolution of conventional one-dimensional ultrafast measurement techniques such as spectral interferometry to that in three-dimensional ultrafast compressive imaging. In this way, both the amplitude and phase of the probe are necessary for a full Fourier transform method, which obtains temporal information with an improved resolution determined by probe spectral bandwidth. The improved temporal resolution potentially enables ultrafast compressive imaging with an effective imaging speed at the quadrillion-frames-per-second level.

Real-time optical time interpolation using spectral interferometry

A simple scheme for all-optical time interpolation using spectral interferometry is put forward that is, in principle, capable of single-shot measurements. In this method, the arrival time of optical timing pulses is encoded into the spectrum of a time-stretched supercontinuum via cross phase modulation. The proof-of-concept test setup points toward femtosecond-level absolute timing capabilities with only minor additions to modern optical clockwork.

Algorithm to filter the noise in the spectral intensity of ultrashort laser pulses

We have developed an algorithm to filter the noise in the spectral intensity of ultrashort laser pulses. The filtering procedure consists of smoothing the noise by using the Savitzky-Golay filter, removing the offset, and using a super-Gaussian window to truncate the frequencies of the spectrum. We have modeled bandwidth-limited ultrashort pulses with Gaussian modulated frequencies to show the estimation of the carrier wavelength, reconstruction of the intensity pulse profile, and pulse duration after applying the algorithm. Theoretical results are presented for pulse durations between 5 fs and 100 fs with a carrier wavelength of 825 nm and three different amounts of signal-to-noise ratio (SNR): 30 dB, 20 dB, and 15 dB, normally found in experiments. The algorithm is also applied to an experimental spectral intensity from a homemade Ti:sapphire laser that produces pulses of about 20 fs at 825 nm at 100 MHz. We will show that using only a low-pass Fourier filter and removing offset is not enough to recover the spectral intensity when a large SNR is present, which may be the case when the ultrashort laser beam has been manipulated to compensate for the group velocity dispersion of an external optical system. In cases like this, the use of the Savitzky-Golay filter prior to the super-Gaussian filter improves the recovery of the carrier wavelength and the spectral intensity. We will also show that the algorithm presented in this paper is suitable for experimental analysis and requires limited user intervention.

Simplified single-shot supercontinuum spectral interferometry

We have experimentally demonstrated a simplified method for performing single-shot supercontinuum spectral interferometry (SSSI) that does not require pre-characterization of the probe pulse. The method, originally proposed by D. T. Vu, D. Jang, and K. Y. Kim, uses a genetic algorithm (GA) and as few as two time-delayed pump-probe shots to retrieve the pump-induced phase shift on the probe [Opt. Express26, 20572 (2018)]. We show that the GA is able to successfully retrieve the transient modulations on the probe, and that the error in the retrieved modulation decreases dramatically with the number of shots used. In addition, we propose and demonstrate a practical method that allows SSSI to be done with a single pump-probe shot (again, without the need for pre-characterization of the probe). This simplified method can prove to be immensely useful when performing SSSI with a low-repetition-rate laser source.

Investigation of Spatial Chirp Induced by Misalignments in a Parallel Grating Pair Pulse Stretcher

Spatial chirp induced by the misaligned gratings and mirrors in a parallel grating pair pulse stretcher can significantly affect the performance of the output pulses. Firstly, a detailed analysis about the spatial chirp of the stretched pulses caused by the misalignments has been carried out using the ray tracing simulation method. According to the simulation results, an adjustment procedure has been summarized to accurately calibrate these misalignments. The proposed method has been successfully applied in a home-made chirped pulse stretcher. By measuring the output pulse with an imaging spectrometer, the results show the stretched pulse has a good linear temporal chirp and little spatial chirp, which demonstrates the good adjustment of the stretcher.

Initial observations of the femtosecond timing jitter at the European XFEL

Intense, ultrashort, and high-repetition-rate X-ray pulses, combined with a femtosecond optical laser, allow pump-probe experiments with fast data acquisition and femtosecond time resolution. However, the relative timing of the X-ray pulses and the optical laser pulses can be controlled only to a level of the intrinsic error of the instrument which, without characterization, limits the time resolution of experiments. This limitation inevitably calls for a precise determination of the relative arrival time, which can be used after measurement for sorting and tagging the experimental data to a much finer resolution than it can be controlled to. The observed root-mean-square timing jitter between the X-ray and the optical laser at the SPB/SFX instrument at European XFEL was 308 fs. This first measurement of timing jitter at the European XFEL provides an important step in realizing ultrafast experiments at this novel X-ray source. A method for determining the change in the complex refractive index of samples is also presented.

Fast-frame single-shot pump-probe spectroscopy with chirped-fiber Bragg gratings

To acquire single-shot pump-probe waveforms for each laser pulse at a high repetition rate and high signal-to-noise ratio, we combined the photonic time-stretch technique and time-encoding method using a chirped-fiber Bragg grating (CFBG) and a grating-pair pulse compressor. By changing the pre-chirping of the probe pulse, a variable time window of the pump-probe traces from 1.4 to 17 ps was demonstrated. The use of a CFBG improved the signal-to-noise ratio of the waveforms by minimizing the loss of probe pulses due to the transmission through a long fiber. These techniques are promising, for example, in applications in multi-timescale pump-probe spectroscopy of irreversible phenomena.

Simplified chirp characterization in single-shot supercontinuum spectral interferometry

Single-shot supercontinuum spectral interferometry (SSSI) is an optical technique that can measure ultrafast transients in the complex index of refraction. This method uses chirped supercontinuum reference/probe pulses that need to be pre-characterized prior to use. Conventionally, the spectral phase (or chirp) of those pulses can be determined from a series of phase or spectral measurements taken at various time delays with respect to a pump-induced modulation. Here we propose a novel method to simplify this process and characterize reference/probe pulses up to the third order dispersion from a minimum of 2 snapshots taken at different pump-probe delays. Alternatively, without any pre-characterization, our method can retrieve both unperturbed and perturbed reference/probe phases, including the pump-induced modulation, from 2 time-delayed snapshots. From numerical simulations, we show that our retrieval algorithm is robust and can achieve high accuracy even with 2 snapshots. Without any apparatus modification, our method can be easily applied to any experiment that uses SSSI.

A single-shot spatial chirp method for measuring initial AC conductivity evolution of femtosecond laser pulse excited warm dense matter

To study the rapid evolution of AC conductivity from ultrafast laser excited warm dense matter (WDM), a spatial chirp single-shot method is developed utilizing a crossing angle pump-probe configuration. The pump beam is shaped individually in two spatial dimensions so that it can provide both sufficient laser intensity to excite the material to warm dense matter state and a uniform time window of up to 1 ps with sub-100 fs FWHM temporal resolution. Temporal evolution of AC conductivity in laser excited warm dense gold was also measured.

Simultaneous streak and frame interferometry for electron density measurements of laser produced plasmas

A system of two collinear probe beams with different wavelengths and pulse durations was used to capture simultaneously snapshot interferograms and streaked interferograms of laser produced plasmas. The snapshots measured the two dimensional, path-integrated, electron density on a charge-coupled device while the radial temporal evolution of a one dimensional plasma slice was recorded by a streak camera. This dual-probe combination allowed us to select plasmas that were uniform and axisymmetric along the laser direction suitable for retrieving the continuous evolution of the radial electron density of homogeneous plasmas. Demonstration of this double probe system was done by measuring rapidly evolving plasmas on time scales less than 1 ns produced by the interaction of femtosecond, high intensity, laser pulses with argon gas clusters. Experiments aimed at studying homogeneous plasmas from high intensity laser-gas or laser-cluster interaction could benefit from the use of this probing scheme.

Ultrafast ellipsometric pump-probe diagnostic of liquid metal surface with chirped continuum probe pulses

We describe our ellipsometric pump-probe experiment to study materials at extreme conditions. To demonstrate the performance, liquid bismuth surface is pumped by intense 25 fs pulse and subsequent evolution of non-equilibrium bismuth plasma is probed by chirped continuum pulse. The shift in the origin-time at continuum spectral component is precisely corrected by comparing chirp behavior estimated from induced phase modulation (IPM) in fused silica to one from liquid bismuth reflectivity measurement. From IPM measurements, it was found that the time resolution of a chirped pulse depends on group delay dispersion at corresponding continuum spectral components. Moreover, due to explicit relation between time and frequency of a chirped probe pulse, pump induced rapid changes are projected onto different probe wavelengths. Using these properties, we investigated polarization dependent reflection dynamics of non-equilibrium bismuth plasma with sub-100 fs temporal resolution and a broader wavelength response. These ultrafast measurements will be useful to study exotic phase transitions at extreme states of matter.

Measurement of the chirp characteristics of linearly chirped pulses by a frequency domain interference method

A linear optical technique for chirp characteristics measurement based on frequency domain interference is developed. This technique can be applied to measure the temporal structure of linearly chirped pulses which have become increasingly important in ultrafast optics. To confirm this technique, an experiment is carried out to measure the chirp rate and duration of a picosecond chirped pulse with an imaging spectrometer.

Flux-limited nonequilibrium electron energy transport in warm dense gold

An abrupt change in energy transport has been observed in femtosecond laser heated gold when the absorbed laser flux exceeds ~7×10(12) W/cm(2). Below this value, the absorbed flux is carried by ballistic motion of nonthermal electrons produced in interband excitation. Above this value energy transport appears to include ballistic transport by nonthermal electrons and heat diffusion by thermalized hot electrons. The ballistic component is limited to a flux of ~7×10(12) W/cm(2). This offers a unique benchmark for comparison with theory on nonequilibrium electron transport.

Measurement of pressure dependent nonlinear refractive index of inert gases

The propagation of high intensity laser beams is excessively affected by optical nonlinear effects, thereby the knowledge of the nonlinear refractive indices of the beam guiding media is indispensable in the design of laser systems and experiments. Apart from undesired self-focusing, several areas of modern laser spectroscopy can utilize optical nonlinearity, from LiDAR measurements to filamentation. In this paper we report on a direct measurement of pressure dependent nonlinear refractive index of Ar, N2, Ne, Xe, and air between 0.05 mbar and 1 bar, based on the powerful technique called spectrally and spatially resolved interferometry. In this way the total value of nonlinear refractive index is measured, that is the sum of all elementary phenomena contributing to the intensity dependent refractivity of the gases.

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.

Time and space resolved interferometry for laser-generated fast electron measurements

A technique developed to measure in time and space the dynamics of the electron populations resulting from the irradiation of thin solids by ultraintense lasers is presented. It is a phase reflectometry technique that uses an optical probe beam reflecting off the target rear surface. The phase of the probe beam is sensitive to both laser-produced fast electrons of low-density streaming into vacuum and warm solid density electrons that are heated by the fast electrons. A time and space resolved interferometer allows to recover the phase of the probe beam sampling the target. The entire diagnostic is computationally modeled by calculating the probe beam phase when propagating through plasma density profiles originating from numerical calculations of plasma expansion. Matching the modeling to the experimental measurements allows retrieving the initial electron density and temperature of both populations locally at the target surface with very high temporal and spatial resolution (~4 ps, 6 μm). Limitations and approximations of the diagnostic are discussed and analyzed.

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.

Picosecond short-range disordering in isochorically heated aluminum at solid density

Using ultrafast x-ray probing, we experimentally observed a progressive loss of ordering within solid-density aluminum as the temperature raises from 300 K to >10{4} K. The Al sample was isochorically heated by a short ( approximately ps), laser-accelerated proton beam and probed by a short broadband x-ray source around the Al K edge. The loss of short-range ordering is detected through the progressive smoothing of the time-resolved x-ray absorption near-edge spectroscopy (XANES) structure. The results are compared with two different theoretical models of warm dense matter and allow us to put an upper bound on the onset of ion lattice disorder within the heated solid-density medium of approximately 10 ps.

Hot and cold electron dynamics following high-intensity laser matter interaction

The characteristics of fast electrons laser accelerated from solids and expanding into a vacuum from the rear target surface have been measured via optical probe reflectometry. This allows access to the time- and space-resolved dynamics of the fast electron density and temperature and of the energy partition into bulk (cold) electrons. In particular, it is found that the density of the hot electrons on the target rear surface is bell shaped, and that their mean energy at the same location is radially homogeneous and decreases with the target thickness.

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.

Equation-of-state measurement of dense plasmas heated with fast protons

Using an ultrafast pulse of mega-electron-volt energy protons accelerated from a laser-irradiated foil, we have heated solid density aluminum plasmas to temperatures in excess of 15 eV. By measuring the temperature and the expansion rate of the heated Al plasma simultaneously and with picosecond time resolution we have found the predictions of the SESAME Livermore equation-of-state (LEOS) tables to be accurate to within 18%, in this dense plasma regime, where there have been few previous experimental measurements.

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

We present the first technique for directly measuring (without assumptions) the spatio-temporal intensity and phase of a train of ultrashort pulses at and near a focus. Our method uses an experimentally simple and high-spectral resolution variant of spectral interferometry (SEA TADPOLE). To illustrate our technique, we measured the spatio-temporal electric field in and around the foci of several different types of lenses. To confirm our results, we also simulated these measurements by numerically propagating a pulse through each of the lenses used. From one set of measurements, we made a movie showing a focusing pulse with severe chromatic aberration.

Single-shot two-dimensional spectral interferometry for ultrafast laser-produced plasmas

Coherent white light was used as a light source for spectral interferometry of ultrafast laser-produced plasmas. Using a narrowband filter, two-dimensional images of field ionization in helium were obtained with a 14 fs time resolution.

Picosecond time-resolved X-ray absorption spectroscopy of ultrafast aluminum plasmas

We have used point-projection K-shell absorption spectroscopy to infer the ionization and recombination dynamics of transient aluminum plasmas. Two femtosecond beams of the 100 TW laser at the LULI facility were used to produce an aluminum plasma on a thin aluminum foil (83 or 50 nm), and a picosecond x-ray backlighter source. The short-pulse backlighter probed the aluminum plasma at different times by adjusting the delay between the two femtosecond driving beams. Absorption x-ray spectra at early times are characteristic of a dense and rather homogeneous plasma. Collisional-radiative atomic physics coupled with hydrodynamic simulations reproduce fairly well the measured average ionization as a function of time.

Complete characterization of a plasma mirror for the production of high-contrast ultraintense laser pulses

Improving the temporal contrast of ultrashort and ultraintense laser pulses is a major technical issue for high-field experiments. This can be achieved using a so-called "plasma mirror." We present a detailed experimental and theoretical study of the plasma mirror that allows us to quantitatively assess the performances of this system. Our experimental results include time-resolved measurements of the plasma mirror reflectivity, and of the phase distortions it induces on the reflected beam. Using an antireflection coated plate as a target, an improvement of the contrast ratio by more than two orders of magnitude can be achieved with a single plasma mirror. We demonstrate that this system is very robust against changes in the pulse fluence and imperfections of the beam spatial profile, which is essential for applications.

Uniform theory of the Talbot effect with partially coherent light illumination

A uniform formulation for the self-imaging of gratings with any kind of partially coherent illumination is developed in terms of the cross mutual spectral density of the partial coherence theory. The formulation includes the time diffractive intensity distribution and the averaged diffractive intensity distribution at self-imaging distances and can be applied to both continuous and temporal illuminations with any kind of spectra. It is found that the averaged intensity distribution is related only to the intensity spectrum of illumination. The continuous polychromatic illumination and the ultrashort laser pulses with or without frequency chirp are then studied by a numerical stimulation. It is shown that the ultrashort laser pulse and the continuous polychromatic illuminations have similar averaged self-image distributions. Thus the Talbot effect may help in the study of the temporal and spectral characteristics of ultrashort laser pulses. An experiment with an LED is given, as well.

Realization of a time-domain Fresnel lens with coherent control

Perturbative chirped pulse excitation leads to oscillations of the excited state amplitude. These coherent transients are governed by interferences between resonant and off-resonant contributions. Control mechanisms in both frequency and time domain are used to modify these dynamics. First, by applying a phase step in the spectrum, we manipulate the phase of the oscillations. By direct analogy with Fresnel zone lenses, we then conceive highly phase-amplitude modulated pulse shapes that slice destructive interferences out of the excitation time structure and enhance the final population.