Spectral Phase Interferometry For Direct Electric-field Reconstruction Research Articles

Fast Spectrum Measurements Using Optical Computing

Traditional spectrometers are too slow for the continuous real-time measurement of rapidly varying spectrum. Dispersive Fourier transformation (DFT) technology replaces diffraction grating and detector array in traditional spectrometers with dispersive elements and photodiodes, and therefore reaches MHz-level spectral capture rate. In addition, frequency-resolved optical gating (FROG) and spectral phase interferometry for direct electric-field reconstruction (SPIDER) are also important ultrafast spectroscopy technologies in relevant fields. However, these approaches have to use mode-locked pulses as probe light, which may cause damages to some samples due to high peak power. Therefore, the requirement for light source restricts the scope of these technologies’ applications. Here, we report a general technique using optical computing for fast spectrum measurements, to overcome the bottleneck of light source in existing ultrafast spectroscopy measurement technologies. The proposed method has no strict requirement on the probe light. It means the common light source could also be applied for fast real-time spectroscopic measurements. In experiments, CW signals with four different optical spectra have been measured at capture speed of 1MHz respectively. The proposed method can overcome the limitations of existing ultrafast spectroscopy technologies in light source, and therefore provide a powerful tool for investigating rapid transient phenomena in many applications.

Complete characterization of ultrafast optical fields by phase-preserving nonlinear autocorrelation

Nonlinear autocorrelation was one of the earliest and simplest tools for obtaining partial temporal information about an ultrashort optical pulse by gating it with itself. However, since the spectral phase is lost in a conventional autocorrelation measurement, it is insufficient for a full characterization of an ultrafast electric field, requiring additional spectral information for phase retrieval. Here, we show that introducing an intensity asymmetry into a conventional nonlinear interferometric autocorrelation preserves some spectral phase information within the autocorrelation signal, which enables the full reconstruction of the original electric field, including the direction of time, using only a spectrally integrating detector. We call this technique Phase-Enabled Nonlinear Gating with Unbalanced Intensity (PENGUIN). It can be applied to almost any existing nonlinear interferometric autocorrelator, making it capable of complete optical field characterization and thus providing an inexpensive and less complex alternative to methods relying on spectral measurements, such as frequency-resolved optical gating (FROG) or spectral phase interferometry for direct electric-field reconstruction (SPIDER). More importantly, PENGUIN allows the precise characterization of ultrafast fields in non-radiative (e.g., plasmonic) nonlinear optical interactions where spectral information is inaccessible. We demonstrate this novel technique through simulations and experimentally by measuring the electric field of ~6-fs laser pulses from a Ti:sapphire oscillator. The results are validated by comparison with the well-established FROG method.

Characterizing ultrashort laser pulses by the rotational Doppler effect

Technological advances in femtosecond laser sources call for the development of increasingly refined characterization tools implying to enrich the existing panel of operable nonlinear interactions. Toward that end, we have recently proposed a variant of SPIDER (spectral phase interferometry for direct electric field reconstruction) based on a nonstandard effect for producing the frequency shear, the so-called rotational Doppler effect. The method called DEER-SPIDER, for Doppler effect E-field replication, has the advantage of producing a spectral shearing at/near the fundamental wavelength, thus allowing operation in the ultraviolet spectral range. The present paper provides a deeper study of this approach. The method is tested under two different challenging conditions, and a thorough theoretical analysis is proposed. Possible improvements and an outlook are also discussed.

Principle and technology of attosecond pulse characterization

Attosecond pulses have potential applications in the fields of physics, chemistry, biology, and medicine owing to the extremely high time resolution brought by their extremely short pulse widths. The generation and measurement technology of attosecond pulses provides a powerful means for the study of electron dynamical process in atoms. Since the date of its birth, the time width of an attosecond pulse has become shorter and shorter, making its measurement a challenging task. Although attosecond pulses are more and more widely used in the study of ultrafast dynamics and more interest is attracted into the field of attosecond science, it is undeniable that there are still difficulties and challenges for the measurement of attosecond pulses. This review is divided into two parts. The first part presents the development of technics for characterizing attosecond pulses, and briefly describes several experimental principles, setups and results for acquiring time-domain information of attosecond pulses, including RABITT (reconstruction of attosecond beating by interference of two-photon transitions) and laser-assisted lateral X-ray photoionization for measuring attosecond pulse train, attosecond streak camera for measuring single attosecond pulses, TIPTOE (tunneling ionization with a perturbation for the time-domain observation of an electric field) for measuring time-domain information of periodic pulses, as well as theoretical proposals such as attosecond cross correlation, asymmetric photoionization method, and SPIDER (attosecond spectral phase interferometry for direct electric-field reconstruction). The second part introduces the principle and structure of inversion algorithms for extracting time-domain information of attosecond pulses from spectrograms obtained with an attosecond streak camera, including FROG-CRAB (frequency resolved optical gating for complete reconstruction of attosecond bursts), PROOF (phase retrieval by omega oscillation filtering), VTGPA (Volkov transform generalized projections algorithm), PROBP-AC (phase retrieval of broadband pulses with autocorrelation) and CVGN (conditional variational generative network). We also evaluate the calculation time and accuracy of the algorithms. Finally, we summarize the experimental and theoretical challenges of the characterization of attosecond pulses, and look forward to the future development of attosecond pulse measurement.

Accurate reconstruction of electric field of ultrashort laser pulse with complete two-step phase-shifting

This paper presents a complete two-step phase-shifting (TSPS) spectral phase interferometry for direct electric-field reconstruction (SPIDER) to improve the reconstruction of ultrafast optical fields. Here, complete TSPS acts as a balanced detection that can not only remove the effect of the dc term of the interferogram, but also reduce measurement noises, and thereby improve the capability of SPIDER to measure the pulses with narrow spectra or complex spectral structures. Some prisms are chosen to replace some environment-sensitive optical components, especially reflective optics to improve operating stability and improve signal-to-noise ratio further. Our experiments show that the available shear can be decreased to 1.5% of the spectral width, which is only about $1/3$ compared with traditional SPIDER.

Simple technique for the compression of nanojoule pulses from few-cycle laser oscillator to 1.7-cycle duration via nonlinear spectral broadening in diamond.

We report on a simple approach for the compression of few-cycle laser pulses generated in an ultrafast laser oscillator to a duration corresponding to 1.7 cycles of near-infrared light (compression factor of 1.44) by nonlinear spectral broadening in diamond and subsequent dispersion compensation using chirped mirrors. After the spectral broadening, the pulse spectrum spans over almost an octave (580-1000nm at the -10 dB level). The pulses are compressed by broadband-chirped mirrors and a wedge pair to a duration of 4.5fs measured by spectral phase interferometry for direct electric-field reconstruction (SPIDER). The properties of the broadened spectrum and their modelling by numerical solution of a 1D nonlinear Schrödinger equation show that the main source of spectral broadening is self-phase modulation, whereas stimulated Raman scattering does not play a significant role.

Unstable and Multiple Pulsing Can Be Invisible to Ultrashort Pulse Measurement Techniques

Multiple pulsing occurs in most ultrashort-pulse laser systems when pumped at excessively high powers, and small fluctuations in pump power in certain regimes can cause unusual variations in the temporal separations of sub-pulses. Unfortunately, the ability of modern intensity-and-phase pulse measurement techniques to measure such unstable multi-pulsing has not been studied. Here we report calculations and simulations finding that allowing variations in just the relative phase of a satellite pulse causes the second pulse to completely disappear from a spectral interferometry for direct electric field reconstruction (SPIDER) measurement. We find that, although neither frequency-resolved optical gating (FROG) nor autocorrelation can determine the precise properties of satellite pulses due to the presence of instability, they always succeed in, at least, seeing the satellite pulses. Also, additional post-processing of the measured FROG trace can determine the correct approximate relative height of the satellite pulse and definitively indicate the presence of unstable multiple-pulsing.

Two-step phase-shifting SPIDER

Comprehensive characterization of ultrafast optical field is critical for ultrashort pulse generation and its application. This paper combines two-step phase-shifting (TSPS) into the spectral phase interferometry for direct electric-field reconstruction (SPIDER) to improve the reconstruction of ultrafast optical-fields. This novel SPIDER can remove experimentally the dc portion occurring in traditional SPIDER method by recording two spectral interferograms with π phase-shifting. As a result, the reconstructed results are much less disturbed by the time delay between the test pulse replicas and the temporal widths of the filter window, thus more reliable. What is more, this SPIDER can work efficiently even the time delay is so small or the measured bandwidth is so narrow that strong overlap happens between the dc and ac portions, which allows it to be able to characterize the test pulses with complicated temporal/spectral structures or narrow bandwidths.

A compact SPIDER system based on a pair of 180° folding right-angle prisms stretcher with a modified reconstruction algorithm

The pulse stretcher, a necessary part of the spectral phase interferometry for direct electric-field reconstruction (SPIDER) system, generates a chirped pulse to meet the quasi-CW condition by introducing optical material dispersion or angular dispersion. In this paper, a compact design of SPIDER with a pulse stretcher consisting of a pair of 180° folding right angle prisms (FRAPs) is proposed. The major advantages of the FRAPs include its insensitivity to misalignment, tunable dispersion in a large range, without inducing angular dispersion, low loss, and aberrationless. Moreover, we propose a modified algorithm with which the spectral phase errors of the recovered electric-field reconstructed with traditional SPIDER algorithm due to dispersion from the splitter of the Michelson interferometer can be alleviated effectually, and the modified algorithm is confirmed by both simulations and experimental measurements of two 800 nm ultrashort pulse chains with 43.5 and 29.8 nm bandwidths, respectively.

Precise measurement of ultrafast laser pulses using spectral phase interferometry for direct electric-field reconstruction

In this work, I present a novel method for measuring the pulse duration of few-cycle pulses using spectral phase interferometry for direct electric-field reconstruction (SPIDER) with high accuracy. These few-cycle pulses were generated due to nonlinear self-phase modulation (SPM) in nonlinear medium (neon gas) using a one meter hollow-fiber. The observed reconstructed pulse intensity autocorrelation function was varied from 5.35[Formula: see text]fs to almost 13[Formula: see text]fs. Moreover, the applied method allows for direct controlling of the output pulse duration through variation of the pulse-width of input pulses at different pressure of neon gas. The observed results indicate that the SPM was enhanced for high neon pressure (2.5[Formula: see text]atm.) and short input pluses (32[Formula: see text]fs) without chirping. The obtained results may give an opportunity to monitor and control ultrafast transit interaction in femtosecond chemistry.

Spectral-phase interferometry for direct electric-field reconstruction applied to seeded extreme-ultraviolet free-electron lasers.

We present a setup for complete characterization of femtosecond pulses generated by seeded free-electron lasers (FELs) in the extreme-ultraviolet spectral region. Two delayed and spectrally shifted replicas are produced and used for spectral phase interferometry for direct electric field reconstruction (SPIDER). We show that it can be achieved by a simple arrangement of the seed laser. Temporal shape and phase obtained in FEL simulations are well retrieved by SPIDER reconstructions, allowing to foresee the implementation of this diagnostics tool on existing and future sources. This will be a significant step towards an experimental investigation and control of FEL spectral phase.

Phase retrieval via regularization in self-diffraction-based spectral interferometry

A novel variant of spectral phase interferometry for direct electric-field reconstruction (SPIDER) is introduced and experimentally demonstrated. Unlike most previously demonstrated variants of SPIDER, our method is based on a third-order nonlinear optical effect, namely self-diffraction (SD), rather than the second-order effect of sum-frequency generation. On the one hand, SD substantially simplifies phase-matching capabilities for multioctave spectra that cannot be hosted by second-order processes given manufacturing limitations of crystal lengths in the few-micrometer range. However, on the other hand, SD SPIDER imposes an additional constraint as it effectively measures the spectral phase of a self-convolved spectrum rather than immediately measuring the fundamental phase. Reconstruction of the latter from the measured phase and the spectral amplitude of the fundamental turns out to be an ill-posed problem, which we address by a regularization approach. We discuss the numerical implementation in detail and apply it to measured data from a Ti:sapphire amplifier system. Our experimental demonstration used 54 fs pulses and a 500 μm thick BaF2 crystal to show that the SD SPIDER signal is sufficiently strong to be separable from stray light. Extrapolating these measurements to the thinnest conceivable nonlinear media, we predict that bandwidths well above two optical octaves can be measured by a suitably adapted SD SPIDER apparatus, enabling the direct characterization of pulses down to single-femtosecond pulse durations. Such characteristics appear out of range for any currently established pulse measurement technique.

Characterizing inner-shell with spectral phase interferometry for direct electric-field reconstruction.

In many atomic, molecular and solid systems, Lorentzian and Fano profiles are commonly observed in a broad research fields throughout a variety of spectroscopies. As the profile structure is related to the phase of the time-dependent dipole moment, it plays an important role in the study of quantum properties. Here we determine the dipole phase in the inner-shell transition using spectral phase interferometry for direct electric-field reconstruction (SPIDER) with isolated attosecond pulses (IAPs). In addition, we propose a scheme for pulse generation and compression by manipulating the inner-shell transition. The electromagnetic radiation generated by the transition is temporally compressed to a few femtoseconds in the extreme ultraviolet (XUV) region. The proposed pulse-compression scheme may provide an alternative route to producing attosecond pulses of light.

Accurate characterization of complex pulses by delay-controlled fringe-free interferometry of spectral high-resolution technique

We discuss the disadvantage in conventional Spectral Phase Interferometry for Direct Electric-field Reconstruction (SPIDER) technology in complex femtosecond pulse measurement. An improved version of conventional technology named DC-FISH is presented, where single replica of the unknown pulse upconverts synchronously with two frequency-shifted narrow-banded long pulses. The spectral phase of the unknown pulse can be directly calculated from the fringe-free spectra with the introduction of a suitable small delay between the upconverted pulses. The numerical simulation results are achieved to identify a higher efficiency and lower requirements on measurement in novel approach.

Spectral phase measurement of complex pulses using delay controlled fringe free interferometry technique

The shortcomings in complex femtosecond pulse measurement of conventional spectral phase interferometry for direct electric-field reconstruction (SPIDER) are commented in this paper. To solve the problem, we propose an improved version of SPIDER, where single replica of the unknown pulse upconverts synchronously with two frequency-shifted narrow-banded long pulses. With the introduction of a suitable small delay between the upconverted pulses, the spectral phase of the unknown pulse can be directly calculated from the fringe-free spectra and Fourier-transform filtering is not required. The results of numerical simulation show that the accuracy of the new method in complex pulse measurement is higher than conventional SPIDER.

Spectral phase characterization of ultrashort pulse using fringe free interferometry

There are presented analytical and experimental results of a novel method which enables significant simplifications in spectral shearing interferometry as applied for ultrashort optical pulse measurements. The method attempts to improve the superiority in conventional Spectral Phase Interferometry for Direct Electric-field Reconstruction (SPIDER). It doesn’t split a test pulse into two parts, but compensates for the delay time between two quasi-monochromatic frequency components in a chirped pulse with spectral and temporal shear to produce an interferogram without fringe. Fringe free interferograms could simplify data processing procedures and reduce the restriction on resolution of spectrometers. The experimental setup avoids the influence of material dispersion with real-time and single-shot nature, and could be made up as a miniaturization measurement device. Although being short of the beauties in SPIDER, it still could be an optional femtosecond pulse measurement method in certain conditions.

THE AMPLITUDE AND PHASE MEASUREMENTS OF FEMTOSECOND PULSE USING FRINGE FREE INTERFEROMETRY OF SPECTRAL HIGH-RESOLUTION METHOD

In this paper, we present analytical and experimental results of a novel method which enables significant simplifications in spectral shearing interferometry as applied for ultrashort optical pulse measurements. The method attempts to improve the superiority in conventional spectral phase interferometry for direct electric-field reconstruction (SPIDER). It does not split a test pulse into two parts, but compensate for the delay time between two quasi-monochromatic frequency components in a chirped pulse with spectral and temporal shear to produce an interferogram without fringe. Fringe free interferogram could simplify data processing procedure and reduce the restriction on resolution of spectrometer. The experimental setup avoids the influence of material dispersion with real-time and single-shot nature, and could be made up as a miniaturization measurement device. Although being short of the beauties in SPIDER, it still could be an optional femtosecond pulse measurement method in certain condition.

Pulse-shape instabilities and their measurement

Multi-shot pulse-shape measurements of trains of ultrashort pulses with unstable pulse shapes are studied. Measurement techniques considered include spectral-phase interferometry for direct electric-field reconstruction (SPIDER), second harmonic generation frequency-resolved optical gating (FROG), polarization gate FROG, and cross-correlation FROG. An analytical calculation and simulations show that SPIDER cannot see unstable pulse-shape components and only measures the coherent artifact. Further, the presence of this instability cannot be distinguished from benign misalignment effects in SPIDER. FROG methods yield a better, although necessarily rough, estimate of the pulse shape and also indicate instability by exhibiting disagreement between measured and retrieved traces. Only good agreement between measured and retrieved FROG traces or 100% SPIDER fringe visibility guarantees a stable pulse train.

Retrieval of the amplitude and phase of the dipole matrix element by attosecond electron-wave-packet interferometry

We extend the ideas of wave-packet interferometry [Remetter et al., Nat. Phys. 2, 323 (2006)] to implement the algorithm of spectral phase interferometry for direct electric-field reconstruction (SPIDER) for characterizing the amplitude and phase of electron wave packets. Single-photon ionization by an attosecond pulse launches an electron wave packet in the continuum. Ionization by a train of two attosecond pulses in the presence of a moderate infrared pulse creates an interferogram in the final photoelectron momentum distribution. From the interferogram, the complex electron wave function can be reconstructed. If the pulses are well characterized, the amplitude and phase of the bound-free dipole matrix element can be reconstructed over a wide energy range. This is demonstrated by application of the retrieval method to momentum distributions obtained by numerical solution of the time-dependent Schr¨ odinger equation. The case of Coulombic potentials requires appropriate treatment of

Adaptive Generation and Diagnostics of Linear Few-Cycle Light Bullets

Recently we introduced the class of highly localized wavepackets (HLWs) as a generalization of optical Bessel-like needle beams. Here we report on the progress in this field. In contrast to pulsed Bessel beams and Airy beams, ultrashort-pulsed HLWs propagate with high stability in both spatial and temporal domain, are nearly paraxial (supercollimated), have fringe-less spatial profiles and thus represent the best possible approximation to linear “light bullets”. Like Bessel beams and Airy beams, HLWs show self-reconstructing behavior. Adaptive HLWs can be shaped by ultraflat three-dimensional phase profiles (generalized axicons) which are programmed via calibrated grayscale maps of liquid-crystal-on-silicon spatial light modulators (LCoS-SLMs). Light bullets of even higher complexity can either be freely formed from quasi-continuous phase maps or discretely composed from addressable arrays of identical nondiffracting beams. The characterization of few-cycle light bullets requires spatially resolved measuring techniques. In our experiments, wavefront, pulse and phase were detected with a Shack-Hartmann wavefront sensor, 2D-autocorrelation and spectral phase interferometry for direct electric-field reconstruction (SPIDER). The combination of the unique propagation properties of light bullets with the flexibility of adaptive optics opens new prospects for applications of structured light like optical tweezers, microscopy, data transfer and storage, laser fusion, plasmon control or nonlinear spectroscopy.