Spectral Phase Interferometry For Direct Electric-field Reconstruction Research Articles

Coherent artifact in modern pulse measurements

We simulate multishot intensity-and-phase measurements of unstable trains of complex ultrashort pulses using second-harmonic-generation (SHG) frequency-resolved optical gating (FROG) and spectral-phase interferometry for direct electric-field reconstruction (SPIDER). Both techniques fail to see the pulse structure. But FROG yields the correct average pulse duration and suggests the instability by exhibiting significant disagreement between measured and retrieved traces. SPIDER retrieves the correct average spectral phase but significantly underestimates the average pulse duration. In short, SPIDER measures only the coherent artifact. An analytical calculation confirms this last fact.

Use of photoelectron energy spectrum transfer equation for the measurement of a narrowband XUV pulse

To study the time evolution of a molecular state in an ultra-fast chemical reaction, the use of shorter pulses with higher photon energy and narrower bandwidth for both pump and probe is necessary. However, quick and precise measurement of their detailed time structures is a challenge. Over the last decade, great efforts have been made to measure an attosecond extreme ultraviolet (XUV) pulse. To date, several methods have been developed to measure the pulse duration and completely reconstruct it. The attosecond spectral phase interferometry for direct electric field reconstruction (SPIDER) and attosecond frequency-resolved optical gating (FROG) techniques are often used. However, these methods use state-of-the-art experimental set-ups and complicated data analysis procedures. To develop attosecond metrology for practical use (e.g. timing, measurement, evaluation, calibration, optimization, pumping, probing), we propose a quick and analytical method to precisely observe an attosecond XUV pulse with laser-assisted photo-ionization. The method is based on determining the laser-related phase of each streaked electron and using a transfer equation for one-step pulse reconstruction without any time-resolved measurements, iterative calculations, or data fitting procedures. Temporal errors of the pulse reconstruction are calculated from the XUV bandwidth. Because the transfer equation establishes a direct connection between the XUV pulse properties, the crucial laser parameters (peak intensity, phase, carrier envelope phase), the atomic ionization potential, and the measured photoelectron energy spectrum, we can use it to study any one of these properties from other known information and probe the dynamic processes of an ultra-fast reaction.

Sub-picosecond phase-sensitive optical pulse characterization on a chip

The recent introduction of coherent optical communications has created a compelling need for ultra-fast phase-sensitive measurement techniques operating at milliwatt peak power levels and in time scales ranging from sub-picoseconds to nanoseconds. Previous reports of ultrafast optical signal measurements in integrated platforms[8-10] include time-lens temporal imaging on a silicon chip[8,9] and waveguide-based Frequency-Resolved Optical Gating (FROG). Time-lens imaging is phase insensitive while waveguide-based FROG methods require the integration of long tuneable delay lines - still an unsolved challenge. Here, we report a device capable of characterizing both the amplitude and phase of ultrafast optical pulses with the aid of a synchronized incoherently-related clock pulse. It is based on a novel variation of Spectral Phase Interferometry for Direct Electric-Field Reconstruction (SPIDER)that exploits degenerate four-wave-mixing (FWM) in a CMOS compatible chip. We measure pulses with <100mW peak power, a frequency bandwidth >1THz, and up to 100ps pulsewidths, yielding a time-bandwidth product (TBP)>100.

Characterization of high-intensity sub-4-fs laser pulses using spatially encoded spectral shearing interferometry

We report on the full amplitude and phase characterization of high-intensity few-cycle laser pulses generated in a single-stage hollow core fiber system with subsequent compression by ultrabroadband chirped mirrors. We use a spatially-encoded arrangement (SEA) spectral phase interferometry for direct electric field reconstruction (SPIDER) with spectral filters for ancilla generation to characterize the sub-4 fs pulses with spatial resolution.

Application of single-beam homodyne SPIDER for the control of complex spectral phase profiles

We investigate the range of application of single-beam homodyne spectral phase interferometry for direct electric field reconstruction (SPIDER) for multiphoton microscopy. Simulations and experimental studies performed on model spectral phase profiles show that the phase reconstruction technique used in this method makes the phase retrieval quality highly sensitive to the complexity of the profile. In addition, we show that the use of iterative processes is likely to deteriorate the phase retrieval quality, especially for strongly varying phase profiles. These effects are illustrated and quantified for sinusoidal and quadratic spectral phase profiles.

Real-time pulse length measurement of few-cycle laser pulses using above-threshold ionization

The pulse lengths of intense few-cycle (4-10 fs) laser pulses at 790 nm are determined in real-time using a stereographic above-threshold ionization (ATI) measurement of Xe, i.e. the same apparatus recently shown to provide a precise, real-time, every-single-shot, carrier-envelope phase measurement of ultrashort laser pulses. The pulse length is calibrated using spectral-phase interferometry for direct electric-field reconstruction (SPIDER) and roughly agrees with calculations done using quantitative rescattering theory (QRS). This stereo-ATI technique provides the information necessary to characterize the waveform of every pulse in a kHz pulse train, within the Gaussian pulse approximation, and relies upon no theoretical assumptions. Moreover, the real-time display is a highly effective tool for tuning and monitoring ultrashort pulse characteristics.

Crystal-dithering method applied to spectral phase interferometry for direct electric-field reconstruction (SPIDER) for sensitivity enhancement of the pulse phase measurement

The application of a crystal-dithering technique to the spectral phase interferometry for direct electric-field reconstruction (SPIDER) was experimentally demonstrated. Applying a crystal-dithering technique to SPIDER resulted in the improvement of the measurement sensitivity. In our approach, a 20μm-thick nonlinear crystal for a thin-crystal SPIDER method was replaced by a 100μm-thick crystal, and the crystal was dithered. The improvement was confirmed by comparing the statistical error of the crystal-dithering SPIDER to the statistical error of the thin-crystal SPIDER method. The dispersion of a BK7 plate was investigated to evaluate the reliability of the proposed approach.

Real-time Temporal Characterization and Performance Optimization of a kHz Femtosecond Ti:Sapphire Laser Using a Comprehensive SPIDER

A comprehensive real-time spectral phase interferometry for direct electric field reconstruction (SPIDER) apparatus for characterizing femtosecond laser pulses is demonstrated. The SPIDER provides the temporal profiles of femtosecond laser pulses, reconstructed at the speed of 3.5 Hz, with parameters of the spectral phase such as group delay dispersion and third-order dispersion. The apparatus is applied successfully to optimize the spectral dispersion of a kHz femtosecond Ti:Sapphire laser by adjusting a grating compressor in real time.

Theory and design of two-dimensional spectral shearing interferometry for few-cycle pulse measurement

We provide a detailed discussion of our recently developed pulse characterization technique for few-cycle pulses, called two-dimensional spectral shearing interferometry (2DSI). Based on spectral phase interferometry for direct electric-field reconstruction (SPIDER), 2DSI is relatively simple to implement, but requires no interferometer delay or scan calibration. We show simulations of 2DSI in the presence of noise and find that it retains the favorable noise performance of spectral shearing methods, performing identically to standard SPIDER for a given measurement time. The optimal choice of experimental parameters is discussed, with results applicable to any spectral shearing method. Experimental considerations when building and operating a 2DSI are provided, with results shown for a 4.9 fs pulse, verifying the accuracy and precision of the 2DSI.

Characterization of attosecond XUV pulses utilizing a broadband UV~VUV pumping

We propose a simple scheme to characterize attosecond extreme ultraviolet (XUV) pulses. A broadband ultraviolet (UV) approximately vacuum ultraviolet (VUV) pump pulse creates a coherent superposition of atomic bound states, from which photoionization takes place by the time-delayed attosecond XUV probe pulse. Information on the spectral phase of the XUV pulse can be extracted from the phase offset of the interference beating in the photoelectron spectra using a standard SPIDER (spectral phase interferometry for direct electric-field reconstruction) algorithm. We further discuss the influence of the chirp and polychromaticity of the pump pulse, and show that they do not spoil the reconstruction process. Since our scheme is applicable for various simple atoms such as H, He, and Cs, etc., and capable of characterizing attosecond XUV pulses with a pulse duration of a few hundred attoseconds or even less, it can be an alternative technique to characterize attosecond XUV pulses. Specific numerical examples are presented for the H atom utilizing the 2p and 3p states.

Characterization of chirped pulses with modified-zero-additional-phase spectral phase interferometry for direct electric-field reconstruction

At present, pulse measurement systems based on spectral phase interferometry for direct electric-field reconstruction (SPIDER) may have problems in chirped pulse characterization. In this paper we propose and demostrate a Modified-ZAP SPIDER system to solve this problem. Femtosecond pulses from a KLM Ti:sapphire laser and the chirped pulses obtained by broadening by a 80 mm BK7 glass block are respectively measured. The experimental results show that the novel MZAP-SPIDER system performs well in chirped pulse measurement.

Two-beam SPIDER for dual-pulse single-shot characterization

We describe an innovative design of the spectral-phase-interferometry-for-direct-electric-field-reconstruction (SPIDER) technique applicable to the simultaneous measurement of the electric field of two ultrashort pulses, e.g., a reference and probe pulse. We demonstrate the utility of the device by measuring material dispersion in a single shot by subtracting the reconstructed phase of a dispersed pulse and a reference pulse and by quantifying phase differences arising from nonlinear effects. Our two-beam technique is particularly suitable for use in experiments performed on high-energy, ultrafast laser systems operating in a single-shot mode with significant pulse-to-pulse variations.

Ultrashort pulse characterization by spectral shearing interferometry with spatially chirped ancillae

We report a new version of spectral phase interferometry for direct electric field reconstruction (SPIDER), in which two spatially chirped ancilla fields are used to generate a spatially encoded SPIDER interferogram. We dub this new technique Spatially Encoded Arrangement for Chirped ARrangement for SPIDER (SEA-CAR-SPIDER). The single shot interferogram contains multiple shears, the spectral amplitude of the test pulse, and the reference phase, which is accurate for broadband pulses. The technique enables consistency checking through the simultaneous acquisition of multiple shears and offers a simple and precise calibration method. All calibration parameters--the shears, and the upconversionfrequency--can be accurately obtained from a single calibration trace.

Improved ancilla preparation in spectral shearing interferometry for accurate ultrafast pulse characterization

We report a version of spectral phase interferometry for direct electric field reconstruction (SPIDER), in which spectral filters are used to produce the quasi-monochromatic fields required for upconversion. The advantages of this approach include improved calibration accuracy, robustness for strongly chirped input pulses, simplicity, and compactness. We verify the technique experimentally by measuring the spectral chirp of a grating compressor using a spatially encoded arrangement (SEA-)SPIDER.

Single-beam homodyne SPIDER for multiphoton microscopy

We report a new version of spectral phase interferometry for direct electric field reconstruction (SPIDER) requiring only a single phase-shaped laser beam. A narrowband probe pulse is selected out of a broadband ultrafast laser pulse by a phase pulse-shaping technique and mixed with the original broadband pulse to generate a second-harmonic generation (SHG) signal. Using another SHG signal solely generated by the broadband pulse as a local oscillator, the spectral phase of the broadband laser pulse can be analytically retrieved by a combination of double-quadrature spectral interferometry and homodyne optical technique for SPIDER (HOT SPIDER). An arbitrary spectral phase at the sample position of a microscope can be compensated with a precision of 0.05 rad over the FWHM of the laser spectrum. It is readily applicable to a nonlinear microscopy technique with a phase-controlled broadband laser pulse.

Analysis and mitigation of systematic errors in spectral shearing interferometry of pulses approaching the single-cycle limit [Invited

We derive an analytical approximation for the measured pulse width error in spectral shearing methods, such as spectral phase interferometry for direct electric-field reconstruction (SPIDER), caused by an anomalous delay between the two sheared pulse components. This analysis suggests that, as pulses approach the single-cycle limit, the resulting requirements on the calibration and stability of this delay become significant, requiring precision orders of magnitude higher than the scale of a wavelength. This is demonstrated by numerical simulations of SPIDER pulse reconstruction using actual data from a sub-two-cycle laser. We briefly propose methods to minimize the effects of this sensitivity in SPIDER and review variants of spectral shearing that attempt to avoid this difficulty.

Characterization of mid-infrared femtosecond pulses [Invited

We review different methods for characterizing mid-infrared femtosecond pulses, including linear methods such as electro-optic sampling, time- and frequency-domain interferometry, and nonlinear self-referenced methods such as frequency-resolved optical gating (FROG) and spectral phase interferometry for direct electric-field reconstruction (SPIDER). Of particular interest are methods based on upconversion through nonlinear mixing with chirped 800 nm pulses, enabling a complete measurement of mid-infrared pulses with visible-light spectrometers.

Gold-SPIDER: spectral phase interferometry for direct electric field reconstruction utilizing sum-frequency generation from a gold surface

We report on a version of spectral phase interferometry for direct electric field reconstruction (SPIDER) that uses no nonlinear crystals, instead relying on the harmonic signal from a gold mirror. Surface harmonic generation holds the promise of being able to upconvert extremely broad bandwidths over a large tuning range, thus providing access to both extremely short pulses and wavelengths outside of traditional methods. In this proof of principle demonstration, SPIDER traces for chirped and transform-limited 55 fs pulses are presented.

Characterization of a broadband pulse for phase controlled multiphoton microscopy by single beam SPIDER

We present what we believe to be a new version of spectral phase interferometry for direct electric field reconstruction (SPIDER) using only a single-phase and polarization controlled laser beam. Two narrow pulses and one broadband pulse are selected out of an ultrafast laser pulse by a polarization and phase control technique to generate second harmonic generation (SHG) signals, which are equivalent to a spectral shear interferogram in the conventional SPIDER method. The spectral phase of the broadband laser pulse is extracted analytically with double quadrature spectral interferometry (DQSI). An arbitrary spectral phase can be retrieved with great precision and compensated in situ at the sample position of a microscope. This new method requires no separate reference beam and is suitable for nonlinear optical microscopy with a phase controlled laser pulse.

Fractional-order Fourier analysis for ultrashort pulse characterization

We report what we believe to be the first experimental demonstration of ultrashort pulse characterization using fractional-order Fourier analysis. The analysis is applied to the interpretation of spectral interferometry resolved in time (SPIRIT) traces [which are spectral phase interferometry for direct electric field reconstruction (SPIDER)-like interferograms]. First, the fractional-order Fourier transformation is shown to naturally allow the determination of the cubic spectral phase coefficient of pulses to be analyzed. A simultaneous determination of both cubic and quadratic spectral phase coefficients of the pulses using the fractional-order Fourier series expansion is further demonstrated. This latter technique consists of localizing relative maxima in a 2D cartography representing decomposition coefficients. It is further used to reconstruct or filter SPIRIT traces.