Frequency-resolved Optical Gating Trace Research Articles

Optimal feedback control of two-photon fluorescence in Coumarin 515 based on genetic algorithm

An optimal feedback control of two-photon fluorescence in the Coumarin 515 ethanol solution excited by shaping femtosecond laser pulses based on genetic algorithm is demonstrated experimentally. The two-photon fluorescence intensity can be enhanced by ∼20%. Second harmonic generation frequency-resolved optical gating traces indicate that the optimal laser pulses are positive chirp, which are in favor of the effective population transfer of two-photon transitions. The dependence of the two-photon fluorescence signal on the laser pulse chirp is investigated to validate the theoretical model for the effective population transfer of two-photon transitions. The experimental results appear the potential applications in nonlinear spectroscopy and molecular physics.

Interferometric frequency-resolved optical gating

We demonstrate a novel variant of frequency-resolved optical gating (FROG) that is based on spectrally resolving a collinear interferometric autocorrelation rather than a noncollinear one. From the interferometric FROG trace, one can extract two terms, the standard SHG-FROG trace and a new phase-sensitive modulational component, which both allow for independent retrieval of the pulse shape. We compare the results of both methods and a separate SPIDER measurement using 6.5-fs pulses from a white-light continuum. We find that the novel modulational component allows for robust retrieval of pulse shapes in the few-cycle regime. Together with the added cross-checks, our method significantly enhances choices for pulse characterization in this regime.

Feedback Control for Accurate Shaping of Ultrashort Optical Pulses prior to Chirped Pulse Amplification

Through experiments, we demonstrate accurate pulse shaping of femtosecond optical pulses in both amplitude and phase, prior to chirped pulse amplification. The nonlinear transfer function of the amplifier was compensated with feedback control referring to the amplified pulse shape measured by frequency resolved optical gating (FROG) or temporal analysis, by dispersing a pair of light e fields (TADPOLE). In FROG-referring control, the pulse shaper is adaptively controlled using a control index calculated from the two-dimensional FROG trace image, while in TADPOLE-referring control, the shaping phase-mask is corrected only a few times using the reconstructed spectrum phase of the output pulse. The performance and limitations of pre-shaping systems are discussed by comparing two pulse shaper devices, namely a liquid-crystal spatial light modulator and an acoustic optical phase dispersion filter, two pulse measurement techniques, and two feedback control schemes.

Beyond error bars: Understanding uncertainty in ultrashort-pulse frequency-resolved-optical-gating measurements in the presence of ambiguity

Previously we showed that the "bootstrap method," a well-known statistical technique, can be used to automatically compute error bars in ultrashort pulse measurements using frequency-resolved optical gating (FROG) without the need for additional measurements or traditional error analysis. Here we extend the bootstrap method to pulse measurement in the presence of ambiguities, where traditional error bars would give misleading information. As a result, we provide a new approach to displaying this uncertainty, which nicely reveals the richness of information available (or perhaps unavailable) in a FROG trace (or other measurement) in the presence of ambiguities.

Determining error bars in measurements of ultrashort laser pulses

We present a simple and automatic method for determining the uncertainty in the retrieved intensity and phase versus time (and frequency) due to noise in a frequency-resolved optical-gating trace, independent of noise source. It uses the “bootstrap” statistical method and also yields an automated method for phase blanking (omitting the phase when the intensity is too low to determine it).

Real time femtosecond optical pulse measurement using a video-rate frequency-resolved optical gating system

We describe an improved instrument for measuring at video rate (30 frames per second) the second-harmonic frequency-resolved optical gating trace of femtosecond pulses from a mode-locked laser oscillator. The system comprises separate scanning acquisition and pulse retrieval elements which together enable the exact pulse profile to be viewed in real time with a typical refresh rate of 1 Hz. Details are given of the optical system used, the electronic synchronization circuits and the acquisition and retrieval software employed.

Real-time inversion of polarization gate frequency-resolved optical gating spectrograms.

Frequency-resolved optical gating (FROG) is a technique used to measure the intensity and phase of ultrashort laser pulses through the optical construction of a spectrogram of the pulse. To obtain quantitative information about the pulse from its spectrogram, an iterative two-dimensional phase retrieval algorithm must be used. Current algorithms are quite robust but retrieval of all the pulse information can be slow. Previous real-time FROG trace inversion work focused on second-harmonic-generation FROG, which has an ambiguity in the direction of time, and required digital signal processors (DSPs). We develop a simplified real-time FROG device based on a single-shot geometry that no longer requires DSPs. We use it and apply the principal component generalized projections algorithm to invert polarization gate FROG traces at rates as high as 20 Hz.

Adaptive pulse shaping of phase and amplitude of an amplified femtosecond pulse laser by direct reference to frequency-resolved optical gating traces

By adaptive control of both spectral phase and amplitude of seed pulses with an acousto-optic programmable dispersion filter located before a pulse stretcher, accurate pulse shaping was achieved for ultrashort laser pulses delivered through a regenerative amplifier. Two-dimensional patterns obtained from frequency-resolved optical gating were used for calculating cost functions in an adaptive control algorithm without pulse shape reconstruction during the control of pulse shape.

Ultrashort-laser-pulse measurement using swept beams

We demonstrate a frequency-resolved optical gating (FROG) device that uses a sweepshot geometry that combines the advantages of multishot and single-shot pulse-measurement devices, has only one moving part, a galvanometer, and requires no computer control. Like a multishot device, it focuses the beam to a small spot (rather than a line focus) and has a high intensity in the nonlinear medium. Like single-shot devices, it makes measurements quickly, generating an entire FROG trace on a single camera screen (rather than requiring many camera downloads).

Effect of third-order dispersion on the phases of solitonlike Cr^4+ : YAG-laser pulses characterized by the second-harmonic generation frequency-resolved optical gating method

The effect of third-order dispersion on solitonlike operation of the L-fold cavity Cr4+:YAG laser is studied. Dispersion equations are derived to the fourth order for an L-fold cavity, and dispersion values for a Cr4+:YAG laser are calculated. Third-order dispersion is found to be comparable with the second-order dispersion in a 60-fs-class Cr4+:YAG laser, and fourth-order dispersion is negligible. The temporal and spectral phases of a 60-fs pulse are calculated from the dispersion properties of the cavity. The spectral phase is constant, despite considerable third-order dispersion. A second-harmonic generation (SHG) frequency-resolved optical gating (FROG) trace is calculated for the simulated pulse. The SHG spectrum has a tail to the short-wavelength side at zero delay, consistent with experimental results. The calculated phase and the FROG trace should be recognized as characteristic of the third-order-dispersion effect on solitonlike lasers.

Convergence test for inversion of frequency-resolved optical gating spectrograms

We describe a new and simple method to aid in the analysis of retrieved pulses from inverted frequency-resolved optical gating (FROG) traces. The analysis can separate noise from distortion and shows that distortion is more deleterious to the retrieved pulse than is pure noise. The analysis relies on the fact that FROG traces can be constructed from a single outer product of two vectors, whereas distortion and noise require the sum of a series of outer products.

Optical heterodyne detected spectrograms of ultrafast nonresonant electronic responses

The dispersed optical heterodyne detected (OHD) birefringence and dichroism that result from the electronic response of nonresonant materials are described for a number of ultrafast pulse shapes. The OHD spectrograms that correspond to these dispersed instantaneous electronic responses display detuning oscillations along both the interpulse delay and the probe frequency dimensions. The frequency of these oscillations depends only on the detuning of the selected Fourier component of the probe pulse from the carrier frequency and the pulse shapes. This effect is demonstrated for Gaussian, sech2, and one-sided exponential probe pulses. For each of these pulse shapes the OHD spectrograms exhibit a characteristic dependence on detuning frequency. The effects of linear chirp on these OHD spectrograms are also considered. Experimentally observed nonresonant electronic spectrograms are compared with theory. These OHD spectrograms are also compared with the well-known frequency-resolved optical gating traces. Analysis of the OHD spectrograms may provide a more useful approach for the characterization of ultrafast pulses because of the phase-specific, amplitude level origin of these responses.

Complete characterization of a self-mode-locked Ti:sapphire laser in the vicinity of zero group-delay dispersion by frequency-resolved optical gating

The intensity and the phase of ultrashort pulses from a self-mode-locked Ti:sapphire laser operating in the vicinity of zero group-delay dispersion (GDD) have been completely characterized by the technique of frequency-resolved optical gating (FROG). For small values of negative GDD, the appearance of a dispersive wave in the pulse spectrum is manifested in the measured FROG trace, and pulse retrieval directly shows its association with a broad leading-edge pedestal. For positive GDD, we confirm previous experimental observations of picosecond pulses with large positive chirp and report a new operating regime in which the output pulses are of picosecond duration but are intensity modulated at 20 THz. The physical origin of this modulation is discussed by analogy with similar effects observed during pulse propagation in optical fibers, and the experimental results are compared with a model of intracavity four-wave mixing about the cavity zero GDD wavelength.

Recent progress toward real-time measurement of ultrashort laser pulses

Frequency-resolved optical gating (FROG) is a technique that produces a spectrogram of an ultrashort laser pulse optically. While a great deal of information about the pulse can be gleaned from its FROG trace, often it is desirable to obtain of the pulse information immediately, in real time. Quantitative information about the guise is not readily obtainable from its spectrogram without the use of a two-dimensional phase retrieval algorithm. While current algorithms are quite robust, retrieval of all the pulse information can be slow. In this paper, I describe a recently developed FROG trace inversion algorithm called Principal Component Generalized Projects that is fast, robust, and can invert FROG traces in real time. A femtosecond oscilloscope based on second-harmonic generation FROG is also described that uses this new algorithm to rapidly (up to 2.3 Hz) and continuously display the intensity and phase of ultrashort laser pulses.

Practical issues in ultrashort-laser-pulse measurement using frequency-resolved optical gating

We explore several practical experimental issues in measuring ultrashort laser pulses using the technique of frequency-resolved optical gating (FROG). We present a simple method for checking the consistency of experimentally measured FROG data with the independently measured spectrum and autocorrelation of the pulse. This method is a powerful way of discovering systematic errors in FROG experiments. We show how to determine the optimum sampling rate for FROG and show that this satisfies the Nyquist criterion for the laser pulse. We explore the low- and high-power limits to FROG and determine that femtojoule operation should be possible, while the effects of self-phase modulation limit the highest signal efficiency in FROG to 1%. We also show quantitatively that the temporal blurring due to a finite-thickness medium in single-shot geometries does not strongly limit the FROG technique. We explore the limiting time-bandwidth values that can be represented on a FROG trace of a given size. Finally, we report on a new measure of the FROG error that improves convergence in the presence of noise.

Frequency-resolved optical gating with the use of second-harmonic generation

We discuss the use of second-harmonic generation (SHG) as the nonlinearity in the technique of frequency-resolved optical gating (FROG) for measuring the full intensity and phase evolution of an arbitrary ultrashort pulse. FROG that uses a third-order nonlinearity in the polarization-gate geometry has proved extremely successful, and the algorithm required for extraction of the intensity and the phase from the experimental data is quite robust. However, for pulse intensities less than ~1 MW, third-order nonlinearities generate insufficient signal strength, and therefore SHG FROG appears necessary. We discuss the theoretical, algorithmic, and experimental considerations of SHG FROG in detail. SHG FROG has an ambiguity in the direction of time, and its traces are somewhat unintuitive. Also, previously published algorithms are generally ineffective at extracting the intensity and the phase of an arbitrary laser pulse from the SHG FROG trace. We present an improved pulse-retrieval algorithm, based on the method of generalized projections, that is far superior to the previously published algorithms, although it is still not so robust as the polarization-gate algorithm. We discuss experimental sources of error such as pump depletion and group-velocity mismatch. We also present several experimental examples of pulses measured with SHG FROG and show that the derived intensities and phases are in agreement with more conventional diagnostic techniques, and we demonstrate the high-dynamic-range capability of SHG FROG. We conclude that, despite the above drawbacks, SHG FROG should be useful in measuring low-energy pulses.

Comparison of ultrashort-pulse frequency-resolved-optical-gating traces for three common beam geometries

We recently introduced frequency-resolved optical gating (FROG), a technique for measuring the intensity and phase of an individual, arbitrary, ultrashort laser pulse. FROG can use almost any instantaneous optical nonlinearity, with the most common geometries being polarization gate, self-diffraction, and second-harmonic generation. The experimentally generated FROG trace is intuitive, visually appealing, and can yield quantitative information about the pulse parameters (such as temporal and spectral width and chirp). However, the qualitative and the quantitative features of the FROG trace depend strongly on the geometry used. We compare the FROG traces for several common ultrashort pulses for these three common geometries and, where possible, develop scaling rules that allow one to obtain quantitative information about the pulse directly from the experimental FROG trace. We illuminate the important features of the various FROG traces for transform-limited, linearly chirped, self-phase modulated, and nonlinearly chirped pulses, pulses with simultaneous linear chirp and self-phase modulation, and pulses with simultaneous linear chirp and cubic phase distortion, as well as double pulses, pulses with phase jumps, and pulses with complex intensity and phase substructure.

Improved ultrashort pulse-retrieval algorithm for frequency-resolved optical gating

We report on significant improvements in the pulse-retrieval algorithm used to reconstruct the amplitude and the phase of ultrashort optical pulses from the experimental frequency-resolved optical gating trace data in the polarization-gate geometry. These improvements involve the use of an intensity constraint, an overcorrection technique, and a multidimensional minimization scheme. While the previously published, basic algorithm converged for most common ultrashort pulses, it failed to retrieve pulses with significant intensity substructure. The improved composite algorithm successfully converges for such pulses. It can now retrieve essentially all pulses of practical interest. We present examples of complex waveforms that were retrieved by the improved algorithm.

Using phase retrieval to measure the intensity and phase of ultrashort pulses: frequency-resolved optical gating

We recently introduced a new technique, frequency-resolved optical gating (FROG), for directly determining the full intensity I(t) and phase φ(t) of a single femtosecond pulse. By using almost any instantaneous nonlinear-optical interaction of two replicas of the ultrashort pulse to be measured, FROG involves measuring the spectrum of the signal pulse as a function of the delay between the replicas. The resulting trace of intensity versus frequency and delay yields an intuitive display of the pulse that is similar to the pulse spectrogram, except that the gate is a function of the pulse to be measured. The problem of inverting the FROG trace to obtain the pulse intensity and phase can also be considered a complex two-dimensional phase-retrieval problem. As a result, the FROG trace yields, in principle, an essentially unique pulse intensity and phase. We show that this is also the case in practice. We present an iterative-Fourier-transform algorithm for inverting the FROG trace. The algorithm is unusual in its use of a novel constraint: the mathematical form of the signal field. Without the use of a support constraint, the algorithm performs quite well in practice, even for pulses with serious phase distortions and for experimental data with noise, although it occasionally stagnates when pulses with large intensity fluctuations are used.

Characterization of arbitrary femtosecond pulses using frequency-resolved optical gating

The frequency-resolved optical gating (FROG) technique for characterizing and displaying arbitrary femtosecond pulses is presented. The method is simple, general, broadband, and does not require a reference pulse. Using virtually any instantaneous nonlinear-optical effect, FROG involves measuring the spectrum of the signal pulse as a function of the delay between two input pulses. The resulting trace of intensity versus frequency and delay is related to the pulse's spectrogram a visually intuitive transform containing time and frequency information. It is proven using phase retrieval concepts that the FROG trace yields the full intensity I(t) and phase phi (t) of an arbitrary ultrashort pulse with no physically significant ambiguities. FROG appears to have temporal resolution limited only by the response of the nonlinear medium. The method is demonstrated by using self-diffraction through the electronic Kerr effect in BK-7 glass and 620-nm, linearly chirped, approximately 200-fs pulses of a few microjoules.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>