Frequency-resolved Optical Gating Trace Research Articles

Dispersion scan frequency resolved optical gating for consistency check of pulse retrieval.

Many methods commonly used to characterize ultrafast laser pulses, such as the frequency-resolved optical gating (FROG) or the dispersion scan (d-scan), face problems when they are used on pulses with a spectrum or phase varying within the laser beam cross section or the acquisition time. The presence of such pulse shape variation leads to discrepancy between the measured FROG trace and its reconstructed counterparts. Nevertheless, it is difficult to reliably discern this shape variation because even the distorted experimental FROG trace can be reasonably reproduced by a realistic pulse shape. In this work, we examine and discern the variation of the pulse shape based on a new method, dispersion-scan FROG (D-FROG), which combines the idea of dispersion scanning with the FROG method. This technique provides a means of careful evaluation of the laser pulse based on a set of FROG traces connected by known dispersion changes. Therefore, this method can disclose seemingly correct pulse retrievals from distorted datasets. The D-FROG method can be used as a simple extension of the FROG technique to provide a consistency check able to identify the shortcomings in the pulse characterization.

The Temporal Measurement of Infrared Femtosecond Fiber Laser Pulse with Complex Spectra: SPIDER and FROG

Femtosecond fiber laser pulse (FFLP) is very suitable for precision laser processing (PLP) with the advantages of high power, compact integrated structure, and easy installation. However, with the power increasing, nonlinear optical effects (NOE) of fiber, such as self-phase modulation (SPM), will be greatly enhanced, and the spectra of the output pulse will be very complex, which considerably increases the temporal complexity of FFLP and takes an immeasurable influence on PLP, so it is of great significance to accurately measure the temporal property of FFLP for higher accuracy of PLP. This paper presents a self-referencing spectral phase interferometry for direct electric-field reconstruction based on a single grating stretcher (SGS-SPIDER) with the two-step phase shift (TSPS) method for measuring FFLP with complex and infrared spectra. Meanwhile, we present a modified pulse-retrieval algorithm called an adaptive pulse-retrieval algorithm (APRA) of frequency-resolved optical gating (FROG) to reconstruct the measured pulse accurately. The duration of the reconstructed pulse measured by FROG is 162 fs, whose autocorrelation curve is similar to the measured autocorrelation curve including the picosecond background. The error of the reconstructed FROG trace is 0.42%, which is reliable enough according to the literature experience. Finally, the unique advantages of FROG for measuring complex ultrashort pulses such as FFLP are compared with SPIDER; that is, FROG has a wider spectral phase measuring range than SPIDER. These studies provide a new diagnostic technique for the complete temporal characterization of FFLP with complex spectra and extend the measurement range and application of SPIDER at the infrared wavelength band, which is significant for improving the accuracy of PLP using FFLP.

Pulse Measurement from a Polluted Frequency Resolved Optical Gating Trace Based on Half-Trace Retrieval Algorithm

A half-trace retrieval algorithm based on an extended-ptychographical iterative engine algorithm is proposed to reconstruct the temporal structure of pulse from a polluted and recorded frequency-resolved optical gating (FROG) trace that was modulated by poor spatial profile of output pulses, stray light, or misalignment of the measurement setup. In the proposed algorithm, the probe pulse and the gated pulse were retrieved simultaneously from a recorded FROG trace with a half-delay range, and the measured pulse was obtained by combining the different edges of the probe pulse and the gated pulse. Numerical simulations were carried out to verify the feasibility of the proposed algorithm. A single-shot picoseconds (ps)−THG−FROG setup with a 100-μJ ps laser system and an online ps−SHG−FROG setup in PW laser system were built to test the proposed algorithm experimentally. The results show that the temporal structure of pulses retrieved by the half-trace retrieval algorithm is closer to the real temporal structure than that retrieved by the conventional ptychographical algorithm when the recorded FROG trace is badly polluted.

Eliminating local convergences in FROG retrieval algorithms

The complicated electric field structure of ultrashort pulses as characterized by frequency-resolved optical gating (FROG) algorithms often results in local convergence, which does not accurately represent the actual field pulse. We present an efficient and universal test procedure applicable to any FROG retrieval algorithm that allows recognition of the erroneous local convergence. The 100% efficacy of the procedure is demonstrated using Line-Search FROG algorithm, and comparison is given with the performance of a standard extended ptychographic iterative FROG trace retrieval engine.

Simultaneous Characterization of Two Ultrashort Optical Pulses at Different Frequencies Using a WS2 Monolayer.

The precise characterization of ultrashort laser pulses has been of interest to the scientific community for many years. Frequency-resolved optical gating (FROG) has been extensively used to retrieve the temporal and spectral field distributions of ultrashort laser pulses. In this work, we exploit the high, broad-band nonlinear optical response of a WS2 monolayer to simultaneously characterize two ultrashort laser pulses with different frequencies. The relaxed phase-matching conditions in a WS2 monolayer enable the simultaneous acquisition of the spectra resulting from both four-wave mixing (FWM) and sum-frequency generation (SFG) nonlinear processes while varying the time delay between the two ultrashort pulses. Next, we introduce an adjusted double-blind FROG algorithm, based on iterative fast Fourier transforms between two FROG traces, to extract the intensity distribution and phase of two ultrashort pulses from the combination of their FWM and SFG FROG traces. Using this algorithm, we find an agreement between the computed and observed FROG traces for both the FWM and SFG processes. Exploiting the broad-band nonlinear response of a WS2 monolayer, we additionally characterize one of the pulses using a second-harmonic generation (SHG) FROG trace to validate the pulse shapes extracted from the combination of the FWM and SFG FROG traces. The retrieved pulse shape from the SHG FROG agrees well with the pulse shape retrieved from our nondegenerate cross-correlation FROG measurement. In addition to the nonlinear parametric processes, we also observe a nonlinearly generated photoluminescence (PL) signal emitted from the WS2 monolayer. Because of its nonlinear origin, the PL signal can also be used to obtain complementary autocorrelation and cross-correlation traces.

Targeted generation of complex temporal pulse profiles

A targeted shaping of complex femtosecond pulse waveforms and their characterization is essential for many spectroscopic applications. A 4f pulse shaper combined with an advanced pulse characterization technique should, in the idealized case, serve this purpose for an arbitrary pulse shape. This is, however, violated in the real experiment by many imperfections and limitations. Although the complex waveform generation has been studied in-depth, the comparison of the effects of various experimental factors on the actual pulse shape has stayed out of focus so far. In this paper, we present an experimental study on the targeted generation and retrieval of complex pulses by using two commonly-used techniques: spatial-light-modulator (SLM)-based 4f pulse shaper and second-harmonic generation frequency-resolved optical gating (FROG) and cross-correlation FROG (XFROG). By combining FROG and XFROG traces, we analyze the pulses with SLM-adjusted complex random phases ranging from simple to very complex waveforms. We demonstrate that the combination of FROG and XFROG ensures highly consistent pulse retrieval, irrespective of the used retrieval algorithm. This enabled us to evaluate the role of various experimental factors on the agreement between the simulated and actual pulse shape. The factors included the SLM pixelation, SLM pixel crosstalk, finite laser focal spot in the pulse shaper, or interference fringes induced by the SLM. In particular, we observe that including the SLM pixelation and crosstalk effect significantly improved the pulse shaping simulation. We demonstrate that the complete simulation can faithfully reproduce the pulse shape. Nevertheless, even in this case, the intensity of individual peaks differs between the retrieved and simulated pulses, typically by 10–20% of the peak value, with the mean standard deviation of 5–9% of the maximum pulse intensity. We discuss the potential sources of remaining discrepancies between the theoretically expected and experimentally retrieved pulse.

Fast and direct optical dispersion estimation for ultrafast laser pulse compression.

In ultrashort pulse laser applications, optical dispersion seriously affects the energy concentration in the laser pulse duration and lowers the peak power. Accordingly, this study proposes a rapid dispersion estimation mechanism to facilitate the compensation of optical dispersion using a closed-loop control system. In the proposed approach, the optical dispersion information of the laser pulse is estimated directly from a frequency-resolved optical gating trace without the need for an iterative pulse-retrieval algorithm. In particular, the group delay dispersion (GDD) is determined from frequency and delay marginals, which are related to the laser spectrum and intensity autocorrelation, respectively, using a simple lookup table approach. The accuracy of the estimated GDD results is confirmed via a comparison with the spectral phase distribution of the electric field reconstructed using the principal component generalized projections algorithm. It is shown that the computation time of the proposed direct estimation method is around 13 times faster than that of the traditional iterative algorithm. It thus provides a feasible approach for enabling the real-time compensation of ultrafast laser pulse compression. Moreover, in a multiphoton-excited fluorescence imaging application, the proposed pulse compression mechanism yields an effective improvement in the intensity and contrast of the reconstructed image due to the increased nonlinear optical excitation efficiency of the optimized laser pulses.

Investigation of supercontinuum generation in photonic crystal fiber using bursts of femtosecond pulses

Results of experimental and numerical investigation of supercontinuum generation in polarization maintaining photonic crystal fiber using a burst of two orthogonal polarization femtosecond pump pulses are presented. The initial pump pulse source was a mode-locked Yb:KGW laser generating 52 nJ energy 90 fs duration pulses at 1033 nm with 76 MHz repetition rate. Analysis of cross-correlation frequency-resolved optical gating traces and numerical simulation results reveal that there are slight changes in supercontinuum generation when temporal delay between pump pulses in the burst is changed. Weak dependence of supercontinuum characteristics on temporal distance between the pump pulses is related to supercontinuum generation dynamics which is analyzed in detail.

Convolutional neural network for transient grating frequency-resolved optical gating trace retrieval and its algorithm optimization* *Project supported by the National Key R&D Program of China (Grant No. 2017YFB0405202) and the National Natural Science Foundation of China (Grant Nos. 61690221, 91850209, and 11774277).

A convolutional neural network is employed to retrieve the time-domain envelop and phase of few-cycle femtosecond pulses from transient-grating frequency-resolved optical gating (TG-FROG) traces. We use theoretically generated TG-FROG traces to complete supervised trainings of the convolutional neural networks, then use similarly generated traces not included in the training dataset to test how well the networks are trained. Accurate retrieval of such traces by the neural network is realized. In our case, we find that networks with exponential linear unit (ELU) activation function perform better than those with leaky rectified linear unit (LRELU) and scaled exponential linear unit (SELU). Finally, the issues that need to be addressed for the retrieval of experimental data by this method are discussed.

Coherent artifact and time-dependent polarization in amplified ultrafast erbium-doped fibre lasers

Mode-locked erbium-doped fibre lasers are ultrashort pulsed sources widely studied due to their versatility and multiple applications in the near infrared range. Here we present the experimental study of the emission of a passive mode-locked erbium-doped fibre laser with an amplification stage outside the cavity by means of Frequency Resolved Optical Gating (FROG) and spectral interferometry. Due to shot-to-shot instabilities, the FROG traces can be understood as the combination of two different traces, corresponding to the coherent artifact and the average pulse characteristics. We have modified a Principal Components Generalized Projections Algorithm, in order to make it able to retrieve efficiently both the coherent artifact and the average pulse. In addition, we study the temporal dependence of the polarization, showing that the pulses present time-dependent polarization with a stable spectral relative phase between the horizontal and vertical projections. Up to our knowledge, this is the first experimental study that shows the FROG measurements of unstable pulse trains associated with the coherent artifact and analyses the time-dependent polarization in ultrafast fibre lasers.

Influence of the delay line jitter on the SHG FROG reconstruction.

Frequency-resolved optical gating (FROG) counts among the most used methods to characterize complex femtosecond pulses. The multishot FROG experiment, studied in this work, relies on varying a delay between two replicas of the measured pulse, where the delay accuracy can suffer from delay line imperfections, setup instability, or minimization of the acquisition time. We present a detailed study on the effect of the delay line jitter on the pulse retrieval. We carried out simulations with the jitter values ranging from high-precision delay lines (100 nm) up to extremely unstable measurements (>1000 nm). For three sets of pulses, we quantified criteria assuring reliable reconstruction, using ptychographic algorithm, of a complex pulse based on the experimentally available FROG trace error. We observe that the effect of the jitter scales together with the spectral bandwidth. However, the pulse reconstruction is relatively robust against the jitter and, even for a severe distortion of the FROG trace (e.g., a jitter of 500 nm for broadband pulses), the main features of all pulses are retrieved with high fidelity. Our results provide guidance for the limitations based on the delay imperfections in the FROG experiment.

Reconstructing algorithm for frequency-resolved optical gating based on intelligent seeker optimization

Frequency-resolved optical gating (FROG) is a common technique of ultrashort pulse measurement. It reconstructs the test pulse by an iterative two-dimensional phase retrieval algorithm from a FROG trace. Now the most widely used FROG algorithm is principal component generalized projection (PCGP), yet its accuracy of pulse retrieval drops obviously under noise condition, and its iterative speed slows down significantly as the size of FROG trace increases. Actually, most of ultrashort pulses delivered from ultrafast oscillators and amplifiers as well as created in most scientific experiments are of smooth spectral phases, so that they can be determined by a few of dispersion coefficients. In this paper, we propose a FROG algorithm based on seeker optimization algorithm (SOA). After recording the spectrum of the test pulse, several main dispersion coefficients of the spectral phase of the pulse are searched directly by the SOA algorithm to fit the corresponding FROG trace. Then the shape of the test pulse can be uniquely reconstructed. Since this algorithm mainly operates in a spectral domain and its routine of iteration is much simpler than PCGP’s, faster speed and higher accuracy of pulse retrieval can be expected. In order to prove the advantages of SOA-FROG algorithm, numeral simulations are performed for test pulses with varying dispersion, in the cases without noise and with 1%, 5%, 10%, 20% noise levels, respectively. The simulation results show that the new algorithm performs much better than PCGP in accuracy and iteration speed. In the case without noise, 97% test pulses reach the condition of rigid convergence (FROG error <i>G</i> ≤ 10<sup>–4</sup>) after 1500 iteration circles by using the SOA, with an average FROG error <i>G</i> < 10<sup>–5</sup>. So the accuracy of pulse reconstruction by SOA is at least three orders of magnitude higher than by PCGP. In cases with different noise levels, the accuracy of pulse reconstruction by SOA is also much higher than by PCGP. By means of background-subtraction and filtering on the FROG traces, the retrieved pulse profiles almost accord with reality. Typically for a 256 × 256 FROG trace, SOA-FROG iterates 100.8 circles per second, about 5 times faster than PCGP. After 300 iteration circles by SOA in about 3 s, most of test pulses can finish their routines of reconstruction and reach high accuracy. Besides SHG-FROG, the SOA-FROG algorithm can also be utilized in other FROG techniques based on the 3<sup>rd</sup> order nonlinear optical effects. In summary, the SOA-FROG is expected to be suitable to the real-time pulse measurement with high accuracy in most of application cases. Yet some measures of improvement should be taken to reconstruct complex pulses with rough spectral phases or/and broken spectra.

Reconstruction of an ultrashort laser pulse from flexibly shaped FROG traces via ptychography algorithm

Frequency-resolved optical gating (FROG) is a popular technique for characterizing ultrashort laser pulses. This technique comprises two steps. First, a spectrogram, named FROG trace, is constructed for a pulse by measuring process. Second, an efficient algorithm is employed to retrieve the pulse information from its FROG trace. By expressing an arbitrary FROG trace using matrix multiplication, we confirm that the data on all the complex spectral components constituting the relative pulse are, in principle, encoded in the value of each point of the trace. Considering this fact and the characteristics of the measuring devices, flexibly shaped FROG traces are built by simultaneously applying low-pass filtering and up-sampling along the frequency axis and down-sampling along the delay axis to the conventional square ones. Furthermore, these practical traces can be used for the effective reconstruction of ultrashort laser pulses via the ptychography algorithm. Utilizing this specially designed trace will significantly reduce the difficulty and time-consumption in the first step of the FROG process.

Single-scan, dual-functional interferometer for fast spatio-temporal characterization of few-cycle pulses.

Accurate and fast characterization of spatio-temporal information of high-intensity, ultrashort pulses is crucial in the field of strong-field laser science and technology. While conventional self-referenced interferometers were widely used to retrieve the spatial profile of the relative spectral phase of pulses, additional measurements of temporal and spectral information at a particular position of the laser beam, however, were necessary to remove the indeterminacy, which increases the system complexity. Here we report an advanced, dual-functional interferometer that is able to reconstruct the complete spatio-temporal information of ultrashort pulses with a single scan of the interferometer arm. The setup integrates an interferometric frequency-resolved optical gating (FROG) with a radial shearing Michelson interferometer. Through scanning one arm of the interferometer, both the cross-correlated FROG trace at the central part of the laser beam and the delay-dependent interferograms of the entire laser profile are simultaneously obtained, allowing a fast three-dimensional reconstruction of few-cycle laser pulses.

Development of single-shot frequency-resolved optical gating for characterizing the instantaneous intensity and phase of LFEX laser pulses

Frequency-resolved optical gating (FROG) is a novel means of measuring the fast motion of a critical density surface during relativistic laser–plasma interaction. Herein, we present a design and demonstration results for a new single-shot FROG system and optical transport system for characterizing the instantaneous intensity and phase at the LFEX (Laser for Fast Ignition Experiment) laser facility at the Institute of Laser Engineering of Osaka University. At LFEX, the laser intensity at the vacuum window is intrinsically high because of two unique properties, namely, the large F-number of the off-axis parabolic mirror and the small radius of the interaction chamber. Consequently, to obtain an accurate FROG trace, attention must be paid to spectrum modulation due to self-phase modulation. The appropriate laser intensity for FROG operation was investigated experimentally, and an optical transport system with an energy attenuator composed of reflective optics was designed to eliminate the concern of spectrum modulation from measurements. A FROG trace recorded at LFEX shot with 161 J energy was reconstructed 100 times using an iterative phase-retrieval algorithm. Despite some differences in structure, the reconstructed spectrum agrees reasonably well with the spectrum obtained by a time-integrated spectrometer. This shows that the developed FROG system and the optical transport system can measure the instantaneous intensity and phase of a laser pulse without spectrum modulation.

Adaptive pre-shaping for ultrashort pulse control during propagation in AZO/ZnO multilayered metamaterial at the epsilon-near-zero spectral point

A novel approach to the application of an adaptive pre-shaping algorithm for ultrashort pulse distortion compensation during the propagation in AZO/ZnO multilayered metamaterials (thickness 300-700 nm) at the epsilon-near-zero spectral point is investigated. We show that using the Broyden-Fletcher-Goldfarb-Shanno algorithm to minimize the residual between frequency-resolved optical gating traces of the distorted output pulse and the zero phase pulse of 100 fs duration can yield increased output pulse field strength and a central frequency shift towards the epsilon-near-zero spectral point, which can be of future use for applications in ultrafast communication, signal processing, and super resolution imaging.

Extremely Robust Pulse Retrieval From Even Noisy Second-Harmonic-Generation Frequency-Resolved Optical Gating Traces

We further improve and then demonstrate the reliability of the previously introduced RANA approach for the second-harmonic-generation frequency-resolved optical gating (SHG FROG) phase-retrieval algorithm in the presence of significant noise in the traces. We provide a set of relevant parameters for this approach according to the noise level and trace size. Using it, we achieve 100% convergence for thousands of even extremely complex sample pulses, even when contaminated with the introduced significant noise.

Highly Reliable Frequency-Resolved Optical Gating Pulse-Retrieval Algorithmic Approach

Frequency-resolved optical gating (FROG) is widely used to measure ultrashort laser pulses, also providing an excellent indication of pulse-shape instabilities by disagreement between measured and retrieved FROG traces. FROG, however, requires -- but currently lacks -- an extremely reliable pulse-retrieval algorithm. So, this work provides one. It uses a simple procedure for directly retrieving the precise pulse spectrum from the measured trace. Additionally, it implements a multi-grid scheme, also quickly yielding a vastly improved guess for the spectral phase before implementing the entire measured trace. As a result, it achieves 100% convergence for the three most common variants of FROG for pulses with time-bandwidth products as high as 100, even with traces contaminated with noise. Here we consider the polarization-gate (PG) and transient-grating (TG) variants of FROG, which measure amplified, UV, and broadly tunable pulses. Convergence occurs for all of the >20,000 simulated noisy PG/TG FROG traces considered and is also faster.

Retrieving the coherent artifact in frequency-resolved optical gating

When confronted with a pulse train whose intensity and/or phase versus time varies from pulse to pulse, multi-shot pulse-measurement techniques usually exhibit a coherent artifact (CA), which substantially complicates the interpretation of the measurement. In frequency-resolved optical gating (FROG), such instabilities are indicated by discrepancies between the measured and retrieved FROG traces. Here we consider the simultaneous retrieval of the CA and the average pulse characteristics from a single FROG trace in the limit of significant fluctuations. We use a modified generalized projections algorithm. Two electric fields are simultaneously retrieved, while the data constraint is updated as the algorithm progresses using only the assumption that the trace can be modeled as the sum of two spectrograms, one corresponding to the pulse and the other corresponding to the CA. An additional flat-spectral-phase constraint is added to one of the fields to ensure that it only reacts to the presence of the CA. Using this novel retrieval method, the complete retrieval of the characteristics of pulses in an unstable train from FROG traces is demonstrated.

Frequency-Resolved Optical Gating Recovery via Smoothing Gradient

Frequency-resolved optical gating (FROG) is a popular technique for complete characterization of ultrashort laser pulses. The acquired data in FROG, called FROG trace, is the Fourier magnitude of the product of the unknown pulse with a time-shifted version of itself, for several different shifts. To estimate the pulse from the FROG trace, we propose an algorithm that minimizes a smoothed non-convex least-squares objective function. The method consists of two steps. First, we approximate the pulse by an iterative spectral algorithm. Then, the attained initialization is refined based upon a sequence of block stochastic gradient iterations. The algorithm is theoretically simple, numerically scalable, and easy-to-implement. Empirically, our approach outperforms the state-of-the-art when the FROG trace is incomplete, that is, when only few shifts are recorded. Simulations also suggest that the proposed algorithm exhibits similar computational cost compared to a state-of-the-art technique for both complete and incomplete data. In addition, we prove that in the vicinity of the true solution, the algorithm converges to a critical point. A Matlab implementation is publicly available at https://github.com/samuelpinilla/FROG.