Frequency-resolved Optical Gating Research Articles

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.

Asymmetric interferometric frequency resolved optical gating for complete unambiguous ultrashort pulse characterisation

We propose a modification of the second-harmonic generation frequency resolved optical gating method (SHG-FROG) utilizing asymmetric spectral interferometry (aiFrog) for complete unambiguous reconstruction of ultrashort optical pulse intensity and phase. The large amount of information encoded in the aiFrog trace allows a straightforward calculation of the fundamental pulse spectrum and a direct reconstruction of the pulse envelope and phase. A simple and robust iterative algorithm with fast convergence is developed for pulse reconstruction from the aiFrog trace, taking advantage of large data redundancy and noise averaging. Due to the asymmetry of the setup, our method is free from the known challenges of a standard SHG-FROG (direction-of-time ambiguity, almost identical FROG traces for well separated pulses with different phases and for asymmetric well separated pulses). The method is highly sensitive to the weak satellite pulse of the main pulse, which can be used to track pre- or post-pulses even without full processing of the measured aiFrog trace.

Observation of Ultrashort Laser Pulse Evolution in a Silicon Photonic Crystal Waveguide

Using the sum frequency generation cross-correlation frequency-resolved optical gating (SFG-XFROG) measurement setup, we observed the soliton evolution of low energy pulse in an Si photonic crystal waveguide, and it exhibited the pulse broadening, blue shift, and evident pulse acceleration. The soliton evolution was also investigated by nonlinear Schrödinger equation (NLSE) modelling simulation, and the simulated results agreed well with the experimental measurements. The effects of waveguide length on the pulse evolution were analyzed; the results showed that the pulse width changed periodically with increasing waveguide length. The results further the understanding of the ultra-fast nonlinear dynamics of solitons in silicon waveguides, and are helpful to soliton-based functional elements on CMOS-compatible platforms.

V-FROG—single-scan vectorial FROG

We propose and experimentally demonstrate single-scan vectorial frequency-resolved optical gating (FROG) which characterizes the amplitude, phase and polarization of ultrashort laser pulses using a single measured spectrogram. It is carried out by rotating the polarization of the incoming pulse (using a half-wavelength waveplate), in parallel to scanning the delay between the pulse and its replica in an otherwise ordinary FROG apparatus. A ptychography-based phase retrieval algorithm extracts the full pulse information from the recorded spectrogram. We numerically show that this method is reliable and use it to experimentally reconstruct a pulse with intricate time-dependent polarization. We also show that this method can be used to remove time-reversal ambiguity of second harmonic generation FROG.

FROG-measurement based phase retrieval for analytic signals

While frequency-resolved optical gating (FROG) is widely used in characterizing the ultrafast pulse in optics, analytic signals are often considered in time-frequency analysis and signal processing, especially when extracting instantaneous features of events. In this paper we examine the phase retrieval (PR) problem of analytic signals in CN by their FROG measurements. After establishing the ambiguity of the FROG-PR of analytic signals, we found that the FROG-PR of analytic signals of even lengths is different from that of analytic signals of odd lengths, and it is also different from the case of B-bandlimited signals with B≤N/2. The existing approach to bandlimited signals can be applied to analytic signals of odd lengths, but it does not apply to the even length case. With the help of two relaxed FROG-PR problems and a translation technique, we develop an approach to FROG-PR for the analytic signals of even lengths, and prove that in this case the generic analytic signals can be uniquely (up to the ambiguity) determined by their (3N/2+1) FROG measurements. Phase derivative (or instantaneous frequency) is a significant feature for signal analysis. As an application of our main result, an approach is established to determine the phase derivatives of decaying signals by exploiting the ambiguity.

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.

Solving nonlinear integral equations for laser pulse retrieval with Newton's method

We present an algorithm based on numerical techniques that have become standard for solving nonlinear integral equations: Newton's method, homotopy continuation, the multilevel method, and random projection to solve the inversion problem that appears when retrieving the electric field of an ultrashort laser pulse from a two-dimensional intensity map measured with frequency-resolved optical gating (FROG), dispersion-scan, or amplitude-swing experiments. Here we apply the solver to FROG and specify the necessary modifications for similar integrals. Unlike other approaches we transform the integral and work in time domain where the integral can be discretized as an overdetermined polynomial system and evaluated through list autocorrelations. The solution curve is partially continues and partially stochastic, consisting of small linked path segments and enables the computation of optimal solutions in the presents of noise. Interestingly, this is an alternative method to find real solutions of polynomial systems, which are notoriously difficult to find. We show how to implement adaptive Tikhonov-type regularization to smooth the solution when dealing with noisy data, and we compare the results for noisy test data with a least-squares solver and propose the L-curve method to fine-tune the regularization parameter.

Simulations of wavelength-multiplexed holography for single-shot spatiotemporal characterization of NIF's advanced radiographic capability (ARC) laser.

We simulate the use of a newly developed single-shot wavelength-multiplexed holography-based diagnostic, STRIPED FISH, to fully characterize the as-delivered laser pulses of the National Ignition Facility's Advanced Radiographic Capability (NIF-ARC) laser. To that end, we have performed simulations of the NIF-ARC pulse incorporating (a) a time-integrated spatial-profile measurement and a complete temporal-intensity-and-phase measurement using a frequency resolved optical gating, but without any spatiotemporal pulse characterizations, and (b) simulated first-order spatiotemporal distortions, which could be measured on a single shot if a STRIPED FISH device were deployed.

All-optical single-shot complete electric field measurement of extreme ultraviolet free electron laser pulses

Recent advances in ultrafast extreme ultraviolet (EUV) and x-ray light sources provide direct access to fundamental time and length scales for biology, chemistry, and materials physics. However, such light pulses are challenging to measure due to the need for femtosecond time resolution at difficult-to-detect wavelengths. Also, single-shot measurements are needed because severe pulse-to-pulse fluctuations are common. Here we demonstrate single-shot, complete field measurements by applying a novel version of frequency resolved optical gating. An EUV free electron laser beam creates a transient grating containing the pulse’s electric field information, which is read out with a 400 nm probe pulse. By varying the time delay between two copies of the EUV pump, rather than between the pump and the probe, we separate the needed coherent wave mixing from the slow incoherent response. Because this approach uses photoionization, it should be applicable from the vacuum ultraviolet to hard x rays.

Single-shot dispersion sampling for optical pulse reconstruction.

We present a novel approach to single-shot characterization of the spectral phase of broadband laser pulses. Our method is inexpensive, insensitive to alignment and combines the simplicity and robustness of the dispersion scan technique, that does not require spatio-temporal pulse overlap, with the advantages of single-shot pulse characterization methods such as single-shot frequency-resolved optical gating at a real-time reconstruction rate of several Hz.

Measuring an ultrashort, ultraviolet pulse in a slowly responding, absorbing medium.

Frequency-resolved optical gating (FROG) is a common technique for measuring ultrashort laser pulses using an instantaneous, nonlinear-optical interaction as a fast time-gate to measure the pulse intensity and phase. But at high frequencies, materials are often absorbing and it is not always possible to find a medium with a fast nonlinear-optical response. Here we show that an ultrashort, ultraviolet (UV) pulse can be measured in a strongly absorbing medium, using the absorption as the nonlinear-optical time-gate. To do this, we build on our recent implementation of FROG, known as induced-grating cross-correlation FROG (IG XFROG), where an unknown, higher-frequency pulse creates a transient grating that is probed with a lower-frequency, more easily detectable reference pulse. We demonstrate this with an 800 nm reference pulse to characterize 400 nm or 267 nm pulses using ZnS as the nonlinear-optical medium, which is absorptive at and below 400 nm. By scanning the delay between the two UV pulses which create the transient grating, we show that the phase-sensitive instantaneous four-wave-mixing contribution to the nonlinear signal field can be detected and separated from the slower, incoherent part of the response. Measuring a spectrally-resolved cross-correlation in this way and then applying a simple model for the response of the medium, we show that a modified generalized projections (GP) phase-retrieval algorithm can be used to extract the pulse amplitude and phase. We test this approach by measuring chirped UV pulses centered at 400 nm and 267 nm. Since interband absorption (or even photoionization) is not strongly wavelength-dependent, we expect IG XFROG to be applicable deeper into the UV.

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.

Improving laser standards for three-photon microscopy.

.Significance: Three-photon excitation microscopy has double-to-triple the penetration depth in biological tissue over two-photon imaging and thus has the potential to revolutionize the visualization of biological processes in vivo. However, unlike the plug-and-play operation and performance of lasers used in two-photon imaging, three-photon microscopy presents new technological challenges that require a closer look at the fidelity of laser pulses.Aim: We implemented state-of-the-art pulse measurements and developed innovative techniques for examining the performance of lasers used in three-photon microscopy. We then demonstrated how these techniques can be used to provide precise measurements of pulse shape, pulse energy, and pulse-to-pulse intensity variability, all of which ultimately impact imaging.Approach: We built inexpensive tools, e.g., a second harmonic generation frequency-resolved optical gating (SHG-FROG) device and a deep-memory diode imaging (DMDI) apparatus to examine laser pulse fidelity.Results: First, SHG-FROG revealed very large third-order dispersion (TOD). This extent of phase distortion prevents the efficient temporal compression of laser pulses to their theoretical limit. Furthermore, TOD cannot be quantified when using a conventional method of obtaining the laser pulse duration, e.g., when using an autocorrelator. Finally, DMDI showed the effectiveness of detecting pulse-to-pulse intensity fluctuations on timescales relevant to three-photon imaging, which were otherwise not captured using conventional instruments and statistics.Conclusions: The distortion of individual laser pulses caused by TOD poses significant challenges to three-photon imaging by preventing effective compression of laser pulses and decreasing the efficiency of nonlinear excitation. Moreover, an acceptably low pulse-to-pulse amplitude variability should not be assumed. Particularly for low repetition rate laser sources used in three-photon microscopy, pulse-to-pulse variability also degrades image quality. If three-photon imaging is to become mainstream, our diagnostics may be used by laser manufacturers to improve system design and by end-users to validate the performance of their current and future imaging systems.

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.

Direct reconstruction of two ultrashort pulses based on non-interferometric frequency-resolved optical gating

We describe a non-interferometric ultrashort-pulse measurement technique based on frequency-resolved optical gating (FROG) with which pulses can be reconstructed directly, i.e. non-iteratively. Two different FROG spectrograms are measured, which represent the only information required to reconstruct the amplitudes and phases of two independent input pulses. The direct reconstruction method is demonstrated with a single-shot FROG setup used to obtain the spectrograms generated from two synchronized input pulses. To demonstrate and determine the reconstruction quality for complex pulses, a programmable pulse shaper is used to modify the pulses sourced from a Kerr-lens mode-locked Ti:sapphire oscillator.

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.

Few-cycle optical pulse characterization under phase-mismatching.

The phase-matching bandwidth of nonlinear crystal is of great significance in ultrashort laser pulse characterization. In order to satisfy the phase-matching bandwidth, ultra-thin nonlinear crystals are generally required. However, the significantly reduced conversion efficiency, as well as the machining difficulties, limits its applications. Here, we show that sufficient spectrum bandwidth response can be achieved for a thick crystal when the phase-matching wavelength is tuned outside of the spectral window of the measured pulse. By applying this phenomenon to a single-shot second-harmonic generation frequency resolved optical gating (SHG-FROG) device, we successfully characterized a few-cycle pulse using a 150µmβ-barium borate (BBO) crystal. The accuracy of the method was verified by comparing the conventional pulse retrieving approach with a 5µm BBO crystal, which has a sufficient phase-matching bandwidth.

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.

Broad spectral range few-cycle laser pulses characterization by using a FASI device

Full characterization of few-cycle laser pulses is necessary in many applications. FROG is one of the most widely used full characterization techniques so far, and SRSI is another fresh one with attractive capacity. In this study, we develop a simple device FASI (frequency-resolved optical gating and self-referenced spectral interferometry), which combines the FROG and SRSI in a single device, and both of them are based on the third-order nonlinear effect of transient grating. It is compact with a size of 340 × 240 × 80 mm3. The device owns the advantages of the TG-SRSI method, which can characterize few-cycle pulses with broad spectral range from UV to mid-IR in single-shot mode for well compressed pulses. What’s more, for complex or large chirped pulses, it can also complete the characterization task by using the multi-shot TG-FROG mode. Two few-cycle pulses centered at 800 nm and 1800 nm have been characterized by using this device to verify its ability. It turned out that the proposed FASI device is a powerful tool for broad spectral range few-cycle laser pulses characterization.

Temperature and Pulse-Energy Range Suitable for Femtosecond Pulse Transmission in Si Nanowire Waveguide

We experimentally measured the femtosecond pulse transmission through a silicon-on-insulator (SOI) nanowire waveguide under different temperatures and input pulse energy with a cross-correlation frequency-resolved optical gating (XFROG) measurement setup. The experimental results demonstrated that the temperature and pulse energy dependence of the Si photonic nanowire waveguide (SPNW) is interesting rather than just monotonous or linear, and that the suitable temperature and pulse-energy range is as suggested in this experiment, which will be valuable for analyzing the practical design of the operating regimes and the fine dispersion engineering of various ultrafast photonic applications based on the SPNWs. The research results will contribute to developing the SPNWs with photonic elements and networks compatible with mature complementary metal–oxide–semiconductors (CMOS).