High-sensitivity and high-speed measurements of ultrashort pulses as short as 74 fs at 1.9 µm using a GRENOUILLE device.

Ultrashort laser pulse sources in the wavelength range of 1.8 to 2 µm have many potential applications including medicine, materials processing, and sensing. In the use of such lasers, a crucial task is to measure their pulse's temporal intensity and phase. Such measurement devices are most useful when they are simple to build and operate and also have high speed and high sensitivity. The GRENOUILLE measurement device with few components, no moving parts, sensitivity of hundreds of picojoules, and measurement speed of hundreds of milliseconds, is commonly used to solve this problem at other wavelengths. In this paper, the measurement of ultrashort pulses by a GRENOUILLE device, developed using a silicon matrix sensor, for pulses in the wavelength range of 1.8 to 2 µm has been demonstrated. It is shown that ultrashort pulses with durations of 74 to 900 fs and a maximum spectral FWHM of 85 nm can be measured with this device. The recently developed ultra-reliable RANA approach was used for pulse retrieval from the measured traces. The device's performance was validated by comparing its measurements with those obtained by the robust FROG technique.

Simple single-shot complete spatiotemporal intensity and phase measurement of an arbitrary ultrashort pulse using coherent modulation imaging.

We propose a simple single-shot spatiotemporal measurement technique called coherent modulation imaging for the spatio-spectrum (CMISS), which reconstructs the full three-dimensional high-resolution characteristics of ultrashort pulses based on frequency-space division and coherent modulation imaging. We demonstrated it experimentally by measuring the spatiotemporal amplitude and phase of a single pulse with a spatial resolution of 44 µm and a phase accuracy of 0.04 rad. CMISS has good potential for high-power ultrashort-pulse laser facilities and can measure even spatiotemporally complicated pulses with important applications.

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.

Encoding the complete electric field of an ultraviolet ultrashort laser pulse in a near-infrared nonlinear-optical signal.

We introduce a variation on the cross-correlation frequency-resolved optical gating (XFROG) technique that uses a near-infrared (NIR) nonlinear-optical signal to characterize pulses in the ultraviolet (UV). Using a transient-grating XFROG beam geometry, we create a grating using two copies of the unknown UV pulse and diffract a NIR reference pulse from it. We show that, by varying the delay between the UV pulses creating the grating, the UV pulse intensity-and-phase information can be encoded into a NIR signal. We also implemented a modified generalized-projections phase-retrieval algorithm for retrieving the UV pulses from these spectrograms. We performed proof-of-principle measurements of chirped pulses and double pulses, all at 400 nm. This approach should be extendable deeper into the UV and potentially even into the extreme UV or x-ray range.

100% reliable algorithm for second-harmonic-generation frequency-resolved optical gating.

We demonstrate a novel algorithmic approach for the second-harmonic-generation (SHG) frequency-resolved optical gating (FROG) ultrashort-pulse-measurement technique that always converges and, for complex pulses, is also much faster. It takes advantage of the Paley-Wiener Theorem to retrieve the precise pulse spectrum-half the desired information-directly from the measured trace. It also uses a multi-grid approach, permitting the algorithm to operate on smaller arrays for early iterations and on the complete array for only the final few iterations. We tested this approach on more than 25,000 randomly generated complex pulses with time-bandwidth products up to 100, yielding SHG FROG traces to which noise was added, and have achieved convergence to the correct pulse in all cases. Moreover, convergence occurs in less than half the time for extremely large traces corresponding to extremely complex pulses.

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.

High-speed "multi-grid" pulse-retrieval algorithm for frequency-resolved optical gating.

We use an algorithmic technique called "multi-grid" to improve the speed of convergence of the cross-correlation frequency-resolved-optical-gating (XFROG) pulse-retrieval algorithm for very complex pulses. The multi-grid approach uses a smaller trace (N/4 × N/4) drawn from the original N × N trace for initial iterations, yielding poorer resolution and range, but proceeding ~16 times faster for such iterations. The pulse field rapidly retrieved from this smaller array then provides the initial guess for the larger, full array, significantly reducing the number of iterations required on the full array. We first find that, for simple pulses and their resulting simple traces, the original generalized-projections FROG and XFROG algorithms already converge in less time than is required to plot the retrieved pulse, so speed improvements for them appear irrelevant in general. Considering therefore only complex pulses and their resulting complex traces, we adapted the multi-grid algorithm to XFROG, the technique used for complex pulses whenever possible. We show that extending multi-grid to even smaller arrays is not helpful, but intermediate-size arrays of N/2 × N/2 are, further reducing the number of iterations on the full array and further decreasing convergence time. We obtain a factor of ~7 improvement in speed for very complex pulses with time-bandwidth products of 50 to 90. This approach does not require modifications to the algorithm itself and so can be used in conjunction with essentially all FROG algorithms for improved speed. And it retains FROG's ability to determine the pulse-shape stability in multi-shot measurements.

Complete measurement of spatiotemporally complex multi-spatial-mode ultrashort pulses from multimode optical fibers using delay-scanned wavelength-multiplexed holography.

We introduce a simple delay-scanned complete spatiotemporal intensity-and-phase measurement technique based on wavelength-multiplexed holography to characterize long, complex pulses in space and time. We demonstrate it using pulses emerging from multi-mode fiber. This technique extends the temporal range and spectral resolution of the single-frame STRIPED FISH technique without using an otherwise-required expensive ultranarrow-bandpass filter. With this technique, we measured the complete intensity and phase of up to ten fiber modes from a multi-mode fiber (normalized frequency V ≈10) over a ~3ps time range. Spatiotemporal complexities such as intermodal delay, modal dispersion, and material dispersion were also intuitively displayed by the retrieved results. Agreement between the reconstructed color movies and the monitored time-averaged spatial profiles confirms the validity to this delay-scanned STRIPED FISH method.

Measuring spatiotemporal ultrafast field structures of pulses from multimode optical fibers.

Ultrashort pulses emerging from multimode optical fibers are spatiotemporally complex, because inside these fibers the modes have different spatial intensity patterns and experience different propagation velocities and dispersions. To determine the spatiotemporal field from multimode fibers, we applied a technique for the complete measurement of the output pulses called a spatially and temporally resolved intensity and phase evaluation device: full information from a single hologram. It yields the complete electric field over space and time from multiple digital holograms, simultaneously recorded at different frequencies on a single camera frame. Using femtosecond pulses from a Ti:sapphire laser, we measured the first few linearly polarized modes (LP01, LP11, LP02, and LP21) inside several few-mode fibers. We also generate movies displaying the measured spatial, temporal, and spectral field features.

Visualizing spatiotemporal pulse propagation: first-order spatiotemporal couplings in laser pulses.

Even though a general theory of first-order spatiotemporal couplings exists in the literature, it is often difficult to visualize how these distortions affect laser pulses. In particular, it is difficult to show the spatiotemporal phase of pulses in a meaningful way. Here, we propose a general solution to plotting the electric fields of pulses in three-dimensional space that intuitively shows the effects of spatiotemporal phases. The temporal phase information is color-coded using spectrograms and color response functions, and the beam is propagated to show the spatial phase evolution. Using this plotting technique, we generate two- and three-dimensional images and movies that show the effects of spatiotemporal couplings.

Numerical simulations of holographic spatiospectral traces of spatiotemporally distorted ultrashort laser pulses.

We simulate traces for a catalog of spatiotemporally complex pulses measured using a single-shot complete spatiotemporal pulse-measurement technique we recently developed, called Spatially and Temporally Resolved Intensity and Phase Evaluation Device: Full Information from a Single Hologram (STRIPED FISH). The only such technique ever developed to our knowledge, STRIPED FISH measures the complete spatiotemporal intensity I(x,y,t) and phase ϕ(x,y,t) of an arbitrary laser pulse using an experimentally recorded trace consisting of multiple digital holograms, one for each frequency present in the pulse. To understand the effects of various spatiotemporal distortions on the STRIPED FISH trace, we numerically investigate STRIPED FISH trace features for a catalog of pulses, including the spatially and temporally transform-limited pulse, temporal and spatial double pulses, spherically focusing and diverging pulses, self-phase modulated and self-focusing pulses, spatiotemporally coupled pulses, and pulses with complex structures. As a practical example, we also analyze an experimentally recorded trace of a focusing pulse with spatial chirp. Overall, we find that, from STRIPED FISH's informative trace, significant spatiotemporal characteristics of the unknown pulse can be immediately recognized from the camera frame. This, coupled with its simple pulse-retrieval algorithm, makes STRIPED FISH an excellent technique for measuring and monitoring ultrafast laser sources.

Standards for ultrashort-laser-pulse-measurement techniques and their consideration for self-referenced spectral interferometry.

Issues important for new ultrashort-pulse-measurement techniques include the generation of theoretical example traces for common pulses, validity ranges, ambiguities, coherent artifacts, device calibration sensitivity, iterative retrieval convergence, and feedback regarding measurement accuracy. Unfortunately, in the past, such issues have gone unconsidered, yielding long histories of unsatisfactory measurements. We review these issues here in the hope that future proposers of new techniques will consider them without delay, and, as an example, we address them for a relatively new technique: self-referenced spectral interferometry.

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.

Reliable determination of pulse-shape instability in trains of ultrashort laser pulses using frequency-resolved optical gating.

We describe a reliable approach for determining the presence of pulse-shape instability in a train of ultrashort laser pulses. While frequency-resolved optical gating (FROG) has been shown to successfully perform this task by displaying a discrepancy between the measured and retrieved traces for unstable trains, it fails if its pulse-retrieval algorithm stagnates because algorithm stagnation and pulse-shape instability can be indistinguishable. So, a non-stagnating algorithm-even in the presence of instability-is required. The recently introduced Retrieved-Amplitude N-grid Algorithmic (RANA) approach has achieved extremely reliable (100%) pulse-retrieval in FROG for trains of stable pulse shapes, even in the presence of noise, and so is a promising candidate for an algorithm that can definitively distinguish stable and unstable pulse-shape trains. But it has not yet been considered for trains of pulses with pulse-shape instability. So, here, we investigate its performance for unstable trains of pulses with random pulse shapes. We consider trains of complex pulses measured by second-harmonic-generation FROG using the RANA approach and compare its performance to the well-known generalized-projections (GP) algorithm without the RANA enhancements. We show that the standard GP algorithm frequently fails to converge for such unstable pulse trains, yielding highly variable trace discrepancies. As a result, it is an unreliable indicator of instability. Using the RANA approach, on the other hand, we find zero stagnations, even for highly unstable pulse trains, and we conclude that FROG, coupled with the RANA approach, provides a highly reliable indicator of pulse-shape instability. It also provides a typical pulse length, spectral width, and time-bandwidth product, even in cases of instability.

Optical-parametric-amplification imaging of complex objects.

We used ultrafast Fourier-plane optical-parametric-amplification (OPA) imaging to simultaneously image, wavelength-shift, and amplify complex two-dimensional objects with spatial features from 1.1 to 10.1 line pairs/millimeter (lp/mm) in the vertical dimension and from 2.0 to 16.0 lp/mm in the horizontal dimension, corresponding to a two-dimensional space-bandwidth product (SBP) of ~46,000. This represents an increase in image complexity over previous analogous OPA imaging systems by over three orders of magnitude. We observe both wavelength-shifting the image from 930 nm to a wavelength of 700 nm and image amplification by two orders of magnitude. Our wavelength-shifted image has a SBP of ~30,000.

Complete single-shot measurement of arbitrary nanosecond laser pulses in time.

For essentially all applications, laser pulses must avoid variations in their intensity and phase within a pulse and from pulse to pulse. Currently available devices work very well for both long (>10ns) and short (<100ps) pulses. But intermediate (~ns) pulses remain difficult to measure and, not surprisingly, are the least stable. Here we describe a simple, elegant, complete, all-optical, single-shot device that measures ~ns pulses and that does not require a reference pulse or assumptions about the pulse shape. It simultaneously achieves a very high spectral resolution of <1pm and a very large delay range of ~10ns (several meters of light travel). It accomplishes both goals using high-efficiency, high-finesse etalons: one to generate high angular dispersion for a high-resolution spectrometer, and another to tilt the pulse front by ~89.9° without distorting it in time. Using this device, we completely measure microchip and fiber-amplifier pulses.

All-fiber ultrafast amplifier at 1.9 µm based on thulium-doped normal dispersion fiber and LMA fiber compressor.

The duration reduction and the peak power increase of ultrashort pulses generated by all-fiber sources at a wavelength of [Formula: see text] are urgent tasks. Finding an effective and easy way to improve these characteristics of ultrafast lasers can allow a broad implementation of wideband coherent supercontinuum sources in the mid-IR range required for various applications. As an alternative approach to sub-100 fs pulse generation, we present an ultrafast all-fiber amplifier based on a normal-dispersion germanosilicate thulium-doped active fiber and a large-mode-area silica-fiber compressor. The output pulses have the following characteristics: the central wavelength of [Formula: see text], the repetition rate of 23.8 MHz, the energy per pulse period of 25 nJ, the average power of 600 mW, and a random output polarization. The pulse intensity and phase profiles were measured via the second-harmonic-generation frequency-resolved optical gating technique for a linearly polarized pulse. The linearly polarized pulse has a duration of 71 fs and a peak power of 128.7 kW. The maximum estimated peak power for all polarizations is 220 kW. The dynamics of ultrashort-pulse propagation in the amplifier were analyzed using numerical simulations.

Measuring temporally complex ultrashort pulses using multiple-delay crossed-beam spectral interferometry.

We introduce a spectral-interferometry (SI) technique for measuring the complete intensity and phase of relatively long and very complex ultrashort pulses. Ordinarily, such a method would require a high-resolution spectrometer, but our method overcomes this need. It involves making multiple measurements using SI (in its SEA TADPOLE variation) at numerous delays, measuring many temporal pulselets within the pulse, and concatenating the resulting pulselets. Its spectral resolution is the inverse delay range--many times higher than that of the spectrometer used. Our simple proof-of-principle implementation of it provided 71 fs temporal resolution and a temporal range of 100 ps using a few-cm low-resolution spectrometer.

Measuring extremely complex pulses with time-bandwidth products exceeding 65,000 using multiple-delay crossed-beam spectral interferometry.

We measure the complete electric field of extremely complex ultrafast waveforms using the simple linear-optical, interferometric pulse-measurement technique, MUD TADPOLE. The waveforms were measured with ~40 fs temporal resolution over a temporal range of ~3.5 ns and had time-bandwidth products exceeding 65,000. The approach is general and could allow the measurement of arbitrary optical waveforms.

Highly simplified device for measuring the intensity and phase of picosecond pulses.

We demonstrate an extremely simple frequency-resolved-optical-gating (GRENOUILLE) device for measuring the intensity and phase of relatively long--ps--pulses. In order to achieve the required high spectral resolution and large temporal range, it uses a few-cm-thick second-harmonic-generation crystal in the shape of a pentagon. This has the additional advantage of reducing the device's total number of components to as few as three simple easily aligned optics, making it the simplest device ever developed for complete pulse measurement. We report complete intensity-and-phase measurements of pulses up to 15ps long with a time-bandwidth product of 21.