We extend the time-domain ptychographic iterative engine to generalized spectral phase-only transfer functions. The modified algorithm, i$^2$PIE, is described and its robustness is demonstrated by different numeric simulations. The concept is experimentally verified by reconstruction of a complex supercontinuum pulse from an all normal dispersion fiber.

Summary form only given. Ultrashort laser pulse characterization presents us with an interesting problem since these pulses are temporally too short to directly measure. Indirect measurement of pulses are possible through a variety of pulse reconstruction schemes such as FROG[1], SPIDER[2], MIIPS[3] and many more. Ptychography[4] a lens-less imaging technique in the spatial domain used to reconstruct images from sets of recorded diffraction patterns by application of the ptychographic iterative engine (P1E)[5] was recently migrated to the time-domain[6]. The ptychographic reconstruction algorithm has several advantages such as ease of implementation, quick convergence and being based in in the Fourier transform, the temporal resolution is determined by the spectral bandwidth and the temporal window is determined by the spectral resolution. Further the method does not require a square sample matrix nor a regularly spaced time delayed sample set. Pulse cross -correlation type schemes have been demonstrated using time-domain ptychography [6-11]. In this family of measurements an unknown pulse E(t) is mixed in a non-linear medium (NLM) with a time delayed probe pulse P(t) and an intensity spectrum I(co) is measured, where in some of the above references the probe is known, Fig. 1(a)i, and in some generated from the input pulse Fig. 1(a)ii by applying a filter H. In our latest work we show that one can generalize the PIE algorithm for application to single beam measurements, Fig. 1(a)iii, with excellent results. Here a known phase only transfer function from a set h n , is applied to the input pulse sequentially, in each case recording an intensity spectrum, i(o) = 1g. {[E(t) x h n (t)] 2 }1 2 , ( 1 ) which we refer to as i 2 P1E. Here Jr refers to the Fourier transform and x denotes the convolution operation. Once the pulse is characterized, the transfer function is effectively removed. In Fig. 1(b), (c) and (d) we show an example of a transfer function set, the resultant spectrogram and the reconstructed spectral amplitude and phase respectively. The i 2 P1E method is very versatile, broad in definition and performance is robust.

One of the most robust techniques solving the so-called phase problem in X-ray diffraction imaging is ptychography. It produces the correct real-space image if the illumination beam is known [1], but works even if it is unknown [2]. In 2015 we were the first to extend ptychography to the time domain and further to the reconstruction of temporal objects. In comparison to existing algorithms, ptychography minimizes the data to be recorded and processed, and thereby significantly reduces the computational time for reconstruction.

Dedicated simulations show that the application of time-domain ptychography to angular photo-electron streaking data allows shot-to-shot reconstruction of individual X-ray free electron laser pulses. Specifically, in this study, we use an extended ptychographic iterative engine to retrieve both the unknown X-ray pulse and the unknown streak field. We evaluate the quality of reconstruction versus spectral resolution, signal-to-noise and sampling size of the spectrogram.

Summary form only given. Ptychography, a lens-less imaging technique which reconstructs the spatial phase from measured diffraction patterns, has recently been migrated to the time domain. Time-domain ptychography requires recording several spectral measurements, each with a different relative time delay, of the product of two electrical fields where the one electrical field is seen as a temporal object and the other a temporal probe. Time domain ptychography allows a wide range of temporal objects to be reconstructed with a very versatile range of probe functions. There are at present three reconstruction algorithms which can be used depending on the temporal probe function used. These are variants on the ptychographic iterative engine (PIE). First we have shown that one can apply ptychography in the time domain by migrating the PIE algorithm to a one-dimensional space. For standard time-domain ptychography, the requirement is that the probe pulse is known. We then migrated the extended PIE (ePIE) algorithm to the time domain, and it was demonstrated with an experiment in the attosecond regime. We also showed that if one has some intrinsic knowledge about the probe, as is the case when the probe is derived from the temporal object by application of a known transfer function, the temporal object can be reconstructed. For this case, we developed the intrinsic PIE (iPIE) algorithm and showed that one can use it in order to do pulse characterization.

We demonstrate that time-domain ptychography, a recently introduced ultrafast pulse reconstruction modality, has properties ideally suited for the temporal characterization of complex light pulses with large time-bandwidth products as it achieves temporal resolution on the scale of a single optical cycle using long probe pulses, low sampling rates, and an extremely fast and robust algorithm. In comparison to existing techniques, ptychography minimizes the data to be recorded and processed, and drastically reduces the computational time of the reconstruction. Experimentally we measure the temporal waveform of an octave-spanning, 3.5 ps long supercontinuum pulse generated in photonic crystal fiber, resolving features as short as 5.7 fs with sub-fs resolution and 30 dB dynamic range using 100 fs probe pulses and similarly large delay steps.

This note reports author corrections that were omitted from Appl. Opt.55, 5008 (2016) 10.1364/AO.55.005008 in error during production. The article was corrected online 23 June 2016.

We demonstrate that time-domain ptychography, a recently introduced iterative ultrafast pulse retrieval algorithm, has properties well suited for the reconstruction of complex light pulses with large time-bandwidth products from a cross-correlation frequency-resolved optical gating (XFROG) measurement. It achieves temporal resolution on the scale of a single optical cycle using long probe pulses and low sampling rates. In comparison to existing algorithms, ptychography minimizes the data to be recorded and processed, and significantly reduces the computational time of the reconstruction. Experimentally, we measure the temporal waveform of an octave-spanning, 3.5 ps long, supercontinuum pulse generated in photonic crystal fiber, resolving features as short as 5.7 fs with sub-fs resolution and 30 dB dynamic range using 100 fs probe pulses and similarly large delay steps.

We present a theoretical analysis of laser cutting of metals based on a model originally proposed by Niziev and an extension which includes heat conduction. Specifically, we investigate the dependence of relevant parameters, such as maximum cutting speed, shape of the cutting front et cetera, on wavelength, polarization, and laser beam properties. A special emphasis is on the comparison between results obtained for lasers around 1 μm and CO2 lasers at 10 μm wavelength, respectively. To test the model we compare the numerical solutions for a cold-work steel work-piece to experimental results presented elsewhere. We find good agreement between theoretical and experimental observations. The main differences between laser cutting with 1 and 10 μm lasers arise from the different absorptivity profiles and absorbed intensities. In most of the analysed cases the computed mean absorbed intensities as well as the absorbed intensity profiles show that the energy transfer is more efficient for laser cutting with 1 μm lasers.

We present a derivation and, based on it, an extension of a model originally proposed by V.G. Niziev to describe continuous wave laser cutting of metals. Starting from a local energy balance and by incorporating heat removal through heat conduction to the bulk material, we find a differential equation for the cutting profile. This equation is solved numerically and yields, besides the cutting profiles, the maximum cutting speed, the absorptivity profiles, and other relevant quantities. Our main goal is to demonstrate the model’s capability to explain some of the experimentally observed differences between laser cutting at around 1 and 10 μm wavelengths. To compare our numerical results to experimental observations, we perform simulations for exactly the same material and laser beam parameters as those used in a recent comparative experimental study. Generally, we find good agreement between theoretical and experimental results and show that the main differences between laser cutting with 1- and 10-μm beams arise from the different absorptivity profiles and absorbed intensities. Especially the latter suggests that the energy transfer, and thus the laser cutting process, is more efficient in the case of laser cutting with 1-μm beams.