Coherent artifact in modern pulse measurements

Abstract

We simulate multi-shot intensity-and-phase measurements of unstable ultrashort-pulse trains using frequency-resolvedoptical-gating (FROG) and spectral phase interferometry for direct electric-field reconstruction (SPIDER). Both techniques fail to reveal the pulse structure. FROG yields the average pulse duration and suggests the instability by exhibiting disagreement between measured and retrieved traces. SPIDER under-estimates the average pulse duration but retrieves the correct average pulse spectral phase. An analytical calculation confirms this behavior.When a measurement averages over many different events, it faces an impossible task: providing one result when no single result can be correct. In ultrafast optics, this issue has been particularly problematic for multi-shot intensity-autocorrelation measurements of trains of different complex pulses. The resulting measured autocorrelation trace vs. delay (see Fig. 1) consists of a narrow spike atop a broad structureless background. Given that the task is inherently impossible, it is worth asking what we should expect. The answer is that the technique should yield a pulse with some characteristics of the typical pulse in the train (e.g., its duration) and also give some indication of the stability, or randomness, of the pulses in the train. Although autocorrelation actually does yield some of this information, it yields neither the pulse intensity nor its phase for the case of a stable train of identical pulses and so is now generally considered obsolete.The next question-one whose answer is long overdue-is how more modern pulse-measurement techniques, which do yield the pulse intensity and phase for a stable train of identical pulses, react to an unstable train of random pulses. So here we consider this question for frequency-resolved optical gating (FROG)[2] and spectral-phase interferometry for direct electric-field reconstruction (SPIDER) [3], the latter of which also allows an analytical result.For the simulations, we chose a nonrandom component E() with a flat phase and Gaussian intensity of temporal FWHM 12t, where t is the temporal sampling rate. To E(), we added an equal-energy random component E rand () with the same spectrum, but with random spectral phase, which we then Fourier-filtered (made somewhat less random and hence the resulting pulse shorter) by different amounts to yield two trains of variably structured pulses with different average complexities and durations.[4] The random trains' resulting average pulse lengths (FWHM) were 26t and 54t. Figure 2 shows typical pulses in the two trains. All frequency units are in 2/(Nt), where N is the SPIDER array size (4096).We computed multi-shot traces for secondharmonic-generation (SHG) FROG and SPIDER. FROG involves measuring a self-gated spectrogram of the pulse field, while SPIDER measures a spectral interferogram of the pulse and a frequency-sheared and delayed replica of it. SPIDER requires a frequency shear, , which we chose to be 30/(Nt), and a pulse separation, T, which we chos...

Self-Guided Propagation of Ultrashort Laser Pulses in the Anomalous Dispersion Region of Transparent Solids: A New Regime of Filamentation

“…It is free from the coherence artifact due to shot-to-shot instability that can arise with multi-shot characterization techniques [17]. As the signal-to-noise ratio on the spectrometer was low, the measurements were integrated over ten shots.…”

Unstable and Multiple Pulsing Can Be Invisible to Ultrashort Pulse Measurement Techniques

“…Previous publications addressing instability in SPIDER have included some analytical considerations of averaged SPIDER measurements [7,8], and we will use those calculations as a starting point for considering the specific case of double pulses. Given a spectral shear Ω and an internal pulse separation T in the SPIDER apparatus, a general expression for the ideal SPIDER trace of a single pulse as a function of the pulse complex electric field E(ω) is:…”

“…Recently, a few papers have addressed the unfortunate consequences of averaging over a train of pulses with fluctuating pulse shapes in attempts to measure them using modern ultrashort-pulse measurements [7][8][9][10]. Also, shockingly, modern techniques based on interferometry were found to measure only the coherent artifact.…”

“…As mentioned earlier, simulations of fluctuating pulse shapes have demonstrated that several measurement techniques based on interferometry have considerable difficulty detecting instability and yield only the coherent artifact [7,8]. This is alarming, especially because several popular techniques, including SPIDER, display these problems and so conceal potential instability from the user and can report, for example, pulse lengths considerably shorter than are in fact present.…”

Recent Developments in Experimental Techniques for Measuring Two Pulses Simultaneously

“…Over the years, researchers have proposed different techniques to accomplish this two-pulse measurement task in a single device, such as Blind-FROG [18][19][20], complete reconstruction of attosecond bursts (CRAB) [21,22] very advanced method for phase and intensity retrieval of e-fields (VAMPIRE) [23,24] and Double Blind FROG [25,26]. Several articles have reviewed the commonly used single-pulse measurement techniques [27][28][29][30], so we will focus on the two-pulse measurement problem and review the aforementioned techniques.…”