Complementary ultrashort laser pulse characterizationusing MOSAIC and SHG FROG
Daniel A. Bender1,* and Mansoor Sheik-Bahae2
1Sandia National Laboratories, P. O. Box 5800, Albuquerque, New Mexico, 87185, USA2Department of Physics and Astronomy, University of New Mexico, 800 Yale Boulevard NE,
Albuquerque, New Mexico 87131, USA*Corresponding author: [email protected]
Received March 17, 2010; revised May 27, 2010; accepted May 31, 2010;posted June 7, 2010 (Doc. ID 125649); published June 23, 2010
One of the most common ultrashort pulse characteriza-tion techniques available is second-harmonic generationfrequency-resolved optical gating (SHG FROG). Perform-ing pulse characterization using SHG FROG consists ofan experimental apparatus and an iterative phase retrie-val algorithm to extract the intensity and phase [1]. Theprimary success of SHG FROG is based on its ability toquantitatively characterize short pulses. However, muchcan be learned from a real-time, noniterative algorithmperformed on the SHG FROG dataset, giving a trace thatis both visually sensitive and easily interpreted for thepresence of pulse chirp.Preferably, the SHG FROG trace would give direct in-
sight on the phase of the pulse from a visual inspection.In such a case, no complicated time-consuming iterativeretrieval would be needed. Some thought has been givento visually interpreting the SHG FROG trace. In [2] it wasnoted that a horseshoe shape about zero delay was char-acteristic of excessive third-order dispersion. However,the observation of the horseshoe shape is difficult in thatit is not a background-free estimation. That is, there canbe a significant amount of additional structure in the SHGFROG trace that does not resemble a horseshoe shape.Additionally, a spectrally normalized SHG FROG tracehas been developed [3]. Every autocorrelation trace inthe time domain at its second-harmonic wavelengthvalue is normalized to a peak value of unity. In this ren-dering, a pulse with an arbitrary spectrum and a flat spec-tral phase would give a streak of uniform thickness aboutzero delay. Interpretation of this trace is subjective. Theconfirmation of a uniform thickness for near-transform-limited pulses is visually difficult. Subtle departures fromthe transform limit are likely to go unnoticed, as the traceis not background free.The SHG FROG trace can be made more insightful by
augmenting it with a modified spectrum autointerfero-metric correlation (MOSAIC) trace. Initially, MOSAICwas developed as a real-time spectral filter for second-order interferometric autocorrelaton, producing awaveform visually sensitive to chirp [4,5]. Subsequentadditions to MOSAIC involved efficient algorithm devel-opment, interpretation, and spectral phase retrieval[6–8]. It has recently been shown that MOSAIC can begenerated from a single shot (i.e., noninterferometric)
geometry by making use of the intensity autocorrelation,gðτÞ, and second-harmonic power spectrum, SSHGðωÞ [8]:
SMOSAICðτÞ ¼ gðτÞ − jgpðτÞj; ð1Þ
where gpðτÞ ¼ F−1½SSHGðωÞ� with F−1 denoting the in-verse Fourier transform. If gðτÞ and SSHGðωÞ are mea-sured independently, gpðτÞ should be multiplied by aprefactor (γ ¼ gð0Þ=jgpð0Þj) to ensure SMOSAICð0Þ ¼ 0.The function SMOSAICðτÞ has the unique property of beingequal to zero for all τ when a pulse is unchirped; any de-parture from an unchirped pulse results in a deflectionfrom zero. Here we show SMOSAICðτÞ can be obtained di-rectly from the SHG FROG dataset. No additional experi-mental hardware beyond that necessary to measure theSHG FROG trace is needed. The rendering of MOSAICfrom SHG FROG facilitates direct, immediate insighton pulse chirp. No iterative reconstruction is requiredand, hence, the production of the MOSAIC trace is realtime in all cases, independent of pulse complexity. TheSHG FROG dataset and the generalized projections algo-rithm do a good job of quantitative pulse reconstruction,while MOSAIC performs well as an extremely sensitivequalitative tool for background-free visual pulse chirpcharacterization. The merging of these two techniquesprovides complementary pulse assessment and is thefocus of this Letter.
The generation of MOSAIC from SHG FROG is under-stood by considering the functional form of the SHGFROG spectrogram:
ISHGFROGðω; τÞ ¼����Z
EðtÞEðt − τÞeiωtdt����2; ð2Þ
where EðtÞ is the time-dependent complex electricfield [1]. The spectral segment at zero delay is thesecond-harmonic power spectrum, ISHGFROGðω; τ ¼ 0Þ ¼j R EðtÞ2eiωtdtj2 ≡ SSHGðωÞ, while, by applying theParseval's identity, we note that spectral integration ofthe FROG trace is the intensity autocorrelationRISHGFROGðω; τÞdω ¼ R jEðtÞEðt − τÞj2dt≡ gðτÞ. Therefore,
both constituents of SMOSAICðτÞ in Eq. (1) are easily com-puted from the corresponding FROG trace. Given thatthe FROG trace is measured correctly according to
Eq. (2), its corresponding SMOSAICðτÞ should be sym-metric around—and must vanish at—zero delay (τ ¼ 0)without needing any prefactor (i.e., γ ¼ 1). Therefore,verifying these two MOSAIC conditions by proper align-ment of the FROG experiment is extremely helpful.The MOSAIC trace has been shown to be far more sen-
sitive to displaying pulse chirp than an interferometricautocorrelation [7]. In an analogous way, MOSAIC canbe a more visually sensitive rendering of pulse chirp thanan SHG FROG spectrogram. The enhanced sensitivity isdue to the background-free nature of MOSAIC and is illu-strated in Fig. 1. An unchirped pulse is used for computa-tion of the SHG FROG trace shown in Fig. 1(a). The pulseis symmetric and has a transform-limited duration of≈10 fs (see inset). The case of Fig. 1(b) is generated fromthe same spectral amplitude, but having 10 fs2 of group-delay dispersion. The dispersion gives rise to chirp andpulse broadening in the time domain (see inset). TheMOSAIC trace of Fig. 1(c) is determined from the SHGFROG trace of Fig. 1(a) and immediately confirms thatthe pulse is unchirped without the need for iterativeretrieval. The sensitivity of the MOSAIC trace is apparentfrom Fig. 1(d). While the SHG FROG trace of Fig. 1(b)shows little difference from its unchirped counterpart,the MOSAIC trace illustrates a dramatic difference[shaded area in Fig. 1(d)]. The chirped MOSAIC traceis computed from the SHG FROG dataset and easily dis-plays pulse chirp embedded within the SHG FROG trace.For the particular case depicted in Fig. 1, the normalizedFROG error between the two datasets isG0 ¼ 0:0074. Thenormalized FROG error is computed only over the non-zero area of the FROG trace. Published values of the stan-dard FROG error for retrieved pulses using SHG FROGhave exceeded G > 0:01 [9]. In such instances, MOSAICcould serve as a means of displaying subtle amounts ofpulse chirp.Users of commercial FROG devices are aware the re-
trieval quality can be checked by comparing the mea-
sured and retrieved FROG traces [10]. The sensitivityof MOSAIC can be applied to both measured and re-trieved SHG FROG traces, serving as an additional wayto judge the quality of a retrieval effort. As an example,we use a mode-locked Ti:sapphire laser centered at λ ¼800 nm and a Swamp Optics GRENOUILLE to record theSHG FROG dataset shown in Fig. 2(a). The reconstructedSHG FROG trace is shown in Fig. 2(b). The reconstruc-tion was done using Mesa Photonics VideoFROG soft-ware, version 5.0, with 128 × 128 pixels and returned aFROG error of G ¼ 0:0105. From the SHG FROG data-sets, the corresponding MOSAIC traces are computedand illustrated in Fig. 2(c) for both the measured (solidcurves) and reconstructed (dots) data. While the mea-sured and reconstructed SHG FROG traces appear verysimilar, the measured and reconstructed MOSAIC tracesreveal a more obvious difference. Significant structure inSMOSAICðτÞ can be seen over nearly two decades of signal;see Fig. 2(c), inset. The structure was not faithfully repro-duced in the reconstruction effort and is not noise, as isevident from its symmetry about zero delay. It is impor-tant to note that the comparison of measured and recon-structed MOSAIC traces from SHG FROG datasets caneasily be implemented on pulses already retrieved, be-cause no additional information or measurements areneeded beyond the measured and reconstructed FROGtraces.
For best retrieval results, the SHG FROG trace shouldbe symmetric about zero delay [10]. Consultation of theMOSAIC trace for symmetry can improve retrievalresults. A measured SHG FROG trace produced with aslight misalignment of the beam axis with respect to theoptic axis of the GRENOUILLE is shown in Fig. 3(a). The
Fig. 1. (Color online) Simulated SHG FROG traces from (a) anunchirped and (b) a chirped pulse. The insets show pulse in thetime domain. Corresponding MOSAIC traces produced from theSHG FROG traces: (c) unchirped and (d) chirped. Note the SHGFROG traces appear identical; complementary MOSAIC tracesreveal pulse chirp [shaded area in (d)] without the need foriterative reconstruction.
Fig. 2. (Color online) (a) Measured and (b) reconstructedSHG FROG traces. (c) Comparison of corresponding MOSAICtraces produced from the measured (curves) and reconstructed(dots) FROG datasets. The inset displays SMOSAICðτÞ on a logscale; measured, black curve; reconstructed, light curve.
misalignment is very subtle, and no visual indication isobserved in the SHG FROG trace. A pulse retrieval is per-formed on the SHG FROG dataset, yielding a FROG errorof G ¼ 0:006. Upon computation of the MOSAIC trace,the asymmetry in the measurement becomes clear.Shown in the inset of Fig. 3(a) is an asymmetric MOSAIC.Asymmetry in the shoulder height of SMOSAICðτÞ is due to
the beammisalignment. The difference in height betweenthe two peaks is ≈17% and serves as clear visual indica-tion of beam misalignment along the delay axis. By usingthe MOSAIC trace as a visual gauge, we symmetrizeSMOSAICðτÞ and, hence, the FROG trace, by adjusting themirrors directing the laser beam into the GRENOUILLE.The resulting SHG FROG trace is shown in Fig. 3(b) withthe symmetric SMOSAICðτÞ depicted in the inset. A secondretrieval is performed on the symmetrized SHG FROGdataset and a significantly lower FROG error results: G ¼0:0032. While the retrieval from Fig. 3(a) produced an ac-ceptable error of G ¼ 0:006, we were able to improve theresult by nearly a factor of 2 by using the sensitivity ofMOSAIC to achieve a more favorable alignment. The re-duced error corresponded to a reduction in retrievedpulse width of over 6%. Of note is that the symmetricand asymmetric SHG FROG traces of Fig. 3 appear essen-tially identical; it is the complementary MOSAIC tracethat reveals the imperfection and allows its correction,facilitating more accurate results.
Because of the real-time nature of the MOSAIC compu-tation, optimization of beam alignment can be done priorto pulse retrieval by first examining the MOSAIC trace forsymmetry. Such exceptional sensitivity can further be ap-plied to optimization of pulse compressor geometries(e.g., prism or grating pairs). In these situations, full elec-tric field reconstruction is not needed and all that isrequired is a simple, yet sensitive, measure of pulse chirp.
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Fig. 3. (Color online) (a) Measured SHG FROG trace contain-ing a slight asymmetry from beam misalignment. The insetshows that the MOSAIC traces visually identify the asymmetryas a difference in peak heights. (b) Measured symmetric SHGFROG trace after symmetrizing the MOSAIC trace (inset). Whilethe FROG traces appear identical, the retrieval error was re-duced by nearly a factor of 2 when MOSAIC was used to opti-mize alignment prior to retrieval.
