Measuring ultrashort pulses in the single-cycle ... - OSA Publishing

Akturk et al.

Vol. 25, No. 6 / June 2008 / J. Opt. Soc. Am. B

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Measuring ultrashort pulses in the single-cycle regime using frequency-resolved optical gating Selcuk Akturk,* Ciro D’Amico, and Andre Mysyrowicz Laboratoire d’Optique Appliquée, École Nationale Supérieure des Techniques Avancées—École Polytechnique, CNRS UMR 7639, F-91761 Palaiseau Cedex, France *Corresponding author: selcuk.akturk@ensta.fr Received November 15, 2007; revised February 29, 2008; accepted March 6, 2008; posted March 25, 2008 (Doc. ID 89659); published April 22, 2008 We present a single-shot frequency-resolved optical gating setup for measurements of ultrashort pulse intensity and phase down to single-optical-cycle durations. Several issues stemming from short durations and extreme bandwidths are addressed. We show that after using spectral response correction, the regular FROG algorithm yields reliable pulse retrievals. We demonstrate measurement of pulse widths down to 4.9 fs. © 2008 Optical Society of America OCIS codes: 320.7100, 320.5520, 320.7080.

1. INTRODUCTION With the recent advances in spectral broadening and pulse compression methods, generation of near-singlecycle laser pulses in the visible and near-infrared (NIR) is becoming almost routine [1–3]. Such pulses are of extreme interest for several applications, especially in highharmonic generation and high field physics [4,5]. Several approaches have been presented to achieve such extreme pulse durations and required bandwidths. Among these approaches are filamentation [2,6,7], hollow fiber compression [1,8], and frequency synthesis [9]. In a general sense, these methods are based on increasing the bandwidth and compensating the spectral phase, which can be done passively with chirped mirrors or actively using phase modulators. Regardless of the method, most of the practical difficulties are a direct consequence of the extremely large bandwidths (typically spanning more than one octave) involved. Chirped mirrors, for example, have a limited bandwidth and are difficult to manufacture to match the entire broadened spectra [10]. Proper characterization of the pulse intensity and phase is a crucial part of near-single-cycle pulse generation. Regardless of the compression method, it is always necessary to have feedback to be able to perform the required corrections of the phase distortions and to verify the final pulse duration. As for the generation, the measurement of the near-single-cycle pulses poses certain difficulties. As a result, it is necessary to make improvements and modifications in the existing pulse measurement techniques to adapt to this extreme regime. We will briefly discuss some of these methods below. Note that we will not be concentrating on the measurement of the carrier envelope offset of the pulse electric field, which requires a different approach and for which there are well-established techniques [11,12]. One of the commonly used methods for ultrashort-pulse 0740-3224/08/060A63-7/$15.00

characterization is spectral interferometry for direct electric field reconstruction (SPIDER) [13–15]. The conventional setup requires modifications to eliminate the additional dispersion on the unknown pulse, before the nonlinearity, and to accommodate the pulse bandwidth [16,17] and also to improve the sensitivity in the weaker spectral components [18]. A more important issue with SPIDER measurements, arising particularly in the single-cycle regime, is the requirement of precision calibration and stability of the temporal delay between the two pulses [18,19]. For a single-cycle pulse, for a measurement error of 10%, the delay error must be ⬃10 as! This stringent alignment and calibration requirement can be relaxed by two-dimensional shearing interferometry, which requires multishot measurements and significantly increases the experimental complexity [19]. Another well-established method for ultrashort pulse intensity and phase measurements is frequency-resolved optical gating (FROG) [20,21]. Since its invention, FROG has been demonstrated successfully for various pulse lengths [22,23] and wavelengths [24,25]. Baltuska et al. have shown that FROG also works well in the few-cycle regime, provided that various spectral and temporal weighting factors are taken into account [26,27]. The spectral factors result from the conversion efficiency of the second-harmonic-generation (SHG) crystal and responses of the optical elements. These effects constitute an overall spectral filter, and by carefully calculating this filter, and dividing the experimental FROG trace by it, the standard FROG algorithm yields the correct pulse electric field. In the multishot configuration, the fact that the beams must cross at a finite angle causes a timedomain weighting called geometrical time smearing [26]. It causes the pulse to appear longer than it actually is, and the shorter the pulse, the more significant this effect becomes. Like the spectral effects, this effect can also be © 2008 Optical Society of America

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calculated and extracted from the trace. By performing all these corrections, Baltuska et al. demonstrated FROG measurements of 4.6 fs pulses, generated by spectral broadening in fiber, and compression with a combination of a prism pulse compressor and chirped mirrors [26]. In this work, we present a single-shot FROG configuration, which is capable of measuring pulses down to singlecycle durations. We have used spectral correction schemes similar to the ones mentioned above, but we used different approaches to increase the device response in the short wavelength, where spectral intensity is relatively low. We also used a home-brew spectrometer and UVenhanced, broadband components to address the extreme bandwidth issues. Most importantly, since our setup is single shot, the temporal delay is generated by crossing two beams at an angle in a line focus; hence, it is essentially free of the geometrical time-smearing effects [28,29]. The configuration is practically straightforward to build and relatively easy to align. We describe the setup in detail in Section 2 and the required spectral corrections and calibrations in Section 3. We show some examples of short pulse measurements (down to 4.9 fs) in Section 4. Finally, we present a summary in Section 5.

2. SINGLE-SHOT FROG SETUP FOR SINGLE-CYCLE PULSE MEASUREMENTS In the most general sense, FROG is a frequency-resolved autocorrelation, so it consists of an autocorrelator followed by a spectrometer, whereas practical realization of both parts may differ significantly [21,30,31]. We used a single-shot geometry, where the required delay is generated by crossing two beams in a line focus, at an angle [28], used SHG as the nonlinearity, and built an imaging spectrometer in the Czerny–Turner configuration, using a prism as the dispersive element. Figure 1 shows the top view layout of the FROG setup that we developed, which is capable of measuring, in principle, single-cycle pulses. We addressed several issues associated with the short durations and large bandwidths. Notice first that we used no transmissive element in the autocorrelation part, except for the SHG crystal, in order to avoid additional

Fig. 1. (Color online) Top-view layout of single-shot FROG for measuring pulses in the single-cycle regime. The bi-mirror consists of two rectangular flat mirrors on top of each other, with the input beam centered in between. CM, cylindrical mirror; SM, spherical mirror; HS, horizontal slit; VS, vertical slit.

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group velocity dispersion (GVD). We also used optical components with enhanced qualities in the short wavelengths, as the input pulse has significant spectral distribution in the visible, hence the second harmonic in the UV. The input beam needs to be large enough and reasonably uniform to have a relatively flat spatial distribution at the focus, as required by single-shot measurements [28]. The effect of beam size on the single-shot FROG measurements was studied in detail by Wang [32]. We use beam sizes around 10 mm (at 1 / e of the peak intensity). The input beam first hits a bi-mirror (two flat mirrors on top of each other, with a very small angle between their surfaces) in the center, which spatially divides the beam into two half-circles and crosses them some distance away. In Fig. 1, the beamlets cross in the perpendicular plane. The crossing angle determines both the temporal resolution and the maximum delay window at the detector. We have chosen a crossing angle of ⬃1.3 deg, which is sufficient to both resolve the single-cycle duration and properly cover the pulse pedestal and satellite pulses. As mentioned earlier, this single-shot geometry is immune to geometrical time smearing and causes no artificial weighting on the pulse duration. We also give a brief recipe to ensure a negligible effect of the transverse beam profile on the measurement. We spatially split the beam into two half-circles, and when they cross at the crystal, the lower-intensity wings of one half get mixed with the higher-intensity center of the other. This significantly improves the overall uniformity [32]. One can also easily make some quantitative estimates: first, using a target temporal resolution, the required crossing angle and delay window is calculated. The delay window determines the effective portion of the input beam that will be used. Calling this width weff, and using a Gaussian transverse profile (with the intensity 1 / e width of w0), the ratio of the SHG intensity at the cen2 ter to that at the edges will be exp共−weff / 2w02兲. In our case, a delay window of ⬃100 fs is generated within weff ⬃ 2.5 mm; hence the SHG intensity drop at the edges is only ⬃3%, which would cause negligible temporal weighting. After the bi-mirror, the beam hits a cylindrical mirror [radius of curvature (ROC) of 200 mm], which generates a line focus on the crystal. The SHG crystal is the most critical element in the setup; thus its thickness and angle must be chosen carefully. The crystal should be thin enough to introduce negligible GVD, also thin enough to have sufficient phase-matching bandwidth [equivalently, negligible group velocity mismatch (GVM)]. The GVM is a consequence of the difference between the group velocities at the fundamental and the second-harmonic wavelengths [21], whereas the GVD originates from the different group velocities within the fundamental pulse spectrum. As a result, the GVM is usually a more strict constraint, hence when satisfied, the GVD constraint is also automatically satisfied. It was shown that angle dithering the crystal relaxes the constraint on the GVM and allows for much thicker crystals [33]. For near-singlecycle pulses, however, since the pulse bandwidths typically scan more than an octave, the difference in the group velocities of the two ends of the pulse spectrum be-

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comes comparable with that between the fundamental and second-harmonic frequencies. Thus, angle dithering does not provide much improvement. It also compromises the single-shot capability. Therefore, we have chosen a stationary ␤-barium borate (BBO) crystal with 5 ␮m thickness (manufactured by EKSPLA). This thickness exhibits sufficiently large phase-matching bandwidth and negligible GVD. The crystal edges were both 10 mm long. Figure 2 shows the effect of crystal GVD on a theoretical single-cycle pulse for different crystal thicknesses. It is apparent that the 5 ␮m thick BBO introduces no significant GVD. The phase-matching behavior will be examined in detail later. After the SHG crystal, we have several beams; the generated autocorrelation signal, the unconverted fundamental beamlets, and the two second-harmonic beams generated by two individual beamlets. We need to eliminate all but the first one. The others give rise to a strong background of stray and scattered light. We take advantage of the fact that the autocorrelation signal is emitted in a unique direction, midway between the two beamlets and unwanted SHG beams. After the crystal, we used a spherical mirror 共ROC= 200 mm兲 to image the signal (using the 4-f configuration) to the input slit of the spectrometer stage. At the focal plane of this mirror, the input angle is mapped to position, and as a result, the abovementioned signals form distinctly separated lines. At this position, we place a narrow horizontal slit to filter out the unwanted beams. The slit opening was ⬃0.5 mm, which corresponds to an angular acceptance of 5 mrad at the SHG crystal. At the image plane of the mirror, we place another slit, this one vertical, to serve as the input slit of the spectrometer and further block the remaining scattered light. We have experienced that using these slits properly as filters is very important, as we cannot use a color filter to block the fundamental: due to octavespanning bandwidths, it is principally impossible to have a filter that would block the entire fundamental spectrum and leave the second harmonic intact. The rest of the setup is an imaging spectrometer in the conventional Czerny–Turner configuration. The input

Intensity [a.u.]

1.0

input 5 µm 25 µm 50 µm

0.8 0.6

beam is collimated (in the spectral-resolving direction) with a spherical mirror 共ROC= 200 mm兲 and sent to a prism. Using a grating was not an option due to overlapping of diffraction orders in the spectra. After the prism, we used the final spherical mirror (in f-f configuration) to generate the spectrum on the detector. The detector is a CCD (SONY XCD SX910 UV) with enhanced UV response down to 250 nm. The spectrum is generated on the horizontal axis and the position of the SHG crystal; i.e., the delay is directly imaged on the vertical axis. As a result, the complete FROG trace can be recorded on the CCD, over a single laser shot. The CCD can be externally triggered to capture individual pulses for repetition rates of less than ⬃20 Hz.

3. CALCULATION, MEASUREMENT, AND CORRECTION OF SPECTRAL RESPONSE AND CALIBRATION OF THE DEVICE As mentioned earlier, single-cycle pulses essentially possess bandwidths typically covering the NIR, visible, and even part of the UV. Within such a large range, the nonlinear and linear processes involved in measurements do not have flat spectral responses. The SHG crystal has frequency-dependent conversion efficiency, the mirrors have varying reflectivities over the spectral range, and the quantum efficiency of the CCD is also frequency dependent. As a result, a significant spectral weighting is imposed on the recorded FROG traces. Fortunately, all of the effects mentioned above can be calculated or measured without much difficulty. Baltuska et al. have shown that the effect of the factors mentioned above on the FROG trace can be described as a spectral filter, and the FROG trace can be written as a product of this filter with the ideal trace [26,27]: SHG Imeas共⍀, ␶,L兲 ⬀ R共⍀兲IFROG 共⍀, ␶兲,

0.2

⍀2 nE共⍀兲

⫻sinc2

0.0 -10

-5

0 5 Time [fs]

10

Fig. 2. (Color online) Effect of crystal GVD on a single-cycle pulse for different crystal thicknesses. Note that 5 ␮m thick crystal has negligible effects on the pulse.

共1兲

where Imeas is the measured FROG trace, R共⍀兲 is the SHG is the ideal FROG trace overall spectral filter, and IFROG in the absence of these spectral effects. This implies that, by determining the spectral filter, and dividing the experimental FROG trace by it, one can obtain the ideal trace and use the standard FROG retrieval algorithm [34,35] to extract the intensity and phase of single-cycle pulses. The spectral response can be written as the combined effect of several terms: R共⍀兲 = Q共⍀兲

0.4

A65

冉

2 2 关共nE 共⍀兲 − 1兲共nO 共⍀/2兲 − 1兲2兴2

⌬k共⍀/2,⍀/2兲L 2

冊

,

共2兲

where Q共⍀兲 describes the overall spectral response of the linear components of FROG, including the mirrors and the CCD. The effects of the nonlinearity are described by the following terms: The ⍀2 dependence results directly from solving Maxwell’s equations for the SHG process. The terms in brackets describe the dispersion of the nonlinear susceptibility. Finally, the sinc2 term results from the phase-matching efficiency. Since the Sellmeier coeffi-


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cients are well determined for most common nonlinear crystals, this frequency-dependent conversion efficiency can easily be calculated. The Q共⍀兲 term is better determined experimentally. To determine Q共⍀兲, we used a precalibrated blackbody radiation source (Oriel LSB020) at the input of the FROG and compared the measured spectrum with the calibration reference. This gives a sensitive combined spectral response of all of the linear elements in the setup. Baltuska et al. have also included the effect of frequency-dependent mode size in the overall spectral response [26,27]. This effect, however, depends on the experimental scheme used. In our experiments, we have selected a small portion of the beam (to be measured) using a pinhole. This beam is then collimated and sent to the FROG setup. After the pinhole, larger wavelengths diffract more, and the focused spot size of a Gaussian beam increases with the wavelength and decreases with the input beam size. As a result, after the cylindrical mirror in the FROG setup, the wavelength dependence of spot size cancels out. Single-cycle pulses generated by NIR lasers usually have significant spectral components in the short wavelengths, in the visible or even UV. This poses an important practical consideration in terms of choice of the SHG crystal configuration. For thin crystals, the phasematching efficiency curves are typically centered at the phase-matched wavelength and they have long tails toward the IR, but a very sharp drop on the UV side (see Fig. 3). Even though there is a finite response toward the UV, the oscillations go to zero; hence no signal is generated at those points, making it impossible to use the spectral correction scheme described above. Worse, the responses of detectors typically fall off below 400 nm. To improve the signal strengths in the short wavelengths we used the crystal phase-matching angle close to the desired shortest wavelength. Figure 3 shows the nonlinear response curves [including all of the ⍀-dependent terms in Eq. (2), except for Q共⍀兲] for different crystal angles. We have used a crystal, cut for phase-matching at normal in-

Conversion Efficiency [a.u.]

1.0 0.8

550 nm 650 nm 800 nm

0.6 0.4 0.2 0.0 200 300 400 500 600 Second-Harmonic Wavelength [nm]

Fig. 3. SHG conversion efficiency curves for 5 ␮m thick BBO cut for different phase-matching wavelengths.

1.0 Conversion Efficiency [a.u.]

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0.8

5 µm 10 µm 20 µm

0.6 0.4 0.2 0.0 200 300 400 500 600 Second-Harmonic Wavelength [nm]

Fig. 4. SHG conversion efficiency curves for 5, 10, and 20 ␮m thick BBO crystals. In all cases, the phase-matched wavelength is 550 nm.

cidence at 550 nm (at ⬃45 deg with the optic axis), which provides finite conversion down to a fundamental wavelength of ⬃450 nm. Even though we are calculating and measuring the spectral filter to make the required correction, in practice, it is not possible to correct arbitrarily low responses. The dynamic range of the detector puts a limit on the ratio of the minimum and maximum signals detected. This requires that the spectral filter, hence the nonlinear conversion efficiency, should not exhibit marginal changes within the range of interest. This is determined mainly by the crystal thickness and angle. Figure 4 shows the conversion efficiencies for different crystal thickness. It can be seen that, over the range of our interest (⬃250 to ⬃550 nm in the second harmonic), even 10 ␮m thickness shows too much variation (too low conversion in the IR, and too high in the visible), whereas 5 ␮m gives a more reasonable response. It is evident from Figs. 3 and 4 that the choices of 5 ␮m thickness and phase-matching wavelength of 550 nm provide reasonable signals and conversion over the spectral range of interest, effectively covering fundamental wavelengths from 500 to 1100 nm. This range is sufficient to make reliable measurements down to single-cycle duration. An alternative method for correcting various spectral responses in the FROG setup is to measure an independent spectrum and multiply the measured trace by the ratio of the autoconvolution of this spectrum and the trace frequency marginal [29]. This scheme has the advantage that it takes into account even potentially unknown effects. However, most of the considerations we mention above would still be important. The spectrometer used to measure the independent spectrum should be calibrated carefully for a nonflat response of its elements (grating, detector, etc.). Furthermore, the correction would not work if the FROG signal is too weak; hence the conversion efficiency in the short wavelengths should be improved as described above.

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FROG Trace Center Pixel

900 data linear fit

800 700 600 500 400 300 200 100 0

5 10 15 Mirror Position [µm]

20

Fig. 5. Shift of the center of the FROG trace in the delay axis by moving one of the bi-mirrors. This provides the required delay calibration.

We end this section with the description of the calibration procedure. We have done the wavelength calibration of FROG using a Hg spectral line source, which has a sufficient number of distinct atomic transition lines in the visible and UV. For the calibration of delay, we placed one of the mirrors of the bi-mirror assembly on a precision translation stage. We used a sensitive position detector (Feinpruf Militron, 0.01 ␮m resolution) to detect the relative displacement of the mirror. Moving this mirror introduces a relative delay between the two beamlets, hence causing the shift of the FROG trace center given by this delay. Therefore, the shift of the trace center and the precision measurement of the mirror position give a calibration of the delay step on the detector. Figure 5 shows the measured FROG trace center pixels for varying mirror position. The corresponding delay is found by multiplying the displacement by 2 (for the round trip) and dividing it by the speed of light. We found the resulting delay calibration to be ⬃0.2 fs per pixel. The detector that we use has 960 pixels in the delay dimension, which corresponds to an overall delay window of 192 fs. Therefore, this configuration is sufficient to resolve the fine temporal structure down to a single cycle and to cover a reasonable amount of the pulse pedestal and wings. If necessary, the delay step and window can be easily adjusted by tilting each of the bi-mirrors and changing the crossing angle.

Fig. 6. (Color online) Top, the measured and retrieved FROG traces without doing the spectral correction. The FROG error is 2.1%. Bottom, the measured and retrieved FROG traces after the spectral correction. The FROG error is 0.8%. The retrieved pulse duration is 6.8 fs FWHM. All traces are at 128⫻ 128 grids.

We first demonstrate the effectiveness of the spectral correction described earlier. We record a FROG trace of a short pulse and run the FROG algorithm on the pulse with and without the correction. The top figures in Fig. 6 show measured and retrieved FROG traces without the

4. EXPERIMENTAL RESULTS In this section, we present experimental few-cycle pulse measurements, using the FROG setup and spectral correction schemes described above. In all cases we present here, the pulses are generated by multistage compression by filamentation in argon, with chirped mirror compression after each stage. The compression setup is analogous to these kinds of experiments presented elsewhere [2,3].

Fig. 7. (Color online) Intensity and phase measurements of the shortest pulses we generated. The retrieved pulse duration is 4.9 fs FWHM.

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correction. From the distinct features between the two traces, it is apparent that the algorithm did not fully converge. The FROG error is 2.1% (for a 128⫻ 128 matrix). On the other hand, the figures on the bottom show the retrieval after the correction. The effectiveness of the spectral response correction is evident from the significantly improved convergence. The FROG error in this case is only 0.8%. The retrieved pulse duration is 6.8 fs FWHM. The frequency marginals shown in Fig. 6 also illustrate the improved convergence with the spectral correction. To test the measurements for near-single-cycle pulses, we optimized the compression setup (by adjusting the pressures in the cells) for the shortest pulses at the output. Figure 7 shows the FROG measurements corresponding to the shortest pulses we were able to generate. The measured pulse duration in this case is 4.9 fs FWHM, corresponding to 1.8 optical cycles at 800 nm. Although this was the shortest pulse we could generate with our current setup, the FROG device is readily adapted to cover durations down to a single cycle. To further investigate the quality of our measurements, we have plotted (Fig. 8, top) the frequency and delay marginals for measured and retrieved traces shown in Fig. 7. The very close matches support the reliability of the retrieval. We have also measured an independent spectrum and compared the spectral autoconvolution calculated us-

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ing FROG retrieved and independently measured spectra (Fig. 8, bottom). The overall structures match well, whereas the differences are mainly due to the lower spectral resolution in the FROG setup. Last, we comment on the required input pulse energy and the sensitivity of the device. Even though the SHG is the most sensitive FROG nonlinearity, since we focus the beam cylindrically onto the crystal, and we have to use a very thin crystal, relatively high pulse energies are needed. In our configuration, the minimum detectable pulse energy is ⬃10 ␮J at a single shot. The majority of the compression schemes yield output energies much higher than this (at the millijoule level); thus the low sensitivity does not cause a limitation. For higher repetition rates, weaker signals can be detected by increasing the integration time of the detector and integrating over multiple shots, even though this compromises the single-shot capability. We were able to measure pulses at 100 Hz, with ⬃500 nJ pulse energies, by integrating signals over a few seconds.

5. CONCLUSIONS In conclusion, we demonstrate a single-shot SHG FROG device, which is capable of measuring pulses down to single-cycle durations. The single-shot geometry is free of geometrical time-smearing effects. By measuring and calculating the spectral weighting caused by various elements, the measured trace can be corrected, and the standard FROG algorithm can then retrieve the correct pulse intensity and phase. We demonstrate measurements of pulses as short as 4.9 fs. This scheme provides robust and relatively straightforward characterization of the intensity and phase of pulses in the single-cycle regime and provides very reliable feedback.

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Fig. 8. (Color online) Top, frequency (right) and delay (left) marginals of measured and retrieved FROG traces shown in Fig. 7. Bottom, spectral autoconvolution calculated using FROGretrieved and independently measured spectra.

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