1. Introduction

Recently, ultrashort pulse generation has advanced to pulse durations below 4 fs [1–4]. Despite the variety of methods employed, the generated few-cycle pulses often exhibit a complicated spectral structure, rendering their precise characterization as challenging as their generation. Characterization of sub-4-fs pulses mostly relied on spectral phase interferometry for direct electric-field reconstruction (SPIDER, [3–8]) or on frequency-resolved optical gating (FROG, [2, 9]). Regardless of method used, one particular difficulty lies in measurement of pulses with strong spectral amplitude variations. White-light continua, for example, tend to exhibit sharp drop-outs in the spectrum, with the spectral power density sometimes being reduced by two orders of magnitude compared to neighboring spectral regions. These drop-outs may overexert the dynamic range in the detection, causing effectively a loss of coherence at the drop-out. It has been shown that this can cause artifacts causing erroneous pulse reconstruction, both in FROG and SPIDER [10].

Some authors used great diligence in setting up their characterization, employing intensified CCD cameras and concatenating the SPIDER trace from several scans for an increased spectral resolution [3,11]. Despite these efforts, the demonstrated potential of hollow-fiber compressors, supporting a 2-fs pulse duration [12], has still not been fully exploited. Here we suggest a much simpler way of increasing the dynamic range and the accuracy of the SPIDER method. Our method uses an industrial-grade uncooled line-scan camera and rejects noise by phase-sensitive averaging.

2. Experimental setup

As a testbed for our enhanced SPIDER apparatus we use a two-stage hollow-fiber compressor, widely similar to the one described by Sansone et al. [13]. Both hollow fibers have an identical inner diameter of 250µm. Pulses with 34 fs duration and 600 µJ energy from a 1-kHz Ti:sapphire amplifier system are launched into a first 50cm long hollow fiber filled with 700 mbar argon. The resulting continuum has a Fourier limit of 10 fs. We overcompensate the chirp of the first stage continuum by 6 bounces off standard chirped mirrors, designed for compensation of the 0.5 mm-thick silica Brewster windows. Each bounce compensates for 60 fs ² group delay dispersion (GDD), yielding a GDD of ≈-75 fs ² on the 260-µJ pulses launched into the second compression stage. The second hollow fiber has a length of 60 cm and is operated at 550 mbar, producing an ultrabroadband continuum of 120µJ energy. This continuum is compressed in 20 bounces off 4 ultrabroadband chirped mirrors, which have been manufactured following the back-side coating (BASIC) approach [14] and cover nearly one optical octave from 520 to 1000 nm. A detailed description of these mirrors was given elsewhere [13]. Despite the octave-coverage of the mirrors, we cannot support the full bandwidth of the continuum, which results in a total energy of 20µJ of the compressed pulses after the second stage.

 

Fig. 1. Experimental setup of the high-dynamic range SPIDER. The spectra recorded by the line-scan CCD camera are processed twice by SPIDER phase retrieval, first to separate signal from noise in a lock-in fashion and then a second time for retrieval of the spectral phase from the interferogram.

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A 0.1% fraction of the continuum is split off by an Inconel coated beam splitter for simultaneous measurement of the spectral power density. The remainder is sent into the SPIDER apparatus. In our modified SPIDER setup (Fig. 1), we use a 50 µm thin silica etalon at 70° incidence for broadband generation of two replica pulses at a relative delay Δt=-390 fs in reflection. The transmitted light is sent through a 10 cm long SF10 glass block and used for up-converting the two replicas. For sum frequency generation, we employ a free-standing 30µm thick β-BaB₂O₄ (BBO) crystal. We use a type-II geometry, with a simple achromatic half-wave retarder for polarization rotation in the upconverter arm of the SPIDER setup. Our solid state approach for beam splitting avoids drift problems. Furthermore, our measurement is completely self-referenced by calibrating the spectrograph with the second harmonic (SH) of the two replicas [7,8]. Therefore we do not have to rely on the wavelength calibration of our spectrograph, as some implementations of cross-correlation SPIDER [11,15,16]. Self-referencing also automatically accounts for the 5 fs² GDD, slightly chirping the second replica pulse that travels through the etalon twice. Yet, our setup is much more sensitive than earlier ultrashort-pulse adaptions of the SPIDER technique, given the nearly balanced beam splitting ratio of the etalon. We convinced ourselves that additional satellite pulses due to multiple reflections inside the etalon did not corrupt the measurement result. The satellites chiefly give rise to an additional component in the Fourier transform of the spectrogram, which can easily be removed by filtering. Also, beam displacements are negligible compared to the beam diameter. The SPIDER-signal is analyzed in a half-meter spectrograph with a tall-pixel (13×500µm²) line-scan camera, capable of single shot operation at the full repetition rate of the laser.

3. Measurement and analysis

In the recording of the spectral interferograms shown in Fig. 2, we used a camera integration time of δt=-5ms. We sampled the spectral power density per unit wavelength interval I(λ,t)=dP(λ,t)/dλ of both, the SPIDER and the SH reference measurement, at t _i=-iδt, (i=1…N,N=-10,000). The detection was chopped at f _chop≈85 Hz, i.e. slightly below the Nyquist frequency f ₀=-1/2δt. For noise rejection, we first processed the acquired data by integration over the wavelength λ and subsequent application of the SPIDER algorithm [17] along the temporal delay t for phase retrieval. This reconstructs the phase of the chopper gating function according to

where λ_1,2 are the spectral detection limits of our spectrograph. We then reject the noise for any given wavelength λ₁<λ<λ₂ by integrating the spectral power densities over t

The signal functions are isolated for both, the reference measurement and the SPIDER measurement. This is to be compared to plain integration along t

4. Experimental results and discussion

An experimental comparison between I _ave(λ) and I _signal(λ) for measurement of a spectral interferogram of two pulses is shown in Fig. 2. These two pulses have been created by the two surface reflections of an etalon. With the 10,000 spectra acquired, ideal averaging should yield a factor 100 rejection of additive noise components (e. g. caused by dark noise of the CCD) compared to an individual trace I(λ,t_i). Simple summation of the traces according to Eq. (3), in contrast, sums up both, signal and noise. Therefore, the signal-to-noise ratio stays the same as in a single trace, and only multiplicative noise (e. g. caused by laser fluctuations) is suppressed. Inspection of the traces reveals that phase-sensitive averaging [Eq. (2)] strongly rejects background noise. This dramatic reduction of noise is illustrated for the vicinity of 800THz in the insets of Fig. 2. Note, however, that our method leaves the fringe contrast unchanged in the range of strong signals, e.g. at 700 THz. Fringe contrast is limited by interferometer alignment and ultimately by shot-to-shot variations of the spectral phase. Phase-sensitive averaging can not improve these issues but prevent data corruption from noise leaking into the interferograms as in the gray-shaded zone of Fig. 2.

 

Fig. 2. Measurement of the SH spectral interferogram of two identical pulses. The red trace I _ave(λ) consists of a simple average over 10,000 spectra according to Eq. (3). Note that the fringe contrast vanishes at about 800 THz. The blue trace I _signal(λ) has been processed in a lock-in like fashion, see Eq. (2), significantly increasing the fringe contrast over the entire bandwidth.

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Fig. 3. Phase retrieval from Fig. 2. Colors correspond to the designations in Fig. 2. (a) Spectral phases reconstructed from the interferograms. The phase from the replica delay φ _delay(ν)=-2πνΔt has been subtracted for clarity. (b) Reconstruction of the spectral phase of the pulse by spectrally integrating the differences between SPIDER phase and reference phase.

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Phase retrieval [17] from these interferograms is shown in Fig. 3 (a). Here it becomes clear that the poor signal-to-noise ratio of I _ave(λ) at 800THz leads to a cycle slip artifact, i.e. an erroneous 2π phase jump, when trying to extract the phase from the interferogram. As two nearly identical pulses have been used to generate this interferogram, such a phase jump can neither be explained by small wavelength miscalibrations of the spectrograph nor by the small differential dispersion GDD of the two pulses. This cycle slip indicates a loss of phase coherence in the detection [10]. The effect of the artifact on the SPIDER method is finally demonstrated in Fig. 3 (b), concatenating the difference of the retrieved spectral phases [5]. The loss of coherence in one of the interferograms causes a kink in the reconstructed phase of the pulse, resulting in a totally incorrect assertion of the pulse profile. In contrast, the cycle slip is rejected by phase-sensitive averaging. In fact, similar artifacts now only appear in regions where the spectral power density has dropped to less than 10^-4 of the maximum signal. Effectively, one therefore gains two orders of magnitude of dynamic range, which allows bridging deep drop-outs in the spectrum. It also allows for an extension of sensible phase retrieval deeper into the spectral wings.

It is important to understand that synchronization between chopper and acquisition is not required for exploiting the advantage of phase-sensitive noise rejection, similar to digital lock-ins, where signal and reference are sampled at some fixed internal frequency. The modulation in the spectrally integrated signal P(t) is strong enough for simple meaningful reconstruction of φ _chop(t) as described above, whereas noise dominates in the low-signal portions of the signal in the individual pixels of the CCD.

 

Fig. 4. Differential phase SPIDER measurement. (a) Retrieved phases with different amounts of additional GDD in the beam. The black line shows a reference measurement without additional glass. (b) The spectral phase differences caused by a differential GDD of 10 fs². The calculated phase difference is shown as a magenta line; a fit to the measured data is shown by the green line. The curvature between computation and the fit agrees within 0.5 fs².

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As a further test on the performance of our enhanced SPIDER set-up, we measured SPIDER traces with and without the insertion of additional material dispersion, similar to the test in one of the first demonstrations of the SPIDER technique (Fig. 9 in Ref. [6]). To demonstrate the sensitivity of phase-sensitive averaging with our apparatus, we used a 200µm thin microscope cover slide with a GDD of 10 fs², i.e. roughly 100 times less dispersion than used in the initial demonstration. Our measurements are displayed in Fig. 4. The small additional dispersion of the glass slide is clearly resolvable. The measured differential phase exhibits an rms average deviation from the calculated phase of the glass slide of approximately 200 mrad, similar to the value reported by Iaconis and Walmsley with their much larger dispersion and smaller bandwidth. In our measurements, the GDD of the glass slide is reproduced within about 1 fs ², which is the equivalent of only 20µm of glass or 30 cm of air. It is important to understand that values above a few fs² cannot be tolerated in the characterization of sub-5-fs pulses. Our error margin of 1 fs² translates into a misestimation of <0.1 fs when measuring the duration of a 4-fs pulse. However, a deviation of 3 fs² would already result in a measurement error of 0.5 fs.

Figure 5 finally shows one of the shortest pulses measured with our modified SPIDER apparatus. Figure 5 (a) depicts the measured SPIDER trace. Spectral intensity and phase of the pulse are plotted in Fig. 5 (b). The spectrum encompasses a 240-THz bandwidth, corresponding to a Fourier-limit of 4.2 fs. The phase is rather flat from 300 to 520THz with a single ≈2π step in the center. The reconstructed pulse has a width of 4.3 fs, corresponding to nearly ideal compression with satellite pulses of less than 20% of the main pulse. To our knowledge, these are the shortest pulse ever measured from hollow-fiber compression using only static dispersion compensation with chirped mirrors.

5. Conclusion

We demonstrated an improved SPIDER setup, particularly adapted for the strong spectral modulation of supercontinuum pulses and the accurate characterization of sub-5-fs pulses. Rapid acquisition using line-scan cameras can be exploited for phase-sensitive noise rejection, enlarging the dynamic range of the measured spectral interferograms and avoiding cycle slip artifacts in SPIDER phase retrieval. This method is found superior to simple cumulation of spectra with long integration times. We demonstrate the sensitivity of our approach by measuring small dispersion changes, equivalent to a few tens of microns of additional glass path. We further succeed in accurately characterizing a 4.3-fs pulse with a static approach to ultrabroadband dispersion compensation, yielding an unprecedented width for dispersion compensation of hollow fiber continua by chirped mirrors only. Yet, the high-dynamic range acquisition technique is much more versatile and can easily be extended towards complete homodyne detection of small induced variations of the spectral phase, e.g. for ultrafast spectroscopic measurements [18]. Furthermore, the same dynamic range improvement also appears beneficial for FROG measurements. We are confident that this improvement helps to further exploit the potential of hollow-fiber pulse compression towards single-cycle pulse generation in the visible/near-infrared spectral region.

 

Fig. 5. Demonstration of the measurement of an ultrashort pulse via the double phase retrieval procedure. (a) Measured SPIDER trace. The SPIDER trace is shifted by -331 THz to match the spectral range of the fundamental spectrum. (b) Spectral phase and intensity calibrated spectrum used for the reconstruction of the temporal profile of the pulse (c).

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