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Abstract
In this work, we demonstrate the sensitivity of the frequency-resolved optical switching (FROSt) technique to detect a small amount of spectral phase shift for the precise characterization of ultrashort laser pulses. We characterized fs pulses centered at 1.75 µm that are spectrally broadened up to 700 nm of bandwidth in a hollow-core fiber and subsequently compressed down to 2.3 optical cycle duration by propagation in the air at atmospheric pressure. By inserting thin fused silica windows of different thicknesses in the beam path, we accurately retrieve group delay dispersion (GDD) variations as small as 10 fs2. Such GDD variations correspond to a change of the pulse duration of only 0.2 fs for a Fourier transform limited 2-cycle pulse at 1.75 µm (i.e., 11.8 fs). The capability to measure such tiny temporal variations thus demonstrates that the FROSt technique has sufficient sensitivity to precisely characterize single-cycle pulses.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
With the advance in ultrafast laser technologies, major efforts have been made to generate and characterize high-energy ultrashort laser pulses down to sub-cycle duration [1–3]. The access to such pulses allows, for instance, to generate high harmonic radiation with photon energy in the water window [4,5], ultrashort electron bunches [6–8], or to measure ultrafast dynamics in atoms and molecules [9–11]. The characterization and control of the spectral phase of such pulses is a key step in the outgrowth of these techniques. Indeed, the spectral phase directly impacts the pulse duration and its temporal shape. Accurate control of the spectral phase allows access to high peak power. That is why considerable progress has been made with the development of technologies capable of temporally characterizing and controlling few to single-cycle pulses [12,13]. Nevertheless, characterizing such ultrashort and broadband pulses remains challenging.
Considering, for example, the dispersion scan (D-scan) technique, well-established for the characterization of compressed few-cycle pulses [14], which measures the second harmonic spectrum of the pulse to be characterized while scanning its dispersion: the temporal and spectral profiles in amplitude and phase of the pulse can be extracted from the spectrogram using a phase retrieval algorithm [15,16]. However, the D-scan technique has to respect the phase-matching condition of the second harmonic process across the entire bandwidth of ultra-broadband pulses. This issue is present in all pulse characterization techniques based on a nonlinear process, such as the second harmonic generation frequency-resolved optical gating (SHG-FROG), thus intrinsically limited in phase matching. Note the exception of surface third-harmonic generation FROG (THG-FROG) that doesn’t require phase matching [17]. More complex techniques were developed, such as TIPTOE [18] which uses sub-cycle tunneling ionization in gas to sample a laser field. This particular approach enables the complete temporal characterization waveforms of ultrashort pulses. However, it is limited to pulses close to the Fourier transform-limited (FTL) duration [19]. Another example is electro-optic sampling (EOS) that has been extended to the IR region and provides a complete field characterization of an IR waveform [20] with the requirement to provide a sampling pulse that has a duration shorter than the optical cycle of the pulse to be characterized [21].
In this work, we use an alternative pulse characterization technique, free of phase matching, based on transient absorption in solids [22–24]. FROSt consists of a pump pulse switching the optical transmission of a solid, and this transmission change is probed by the pulse to be characterized. The material has a bandgap energy higher than the photon energy of the probe; the solid then becomes opaque or partially opaque to the probe after its interaction with the pump pulse. In other words, the probe pulse is transmitted, and as the pumping promotes the free carriers’ electron in the conduction band, it leads to an ultrafast drop of the material transmissivity, i.e., the pump creates an optical switch. The spectrum of the probe pulse is measured at the output as a function of its relative delay with the pump pulse. The temporal profile of the probe pulse and the switch function can be extracted from this spectrogram using an iterative ptychographic algorithm. The versatility of FROSt was demonstrated by characterizing ultrashort and broadband pulses with a central wavelength from 0.77 to 10 µm and various energies down to a few nanojoules [25]. Note that a similar technique uses a transmission drop of an ionized solid target called plasma-mirror FROG (PM-FROG) demonstrated the characterization of UV pulses [26], with the cost that the material must be moved from shot to shot. In principle, FROSt is only spectrally limited by the sensitivity of the spectrometer and the transparency range of the material used for the switch. The present work demonstrates the capability of the FROSt technique to detect tiny amounts of spectral phase shift of ultrashort pulses. We show that FROSt is sufficiently accurate for precisely characterizing the spectral phase of ultrashort few-cycle pulses down to single-cycle.
2. Methods
2.1 Experimental setup
The experiment was conducted at the Advanced Laser Light Source (ALLS) located at INRS EMT (Varennes, Canada). The experimental setup and laser parameters are presented in Fig. 1 (a). The 50 Hz Ti:Sa laser system, delivering 37 mJ pulses centered at 800 nm before compression, is used for this study. The main beam is sampled to obtain a lower energy arm (∼1 mJ) used as the pump beam for the FROSt characterization. The remaining energy is used to generate high energy pulses with a central wavelength at 1.75 µm by pumping a three-stage Optical Parametric Amplifier (OPA). The first two stages of the OPA are achieved with a commercial OPA (TOPAS, Light Conversion) that delivers seed pulses with central wavelength at 1.75 µm and 0.25 mJ of energy. This beam is further amplified with a homebuilt OPA stage to reach an energy up to 2.3 mJ [27,28]. The pulse duration measured at this stage with a homebuilt SHG-FROG is 38 fs full width at half maximum (FWHM) in intensity.
Fig. 1. (a) Layout of the experimental setup: The output beam of the Ti:Sa system is split into two parts. The first path is further split into two arms. The first part is used to generate a seed at 1.75 µm with an OPA, and the second part is used as a pump to amplify the seed with a homebuilt OPA stage. After amplification, the pulses centered at 1.75 µm with pulse energy of 2.3 mJ are spectrally broadened in an argon-filled HCF (2.5 m long, inner core diameter of 750 µm). The collimated output of the HCF is attenuated to generate a probe pulse with pulse energy of ∼150 nJ by using the reflections off the two wedges. The probe beam is focused on the zinc selenide plate (ZnSe) by a 100 mm off-axis parabolic mirror. The second path is used to generate the pump beam for FROSt characterization. The pulses are frequency doubled to 400 nm and are focused on the ZnSe plate using f = 600 mm lens. The probe beam was collimated and then coupled in a spectrometer using f = 500 mm lens (b-e) SHG-FROG characterization of the amplified 1.75 µm pulses at the fiber output: (b) Measured and (c) reconstructed SHG-FROG spectrograms(log scale) (d) Retrieved Spectral and (e) temporal profiles of the pulses in intensity (blue line) and phase (orange line). (f) Spectrum before (blue line) and after (red line) the fiber.
The beam is then coupled into a 2.5 m long HCF (few-cycle Inc.), see Fig. 1 (a), with an inner diameter of 750 µm for spectral broadening [29,30]. The fiber is filled with a differential pressure of argon: the entrance is connected to a vacuum pump and the output to the gas inlet. The optimal pressure of argon in our conditions was about 300 mbar. After the fiber, the pulse energy is 1.5 mJ and the spectrum spans from 1.25 to 2.2 µm, see Fig. 1 (f). The spectrum is measured with a near-IR/IR spectrometer (NIR256-2.5, Ocean Optics). The pulse duration before compression measured at the fiber output by SHG-FROG is 40 fs FWHM, see Fig. 1 (b-e).
After the fiber, the collimated beam propagates through 10 m of air at atmospheric pressure for compression down to 13 fs FWHM duration (Fig. 2 a/c) [31]. The pulse energy is then attenuated to 150 nJ with the reflection of two wedges for the FROSt characterization. Several FS windows of known thicknesses are inserted before the beam enters the FROSt setup. The FROSt measurements are obtained by switching the optical transmissivity of a 500 µm thick ZnSe plate. To create the optical switch, the fundamental beam is frequency-doubled to obtain pump pulses with a central wavelength at 400 nm with 500 µJ of energy and 60 fs duration. This ensures that the switch is created at the surface of the ZnSe sample since the photon energy of the pump is above the material bandgap. These pulses are focused with a 600 mm lens on the ZnSe window positioned a few centimeters before the focal spot to avoid damaging the sample and illuminate a much larger area than the size of the focused probe beam. The pump beam diameter on the window is approximately 1 mm. The probe beam is focused on the ZnSe plate with a 100 mm off-axis parabolic mirror at the center of the pump spot. The parabola with a hole is used to reduce to 3 degrees the angle between the pump and the probe beam onto the ZnSe plate, minimizing the pulse front mismatch. The fluence of the pump and the probe beams onto the plate surface are estimated to be 70 and 1 mJ/cm2, respectively. After passing through the ZnSe plate, the probe beam is collimated with another 100 mm off-axis parabolic mirror and is coupled into the near-IR/IR spectrometer with a 500 mm lens.
Fig. 2. (a) Experimental and reconstructed FROSt traces without additional fused silica. (linear scale) (b) Experimental and reconstructed FROSt trace for 6 mm of fused silica. (linear scale) (c) Retrieved temporal (top) and spectral (bottom) profiles of the pulse in intensity (blue line) and phase (orange line) for different thicknesses of fused silica placed in the beam path. The indicated durations are the FWHM of the peak intensity.
Note that special attention was given to the set-up temporal stability between the pump and probe pulses. Indeed, each arm has a length of 22 m. To evaluate the jitter between both arms, the first step to fulfill is to determine the “zero delay”, i.e. when the relative delay between the pump and the probe pulses onto the sample surface is zero. This is found when the intensity of the transmitted probe beam drops by approximately 50% of the contrast of the spectrogram. At this “zero delay” position of the translation stage, the effect of the jitter between the two pulses should be directly observed by measuring the intensity fluctuations from the transmitted probe beam from shot to shot. For instance, considering the average slope of the signal drop, a jitter delay of +2fs (respectively of -2fs) of the pump pulse compared to the probe pulse would result in a signal fluctuation of +-6.7%. We have verified that such instabilities were not observed in the experiment. In addition, we have not observed slow delay drifts as we have regularly verified the “zero delay” position separated in times by tens of minutes. In this experiment, the jitter and slow delay drift between both arms are negligible and no active stabilization was necessary. The spectra at each delay of the FROSt spectrogram were averaged over 10 shots. Each spectrogram was acquired within 1-2 min.
2.2 Results
The objective is to demonstrate the capability of the FROSt technique to precisely characterize very small amounts of spectral phase. To add a small amount of spectral phase to the 13fs pulses, the simplest way is to linearly propagate the pulses through very thin materials of known thicknesses. This strategy mostly adds SOD. Fused silica windows of different thicknesses were used to add a known amount of spectral phase by small increments. The dispersion windows were placed after the two wedges to avoid nonlinear effects during the beam propagation in the windows. The retrieved temporal and spectral profiles of the probe pulses are presented in Fig. 2 (c). For all FROSt acquisitions, it is worth noting that the setup remains untouched: no optimization is needed because the measured signal is not generated from nonlinear conversion. In other words, the amount of FROSt signal is not affected by the intensity variations of the characterized probe pulses.
Reconstructions are made with an iterative ptychographic algorithm to retrieve the temporal profiles of the probe pulses [25]. In the FROSt trace, the spectral phase of the probe pulse is concealed in the cut-off delay of each frequency, whereas the switch effect is observed in amplitude by the transmissivity drop. With the increasing chirp of the probe pulse, the cut-off delay as a function of frequency tends to map the group delay. This effect can be seen by comparing the FROSt trace of a compressed probe pulse (Fig. 2 (a)) and one of a chirped probe pulse (Fig. 2 (b)). A slope corresponding to a negative chirp is observed for the stretched pulse in the spectrogram. However, an iterative reconstruction algorithm is required to extract the complete amplitude and phase of the probe pulse and the switch from the distribution.
To evaluate the accuracy of the FROSt technique, the spectral phases obtained with the reconstruction algorithm are compared with the phase shifts calculated using the Sellmeier equation, as shown in Fig. 3. A total of 6 mm of FS is inserted in the probe beam path with increments varying between 0.2 and 1.0 mm to measure various changes in the spectral phase. The theoretical phase shifts are calculated for each thickness of FS windows (dashed green line). The experimental phase shift (solid orange line) is the difference between spectral phases retrieved with the FROSt technique. The agreement is excellent between the theory and the experiment for all FS thicknesses, even for the phase shift induced by the 0.2 mm window. Therefore, these results demonstrate that the FROSt technique can detect a change as small as 10 fs2 in the group delay dispersion (GDD) of the probe pulse corresponding to the propagation through 0.2 mm of fused silica.
Fig. 3. (blue line) Experimental spectrum of the pulse after attenuation; (orange line) Difference between experimental spectral phase with different FS thickness (dashed green line). The phase shift is calculated theoretically using the Sellmeier equation of FS.
To further quantify this result, the difference between the theoretical and the experimental curve was calculated in terms of GDD, which is more meaningful than a phase error representing the sum of phase difference. For instance, GDD is the lowest order coefficient of the spectral phase affecting the pulse shape. Moreover, the spectral phase shift induced by FS is mostly SOD, we thus use GDD values to evaluate the FROSt accuracy. The GDD as a function of frequency was deduced from the reconstructed phase curve using the following equation:
A weighted averaging using the spectral intensity has been done on this curve to get access to the GDD of the whole pulse:
Table 1. Theoretical (column 1) and retrieve (column 2) GDD are presented for each thickness of FS, the error for each thickness is shown in column 3
To underline the accuracy of FROSt: while a 10 fs2 change in the GDD of the pulse used in this experiment (13 fs, centered at 1.8 µm) does not influence the pulse duration, (increase by 0.2 fs, i.e., 1.7%), the same difference of 10 fs2 would indeed increase the duration of a single-cycle pulse at 1.8 µm from 6 fs to 7.5 fs. This experimental result proves that the FROSt technique has sufficient precision to accurately measure the SOD of single-cycle pulses.
3. Conclusion
To conclude, we have demonstrated the capability of the FROSt technique to precisely characterize ultrashort near-IR pulses centered at 1.75 µm with 700 nm of bandwidth. The FROSt technique can precisely detect small amounts of phase shift. This approach can detect a 10 fs2 variation in the GDD of the probe pulse induced by the linear propagation through a thin FS window of 0.2 mm. Such a tiny GDD amount only corresponds to a variation of less than 2% of the duration of a 13 fs FT limited two-cycle pulse. In addition, the GDD error is 3.5 fs2 over the whole scan, proving that the FROSt technique has effectively sufficient precision to resolve single-cycle pulse.
While characterization techniques based on a nonlinear process (such as SHG) have already demonstrated few-cycle to single-cycle pulse characterization [32,33], i.e., high precision in the spectral phase measurement, these techniques are bandwidth limited to approximately one octave. The unique capability of FROSt lies in the combination of both capabilities to characterize ultra-broadband pulses, only limited by the transparency range of the pumped material and the sensitivity of the spectrometer [25], and to perform high precision spectral phase measurements, as demonstrated in this study. Therefore, the FROSt is a valuable metrology to characterize ultrashort pulses with ultra-broadband spectra such as single-cycle or even sub-cycle pulses.
This technique can also be used in the mid-IR (MIR) region, where remarkable efforts have been made this past decade to generate few-cycle pulses for their applications in strong-field physics, MIR spectroscopy, and biomedical research [34]. Pulse characterization technique in this spectral region is rather complex and limited [35,36], and FROSt can be an alternative to precisely retrieve the spectral phase of single and sub-cycle MIR pulses.
Funding
Fonds de recherche du Québec – Nature et technologies; Natural Sciences and Engineering Research Council of Canada; Canada Foundation for Innovation.
Acknowledgments
A. L. and M. K. thank the NSERC CREATE program for the scholarship. We also thank Antoine Laramée for the technical support in the laboratory.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are available upon reasonable request to the authors.
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