1. Introduction

Important aspects of plasma physics, inertial confinement fusion, and production of coherent X-ray pulses can be revealed from solid-target experiments where laser pulses with relativistic intensities (>10¹⁸ W/cm²) interact with dense matter. Within the interaction volume, hot and dense plasmas are produced for the approximate duration of the laser pulses. These plasmas can reach temperatures up to 1000 eV while retaining densities near those of the initial solid target [1, 2]. The shorter the excitation pulse is, the steeper the plasma density gradient that favors the production of coherent x-ray pulses (high-order harmonics) [3]. Therefore, a femtosecond laser pulse is the ideal candidate to produce hot and dense plasmas before significant hydrodynamic expansion occurs.

High-energy, ultra-short laser pulses can be produced nowadays using chirp pulse amplification technology [4]. When these pulses are focused on target, intensities in the range of 10¹⁹-10²¹ W/cm² [5, 6, 7] are achieved. For such laser systems, weak pre-pulses or even the amplified spontaneous emission (ASE) could still be intense enough to ionize the matter and produce plasmas that expand significantly before the main pulse interacts with the target. Therefore, high-contrast laser pulses are highly preferred for these solid target experiments. Detailed knowledge of the pulse shape and contrast ratio is necessary for a correct analysis of experimental data. While on a nanosecond time scale it is relatively easy to detect the pre-pulses (and eliminate them using a series of Pockels cells), the characterization of the pulse structure with femtosecond accuracy on a sub-nanosecond time scale is still a challenging task.

Several techniques have been devised to measure the temporal profile of femtosecond pulses. Femtosecond streak cameras are very useful for single-shot measurements but typically they have a maximum dynamic range of up to 10³ and they cannot resolve pulses shorter than 100 fs. Another technique to measure even shorter pulses is based on correlating the femtosecond pulse with an identical copy of itself, i.e., to measure the auto-correlation trace [10, 11]. Popular spectrally-resolved auto-correlation methods such as frequency resolved optical gating [8] (FROG) and spectral phase interferometry for direct-field reconstruction [9] (SPIDER) are designed to characterize the pulse structure in a narrow window of ~2 ps and typically do not provide a dynamic range above 10³. Unfortunately, the 2ω signal produced by frequency-doubling does not provide information about the time direction and one cannot distinguish between a pre- or a post-pulse. Removing the direction-of-time ambiguity requires a correlation of the laser pulse with another femtosecond “probe item,” generally a modified version of the same laser pulse, as it is done in a third-order cross-correlator [12, 13].

In a typical 3rd order cross-correlator, the laser beam is split in two arms. In one arm a second-harmonic generation (SHG) crystal is used to produce the probe pulse by frequency-doubling the original 1ω pulse. The resultant 2ω pulse is “scanned” across the unaltered 1ω pulse structure from the other arm and the correlation trace is generated by recording the 3ω signal produced through frequency-mixing in a second crystal, a sum-frequency generation (SFG) crystal. The correlation trace reflects the true pulse structure as long as the 2ω pulse is very “clean”. Because of the quadratic power generation law P(2ω)~P(1ω)² in a SHG crystal, the 2ω pulse could still contain pre- or post-pulses that ultimately produce “ghosts” or spurious signals in the correlation trace. A much cleaner “probe pulse” can be obtained through white-light supercontinuum (SC) production, a strongly nonlinear process that has an abrupt generation threshold. This is the basic principle behind the operation of the supercontinuum cross-correlator (SCCORR) that is described in this paper.

2. Experimental arrangement

The experimental setup shown in Fig. 1 has been assembled on an optical breadboard. The laser pulse to be measured is produced by a Ti:Al₂O₃ laser system [14] operating at a central wavelength of 805 nm. The system, formed by an oscillator, stretcher, regenerative amplifier, 3-pass amplifier and compressor, produces 50-fs pulses at a 10 Hz repetition rate. Only 3 mJ of the energy output of the 200 mJ maximum achievable has been used for the SCCORR.

 

Fig. 1. Experimental setup. Cylindrical lenses are L1 and L2, M are high-reflectors (mirrors), BS beam splitter, SCG supercontinuum generator, SFG sum-frequency generation crystal, and F1 and F2 are 900-nm and 425-nm bandpass filters, respectively.

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The 10-mm diameter laser beam is split in two arms with a beam splitter (BS). Approximately 85% of energy is sent in the reference arm and 15% is directed in the arm where supercontinuum is generated (SC arm). The reference arm contains a delay stage and broadband 805-nm high-reflectors (mirrors, M). In the SC arm there are four optical elements (see Fig. 1): a) cylindrical lens L1 used to produce a line focus; b) 1-mm thick quartz window (SCG) placed at or near the focal plane of L1 to generate the supercontinuum light; c) cylindrical lens L2 used to image this light onto the sum-frequency generation crystal (SFG), and d) filter F1 used to reject the remnant 805-nm light and transmit only a 40-nm bandpass window centered at 900 nm. The part of the SC pulse that passes through filter F1 is mixed at a 15-degree angle in the 1-mm thick, type-I BBO crystal. Although the crystal was originally designed for SHG at 800 nm, it can efficiently produce a sum-frequency signal at 425 nm (1/425nm=1/805nm+1/900nm) when properly phase-matched. The crystal availability was a factor that determined the choice for the 900 nm-centered spectral window of filter F1 (other center wavelengths for F1 can also be selected together with the proper SFG crystal). The 425-nm signal is spatially filtered using an iris diaphragm and spectrally filtered by the 10-nm bandpass filter F2. This signal is further imaged either onto a CCD camera for the single-shot measurement setup, or onto a photomultiplier (PMT) for the multi-pulse, scanning-type measurements.

The difference between the single-shot and the scanning operation of the SCCORR resides in the orientation of the lenses L1 and L2. For the single-shot setup a horizontal line focus of 7 mm×20μm is produced by the lens L1 and imaged by lens L2. The use of a line focus is preferred over a round one since many more photons at 900 nm can be generated and used in the production of the 425 nm signal. Note that significant SC light can also be generated in a large, round spot, if more laser energy is used (few mJ in a ~0.5 cm² spot). Unfortunately, in this case, multiple self-focusing-induced filaments develop at unpredictable locations within the SCG and the cross-correlation process becomes very inconsistent.

The L1 and L2 lenses are set to produce and image vertical line foci when the SCCORR is operated in the scanning (multi-shot) mode. In this setup, the goal is to produce as many 900-nm photons as possible at a fixed position of the delay stage. Consequently, the signal detected by the PMT is also maximized. The temporal profile of the pulse can be measured step-by-step by scanning the delay stage position. With this setup, the highest dynamic range obtained was 10⁸ and this limitation was given by residual photons produced in the SC arm, not by the PMT sensitivity. These 900-nm photons pass through filter F1, a small part of them is frequency-doubled in the SFG crystal and leaks through F2 into the PMT. A higher dynamic range can be obtained if: 1) a longer wavelength than 900 nm is selected in the SC arm; 2) a thicker SFG crystal having a narrow bandwidth is designed to only add the SC and the reference pulse; 3) filter F2 has better rejection for all other wavelengths than the signal. The only disadvantage of using SC at wavelengths longer than 900 nm is that fewer photons are produced [15]. One way to increase the SC generation in the near-IR (more than 10 times) is to use shaped pulses, as described by Schumacher in 2002 [16].

3. Experimental results

The operation of the SCCORR is based on the fact that only the main pulse is able to generate supercontinuum light. The other pre- and post-pulses contained in the pulse structure are weak enough to pass through the SCG and not produce any supercontinuum light. Figure 2 shows the normalized cross-correlation signal amplitude at 425 nm on the CCD camera (single-shot setup) versus the laser pulse energy in the SC arm. The measurement was performed when the delay line was near zero, that is, the pulses in both arms are timed at the SFG crystal and the signal appears in the central part of the CCD window. The energy in the SC arm was reduced from 400μJ to 140 μJ using a calibrated attenuation wheel with fixed time delay. The signal decreased 6 orders of magnitude in between these two points. Below 140μJ the cross-correlation signal reached the CCD noise level. Figure 2 shows that pre- or post-pulses that are only 3 times (or more) weaker than the main pulse are already below the threshold for SC generation and therefore they will not generate “ghosts” in the cross-correlation scans. Another way to verify that the SCCORR signal is due only to the SC production is to slide the SCG slightly out of the line focus without changing the overall delay between the two arms. The intensity of the laser pulse inside the quartz window decreases and the SC generation becomes less efficient. The cross-correlation signal rapidly drops ~500 times when the SCG is 0.5 mm away from focus and then it reaches the 10^-6 noise level if the SCG is moved another 0.5 mm.

 

Fig. 2. Normalized cross-correlation signal on the CCD camera versus laser pulse energy of the SC arm. Calibrated attenuators were used for both the camera and the SC arm.

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In order to show the ability of the cross-correlator to distinguish between pre- and post-pulses, a post-pulse was deliberately produced by inserting a 6.4 mm thick glass plate in the laser beam. The SCCORR scans (with and without the plate) are compared in Fig. 3 to an auto-correlator scan. The auto-correlator setup was made from the SCCORR setup by removing the L1, SCG, L2, F1 and F2 optical components and by tuning the SFG crystal for second harmonic generation at 805 nm.

The top (blue) trace in Fig. 3 shows a typical scan obtained with the SCCORR (no post pulse). All of the “spikes” in this trace (except the ones at ±10 ps) have been identified as reflections in the optical components of the cross-correlator such as the beam splitter, SFG crystal, F1 filter, etc. The background level of ~50 mV is due to the amplified spontaneous emission (ASE) which is approximately 10^-5 of the maximum signal recorded at zero delay. The noise is given by the fluctuations in the laser pulse energy. The actual noise due to the cross-correlator when either one of its arms is blocked is below 2 mV and is due to the PMT and electronic circuitry. For the traces shown in Fig. 3 an OD2.0 attenuation (neutral density) filter was placed on the PMT to keep the signals generated by the post-pulse below the ~3 V saturation level. No selective attenuation was used for the zero delay region (-3 ps to 3 ps) where the PMT signal is saturated.

When the glass plate was placed in the laser beam, a post-pulse with 10^-3 amplitude of that of the main pulse was generated. This post-pulse produced two symmetric “signatures/peaks” on the auto-correlation trace at −64 ps and +64 ps. The position of these peaks is shown in Fig. 3 by the two red arrows. As expected, the auto-correlator cannot resolve the direction of the time axis and just from the auto-correlation trace one cannot determine if the peaks are due to a pre- or a post-pulse. The SCCORR trace, on the other hand, shows only one peak that can be seen in the bottom (black) trace in Fig. 3 at approximately -64 ps (see left black arrow). No signal was recorded on the right-hand side of the trace (near the position marked by the right black arrow) at around +64 ps down to the ASE level. This demonstrates the ability of the SCCORR to remove the time ambiguity and correctly identify pre- or post-pulses in the pulse structure.

 

Fig. 3. Photomultiplier signal of the cross-correlator operating in scanning mode with no post-pulse, top (blue) trace; auto-correlator with post-pulse, middle (red) trace; cross-correlator with post-pulse, bottom (black) trace. To better distinguish the curves, top and middle traces have been displaced by 4 V and 2 V, respectively.

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In addition, the SCCORR setup was converted into a 3rd order cross-correlator setup for comparison purposes. The SHG crystal replaced the SCG plate (to produce 402.5-nm pulses) and a type-I 3ω crystal was used to produce 268-nm pulses (a half-wave plate was also used to rotate the polarization of the infrared pulses in the reference arm). Taking aside the spurious signals generated by secondary reflections from these additional optics, the pulse structure revealed by the 3rd order cross-correlator (including ASE) was found to be similar to that of the SCCORR.

The temporal resolution of the SCCORR has been measured for both the scanning and the single-shot setups. The FWHM of the auto-correlation trace of the pulses sent into the SC-CORR, as measured with a calibrated, commercial auto-correlator, was 70 fs. The FWHM of the cross-correlation trace obtained with the SCCORR scanning setup was 190 fs, as shown in Fig. 4 (a). Figure 4 (b) shows the CCD image of the single-shot SCCORR signal over its entire window of up to 7 ps. The lineout of this image, see Fig. 4 (c), also shows a FWHM of approximately 190 fs. The temporal broadening from 70 fs to 190 fs is due to dispersion in the optical elements present in the SC arm such as the cylindrical lenses and filter F1. A narrower trace can be obtained if reflective optics are used (transmissive optics that were used here allowed an easy conversion SCCORR < - >auto-correlator). The SC generator will then be the only optic responsible for the pulse stretching and since the amount of chirp that the SC is generated with is <10 fs/100 nm [15] and the group velocity dispersion is negligible for thin quartz windows, the temporal resolution of the SCCORR should approach that of the pulse width.

 

Fig. 4. Temporal resolution of the SCCORR in the scanning setup with 20 μm/step (a), single-shot image on the CCD camera (b), and lineout of the image (c).

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4. Conclusion and discussions

We have presented the design for, and the first experiments performed with, a supercontinuum-based cross-correlator (SCCORR). The SCCORR design is similar to that of a second-order autocorrelator with the simple difference that, in one arm, supercontinuum light is generated (in a line focus) and used for the cross-correlation. This simple design allows for an easy, on the spot conversion between auto-correlator and SCCORR operation modes.

The highest dynamic range obtained with the SCCORR using a PMT in a scanning setup was 10⁸. The dispersion-limited temporal resolution of the SCCORR was 190 fs, a factor of 2.7× larger than the auto-correlation width of 70 fs. When operated in the single-shot mode the largest time window attained was 7 ps and the dynamic range was 10⁶. Larger time windows can be obtained with larger diameter beams. For example, if a 50 mm line focus is produced, the window will increase to approximately 35 ps (all optics must be larger in this case, including the SFG crystal). Further increase in the time window size can be obtained with a tilted wavefront in the reference arm. The dynamic range can also be increased (up to 10⁸) if more sensitive detectors are used or more SC light is generated. One way to produce up to 1000 times more SC light is to use a gas as the SCG, for example air [17, 18]. For a single-shot SCCORR with a 35 ps time window the necessary energy/pulse would be only 15-20 mJ, a value easily achievable for low-repetition, high-power femtosecond laser systems.

Compared to a third-order correlator, the SCCORR is, to some extent, wavelength-insensitive because it mixes laser light with supercontinuum light. This becomes important when visible or UV pulses have to be measured. For laser pulses at a λ=527nm wavelength [19], the 3ω signal produced by a third-order correlator would have a wavelength of λ/3=175.6 nm. Production and detection of the λ/3 signal in this part of the electromagnetic spectrum becomes a serious challenge [20]. In contrast, given the broad spectrum of the supercontinuum that extends into IR up to 4.5μm [21], the pulses produced by the SCCORR could have, therefore, wavelengths between λ/2 and λ that are much more convenient to operate with than the λ/3 signal produced by a third-order correlator. Moreover, the SCCORR traces are cleaner than those of a third-order correlator due to the highly nonlinear generation process of the supercontinuum. Pre-or post-pulses that are smaller than one-third of the main pulse were shown not to produce supercontinuum light and therefore do not generate any ghosts in the correlation trace.

This work was supported by the DOE/NNSA-UNR grant DC-FC52-01NV14050 and by the DOE University of California contract for LBNL DE-AC02-05CH11231.