NOTE: The copyright of this paper belongs to SPIE. It is published in the SPIE proceedings #2701.

Second-harmonic generation FROG measurements on a mid-IR free-electron laser

B. A. Richman (1), M. A. Krumbuegel (2), R. Trebino (2)

(1) Stanford Picosecond FEL Center
W. W. Hansen Experimental Physics Laboratory
Stanford University, Stanford, CA 94305-4085
(2) Combustion Research Facility
Sandia National Laboratory
Livermore, CA 94551

ABSTRACT

We present results of second harmonic generation (SHG) frequency-resolved optical gating (FROG) measurements on the mid-IR free-electron laser (FEL) at the Stanford Picosecond FEL Center. These are the first SHG FROG measurements performed in the mid-IR or on an FEL. The observed pulses have an optical wavelength near 5 µm, and the field profiles reconstructed from the FROG trace exhibit narrow-line absorption and freeinduction decay caused by atmospheric water vapor. The SHG FROG signal is easier to isolate than for the polarization gate geometry; hence the SHG traces are not corrupted by a residual background. The experiment used only 10% of the full laser power, and the spectrum and autocorrelation were quickly calculated from the FROG trace, demonstrating the feasibility of using SHG FROG as a real-time diagnostic for the FEL facility.

Keywords: FEL, FROG, SHG, mid-IR, ultrashort pulse, water vapor absorption, freeinduction decay

1. INTRODUCTION

Free-electrons lasers (FELs) [1-2] are now in use at several large laboratories around the world for optical research in spectral domains not readily available from conventional laser systems [3-6]. The Stanford Picosecond FEL Center [4] provides experimenters with a mid-IR FEL [7] and a far-IR FEL [8]. Many of the experiments require a knowledge of the laser pulse field temporal shape and spectrum [5-6]. Although a spectrometer and autocorrelator provide some of this information, it is incomplete and ambiguous. Frequency-resolved optical gating (FROG) is a technique to measure the electric field temporal amplitude and phase profiles unambiguously [9-10].

Previous FROG measurements performed on the mid-IR FEL at Stanford used the common polarization gate geometry [11]. The traces from these measurements, summarized in section 2, were partly corrupted by coherent interference of the desired FROG signal with a background signal (from the original pulse) which could not be completely removed. Also, because the polarization gate is a (weak) third order non-linearity, those measurements required the full power of the laser to obtain a reasonable signal to noise ratio.

The results presented in section 4 demonstrate that FROG using the SHG geometry [12] resolves these problems. The FROG signal is easy to isolate because it travels in a unique direction from the nonlinear crystal. Also, second order nonlinearities are inherently stronger than third order nonlinearities. The SHG FROG traces we obtained were uncorrupted by background signal, and we needed only 10% of the power of the laser beam to acquire traces with a better signaltonoise ratio than their polarization gate counterparts. We also calculated the intensity autocorrelations and spectral intensities directly from the time and wavelength marginals of the FROG traces, where the marginal is defined as the integral of a twodimensional trace over either axis.

Our results show pulses that were distorted by a spectrally narrow water vapor absorption line. The absorption line appears in the pulse spectra, and the pulses have tails from free-induction decay. We compare the SHG FROG traces with polarization gate traces of similar pulses taken last year. The SHG traces are less noisy, and lack negative regions that appear in the polarization gate traces because of the coherent interference of the FROG signal with a background signal.

The quality of the recent data and the low power requirement demonstrate that SHG FROG can make a good real-time diagnostic for the FEL lab, and perhaps replace the existing monochromator and autocorrelator [13].

2. POLARIZATION GATE MEASUREMENT

The polarization gate experiment [11] used a general purpose pump/probe apparatus followed by a monochromator, similar to the SHG apparatus described in section 3. Zinc Selenide Brewster plate polarizers selected the polarization of the gating beam, and isolated the signal beam. The nonlinear medium was a 2 mm Germanium plate. Both the optical delay and monochromator wavelength were scanned mechanically with stepper motors. A PC clone running "LabView¨" [14] managed the experimental control and data acquisition.

The weakness of the nonlinear gating effect necessitated the use of almost all of the laser beam power. Permanent beam splitter plates upstream of the FROG experiment picked off 20% of the power for the mid-IR diagnostics [13].

Germanium is a poor optical material, and partially randomized the polarization of optical beams passing through it. As a result, the polarizers could not completely isolate the weak, desired FROG signal from the ungated pulses. The undesired beam appears most obviously as a background spectrum at very large delays in the FROG trace. As a simple solution, trace points were averaged over large delays as a function of wavelength (outside the delay dependent region of the trace), and subtracted from the entire trace. This background is partially coherent with the FROG signal, however, and interferes with it both constructively and destructively in the trace.

Figure 1(a) shows one of the experimental FROG traces acquired from the FEL with the polarization gate geometry [11]. A narrow water vapor absorption line distorted the optical pulses, and the long tail in the trace evinces the freeinduction decay associated with the absorption. The striped regions indicate negative values, generated by the subtraction of the background spectrum where it interferes destructively with the FROG signal. The maximum depth of these "holes" is more than 10% of the peak value of the trace, indicating that the background signal seriously corrupted the measurement. Negative values were set to zero before inverting the trace. Note that the degree of corruption caused by constructive interference is nontrivial to determine.

The reconstructed temporal intensity (solid) and phase (dashed) in figure 1(b) are relatively smooth and reasonable because of the inherent redundancy of the FROG trace and the robustness of the inversion algorithm10. The main part of the pulse is approximately 1 picosecond long, and the freeinduction tail from the absorption line (at a wavelength of 5.02 µm) occurs 3.5 picoseconds later.


Figure 1: a) Polarization gate FROG trace of pulses which have been distorted by a narrow water vapor absorption line at 5.02 µm wavelength. Striped regions have negative values generated by the subtraction of a background spectrum which was partially coherent with the desired FROG signal. b) The reconstructed temporal amplitude (solid) and phase (dashed) of the trace in (a).

We attempted to eliminate the background problem by trying the self-diffraction gate geometry, in which the signal beam travels in a unique direction from the nonlinear medium, not collinear with the ungated beam. This also involves four-wave mixing, and we used the same 2 mm thick Germanium plate. The self-diffraction gate, however, is not inherently phase matched like the polarization gate, so the diffraction gate requires a thin nonlinear medium to avoid the onset of phase mismatch. Our self-diffraction FROG signal was less than 1% of that of the polarization gate, and was too small to use, either because the Germanium was too thick or because it did not convert well with parallel polarization.

We also considered the second-harmonic generation geometry. SHG FROG has the important advantage that SHG is much easier to accomplish than four-wave mixing, and as with the self-diffraction gate, the signal beam exits the nonlinear medium in a unique direction (and with a wavelength different from that of the original beam), making it easy to isolate. SHG also requires much less power than four-wave mixing, and should be possible with only a small fraction of the laser beam, leaving the rest for other experiments. Its main disadvantage is that the direction of time in the reconstructed temporal profiles is ambiguous, because SHG FROG is based on intensity autocorrelation. For this reason, SHG FROG traces are not intuitive like polarization gate traces.

3. SHG FROG EXPERIMENTAL APPARATUS

Figure 2 is a schematic of the SHG FROG apparatus, which consisted of an intensity autocorrelator followed by a monochromator. Not shown upstream is a 90% reflector for nonlinear spectroscopy experiments that were performed simultaneously with these FROG measurements. The FROG apparatus received the remaining 10% of the beam.


Figure 2: Schematic of the mid-IR FROG apparatus. The first half was an intensity autocorrelator. The output signal of this was fed into a monochromator. Both optical delay and wavelength were scanned mechanically, and each point in the FROG trace was averaged over several thousand optical pulses.

The beam splitter for the autocorrelator was a CaF2 plate coated for approximately 50% reflection. A computer controlled stepper motor delayed one leg of the autocorrelator. A 60¡ paraboloidal reflector (3 inch diameter, 150 mm focal length along beam path) focused and crossed the two beams into the 2 mm thick AgGaSe doubling crystal. This is the same type of crystal used for the permanent diagnostics autocorrelator, and is cut to accommodate phase matching between 3 µm and 8 µm wavelength. This experiment used a wavelength of 5.14 µm. The beams incident on the paraboloid were 8 mm diameter (1/e), and were 5 cm apart. The spot size in the crystal was approximately 100 µm.

A second paraboloid collimated the doubled output, and an iris isolated the crossed beam signal from the single beam signals. A third paraboloid focused the signal beam into a 30 cm McPherson monochromator with resolution of approximately 0.5 nm (out of 2600 nm). Another computer controlled stepper motor set the monochromator wavelength. A photoconductive 1 MHz bandwidth Mercury Cadmium Telluride detector measured the FROG signal, and a plate of PK50 glass (opaque above 3 µm) in front of it blocked any residual fundamental. The detector amplifier was damaged and had a large offset that was subtracted after digitization.

A PC clone computer running "LabView¨" [14] digitized this signal at a 100 kHz sampling rate, averaged over several thousand samples, and then adjusted the delay and wavelength stepper motors for the next point in the FROG trace. The computer also monitored a power reference signal from the user diagnostics and accepted only those points for which this reference was within a preset window. Most scans were arrays of 64 delays by 64 wavelengths, and each took 20 minutes to complete. This is more than twice as fast as for the polarization gate, because the signal was less noisy and required less averaging.

A low pass filter was first applied to the traces before inversion. Then the optical pulses were reconstructed using the method of generalized projections [10].

4. SHG FROG EXPERIMENTAL RESULTS

Figure 3(a) shows an experimental SHG FROG trace of FEL pulses of 5.14 µm wavelength. The trace is very symmetric about the average delay of 5 picoseconds, which is a good indication that the optical pulses did not change over the course of the scan. The gray areas are small negative values that result from the offset subtraction. The noise (estimated from the negative values) is about 3% of the peak value of the trace, which is slightly less than that of the polarization gate scans taken previously. The trace is not nearly elliptical, hence the pulses that generated it must be somewhat complex.

The trace was spatially filtered, and the optical pulses reconstructed. The reconstructed FROG trace matches very closely with the experimental trace. The temporal intensity (solid) and phase (dashed) in figure 3(b) show freeinduction decay similar to that in figure 1(b). The water vapor absorption line in this case is at 5148 nm. The main peak is 1 picosecond long, and the freeinduction decay occurs 2 to 3 picoseconds later. The phase changes (quadratically) by less than a radian over the main peak, so the chirp (from the quadratic component) is very small. The wavelength calculated from the slope of the phase (instantaneous frequency) over the free-induction tail is 5147±5 nm and matches that of the absorption line.

Figure 3(c) shows the reconstructed spectral intensity (solid) and phase (dashed), compared with the deconvolved spectrum (hashed). The reconstructed curves are very smooth because of the trace filtering, however, the absorption line still appears (as a shoulder) at 5.15 µm. The phase changes by only a radian over the spectrum, so the pulses are nearly transform limited except for the absorption. The deconvolved spectrum is closest to a direct spectral measurement of the laser at the FROG apparatus (the user diagnostics [13] were purged with dry Nitrogen gas, and did not show the absorption). The spectral marginal of the SHG FROG trace equals the self-convolution of the spectral intensity, thus taking the square root of the FFT of the spectral marginal and then the inverse FFT recovers the spectrum. We resolved the sign ambiguity of the square root by choosing the phase differences between consecutive FFT points to be less than ¹. The plotted curve was calculated from the raw experimental FROG trace with no filtering, and although noisy, still clearly shows the absorption line. The noise is twice the typical noise of the user diagnostics spectrum.

Figure 3(d) compares the reconstructed autocorrelation (solid) with the delay marginal of the experimental FROG trace (hashed). The delay marginal is mathematically identical to the autocorrelation. The two curves match almost perfectly.


Figure 3: (a) Experimental SHG FROG trace of 5.14 µm pulses from the FEL. (b) Reconstructed temporal intensity (solid) and phase (dashed) from (a) using generalized projections. (c) Reconstructed spectral intensity (solid) and phase (dashed) compared with spectrum obtained by deconvolution of the FROG trace spectral marginal (hashed). (d) Autocorrelation of the reconstructed data in (b) (solid) compared with the delay marginal of the trace (hashed).

5. SUMMARY

We have acquired SHG FROG traces with the mid-IR FEL at Stanford, the first time this was done in the mid-IR or on an FEL. The reconstructed pulses exhibit a narrow water vapor absorption line, and associated free-induction decay. The traces are less noisy than their polarization gate counterparts because of both a larger signal and lack of a coherent background signal. The SHG scans of 64x64 points took 20 minutes, which was twice as fast as for the polarization gate, and SHG requires only 10% of the total beam power, so that other experiments may use the rest. Intensity autocorrelation and spectral intensity are easily calculated directly from the trace. These properties could permit SHG FROG to replace the existing diagnostics.

6. ACKNOWLEDGMENTS

The authors wish to thank C. Rella for the use of his data acquisition software, and the operating staff of the SCA/FEL laboratory. Work supported in part by the Office of Naval Research, Contract #N0001491C0170.

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Updated 2/5/96 by
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