Generation and measurement of ultrashort pulses from the Stanford Superconducting Accelerator free-electron laser

B. A. Richman (1), K. W. DeLong (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

Keywords: FEL, FROG, mid-IR, ultrashort pulse, pump-probe, water vapor absorption

1. INTRODUCTION

The Superconducting Accelerator (SCA) mid-IR FEL at the Stanford Picosecond FEL Center has lased from 3.7 µm to 10.3 µm wavelength. The SCA is an RF linac, and the FEL produces pulses which range in length from 700 fs to 2 ps. These pulses are 50 to 100 optical periods long. Chemical pump/probe and photon echo experiments take full advantage of both the short pulses and the spectral tunability. Knowledge of the pulse temporal shape is necessary to interpret results of such experiments properly, and autocorrelation measurements are often inadequate. Frequency resolved optical gating (FROG) provides this information [7,8].

Water vapor and carbon dioxide in the atmosphere have strong absorption lines in the mid-IR. CO2 has closely spaced lines around 4.3 µm wavelength and water vapor has lines covering the region from 5 µm to 7 µm. Even careful precautions cannot completely eliminate the effects of these lines on optical beams. FROG quantifies the pulse distortion caused when the spectral width of the optical pulse is much larger than the width of the absorption lines. Both absorption and free-induction decay reshape the pulse.

In this paper, we first introduce the FEL and briefly explain its unique abilities and behavior, specifically, those of the SCA mid-IR FEL. Second, we review the basic principles of FROG and defer the reader to detailed papers for complete information [7-9]. Third, we describe the experimental apparatus and detail features specific to working with the FEL and in the mid-IR. Fourth, we show results of FROG measurements of a nearly transform limited pulse, and a chirped pulse distorted by a water vapor absorption line.

2. FEL FUNDAMENTALS AND THE SCA MID-IR FEL

Unlike conventional lasers, FELs are classical devices. In the most common type of FEL, a sinusoidal magnetic field (wiggler) forces a relativistic charged particle beam (usually electrons) to oscillate transversely in space (and time for each particle). This transverse oscillation permits the interaction with collinear radiation.

Figure 1 shows a hypothetical FEL using an electron beam as the lasing medium. The laser consists of the wiggler magnet with two jaws, the beam running between them, and two resonator mirrors. Four dipole magnets steer the electron beam around each mirror. A dielectric end mirror, hole end mirror, or Brewster plate accomplish output coupling. The electron beam, and for simplicity the entire resonator, are in high vacuum. An accelerator supplies the electron beam, and the beam is "dumped" after use. Some future FELs will use storage rings instead, either to improve efficiency or to obtain UV and X-rays.

Figure 1: Hypothetical FEL schematic showing the basic components. The FEL consists of the wiggler magnet with a sinusoidal magnetic field, which induces a sinusoidal trajectory on the electrons. This transverse motion permits interaction with the laser radiation. The electrons travel nearly synchronously with the radiation down the wiggler (from left to right in this figure). Two end mirrors provide laser feedback, and dipole "chicane" magnets steer the electron beam around the mirrors. Two possible output coupling methods are by an end mirror or Brewster plate (common in the mid and far-IR). Currently, the Stanford mid-IR FEL uses a partial reflector for output coupling. The entire electron beam-line and optical resonator are in high vacuum, and the wiggler magnet fits snugly against the outside of the vacuum chamber.

The gain mechanism in the FEL is also classical. The wiggler field forces the electrons to move with or against any extant transverse electric field. The electric field either accelerates the electrons and loses energy to them, or decelerates them, which enhances the field. Which occurs (and how much) is a function of the relative phase of each electron's wiggler oscillation and the local radiation field,

where z is the direction of propagation and k and w are the wave number and angular frequency of the radiation. If -¼/2¼/2 then the electron is accelerated, and if ¼/23¼/2 then it is decelerated. In most FELs, the electrons enter the wiggler uniformly distributed over a distance much greater than the optical wavelength. The electrons are "unbunched." The interaction in the first part of the wiggler serves to modulate the energy of the electrons on the optical wavelength scale. Then the energy dispersion of the wiggler magnet serves to bunch the electrons. Finally, these bunches radiate coherently into the extant radiation field, resulting in optical gain or loss depending on the phase of the bunches. As a result, the gain curve is proportional to the derivative of the spontaneous spectrum. It is antisymmetric: gain is positive for most frequencies less than on resonance, and gain is negative for most frequencies greater than on resonance. The fractional width is 1/(2N). The gain curve as a function of electron energy is also antisymmetric, and gain is positive for most energies higher than resonance.

Currently, all mid-IR FELs use RF linacs as the source of the electron beam. RF linacs produce a pulsed particle beam at the RF frequency (or subharmonic thereof) and the pulses are a few degrees in length. The SCA generates electron "micropulses" at the rate of 11.8 MHz and each is approximately 1 ps long. (The RF frequency is 1.3 GHz.) The laser pulses are approximately the same length. Note that the laser is mode locked to the linac micropulse rate, and the resonator round trip frequency must match it. The laser will lase if the resonator length is within approximately 1 or 2 wavelengths of exact synchronism.

The SCA also has a "macropulse" structure, which is the time duration of the RF. The macropulse can be 1 ms to 4 ms and the repetition rate is usually 10 Hz. RF power dissipation, which may cause the linac to overheat, limits the macropulse length and rate. The laser starts up from noise at the beginning of each macropulse.

The resonant frequency is a quadratic function of electron energy and the radiation and electrons travel almost in unison. Thus the instantaneous frequency of the laser pulses may be tailored by modulating the energy. Since the electrons "slip" behind the radiation by N optical periods as both travel through the wiggler, the frequency must stay within one gain bandwidth of all the electrons in this distance, and hence cannot change faster than f/(2N) within the distance Nl, known as the slippage distance. The SCA mid-IR FEL has 72 periods.

Besides electron energy modulation, the saturation mechanism in FELs can also affect the optical pulse [10]. The following explanation is oversimplified or brevity. Extraction occurs through a form of electron synchrotron oscillation (different from the optical oscillation). As the electrons travel through the wiggler, they execute a fraction of one oscillation. As the laser saturates, this fraction increases, up to a maximum of half the oscillation. The synchrotron frequency mixes with the optical frequency to generate sidebands. The long-wavelength sideband may experience gain on successive passes and the optical pulses become amplitude modulated with a period of approximately one slippage.

3. FROG BASICS

The most common form of FROG is the "polarization gate" geometry. The FROG trace is the spectrum of a third order autocorrelation. Figure 2 is a schematic of the optical layout used in the actual experiment. The laser (with field E(t)) is split into two beams, and the polarization of one beam, the gate, is rotated by 45deg and delayed by a time t with respect to the second. The two beams are then crossed in a 4-wave mixing medium with the nonlinear interaction,

The output beam, the signal, is collinear with the second beam but its polarization is rotated by 90deg. It can be isolated with a polarizer. The FROG trace is the spectrum of the signal and is a function of both wavelength (frequency) and time delay.

Since the square magnitude of the gate pulse will be somewhat shorter than the original pulse, it samples only a portion of the pulse duration in the second beam. Hence the signal maintains both instantaneous amplitude and frequency information from the original pulse. The FROG trace is similar to a spectrogram, and can be inverted to recover the pulse amplitude and phase temporal profiles.

Inversion is currently accomplished using a combination of the original inversion algorithm [7] and generalized projections [9]. The method of generalized projections can invert complex or noisy traces for which the basic algorithm fails to converge to an answer.

4. THE FROG EXPERIMENT ON THE MID-IR FEL

Figure 2: Schematic of the FROG experimental layout. A CaF2 plate reflects Å10% of the laser beam, which is delayed with respect to the remaining beam, which passes through a 45¡ polarizer appropriate for the polarization gate geometry. A paraboloidal reflector focuses and crosses the beams in a 1 mm thick Germanium plate that provides the optical nonlinearity. The optical pulses at the plate are approximately 1 ps long, contain 200 nJ of energy, and focus to a 80 µm rms half-width spot. Polarizers after the plate isolate the signal beam, and the monochromator analyzes it. A computer collects the data and controls stepper motors which drive the optical delay and monochromator.

A single element 1 mm diameter, 1 MHz bandwidth Indium Antimonide (InSb) detector (or Mercury Cadmium Telluride: MCT) was used to measure the FROG signal at the monochromator output. Although FROG measurements in the near IR and shorter wavelengths use a two-dimensional array detector and an imaging spectrometer to obtain an entire FROG trace with one laser pulse, this proved to be too expensive for us in the mid-IR. We required time resolution within the 2 ms FEL macropulses because the micropulses can evolve during that time. A large two-dimensional InSb array costs at least $20K and is not easily synchronized to the FEL macropulses. InSb is not sensitive to wavelengths greater than 5.5 µm, where we must use MCT detectors, and large MCT arrays are almost nonexistent. Therefore we had to acquire the FROG trace with a two-dimensional scan of both optical delay and wavelength. A reference signal (of the initial beam) was monitored to ensure that the laser power did not fluctuate during each scan. A 486 PC computer running "LabView¨" [11] controlled the stepper motors and collected the data. The software rejected and retook data points whose reference signal was not within a tolerance window set by the user. Since the laser may evolve in time during each macropulse, only part of each macropulse was used, about 0.5 ms long, and always the same section in each. Typically, each delay/wavelength data point was the average of 4 macropulse sections. Each 32x32 scan took less than 10 minutes. We obtained some of the data presented here before the monochromator was motorized. Those scans each took 20 minutes and have only 16 wavelengths.

Germanium is not an ideal optical material, and scatters the polarization of the beams. The resulting "leakage" through the polarizers was typically 20% to 100% of the desired gated signal before entering the monochromator. The spectrum of the leakage adds to the FROG data partially coherently. For simplicity, however, we assumed that the leakage was incoherent. We extended the delay scan beyond where the spit beams overlapped temporally, calculated the leakage spectrum as the average of the first and last 4 delay points at each wavelength (where the FROG signal was presumably zero) and subtracted it from the FROG trace.

Atmospheric absorption lines of CO2 and water vapor cover a large fraction of the mid-IR spectrum. The laser beam is preferably kept in vacuum or in a purge with an inert gas such as dry nitrogen or argon. At the Stanford Picosecond FEL Center, the optics transport lines between the laser and each of the experimental rooms are evacuated to 10 µm to 100 µm pressure. The diagnostic system through which the beam passes before going to the rooms is purged with dry nitrogen, and the table on which we performed the FROG measurement can also be purged, but purging is inconvenient and was not done for these experiments. As with any vacuum or purge system, water adsorbed to surfaces takes a few hours to evaporate fully, although most of it dissipates in a few minutes.

5. FROG MEASUREMENT RESULTS

Figure 3: a) Experimental FROG trace of a nearly transform limited FEL pulse. The solid line traversing the trace is the average wavelength as calculated directly from the trace data. This is an approximate indicator of the instantaneous wavelength. b) Pulse temporal intensity (solid) and phase (dotted) computed using the inversion algorithm. The chirp is -7 nm/ps. c) Comparison of computed (solid) and experimental (diagnostic; hashed) autocorrelations. The computed is slightly wider than the diagnostic. d) Computed spectral intensity (solid) and phase (dotted), and diagnostic spectrum (hashed). Note the diagnostic spectrum shows some water vapor absorption (at 5023 nm).

Figure 3(d) shows the computed spectral intensity (solid) and phase (dotted) and compares with the diagnostic spectrum (hashed). A small calibration offset between the two monochromators used is evident. The diagnostics calibration is more accurate than that of the FROG trace. A weak water absorption line appears at 5023 nm in the diagnostics data, but apparently has not disrupted the pulse shape significantly. The rms spectral half-width of the computed pulse is 14Ênm which is 0.3% of the center wavelength, and the rms width from the diagnostics is 19 nm or 0.4%. The computed rms time-bandwidth product is 0.6 (theoretical minimum is 0.5) and that calculated from the diagnostics is 0.8. Note that the chirp from 3(b) amounts to approximately one fourth of the rms spectral full-width over the 1 ps rms full-width pulse length.

Figure 4 shows an example of a chirped pulse further distorted by a water vapor absorption line at 5023 nm. The FROG trace in figure 4(a) clearly reveals both of these attributes. The average wavelength curve through the main part of the trace indicates a chirp of -21 nm/ps. The tail of the FROG trace at large delays has an instantaneous wavelength of 5023 nm, a water absorption line, and corresponds to free induction decay. This trace has only 16 wavelengths which were selected manually over 20 minutes, but the spectral resolution and noise are still adequate to characterize the pulse.

Figure 4: a) Experimental FROG trace of a pulse with a chirp and distorted by water vapor absorption. The solid line is the average wavelength as calculated directly from the trace data, and indicates a chirp of -21 nm/ps. Water vapor free induction causes the tail of the trace. b) Computed temporal intensity (solid) and phase (dotted). Note free induction decay, and strong parabolic phase, which corresponds to a chirp of -21 nm/ps. c) Comparison of computed (solid) and experimental autocorrelation (hashed). Absorption in the air between the autocorrelator and the FROG setup causes the large difference. d) Spectral intensity (solid) and phase (dotted), and diagnostic spectrum (hashed). Note strong absorption at 5023 nm in each.

Figure 4(d) illustrates the computed spectral intensity (solid) and phase (dotted) and compares with the diagnostics spectrum (hashed). The water line at 5023 nm is obvious in both intensity curves. The computed spectrum rms full-width is 42 nm, compared with 32 nm calculated from the diagnostics curve. The chirp corresponds to a 1% spectral change over the pulse rms full-width, and accounts for most of the spectral width. The computed time-bandwidth product is 2.2 which compares poorly with the diagnostics value of 0.8.

The free induction tail of this pulse can effectively reduce the time resolution and confuse the results of spectroscopic experiments such as pump/probe or photon echo. The chirp is also usually undesirable, although we may tailor it by adjusting the linac for quantum control experiments or others which require a chirp.

6. CONCLUSION

The discussion of basic FEL theory serves to familiarize the reader with the differences between the FEL and conventional laser sources. We describe experimental details that are specific to working with the FEL pulse structure and among the mid-IR absorption lines.

The experimental results include examples of nearly transform limited pulses, chirped pulses, and pulses reshaped by a water vapor absorption line and associated free induction decay. The rms pulse length and spectral width computed from the FROG traces are within 20% of those values obtained from independent diagnostic spectral and autocorrelation data for nearly transform limited pulses.

7. ACKNOWLEDGMENTS

8. REFERENCES

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11. "LabView" is a trademark of National Instruments Corporation.
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