We previously described the use of white-light continuum pulses that permitted spectroscopic measurements with time resolution in the subpicosecond regime [1]. We report here white-light continuum pulses that permit spectroscopic measurements with a time resolution as short as 80 fs. The physics of the continuum-generation process simplifies for our 80-fs pump pulses as compared with earlier continuum generation. In particular, we find temporal, spatial, and spectral properties that are consistent with self-phase modulation within the leading and trailing edges of the pump pulse having a prominent role in generation of the continuum.

The apparatus that we use for generating and measuring our continuum pulses employs only reflective optics and thin generating and analyzing media (Fig. 1). The temporal distribution of the continuum is thus determined primarily by the generation mechanism rather than by group velocity dispersion in the generating or analyzing medium or optics. A pulse at 627 nm of 80-fs duration from our colliding-pulse mode- locked laser [2] is amplified to gigawatt power [3] and divided into a pump and a reference pulse. The pump pulse is focused at f/12 into a thin (500-m m) jet of ethylene glycol by a 25-cm-radius focusing mirror yielding intensities of 10^13-10^14 W/cm^2 at the jet at a repetition rate of 10 Hz. Aluminum coatings are used on the mirrors, which reflect the continuum and dielectric or aluminum coatings on the other mirrors. We determine the temporal distribution of the continuum by cross-correlating the continuum pulse with the reference pulse, which is delayed by a stepper-motor-driven stage. A thin (100-m m) KDP crystal is used to upconvert the continuum light. The finite bandwidth of the KDP crystal for phase-matched upconversion and the angular orientation of the c axis select a tunable region of the continuum. An OMA2 optical multichannel analyzer detects the upeonverted signal and measures the up-converted wavelength. By varying the orientation of the KDP crystal, we map out the temporal distribution of the continuum with a series of cross-correlation functions taken over the spectral range reached by our KDP crystal (0.43-1.09 m m).
 
 

We expect the physics of our continuum generation to differ from previous continuum generation because our pump pulse is approximately 2 orders of magnitude shorter in duration than in earlier work by others [4-8]. The consequence is that self-phase modulation, which increases in importance with decreasing pulse durations takes a more prominent role while less easily controlled processes, such as parametric amplification of quantum noise [5] and self focusing," which do not depend explicitly on pulse duration, decrease in relative importance. Avalanche ionization is also less likely because the threshold for that effect increases with decreasing pulse duration [6,8].

Our observations are consistent with these expected changes in relative importance of the various physical mechanisms. We observe, e.g., that the temporal dis- tribution of the continuum is typical of self-phase modulations (Figs. 2 and 3). The red-shifted portion of the continuum coincides with the leading edge of the pump pulse, whereas the blue-shifted portion of the continuum coincides with the trailing edge of the pump pulse (Fig. 2). (We show the pump-pulse autocorrelation at an intensity below threshold for continuum generation. At the intensity used to generate the continuum, the pump pulse is temporally broadened by ~2x, presumably because of multiphoton absorption.) We also observe that the continuum spectrum is independent of emission angle. This absence of angular dependence is characteristic of self-phase modulation but not of continuum generation by four-photon para- metric amplification [4,5,7]. We also see no clear evidence for avalanche ionizations [6]. Finally, we observe only a small time sweep of the continuum, which is consistent with the small amount of group velocity dispersion in our thin jet.

A more complete plot of the temporal distribution of the continuum is shown in Fig. 3. The uncorrected data, data corrected for the time delay in the KDP crystal (these points are connected by a solid line), and data corrected for both KDP delay and group velocity dispersion in the jet are shown. Because the portion of the continuum in the immediate vicinity of the pump does not exhibit sharply defined peaks in time, we have not attempted to give data in the region. The principal points to be made are as follows. (1) The red portion of the continuum occurs in the vicinity of the leading edge of the pump pulse. (2) The blue portion of the continuum occurs in the vicinity of the trailing edge of the pump pulse. (3) The chirp of the continuum is small, amounting to a temporal shift of <10 fs/1000 A in the red and <30 fs/1000 A in the blue. (4) The temporal shifts that are due to group velocity dispersion in the generating or analyzing medium are small compared with the 80-fs pulse duration.
 
 

In general, we find that the continuum is generated with high efficiency (~50%) and retains the directional properties of the pump pulse with the exception that, for our f/12 pump, the angular divergence increases by 2X. Calculations indicate that a lensing effect and some phase-matched four-photon parameteric amplification at small angles to the pump beam could both contribute to this increase in angular divergence.
 
 

The continuum energy per unit bandwidth as a function of frequency is shown in Fig. 4. The slower decrease of intensity to the blue as compared with the red region of the spectrum is a consistently reproducible feature. We have calculated the degree of frequency broadening that is due to self-phase modulation expected for our pulses by using a nonlinear Schrodinger equation description [10], which includes the effects o group velocity dispersion and pulse reshaping. For intensities of 10^13-10^14 W/cm^2 we predict broadening of ~10-100% of the optical frequency because of self-phase modulation. The extremely large frequency broadening that we observe suggests that additional mechanisms, such as four-photon parametric mixing, [5] also contribute.

The magnitude, the temporal response, and the spectral dependence of the nonlinear frequency shifts are consistent with an assignment of n(2) as being due to an optically induced distortion of the electronic charge distribution, i.e., the electronic hyperpolarizability. We measure these properties of n(2) in pump-probe experiments in which a second liquid sample replaces the
 
 

KDP crystal. A portion of the continuum pulse selected by a bandpass filter is passed through a region of the sample excited by the reference pump pulse. The spectrum of the transmitted probe is then examined by the optical multichannel analyzer. We find, e.g., that the probe pulse is upshifted when it coincides with the leading edge of the pump pulse, downshifted when it coincides with the trailing edge, and frequency broadened to both the red and the blue when it coincides with the pulse peak with a modulated spectrum characteristic of the self-phase modulation process [7,9]. We observe similar spectral shifts for a wide variety of liquids, including ethylene glycol, water, D₂0, CCl₄, and a number of fluorocarbons. We also observe little or no delay in the frequency shift of the probe, indicating that the principal part of the medium response is comparable with or faster than our pump pulse in those liquids [11]. We find a value of n(2) typical of that for an electronic hyperpolarizability, ~1 X 10^-13 esu [8]. We also observe a significant increase of n(2) with increasing probe frequency. This frequency dependence of n(2) accounts at least in part for the greater extension of the continuum to the blue.
 
 

We conclude that the short duration of our pump pulses provides a number of important improvements in white-light continuum generation. Not only do we obtain continuum pulses that permit spectroscopic measurements with a time resolution of 80 fs, but the physics of the generation process is simplified in ways that make the continuum pulses more reproducible from pulse to pulse and more spatially uniform. We also anticipate that the feasibility of extending these techniques to short lengths of optical fibers [l2] will permit further improvements in spatial uniformity, pulse reproducibility, and repetition rate.
 
 

Special thanks are due to F. A. Beisser for essential technical support.
 
 

References
 
 

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11. We do observe evidence for a delayed component of n2 in CC14. Greene has also reported a delayed component of n2 in CS2- [B. 1. Greene, in Picosecond Phenomena III, A. Laubereau and K. B. Eisenthal, eds. (Springer-VerW, New York, 1982).

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