plates that are thin enough (250 jm) to be both inexpensive and dispersion free. ... theless pulse-width measurement in the UV remains problematic compared ...
April 1, 1991 / Vol. 16, No. 7 / OPTICS LETTERS
499
Two-photon absorption in diamond and its application to
ultraviolet femtosecond pulse-width measurement J. I. Dadap, G. B. Focht, D. H. Reitze, and M. C. Downer Department
of Physics, University of Texas at Austin, Austin, Texas 78712
Received November 15, 1990; accepted January 28, 1991 Intensity-dependent transmission measurements of 310-nm femtosecond pulses show that diamond has a twophoton absorption coefficient of 0.75 + 0.15 cm/GW, in approximate agreement with universal scaling formulas for
two-photon absorption in diamond-structure materials. We then demonstrate that two-photon absorption is strong enough to permit simple measurements
of ultraviolet femtosecond pulse widths in single-crystal diamond
plates that are thin enough (250jm) to be both inexpensive and dispersion free. Autocorrelation measurements of 10-50-nJ, 0.18-1.4-ps pulses are presented. The method requires no phase matching and can be applied to pulses in the wavelength range of 220-550 nm.
Recently a number of new femtosecond sources have
been developed at near-UV wavelengths,1-6 which has opened new applications in ultrafast molecular spectroscopy7 and high-energy-density physics.8 These sources include intracavity frequency-doubled dye lasers'-4 and high-power excimer amplifiers.5'6 Nevertheless pulse-width measurement in the UV remains problematic compared with routine autocorrelation measurements in the visible and near-infrared based on phase-matched second-harmonic generation in transparent crystals. The lack of frequency-doubling crystals in the UV necessitates alternative, usually less convenient and more expensive, methods. For example, measurements based on third-harmonic generation in gases require detection of a vacuum-UV autocorrelation signal. Cross correlation with visible pulses by phase-matched sum-frequency mixing in beta-barium borate4 is restricted to X > 300 nm and suffers from group-velocity walk-off between the UV and visible pulses. In measurements based on twophoton fluorescence,9 photoionization,' 0 photoconductivity," or photoemission, the autocorrelation signal is superimposed onto a strong background. A recently developed method for third-order autocorrelation measurements of UV pulses, based on degenerate four-wave mixing in fused silica, overcomes many
of the problems of other methods, although it has been demonstrated only for microjoule and higher-energy UV pulses. 12
220 nm, a range that includes most currently available UV femtosecond sources. Our measurements with 310-nm, 10-50-nJ pulses of duration 100 fs < tp < 2 ps show that they induce TPA in diamond strong enough for autocorrelation measurements within path lengths of 0.25 mm, small enough that temporal broadening from group-velocity dispersion is negligible, and small enough that the diamond samples needed are available commercially at inexpensive prices. In fact, for UV pulses with a peak intensity of >25 GW/cm2 , the transmission decrease caused by TPA in a 0.25-mmthick diamond crystal is easily visible to the naked eye. Autocorrelation is achieved by measuring the transmission decrease of a weak probe induced by a strong pump as a function of time delay. Although not background free, the relevant signal is easily separated completely from the background when necessary by use of conventional lock-in detection methods. Maximum UV pulse fluence is limited only by the optical damage threshold of diamond, which is among the highest of all materials (e.g., 0.5 J/cm 2 for 90-fs, 620-
nm pulses1 3 ). Because phase matching is not required, beam alignment with respect to crystalline axes is not critical. Consequently we believe that this method can provide simple, accurate, low-cost autocorrelation measurements for nearly all currently available UV femtosecond sources. For the measurements presented here, 70-fs pulses at 620 nm were generated in a colliding-pulse mode-
In this Letter we demonstrate a simple, low-cost method for obtaining second-order autocorrelation measurements of femtosecond pulses at least as far as 220 nm in the UV, and at a pulse energy at least as low as the nanojoule regime, by using two-photon absorption (TPA) in diamond. Although two-photon processes formed the basis of some of the earliest mea-
locked dye laser, amplified at 5-kHz repetition rate to
gap insulators has not to our knowledge been exploited to characterize pulses from the wide range of recently
focus) in a 0.25-mm-thick
surements of visible ultrashort pulses, 9 TPA in wide-
developed UV femtosecond sources. 1- 6 Because undoped diamond has a wide band gap (5.45 eV), no linear optical absorption occurs at wavelengths of X > 0146-9592/91/070499-03$5.00/0
0.5-,uJ energy in a dye amplifier,1 4 then frequency dou-
bled in a 300-,gm-thickKDP crystal to generate linearly polarized 310-nm femtosecond pulses at energies of as much as 50 nJ. To determine the TPA coefficient ITPA, a single beam of 135-fs UV pulses was focused to a spot diameter of 15 ,um (determined by measuring transmission past a knife edge translated across the type Ha single diamond
(110) crystal purchased from Dubbledee Diamond Corporation, and the transmission was measured as a function of intensity. The pulse width was determined separately by a pump-probe measurement as © 1991 Optical Society of America
500
-'-
OPTICS LETTERS / Vol. 16, No. 7 / April 1, 1991
0.70
at a number of wavelengths.16-'8 Van Stryland et al.17 have shown that the measured ITPA of these semiconductors is predicted by a single universal formula [Eqs. (1) and (2) of Ref. 17] that relates /TPA to a small set of material parameters: photon energy hv, band gap Eg, refractive index n, a nearly material-independent momentum parameter Ep- 21 eV, and a dimensionless proportionality constant K = 3100 determined by fitting the measured ITPA values. Diamond, unlike the semiconductors considered by Van Stryland et at.,'7 is an indirect-gap material. Nevertheless the direct gap Edir= 7.3 eV is expected to provide the relevant scaling parameter because the optically coupled states are directly linked at our photon energy
0.60 -
0 en 0 5 0 M .
t
en
Z 0.40
t
0.30
-
(i.e., 2hv > Edir). However, with hv = 4.0 eV, n(4.0 eV)
me
0.20 F )
50 100 1150 INSIDE INTENSITY (GW/CM 2 )
Fig. 1. Transmission of single 135-fs, 310-nm pulses through a 250-Atm-thicksingle-crystal diamond sample as a function of peak intensity inside the sample. The curves represent the calculated transmission with TPA coefficients.
described below. The power of the transmitted beam was then measured with a photodiode as the incident beam power, measured with a calibrated reference photodiode, was varied. Figure 1 shows the sample transmission as a function of the peak intensity (1 R)Io of the UV pulse inside the sample. At low intensities, the transmission T = (1 - R)2 = 0.66 is determined solely by the reflectivity R of the front and back surfaces. However, T drops monotonically to 0.42 as (1 - R)10 reaches 150 GW/cm2 . If we assume TPA to be the only absorption mechanism and neglect dispersive broadening of the pulse within the diamond, then the transmitted intensity of each point of the pulse spatial and temporal profile I(r, t) can be calculated from dI(r, t)/dz = -1TPAI 2(r, t), which on integration yields
T= (1-R) 2
Jdr2irr
+"
10 (r, t)dt
J 1 + ITPAL(l
-
R)10(r, t)
The curves through the data in Fig. 1 show the calculated transmission T versus (1 - R)Io for three #TPA values, with the assumption that Io(r, t) = Io exp(-r 2 / ro2 )sech2 (1.763t/tp). No polarization dependence was observed. T is well described by OTPA = 0.75 i 0.15 cm/GW. A separate check for defocusing or self-focusing induced by n2 over our intensity range with a Zscan' 5 technique yielded negative results. Scaling laws for multiphoton absorption' 6 predict that threephoton absorption is unimportant for I < 1013W/cm2 . We conclude that TPA is the dominant nonlinearity over the intensity range shown in Fig. 1.
To our knowledge #TPA of diamond has not previously been measured. Nevertheless #TPA of numerous structurally identical direct-gap semiconductors with band gaps between 1.4and 3.7 eV have been measured
= 2.6, and Ep and K values as above, Eqs. (1) and (2) of Ref. 17 yield #TPA = 0.59 cm/GW for Eg = Eindand 0.10 cm/GW for Eg = Edir. Both values are within an order of magnitude of our measured #TPA, but surprisingly use of Eindyields better agreement. This discrepancy may signify that the parameters K and Ep are larger in diamond than in narrower-gap diamond-structure materials. A related example of a similar discrepancy is the case of TPA in silicon with 2hv
4 eV >
Edir,
where the measured18 I3TPA (36 cm/GW) is significantly higher than that predicted by Ref. 17 with Eg = Edir and other parameters as given above because nearly parallel valence and conduction bands in the X valley separated by -4 eV yield a much higher joint density of states than in the simpler parabolic band model used in deriving the universal formula. However, we have not identified the source of the smaller discrepancy in diamond. The time dependence of the absorption and the duration of the UV pulses were measured by a pumpprobe experiment. A weak probe beam was separated from the pump with a beam splitter, passed through a variable delay path, and focused with a separate lens at an incidence angle of approximatley 30° onto the pump focal spot. With this geometry the region of pump-probe overlap was much shorter than the sample thickness. However, the probe could be conveniently separated from the pump with any polarization, and the magnitude of the probe transmission decrease was limited to a few percent, thus avoiding distortion of the autocorrelation signal from saturation. Overlap and signal are easily increased by using collinear propagation through the sample and orthogonal polarizations. Although lock-in detection was used, signals large enough to be measured without synchronous detection were obtained at our highest pump intensities. Figure 2 presents time-resolved differential transmission (AT/T)probe(At)data for a probe polarized orthogonally (filled circles) and parallel (open circles) to the pump. The signal is virtually independent of mutual pump-probe polarization. For the data shown, a 25-nJ pump pulse was focused to a 15-,tm-diameter beam waist, and the maximum signal corresponds to a 3.5% drop in probe transmission, consistent with the signal expected for I3 TPA = 0.75 cm/GW and the -10,umlength of the overlap region of the pump and probe beam waists. To within experimental error, (AT/ T)probe(At)is temporally symmetric, returning to its
April 1, 1991 / Vol. 16, No. 7 / OPTICS LETTERS
501
This research was supported by the National Sci-
0
ence Foundation
(grant DMR-8858388), the U.S. Air
Force Office of Scientific Research (contract F4962089-C-0044), and the Robert A. Welch Foundation (grant F-1038).
8 TPA across the direct
gap can be stronger than linear absorption across the indirect gap. TPA in still wider-gap materials (e.g., fused silica, alkali halides, and alkaline earth fluorides) provides an alternative way of extending the 6 7 method to shorter wavelengths, although theory'> ,1> and experiment 2 0 show that
I
3
TPA becomes
rapidly
smaller as the band gap increases. Consequently diamond appears to be the material of choice in the wavelength range of most currently available UV femtosecond sources.
Opt.
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