Frequency resolved optical gating in the UV using the electronic Kerr effect

Transcription

1 Appl. Phys. B 63, (1996) Frequency resolved optical gating in the UV using the electronic Kerr effect K. Michelmann, T. Feurer, R. Fernsler, R. Sauerbrey Institut fu r Optik und Quantenelektronik, Friedrich-Schiller-Universität Jena, Max-Wien-Platz 1, D-7743 Jena, Germany Fax: 49-() , michelmann@qe.physik.uni-jena.de Received: 24 June 1996/Accepted: 1 July 1996 Abstract. A phase-sensitive single-shot autocorrelator (FROG) for the UV spectral region based on the electronic Kerr effect is demonstrated. Since the Kerr shutter technique leads to a third-order autocorrelation function, information about pulse asymmetries and pulse structures along with the temporal phase can be obtained. PACS: 42.6.By; k; Fm Over the past few years there has been considerable progress in the development of femtosecond lasers. Pulse widths as short as 8 fs [1] can routinely be generated and pulse energies up to several joules [2] have been reached for a number of wavelengths leading to peak intensities of several hundreds of terawatts. In order to reach a bandwidth-limited pulse, temporal phase variations due to intracavity material have to be compensated and for highintensity systems stretcher compressor combinations have to be optimized. On the other hand, there are experiments such as coherent control of wavepacket dynamics [3, 4] where the laser pulse should have a well-defined temporal phase or amplitude modulation. This can be obtained by various means such as prism or grating combinations [5, 6] or liquid-crystal matrices [7]. In all cases, however, it is necessary to have adequate diagnostics that are able to fully determine the electric field of the laser pulse. Since electronic devices and even the fastest streak cameras (maximum resolution &.5 ps [8]) do not have the necessary temporal resolution, autocorrelation or crosscorrelation techniques have to be used. The measured correlation traces are related to the original pulse by some mathematical transformation and in order to retrieve the complete electric field the inverse operation has to be performed. In most of the correlation measurements, some information on the original pulse is lost (mostly phase information) and there has been an extensive search over the past years for techniques that are able to retrieve the complete electric field. One of the most successful approaches so far is called Frequency-Resolved Optical Gating (FROG) [9]. Iterative algorithms have to be used to compute the electric field from the recorded FROG trace [1]. Using a third-order effect, i.e. the electronic Kerr effect, as the gating mechanism leads to very intuitive FROG traces and by calculating moments of low order, good estimates of the phase-modulation can be obtained. Besides the search for appropriate correlation techniques, progress has been made to extend the wavelength region for correlation techniques from the visible to shorter wavelengths. Since second-harmonic generation in crystals is not possible in the UV, other techniques have been investigated such as two-photon fluorescence [11, 12], three-photon fluorescence [13], two-photon ionization [14], two-photon absorption [15], and degenerate four-wave mixing [16]. In the present publication, we present a single-shot PG-FROG (PG: polarization gating) technique for the UV spectral range, i.e. 248 nm. 1 Principle of measurement The electronic Kerr effect as a nonlinear effect for subpicosecond pulse-width measurements in the UV spectral region has been used by Albrecht et al. [17, 18], first for multishot correlation measurements and subsequently for single-shot correlation measurements. In both cases, the third-order correlation function is recorded. A schematics of the experimental setup is shown in Fig. 1. The basic idea of a PG-FROG is that a Kerr medium is placed between two crossed polarizers (polarizers 1 and 2). In principle, all wide band gap materials such as CaF, BaF, LiF, MgF and fused silica are potential candidates for autocorrelation measurements in the deep UV. The incoming beam is split into two replicas by the beam splitter. One of them (probe beam) traverses the two crossed polarizers with the Kerr medium in between and simultaneously the pump beam (intensity ratio pump:probe"1:1) is incident on the Kerr medium under a small angle. Its direction of polarization has been

2 486 λ/2 plate 1 % 9 % Beam splitter Cylindrical lense Cylindrical lense Pump (45 pol) Probe (s-pol) Kerr-medium Polarizer 2 (p-pol) E sig(t, τ) τ FROG-signal Spectrometer τ ω Polarizer 1 (s-pol) Fig. 1. Experimental setup of the PG-FROG. The incoming pulse is split into two replicas (intensity ratio 1: 1). The direction of polarization of the pump beam is rotated by 45 with respect to the probe beam. The probe beam passes a pair of crossed polarizers with the Kerr medium in between. If both pulses overlap the induced birefringence causes a change of the polarization of the probe beam. The transmission through the crossed polarizers is therefore proportional to the spatiotemporal overlap of the two beams. rotated (λ/2-plate) by 45 with respect to the direction of polarization of the probe beam. If both pulses overlap temporally and spatially, the induced birefringence by the pump beam causes a change of polarization of the probe beam that is proportional to the pump intensity. The transmission through the crossed pair of polarizers is therefore proportional to the spatiotemporal overlap of the pump beam and the probe beam. If cylindrical lenses are used to focus both beams, the temporal delay between the two pulses is mapped on to the spatial coordinate of the line focus and a single-shot autocorrelation trace is obtained. The temporal resolution is mainly determined by the angle between the two pulses and the spatial resolution of the detection system. The autocorrelator can be easily calibrated by introducing a known temporal delay to the probe beam and observing the shift of the autocorrelation trace. The line focus is then imaged on to the entrance slit of a spectrometer (resolution +25 at 248 nm) and the two-dimensional FROG trace is subsequently recorded by a CCD camera. The laser pulse stems from a femtosecond KrF laser system that delivers 5 fs pulses with energies up to about 15 mj. Before entering the autocorrelator, the pulse traverses a two-prism (CaF ) compressor having a transmission of about 4%. The size of the line focus (focal length 2.5 cm) at the position of the Kerr medium (fused silica) is 8.2 mm and the energy of the pump beam is )1 μj leading to a peak intensity of about 1 GW/cm. In the case of fused silica, the upper limit [determined by the validity of the linear approximation of ¹(t) in 2] is about 5 GW/cm. The angle between the two incident beams is 8, and the time window therefore is 3.7 ps. For an angle of 8, the walk off distance at the end of the Kerr medium (2 mm) is about 3 fs, and thus neglegible for pulses on the order of some hundred femtoseconds. 2 Theory The electronic Kerr effect is a third-order effect and can be considered instantaneous as long as the response time of the susceptibilities involved is shorter than the temporal width of the laser pulse. If this is not the case, the convolution between the electric fields and the susceptibilities is measured. For isotropic materials, the susceptibility tensor χ has three independent components. Probe and pump pulse both propagate in the z-direction and the pump pulse is polarized in the x-direction. The direction of polarization of the probe beam is tilted by 45 with respect to the pump beam. Hence, the change of the index of refraction is approximately Δn &χ E, Δn &χ E, (1) where n and n are the indices of refraction parallel and perpendicular to the direction of polarization of the pump beam and E is the electric field of the pump beam. If χ and χ have different values, the polarization of the probe beam changes and is usually elliptically polarized after traversing the Kerr medium. Therefore, the transmission of the Kerr shutter (polarizer 2, Kerr medium, analyser) ¹(t) is ¹(t)"sin ( Φ(t)), Φ(t)"2π Δn (t) l, λ Δn "Δn!Δn &I (t), (2) where l is the thickness of the crystal and λ the vacuum wavelength of the probe beam. Supposing that the phase shift Φ(t) is small so that sin(φ)+φ is valid, the timeintegrated signal for a given delay τ between pump and probe beam is K(τ)& dti (t) I (t!τ) (3)

3 487 which corresponds to the third-order autocorrelation function G in the case of I (t)&i (t). The electric field is represented by a transient amplitude A(t) and a time-varying phase Φ(t), E(t)"A(t) exp [!iφ(t) ]. (4) The intensity I(t) and the instantaneous frequency ω(t) can be derived from (4): I(t)& E, (5) ω(t)" dφ dt. (6) The experimentally obtained FROG trace S(τ, ω) is equivalent to the spectrogram of the laser pulse [19, 2] and for the present conditions using the electronic Kerr effect as the gating mechanism, S(τ, ω)" dte(t) E(t!τ) e ω. (7) From the FROG trace, two useful quantities can be obtained: the third-order autocorrelation function G (τ) (zeroth-frequency moment) and the first-frequency moment m ω (τ) [19, 2], G (τ)" dω S(τ, ω), (8) dωω S(τ,ω) m ω (τ)". (9) dωs(τ,ω) The third-order autocorrelation function yields a zeroorder estimation on the temporal width of the pulse and the first-frequency moment indicates the phase modulation of the pulse. Assuming a Gaussian pulse shape, the first-frequency moment is equal to the instantaneous frequency stretched by a factor of, i.e. m ω (t)"ω( t). It is also independent of the beam profile of the pump beam and therefore a quite powerful tool to estimate the phase modulation even for inhomogeneous beam profiles. In order to accurately obtain the complete electric field of the pulse, iterative algorithms [2] have to be used. These algorithms, however, need FROG traces that are free from systematic errors, such as spatial chirp or profile distortions in the focus. 3 Results and discussion Figure 2 shows three measured FROG traces from pulses that emerge from the above-mentioned prism compressor corresponding to different prism separations 72, 12, and 132 cm, respectively. The pulse entering the prism compressor has an almost linear positive chirp due to Selfphase Modulation (SPM). It can be clearly seen that for short prism separations (Fig. 2a), the wavelength is decreasing with time and hence indicating a positive chirp. Closer to the optimum prism separation (Fig. 2b), the pulse has a smaller-phase modulation. Increasing the distance between the two prisms even further (Fig. 2c), the phase modulation is overcompensated and a negative chirp can be seen. In Figs. 2d f, the third-order autocorrelation trace obtained from the FROG traces in Fig. 2a c, following (8) is shown along with the first-frequency moment [see (9)]. The dip in the autocorrelation function is probably due to an inhomogeneous beam profile of the pump beam rather than an amplitude modulation of the pulse. The quality of the spatial beam profile of the experimental experimental experimental a - b - c Mean frequency/ d e f Third order correlation function Fig. 2a f. Experimentally obtained FROG traces from a 5 fs KrF laser pulse that has self-phase modulation. The pulse traverses a prism compressor consisting of two CaF prisms at three different prism seperations a) 72 cm, b) 12 cm and c) 132 cm. d) f) show the corresponding third-order autocorrelation trace and the first-frequency moments. Assuming a Gaussian pulse shape a linear chirp of a, d) (55$1) ps,b,e) (2$5) ps, and c, f) (!3$1) ps can be derived.

4 a experimental calculated instantaneous frequency first frequency moment c b calculated third order correlation function d 1. calculated.8 experimental Fig. 3. a Experimentally obtained FROG trace of a nearly transform limited pulse. b the calculated FROG trace of the reconstructed pulse. c the firstfrequency moment of the experimental FROG trace and the reconstructed instantaneous frequency. d the measured and calculated third-order autocorrelation trace. excimer laser system yields systematic errors in the FROG trace that limit the possibility to use iterative algorithms to reconstruct the electric field. A simple method to obtain an estimation of the phase modulation of the three pulses is to use the proportionality of the phase modulation to the first-frequency moment. In the case of a linearly chirped Gaussian pulse, a linear chirp of (a) (55$1) ps, (b) (2$5) ps, and (c) (!3$1) ps is obtained. If the seed pulse of the final amplifier is attenuated by a factor of about 1, almost no SPM occurs and the pulse emerging from the amplifier should be close to transform limited. The corresponding FROG trace of such a pulse can be seen in Fig. 3a. The arrow indicates a part of the FROG trace (τ') where the profile exhibits strong fluctuations. The best approximation to the experimental data obtained by using the iterative algorithm described in [2] is shown in Fig. 3b. The RMS, a measure of the quality of the solution, τ, ω(s (τ, ω)!s (τ, ω)) RMS" (1) N τ N ω (number of sample points: N τ "N ω "128) for more than 5 iterations is about 1.5% which is as mentioned before mainly due to the spatial pump and probe beam profile along the line focus that leads to artificial structures in the FROG trace. Figure 3c shows the reconstructed instantaneous frequency ω(t) of the laser pulse and the firstfrequency moment (see (9)). The iterative algorithm is able to reconstruct phase and amplitude quite accurate for the undistorted regions in the FROG trace (negative delay times). This can also be seen by comparing the measured (see (8)) and calculated third-order autocorrelation traces in Fig. 3d. For positive delay times, the error is somewhat more substantial due to the inhomogeneous beam profile. It can be seen that at times where the intensity is non-zero, the first-frequency moment is flat, indicating that the pulse has no chirp and therefore is transform-limited as expected. 4 Conclusion A single-shot phase-sensitive FROG autocorrelator in the UV region (248 nm) has been demonstrated. Since most high-power systems have repetition rates of several shots per second iterative algorithms are too slow in order to fully reconstruct the electric field in real time. It has been shown that calculating two moments from the measured FROG trace leads to a fast estimation of the temporal width and phase modulation of the pulse and is therefore suitable for on-line monitoring of the temporal-pulse shape. This procedure can also be used for lasers that have a non-uniform spatial beam profile, such as excimer lasers. Acknowledgement. The authors gratefully acknowledge support for this research from the Deutsche Forschungsgemeinschaft (SA 325/ 3-1). References 1. A. Stingl, M. Lenzner, Ch. Spielmann, F. Krausz, R. Szipöcs: Opt. Lett. 2, 62 (1995) 2. M.D. Perry, F.G. Patterson, J. Weston: Opt. Lett. 15, 381 (1991) 3. B. Amstrup, G. Szabo, R. Sauerbrey, A. Lo rincz: Chem. Phys. 188, 87 (1994) 4. B. Kohler, V.V. Yakovlev, J. Che, J.L. Krause, M. Messina, K.R. Wilson, N. Schwentner, R.M. Whitnell, Y. Yan: Phys. Rev. Lett. 74, 336 (1995) 5. Z. Bor, B. Racz: Opt. Commun. 54, 165 (1985) 6. K. Osvay, I.N. Ross: Opt. Commun. 15, 271 (1994)

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