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The Measurement of Few-Cycle Pulse Duration Is a Real Challenge Even with the Most Powerful Technique

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The Measurement of Few-Cycle Pulse Duration Is a Real Challenge Even with the Most Powerful Technique 5 Technological basis for the primary sources The measurement of few-cycle pulse duration is a real challenge even with the most powerful technique. The reasons for this are the required ultra-broad phase matching bandwidth, ideally all-reflective setup and minimal introduced dispersion by the generation of the non-linear signal. There are some versions of FROG as SHG [12] and TG [13] that under special conditions – such as few-µm thick non-linear medium – can support pulses with about a single optical cycle duration [14]. A much more complex, but even more detailed technique for sub-2-cycle pulses is based on the generation of a single XUV attosecond pulse and using the laser electric fields to shift the energy spectrum of free electrons produced by the XUV probe pulse. Measuring the electron spectrum as a function of the delay between the laser and the XUV pulse a so called “attosecond streaking" curve is obtained [15]. This determines the electric field of the laser and even the absolute phase or carrier envelope phase and the strength of the electric field in the point of measurement. Attosecond streaking belongs to the conventional approaches that to characterize a short pulse uses an even shorter pulse. At the end of this brief overview the complete measurement of long pulse durations (100 ps– 1 ns) with large time-bandwidth product (TBP) is discussed. It should be noted that a fast photodiode with an oscilloscope can measure the temporal intensity without the phase for these pulse durations – assuming there are no fast changes. This might be regular task in chirped pulse amplification systems to determine the temporal structure of the stretched pulse. A very simple, robust and linear technique is based on spectral interferometry. In this approach the pulses are split before stretching, one replica is stretched then the two pulses are combined with a variable delay between them and sent to a spectrometer. The spectrum will be obtained with an interference pattern at the wavelength, which arrives at the same time as the short pulse. This way the long stretched pulse is sampled and its group delay is determined as a function of the wavelength [16]. Recently, even spectral interferometry has been improved that it can measure long pulses with large TBP [17]. Bibliography [1] Sala K. L., Kenney-Wallace G. A. and Hall G. E., IEEE Jour. Quant. Electr. 16, 990 (1980. Herrmann D., Tautz R., Tavella F., Krausz F. and Veisz L., Opt. Expr. 18, 4170 (2010). [2] Etchepare J., Grillon G. and Orszag A., IEEE Jour. Quant. Electr. 19, 775 (1983. Janszky J. and Corradi G., Opt. Commun. 60, 251 (1986). [3] Diels J. C. M. et al., Appl. Opt. 24, 1270 (1985). [4] Trebino R., Frequency-Resolved Optical Gating: The Measurement of Ultrashort Laser Pulses (Kluwer Academic Publishers, Norwell, USA, 2000; http://www.physics.gatech.edu/frog/. [5] DeLong K. W. et al., JOSA B 11, 2206 (1994). [6] Trebino R. et al., Rev. Sci. Instr. 68, 3277 (1997). [7] O’Shea P., Kimmel M., Gu X. and Trebino R., Opt. Lett. 26, 932 (2001). [8] Iaconis C. and Walmsley I. A., Opt. Lett. 23, 792 (1998. Iaconis C. and Walmsley I. A., IEEE Jour. Quant. Electr. 35, 501 (1999). [9] Lozovoy V. V., Pastirk I. and Dantus M., Opt. Lett. 29, 775 (2004. XuB.,GunnJ.M.,DelaCruzJ.M.,LozovoyV.V.,DantusM.,JOSAB23, 750 (2006). [10] Oksenhendler T., Coudreau S., Forget N., Crozatier V., Grabielle S., Herzog R., Kaplan D. and Gobert O., App. Phys. B 99, 7 (2010). [11] Minkovski N., Petrov G. I., Saltiel S. M., Albert O. and Etchepare J., JOSA B 21, 1659 (2004). [12] Baltuska A., Pshenichnikov M. S. and Weirsma D. A., IEEE Jour. Quant. Electr. 35, 459 (1999. Baltuska A., Fuji T. and Kobayashi T., Opt. Lett. 27, 306 (2002). 244 www.extreme-light-infrastructure.eu 5.3 Diagnostics of Laser Parameters [13] Graf U., Fieß M., Schultze M., Kienberger R., Krausz F. and Goulielmakis E., Opt. Expr. 16, 18956 (2009). [14] Cavalieri A. L. et al, New J. Phys. 9, 242 (2007). [15] Goulielmakis E. et al., Science 305, 1267 (2004). [16] Dou T. H., Tautz R., Gu X., Marcus G., Feurer T., Krausz F. and Veisz L., Opt. Expr. 18, 27900 (2010). [17] Cohen J., Bowlan P., Chauhan V. and Trebino R., Opt. Expr. 18, 6583 (2010) 5.3.2 CEP measurement and stabilization The time dependence of the electric field of a laser pulse can be written as: E(t)=E0(t)cos(ωt+ ϕ),whereE0(t) is the envelope function of the field, ω is the angular frequency of the carrier wave, and ϕ is the Carrier-Envelope-Phase (CEP). Figure 5.11: Influence of the CEP on the electric field of a few-cycle pulse; cosine waveform ϕ =0 (red solid line), sine waveform ϕ = π/2 (blue dotted line). It follows from this equation than only in the few-cycle regime (the pulse contains only few oscillations of the carrier wave of the field), the CEP plays a key role, as only when the pulse duration determined by the envelope is comparable to the period of the carrier wave, the electric field form is significantly affected by the CEP (see Fig. 5.11). The CEP, plays a fundamental role for extreme non-linear optics effects as these processes are driven by the precise electric field form rather than by the envelope as in conventional non-linear optics. The reliable generation of isolated attosecond pulses requires the control of the CEP of ultrashort pulses as already demonstrated for high-order harmonic generated in gas [1]; the control of the CEP is expected to play a fundamental role also for the generation of isolated attosecond pulse on solid targets [2]. Application of isolated attosecond pulses for time resolved experiments, therefore, requires measurement and stabilization of the CEP. Several techniques have been proposed and experimentally applied to monitor and control this parameter. The techniques used for the determination of the CEP and the CEP drift will be discussed in the following sections devoted to the methods implemented to stabilize the CEP in amplified laser systems. CEP measurement In situ determination of the CEP requires an extreme nonlinear optics process whose outcome is directly linked to the precise electric field value. The process of Above-Threshold Ionization (ATI) and High-order Harmonic Generation (HHG) are ideal candidates to accomplish this task. The influence of the CEP on extreme nonlinear phenomena was first demonstrated on ATI in www.extreme-light-infrastructure.eu 245 5 Technological basis for the primary sources 2001 [3], and since then ATI based CEP measurement using a so called Stereo-ATI phase-meter evolved to a well established technique. Recently with such an apparatus it became possible to determine the CEP of single laser pulses consecutively up to several kHz repetition rates [4]. The method is based on the measurement in opposite directions (left-right or up-down) of the photoelectron spectra generated by re-scattering on the parent ion of the electrons freed by an intense laser field. The number and the energy of the electrons emitted in the left-right directions strongly depends on the maximum of the electric field pointing in that direction. As the CEP determines the ratio of the peak electric field in opposite directions, ATI is a well suited approach for the determination of the CEP of few-cycle pulses. For this purpose an asymmetry parameter, given by the difference of the numbers of electrons emitted in the two directions divided by the total number of electrons, can be introduced. The value of this parameter depends on the energy range of the photoelectrons. By proper choice of the energy ranges, each CEP value can be associated to two asymmetry parameters calculated in different energy ranges. Tagging the CEP of each single laser shot recently made possible the study of phase dependent phenomena at 3-kHz repetition rate without the need for phase stabilization [5]. Even though the envisaged ELI few-cycle lasers are planned to operate phase stabilized, CEP-tagging can be used as an alternative approach to perform CEP-dependent experiments. The HHG process is also sensitive to the CEP; however due to phase matching effects, the harmonic spectra measured for different CEPs cannot be directly linked to the single atom re- sponse and extraction of the CEP from the experimental data can present additional difficulties. Nevertheless it has been demonstrated that, under proper conditions, this method can be used to determine the CEP of the driving pulse, even for relatively long (≥10 fs) pulses; however always with a π phase ambiguity [6] as the HHG process is not influenced by a π change of the driving electric field. Other effects such as terahertz generation [7] and non-sequential double ionization [8] are affected by the CEP and could be implemented to determine its value. It is important to observe that due to intensity levels that will be reached by the laser system envis- aged in ELI, the motion of the electron will be dominated by relativistic effects and therefore the characteristics of the HHG and ATI processes will be strongly modified. These methods can serve for monitoring the CEP of a low intensity leak from the main pulse, and thus determine the CEP with an offset ambiguity at the interaction; for the determination of the CEP in situ new effects and new approaches will be required, such as the angular distributions of photons emitted via multiphoton Compton scattering, as recently proposed [9]. For many applications, it is important to characterize the CEP drift, i.e.
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