Minimizing attosecond CEP jitter by carrier envelope phase tuning

. Minimizing the CEP jitter of isolated attosecond pulses (IAP) will be important for future applications. This jitter is experimentally and theoretically investigated and can be minimized when the driving pulse is near its Fourier limit but with slightly negative chirp. Thus, understanding and characterization of the CEP jitter of IAPs is a first step towards exact control of the electric field of IAP pulses.


Introduction
The generation of isolated attosecond pulses (IAP) by high harmonic generation (HHG) requires ultrafast carrier envelope phase (CEP) stabilized optical driving pulses. The optical dispersion and the CEP of these pulses are usually controlled by a pair of wedges [1]. For a given optical dispersion ( D ), a residual jitter of the CEP ( CEP ) of the driving laser still remains. In this work we assume the CEP jitter of the driving laser is the main source of CEP jitter of the generated IAPs ( atto ). This effect will be analyzed experimentally and theoretically by solving the time-dependent Schrödinger equation (TDSE).

CEP-Scans: Experimental
We use a CEP-stabilized sub-6 fs few-cycle Ti:Sa laser system to generate isolated attosecond pulses by amplitude gating and spectral filtering of the HHG cut-off region [2]. Experimentally, the CEP is controlled by a pair of wedges introducing either a positive or negative chirp to a Fourier-limited pulse by material dispersion. The CEP stabilization and control are realised with a f-to-0f interferometer in the oscillator and a f-to-2f interferometer in the amplifier averaging over 30 shots. For this laser system, the CEP jitter was measured to be 60 mrad. A neon-gas filled hollow-core fiber spectrally broadens the pulses and a set of chirped mirrors compresses the octave spanning spectrum to Fouriertransform-limited pulses of 5.9 fs. The beam is focused into a neon filled target with a * Corresponding author: Thorsten.Uphues@cfel.de propagation length of ~2 mm for HHG. HHG spectra were recorded over many CEP periods ( Fig. 1), with a slit grating spectrometer to identify the highest cut-off energy in the HHG spectrum. We estimate the cut-off bandwidth by a simple intensity model [3] in perfect agreement with the half-cycle cut-off model [4]. The classical cut-off depends linearly on the ionization potential of the medium (I p ) and the instantaneous intensity (I) resulting in E cut − I p ∝ λ 2 I [5]. Thus the simple relation describes the energy range of the continuum, where I max1 and I max2 are the values of the intensity maxima of the two neighbouring half-cycles contributing to the highest energy part of the HHG process.

CEP-scans: Simulations
For this work we simulated optical pulses with a bandwidth supporting 3.8 fs and an intensity of 4·10 14 W/cm 2 . The results of a simulated CEP-scan for IAPs are shown in Fig. 2a and 2b; where the left upper panel displays the time dependence of the IAPs as a function of  D (Fig. 2a) and the lower three panels (Fig. 2b) show the time dependence, where the wedge position is fixed at a given  D , and the CEP phase  CEP of the driving laser is varied over a range from 50 to 50 mrad. For the negatively and the positively chirped pulses, CEP jitter can lead to the formation of two attosecond pulses with a probability of ~50%. In the Fourier limited case ( D = 0, Fig. 2b, center), it is possible to generate a single IAP independent of CEP jitter within the considered range.
The influence of the CEP-jitter of the driving laser on the CEP of the IAP ( atto ) is depicted in Fig. 2c and 2d. Three positions from a CEP-scan of the driving laser at  D = 2and 0 rad are considered. For each  D , the dependence of  atto on driving laser CEP without dispersion is calculated (Fig. 2c). In each case, the dependency is found to be approximately linear over the considered  CEP range; the slopes of the linear dependency are provided in Fig. 2c. For the strongest up-and down-chirp, the slopes are steeper than the slope at  D = 1 rad. For further analysis corresponding histograms are generated for the CEP jitter of the IAP ( atto ), assuming a CEP-jitter of the driving laser from 100 to 100 mrads (Fig. 2d). The minimum attosecond CEP jitter is observed for the case of  D close to 1 rad.   [2,3]).
In this work the possibility to optimize the driving laser's spectral phase  D to generate ideally stable attosecond pulses using TDSE simulations including dispersion-free jitter  CEP was demonstrated. Generally, by changing  D in a CEP-scan, a value for a theoretical minimum of the CEP jitter of the attosecond pulses  atto can be identified. This value is accessible in the experiment by choosing the corresponding dispersion controlled by a pair of wedges. According to our simulations, a slight negative chirp of near 1 rad yields optimal IAP formation and stability.