Precise Control of the Pulse-to-Pulse Carrier-Envelope Phase in a Mode-Locked Laser
Using a coherent frequency domain technique, we lock the relative pulse-to-pulse carrier-envelope phase of a 15-fs pulse produced by a mode-locked Ti:Sapphire laser to various rational integer fractions of 21π.
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JILA, University of Colorado and National Institute of Standards and Technology, Boulder, CO 80309-0440 USA Bell Laboratories, Lucent Technologies, 700 Mountain Avenue, Murray Hill, NJ 070974
Abstract. Using a coherent frequency domain technique, we lock the relative pulse-to-pulse carrier-envelope phase of a 15-fs pulse produced by a mode-locked Ti:Sapphire laser to various rational integer fractions of 211".
With generation of optical pulses approaching the single cycle regime [1], control over the phase of the carrier with respect to the pulse envelope is becoming increasingly relevant, particularly in extreme nonlinear optics. A number of strong field processes in nonlinear optics have been either predicted and/or observed to be dependent on the relative carrier-envelope phase [2] including high harmonic/soft x-ray generation [3-5], attosecond pulse generation [6], and abov'e-threshold ionization [7] The physical origin of this relative carrier-envelope phase is the difference between the cavity-averaged group velocity (v g ) and phase velocity (vp ). After each round trip, the phase slip between the carrier and envelope of subsequent pulses is, f1¢ =
[~ Vg
-
~]w mod (211"), vp
(1)
where l is the cavity length and w is the carrier frequency of the pulse. In general, f1¢ is not zero and moreover fluctuations in the laser's operational parameters (e.g. cavity length, intracavity power, dispersion) vary Vg and vp by different amounts, effectively randomizing the relative carrier-envelope phase from pulse to pulse emitted by an unstabilized mode-locked laser. In this work we demonstrate, using both temporal cross-correlations and frequency domain measurements, precise control over the the pulse to pulse relative carrier-envelope phase (f1¢) of a Kerr-Lens mode-locked Ti:Sapphire laser. [8] To obtain this phase control, we employ stabilization techniques that were first developed when mode-locked lasers were utilized in optical frequency metrology applications. [9,10] Further discussion of this emerging application of ultrafast lasers is included in the end of this paper. 74
T. Elsaesser et al., Ultrafast Phenomena XII © Springer-Verlag Berlin Heidelberg 2001
The definition of LJ.¢ is shown schematically in Fig. 1. It is important to note LJ.¢ is not the absolute carrier-envelope phase of the pulse, rather it is the pulse to pulse carrier-envelope phase. The absolute phase, ¢, of the mth pulse is given by ¢(m) = ¢o + mLJ.¢ where ¢o is unknown constant phase offset and m is an integer labeling individual pulses. Using the frequency domain technique described below, LJ.¢ can be stabilized. However, the absolute carrier-envelope phase cannot determined. A similar, but refined measurement or an additional technique, such as above threshold ionization [2], is necessary to measure and control ¢o. In the frequency domain LJ.¢ shows up as a frequency offset (15) of the fs laser's nth frequency comb mode (In) from a harmonic of the pulse repetition rate frep (i.e., fn = nfrep + 15, see Fig. 1). The offset freque
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