Direct Measurement of the Carrier-Envelope Phase of a Few-Cycle Laser Pulse by Interference between Surface Harmonics
Atsushi Ishizawa and Hidetoshi Nakano
Optical Science Laboratory
The carrier-envelope phase (CEP) is the phase of the carrier wave at the maximum of the envelope. The timing of the oscillation cycles within a light pulse plays a role in the interaction of light with matter when the duration of the pulse becomes comparable to the light oscillation period. Therefore, it is necessary to control the CEP of few-cycle laser pulses in order to apply nonlinear spectroscopy.
To date, it has been observed that high-order harmonic generation  and above-threshold ionization are sensitive to the CEP. Almost all previous direct measurements of the CEP have relied on strong-field processes using 100-µJ amplified laser pulses, which are available only at low repetition rates in a vacuum chamber equipped with a specialized detector. Therefore, only a few laboratories have been able to measure the CEP.
We demonstrated a measurement that provides direct information about the CEP of a few-cycle laser pulse. In any f -to-2f or 2 f -to-3f spectrum interferogram method using a nonlinear crystal, there is a certain unknown phase shift in the measured value because of the linear dispersion in the SHG crystal. We have devised a way of directly measuring the CEP using the interference between the second and third harmonics from the surface of a solid. Both harmonics have a π/2 phase shift relative to the fundamental optical field when they are generated from the surface of a solid. This means the interference signals do not include a constant offset phase component and can therefore be used to measure the CEP directly. This method uses pulses with a low energy of less than 1 µJ, and it’s very easy to set up the equipment and perform the measurement in air. The spectrum of the laser pulse is shown in Fig. 1. In this experiment, a 5-fs 1-µJ laser pulse was focused on a glass target at the incident angle of 45°. Even and odd harmonics were generated due to the broken symmetry of an interface. The second and third harmonic spectrums overlap in the ultra-violet region. Figure 2 shows a series of interference signals of different phases. The signals cyclically move up and down with the CEP, which has a period of 2π rad. We will be able to achieve stabilization of the CEP of a few-cycle amplified laser pulse by detecting it using this method.
 A. Baltuska, et al., Nature. 421 (2003) 611.
 A. Ishizawa and H. Nakano, Jpn. J. Appl. Phys. 45 (2006) 4087.
Fig. 1 Measured spectrum of a few-cycle laser pulse.
Fig. 2 Dependence of the CEP on the interference intensity.
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