Measurement and Control of Carrier-Envelope Phase in Femtosecond Ti:sapphire Laser

The emergence of few-cycle laser pulses induced enormous interests on the nonlinear phenomena, such as above-threshold ionization[1~3], high harmonic generation[4, 5] and isolated attosecond generation[6~13] etc. The state-of-the-art few-cycle laser generators, like Kerr-lens mode-locked Ti:sapphire lasers, have delivered directly from oscillator optical pulses with the duration of 5fs [14,15], which corresponds to less than two optical cycles in the near infrared wavelength range. At such short pulse duration, the peak electric field strength of the laser depends strongly on the relative phase between the carrier and the envelope of the pulse. This relative phase is the carrier-envelope phase (CEP). The CEP occurs in the ultrashort pulses, for longer pulses, in general it is not ignored because of the neglectable role. However, the CEP will become significant on the laser matter interaction for few-cycle pulses. It is obvious that the CEP plays an important role in physical processes stated above, especially in attosecond generation schemes, such as interaction between the inert gases and the few-cycle intense pulses [6, 7]and Fourier coherent synthesis among ultrashort lasers with different wavelength[16,17], controlling the CEP is always an important prerequisite. In fact, the CEP from pulse to pulse in a pulse train that emitted by a mode-locked femtosecond laser is different because of dispersion. The group and phase velocity will differ and cause CEP evolve rapidly when propagating through materials inside the cavity, such as Ti:sapphire crystal, coating mirrors and prisms etc. The pulse-to-pulse CEP change is the carrier-envelope phase offset (CEO). Up to now, several methods have been developed to measure and control the CEO of femtosecond laser pulses train in the frequency domain[18~26]. In this chapter, we will introduce two schemes for measuring the CEO frequency of pulses in femtosecond Ti:sapphire laser. The first and the most widely used technique is the self-reference method, also be termed the f-to-2f method [19~21]. It is to measure the interference beat frequency between the high frequency and the frequencydoubled low frequency spectral components of an octave spanning spectrum. Normally, a photonic crystal fiber (PCF)[27~31] is used to broaden the laser spectrum to octave-spanning bandwidth in such f-to-2f CEO frequency measurement scheme. Although the PCF has advantage of high nonlinear coefficient be easy to generate supercontinuum spectrum by