Abstract
Progress in ultrafast science and technology has pushed the temporal resolution to subfemtosecond and attosecond region (Kienberger el at., 2002; Fleischer & Moiseyev, 2006; Corkum & Krausz, 2007; Goulielmakis el at., 2007) and technology exploration in ultrashort pulse generation has made it possible to equip femtosecond lasers that are only a few cycles in duration (Xu el at., 1996; Shirakawa el at., 1999; Rulliere, 2005; Mauritsson el at., 2006; Sansone el at., 2006). Coherent control experiments now use precisely shaped optical pulses with sub-femtosecond timing jitters to steer coherent evolution governed by the interaction of coherent light with matter towards quantum paths for desired dynamic processes (Kitzler el at., 2002;Tong el at., 2003; Bandrauk el at., 2005). Precise control and synchronization of ultrashort pulses are essential for many other applications in ultrafast laser spectroscopy (Drescher el at., 2002; Hannaford, 2005; Cavalieri el at., 2007), Fourier synthesis of light pulses or optical waveforms (Jones el at., 2000; Shelton el at., 2001; Supradeepa el at., 2008), multi-color pump-probe investigations (Schoenlein el at., 2000; Son el at., 2002; Manzoni el at., 2006; Gu el at., 2009), coherent anti-Stokes Raman scattering microscope (Jones el at., 2002; Potma el at., 2002), difference frequency mixing for mid-infrared generation (de Barros el at., 1995; Kaindl el at., 2000) and terahertz source generation (Kitaeva, 2008; a. Sell el at., 2008; b. Sell el at., 2008), and so forth. Recently, significant breakthrough has been made in ultrafast laser technology and precision frequency metrology (Hentschel, el at., 2001;Udem el at., 2002; Schibli el at., 2004) with the innovation concept of simultaneous control in both time and frequency domain developed in femtosecond combs (Shelton el at., 2001; Ma el at., 2004). This technique is versatile in controlling ultrashort mode-locked lasers by translating precision control over mode frequencies into ultra-stable control in the time domain, which may eventually facilitate accurate synchronization of multicolor mode-locked lasers desired for coherent optical synthesis to extend the pulsed laser spectrum (Jones el at., 2000; Shelton et al., 2001; Bartels el at., 2004). Rapidly growing interest has been focused in recent years on synchronizing independently mode-locked multi-color lasers with improved synchronization accuracy and robustness, sufficiently low time jitters, as well as large tolerance to disturbance (Kawamura el at., 2000; Rudd el at., 2005; Baudelet el at., 2006). In general, pulse synchronization requires independent lasers to be mode-locked at exactly the same repetition rate. As the repetition rate (fr) depends linearly on the effective cavity length (Leff), fr=c/Leff (c, the speed of light in vacuum), a feed-back locking system is indispensible for laser synchronization to compensate for the unavoidable cavity variations. In accordance with the feedback methods,
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