Self-phase-modulated coherent

Besides the phase of the fundamental mode, strictly speaking, the preferred phase, many other characteristics have been studied in [226]. Because a large mismatch was chosen, they have lacked any trend, but an interesting oscillatory behavior has been discovered for the initial two-mode coherent state. Within each period, the phase-matched second-harmonic and second-subharmonic generation processes can be prepared. The model of an ideal Kerr-like medium [223] have been considered for a comparison with cascaded quadratic non-linearities. It follows that these nonlinearities exhibit not only self-phase modulation in the fundamental mode but also a cross-phase modulation of the modes that can be considered for a nondemolition measurement. 

The spectral width Aty can be further increased by focusing the laser pulses into a special optical fiber, which consists of a photonic crystal (Fig. 9.88) where by self-phase modulation the spectrum is considerably broadened and extends over one decade (e.g., from 1064 nm to 532 nm) (Fig. 9.89). This corresponds to a frequency span of 300 THz [1327] It was found by interference experiments, that the coherence properties were preserved in this broadened spectmm, i.e. the nonlinear processes in the optical fiber did not destroy the coherence of the original frequency comb. 

Phase-modulated coherent pulse such as due to self-phase modulation has a common feature with incoherent light in that it has broad band-width whose reciprocal is much shorter than the light duration. It, therefore, is expected to play the same role as incoherent light in some nonlinear transient spectroscopy. This expectation has also been confirmed by preliminary theoretical and experimental study. 

Soliton ring fiber lasers can be also realized with active mode locking by polarization modulation [11.77], or by additive-pulse mode locking (APM). In the latter technique the pulse is split into the two arms of an interferometer and the coherent superposition of the self-phase modulated pulses results in pulse shortening [11.55]. 

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