Abstract

The parametric decay (or fluorescence) of an intense wave may occur through three-photon [ω = (ω + Ω) + (ω − Ω)], or four-photon [ω + ω = (ω + Ω) + (ω − Ω)] processes, respectively. The bandwidth of the parametric fluorescence is determined by dispersion through the wave-vector selection rules (i.e., k_ω = k_Ω + k_−Ω, or 2k_ω = k_Ω + k_−Ω). Whenever the amplification process is tuned by the pump intensity, the parametric decay is equivalent to modulational instability (MI).2 On the other hand, it is well known that coupling of two more intense waves commonly occurs under a wide variety of interactions [second-harmonic generation (SHG), three-wave and four-wave mixing, nonlinear polarization rotation (NPR), directional coupling of guided modes, etc.].3,4 In the cw regime, these interactions generally lead to periodic exchange of energy among the waves.5 However, the stability of wave coupling against the parametric decay in the presence of dispersion has not been investigated to date. By means of a general approach to this problem, we show here that MI sets a fundamental limit to the maximum useful interaction length for parametrically coupled beams.

© 1997 Optical Society of America