Abstract

Second-order nonlinear interactions¹ are some of the most basic, best known, and widely used processes in nonlinear optics. They can be viewed as a three-wave mixing, whereby waves at only three interacting frequencies (ω₁, + ω₂, = ω₃) are phase matched. In the general case, these interactions presume energy exchange among all three waves. It is known also that there are special regimes of three-wave mixing (which could he regarded as nonlinear eigenmodes) whereby there is no energy exchange among any of those three waves; these no-interaction modes are usually of no interest in frequency transformation or amplification applications. We showed, however, that the interaction among the three waves in these eigenmodes is still manifesied by linear (with respect to the distance of propagation) phase change in each of the waves as they propagate. For these χ⁽²⁾ eigenmodes to occur, a certain relationship should be prearranged among all three intensities (and phases) of the waves. The peculiar phase property of these eigenmodes is essentially equivalent to the amplitude-dependent and phase-sensitive change of phase velocity of each of the waves (with their intensities unchanged) as they propagate. This property makes the χ⁽²⁾ eigenmodes ideal candidates for χ⁽²⁾ cross-induced nonlinear refraction, i.e., amplitude-dependent phase velocity, emulating the third-order nonlinear refractive index, particularly, in cascade² second-harmonic generation (SHG). The eigenmodes constitute the only second-order nonlinear process with unchanging amplitude and with the phase changing linearly with the distance of propagation, and thus they are the only true example of nonlinear refraction. Compared with the modes in which only SHG is used,² the eigenmodes offer broader opportunities involving in the general case three waves with more independently controllable parameters.

© 1993 Optical Society of America