Effective cubic nonlinearity, photoinduced anisotropy, and elliptically polarised cnoidal waves upon frequency doubling

The peculiarities of the effective cubic nonlinearity are analysed upon second harmonic generation in a medium with a quadratic nonlinearity. It is shown that in this case, the polarisation state of the pump wave changes during its propagation due to additional effective photoinduced anisotropy of propagation constants of two orthogonally polarised pump components. Depending on the initial conditions, either an elliptically polarised cnoidal wave is produced (the polarisation state of pump radiation periodically changes from linear to elliptic and vice versa) or a passage occurs to an aperiodic polarisation "chaos".