Dynamical Model of Harmonic Generation in Centrosymmetric Semiconductors at Visible and UV Wavelengths

We study second and third harmonic generation in centrosymmetric semiconductors at visible and UV wavelengths in bulk and cavity environments. Second harmonic generation is due to a combination of spatial symmetry breaking, the magnetic portion of the Lorentz force, and quadrupolar contributions from inner core electrons. The material is assumed to have a nonzero, third-order nonlinearity that gives rise to most of the third harmonic signal. Using the parameters of bulk silicon we predict that cavity environments modify the dependence of second harmonic generation on incident angle, while improving third harmonic conversion efficiency by several orders of magnitude relative to bulk silicon. This occurs despite the fact that the harmonic signals may be tuned to a wavelength range where the dielectric function of the material is negative: A phase-locking mechanism binds the generated signals to the pump and inhibits their absorption. These results point the way to alternative uses and flexibility of materials such as silicon as nonlinear media in the visible and UV ranges