Optical second-harmonic generation in lossy media: Application to GaSe and InSe.

Abstract

The paper deals with optical second-harmonic generation in a medium absorbing the second-harmonic radiation, and where phase matching between the fundamental and second-harmonic radiation is not necessarily achieved. We first take the waves to be in the form of traveling waves, and describe the damping of the fundamental beam due to harmonic creation. It is found that both second-harmonic absorption and phase mismatch enhance the depletion length of the pump wave. Before depletion, the second-harmonic output power is independent of the traversed thickness if it exceeds the second-harmonic attenuation length. When depletion occurs, the second-harmonic output power is constant, instead of quadratic, in the input power. Next, second-harmonic generation in a plane-parallel plate of lossy material is envisaged in the case of normal incidence, including the multiple reflections expected in high-reflectance materials. The expressions of the harmonic output intensity, transmitted or reflected, of this paper and from the conventional treatment, are compared. The deviation is noticeable in the case of the transmitted harmonic power, and may be considerable in the case of the reflected power. Last, measurements of the second-harmonic output intensity in GaSe and InSe are reported at a fundamental wavelength of 1.06 \ensuremath{\mu}m. The sample dependence is in good agreement with our theory, which in turn is applied to derive new values of the nonlinear optical susceptibilities in the layered-structured III-VI materials. The treatment is fully analytical and may be applied to a wealth of materials.