The third-order nonlinear optical coefficients of Si, Ge, and Si1−xGex in the midwave and longwave infrared

Abstract

Using a combination of semiconductor theory and experimental results from the scientific literature, we have compiled and plotted the key third-order nonlinear optical coefficients of bulk crystalline Si and Ge as a function of wavelength (1.5−6.7 μm for Si and 2–14.7 μm for Ge). The real part of third-order nonlinear dielectric susceptibility (χ⁽³⁾′), the two-photon absorption coefficient (β_TPA), and the Raman gain coefficient (g_R), have been investigated. Theoretical predictions were used to curve-fit the experimental data. For a spectral range in which no experimental data exists, we estimate and fill in the missing knowledge. Generally, these coefficient-values appear quite useful for a host of device applications, both Si and Ge offer large χ⁽³⁾′ and g_R with Ge offering the stronger nonlinearity. In addition, we use the same theory to predict the third-order nonlinear optical coefficients of Si_1−xGe_x alloy. By alloying Si and Ge, device designers can gain flexibility in tuning desired optical coefficients in between the two fundamental components based upon their application requirements.