Four-Wave Spectroscopy of Shallow Donors in Germanium

Abstract

In recent years, four-wave mixing spectroscopy (FWMS) with tunable lasers has emerged as a powerful technique for the study of optical excitations in gases, liquids and solids. In a simple version of FWMS, two laser beams, say, at frequencies ω1 and ω2 interact in the medium of interest to generate radiation at the frequency ω4 = 2ω1 — ω2. All the processes leading to output at ω4 can be derived by a third-order nonlinear susceptibility tensor X(3) ijkl(-ω4, ω1, ω1, -ω2) which is a polar tensor of 4th order. It should be pointed out X(3) does not vanish identically for any symmetry group. In contrast, the second-order nonlinear susceptibility tensor X(2) is identically zero for all media except non-centrosymmetric crystals. Thus, phenomena involving X(3) can be studied in all media: gases, liquids and solids.