Multiphoton absorption in germanium using pulsed infrared free-electron laser radiation

We report wavelength- and intensity-dependent transmission measurements of intense mid-infrared radiation from the Vanderbilt free-electron laser in single-crystal Ge(100) in the wavelength range of 2.8-5.2 μm. This range accesses both the direct and indirect energy gaps in Ge, requiring in each case either two or three photons (2PA or 3PA) for absorption. Large changes in the multiphoton absorption rate are seen at the direct-to-indirect and 2PA-to-3PA transitions. Photon interactions are dominated by free-carrier absorption (FCA), primarily due to holes. The entire absorption process is modeled with the two- and three-photon absorption coefficients (β and γ) as fitting parameters. Using newly measured values of the low-intensity FCA cross sections, we find a best fit to the data at 2.8 μm that is in agreement with theory and previous measurements. We report a ratio of 175 for β across the direct-to-indirect transition, and a ratio of 5 across the same transition for γ. These ratios are independent of systematic variations in free-carrier cross sections and beam diameter.