Two- and three-photon absorption of germanium in the mid-infrared

We have studied the nonlinear optical response of crystalline germanium using high-power infrared picosecond laser pulses at wavelengths ranging from 2.8 $\mu $m to 5.2 $\mu $m. Transmittance as a function of fluence at 2.8 $\mu $m and 4.4 $\mu $m were fitted by using two- and three-photon absorption, respectively. Data at 3.2, 3.6, and 4.0 $\mu $m, however, required consideration of simultaneous two- and three- photon absorptions in order to fit the experimental data. Transmittance as a function of wavelength further supports the onset of the two- and three-photon absorption at appropriate wavelengths.