Scientists have shown that at a wavelength of 5 µm the dominant way germanium changes the speed of light is through an instantaneous Kerr nonlinearity. When a short, 127‑fs pulse of 5‑µm light shines on germanium, the phase of a second, identical pulse shifts exactly in step with the pump pulse intensity and disappears when the two pulses no longer overlap. The phase shift increases linearly with pump power, giving a nonlinear refractive index of 0.87 × 10⁻¹⁷ m²/W.

To measure this, the team used field‑resolved degenerate pump–probe spectroscopy. Both pump and probe come from the same mid‑infrared pulse, so they travel together without timing mismatch. An electro‑optic sampling detector records the full electric‑field waveform of the probe at each delay time. Fourier analysis of these waveforms directly yields the change in transmission and phase caused by the pump. By varying the pump intensity in five steps and repeating each measurement three times, the researchers confirmed that the phase shift scales linearly without any delayed tail.

The experiment was deliberately kept below the threshold that would generate free carriers. In this low‑intensity regime the measured response comes only from bound‑electron (Kerr) effects, so the reported nonlinear index is purely refractive. However, at higher intensities carriers would be injected and the measured response would change.

These findings give a precise, time‑resolved measurement of germanium’s nonlinear refractive index at 5 µm, a key parameter for mid‑infrared photonic devices.