Femtosecond spectroscopy of acoustic frequency combs in the 100-GHz frequency range in Al/Si membranes

Acoustic frequency combs are optically excited and detected in silicon membranes covered with thin aluminum layers by femtosecond pump-probe spectroscopy. The various frequency combs consist of 11 up to 45 modes ranging in frequency from 10 up to 500 GHz. Evaluating the different modes of the combs allows us to quantify the dynamic properties of this two-layer system with great precision. Deviations of the frequencies of higher modes from a linear relation can be quantitatively understood. The time domain traces show clearly defined pulses which are detected in regular time intervals after each roundtrip in the acoustic cavity formed by the membrane and the metal film. By analyzing the individual reflected pulses and their evolution in time, damping times for the whole frequency range are determined. We analytically derive a deviation of the individual comb modes from integer values of the fundamental frequency which is corroborated by the experiments.