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Two techniques that employ equally spaced trains of optical pulses to map anoptical high frequency into a low frequency modulation of the signal that canbe detected in real time are compared. The development of phase-stable opticalfrequency combs has opened up new avenues to metrology and spectroscopy. Theability to generate a series of frequency spikes with precisely controlledseparation permits a fast, highly accurate sampling of the material response.Recently, pairs of frequency combs with slightly different repetition rateshave been utilized to down-convert material susceptibilities from the opticalto microwave regime where they can be recorded in real time. We show how thisone-dimensional dual comb technique can be extended to multiple dimensions byusing several combs. We demonstrate how nonlinear susceptibilities can bequickly acquired using this technique. In a second class of techniques,sequences of ultrafast mode locked laser pulses are used to recover pathways ofinteractions contributing to nonlinear susceptibilities by using aphoto-acoustic modulation varying along the sequences. We show that thesetechniques can be viewed as a time-domain analogue of the multiple frequencycomb scheme. %We compare the two techniques: in both, an optical high frequencyis mapped into a low frequency modulation of the signal that can be detected inreal time.

Linear and Nonlinear Time- and Frequency-Domain Spectroscopy with Multiple Frequency Combs