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Pulse Trains and Frequency Combs

Ultrashort pulses are usually generated in the form of periodic pulse trains, where pulses follow each other on a time scale of picoseconds or nanoseconds. If not only the intensity pattern but also the full electric field (including the oscillation phase) are periodically repeated, the Fourier spectrum of the pulse train is a frequency comb. This means that the spectrum consists of discrete lines, which are (for an infinite and noiseless pulse train) infinitely narrow. If the height of each pulse in a graph is taken to be proportional to the optical power, the envelope has the shape of the spectrum of a single pulse. The spacing of the lines is identical to the pulse repetition frequency.

The discrete nature of the spectrum of a pulse train is sometimes considered to be an artificial property of the Fourier transform. However, it strongly corresponds to physical reality. The comb frequencies are those for which a narrowband oscillator can be coherently excited by subsequent pulses. When such a resonator is tuned to a different frequency, different pulses will excite its oscillation with different phases, and so the overall excitation cannot be strong.

The number of lines in the spectrum increases for an increasing ratio of the pulse period and pulse duration.