Carrier-envelope phase

The carrier-envelope phase (CEP) or carrier-envelope offset (CEO) phase is an important feature of an ultrashort laser pulse and gains significance with decreasing pulse duration, in a regime where the pulse consists of a few wavelengths.

Physical effects depending on the carrier-envelope phase fall into the category of highly nonlinear optics.

is the phase between the carrier wave and the position of the intensity envelope of the pulse (cf.

In a train of multiple pulses it is usually varying due to the difference between phase and group velocity.

This makes it possible to perform a multi-shot measurement of the CEP, for example by using an f-2f interferometer.

Here, the pulses to be measured are broadened to a bandwidth of at least one octave.

A long-wavelength part of the pulse is frequency doubled and the beat note between it and the short-wavelength part of the fundamental pulse is measured.

With a phase-locked loop, a property of the laser oscillator such as the optical path length can be adjusted correspondingly to the obtained offset frequency and thus the phase can be stabilized.

CEP in the time domain: A pulse train of five consecutive pulses with linearly varying CEP is depicted. Depending on its value the relative delay between the carrier (black) and the envelope (blue dashed) is different.
CEP in the frequency domain: The frequency spectrum of the above pulse train is a frequency comb which shows an offset if it is continued until a frequency of zero. This offset is the carrier-envelope frequency , and is the repetition rate