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.

CEP in the time domain

The CEP

ϕ

0

{\displaystyle \phi _{0}}

is the phase between the carrier wave and the position of the intensity envelope of the pulse (cf. figure in the time domain). In a train of multiple pulses it is usually varying due to the difference between phase and group velocity. The time, after which the phase increases resp. decreases by

2

π

{\displaystyle 2\pi }

is called

T

C

E

O

{\displaystyle T_{\mathrm {CEO} }}

. Ideally, it is an integer multiple of the duration

T

r

e

p

{\displaystyle T_{\mathrm {rep} }}

between two pulses and the pulses are picked at the corresponding rate to obtain a constant phase over all picked pulses. Besides this linear evolution, fluctuations which are common in conventional femtosecond laser systems usually cause a nonlinear shot-to-shot fluctuation of the CEP. This is why measuring and controlling it is very important for many applications.

CEP in the frequency domain and measurement

In the frequency domain, a pulse train is represented by a frequency comb.