carrier-envelope phase

File:PulseTrain-CEOPhase.svg

The CEP $\backslash phi\_0$ 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 $2\; \backslash pi$ is called $T\_\backslash mathrm\{CEO\}$. Ideally, it is an integer multiple of the duration $T\_\backslash mathrm\{rep\}$ 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.

File:FrequencyComb-CEOphase.svg

In the frequency domain, a pulse train is represented by a frequency comb. Here, the carrier-envelope frequency $f\_\backslash mathrm\{CEO\}=\backslash frac\{1\}\{T\_\backslash mathrm\{CEO\}\}=\backslash frac\{\backslash mathrm\{d\}\; \backslash phi\_0\}\{\backslash mathrm\{d\}\; t\}$ is exactly the offset frequency of the pulse train, cf. figure. 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. This is better known as the offset phase.

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.

• {{cite web|last1=Paschotta|first1=Rüdiger|title=Carrier-envelope offset, CEO frequency, CEP, absolute phase|url=http://www.rp-photonics.com/carrier_envelope_offset.html|website=Encyclopedia of Laser Physics and Technology|accessdate=5 May 2015}}
• {{cite journal|last1=Krausz|first1=Ferenc|last2=Ivanov|first2=Misha|title=Attosecond physics|journal=Reviews of Modern Physics|date=2 February 2009|volume=81|issue=1|pages=163–234|doi=10.1103/RevModPhys.81.163|bibcode = 2009RvMP...81..163K |url=https://nrc-publications.canada.ca/eng/view/fulltext/?id=1245a958-9c93-4116-bfdb-f447e8a53c48}}

Category:Nonlinear optics