Carrier envelope phase

The carrier envelope phase (TE phase, Eng. Carrier-envelope (offset) phase , CE-phase or CEP , CEO-phase ) is a property of a light pulse that is relevant when its duration is only a few periods .

The PD phase is important in generating a frequency comb . Physical effects that depend on the PD phase fall into the area of ​​"extreme non-linear optics ".

PD phase in the time domain

The carrier-envelope phase in the time domain: A pulse train consisting of five consecutive light pulses is shown. Depending on the value of the PD phase , the relative position of the carrier wave (black) differs in relation to the intensity envelope (blue dashed) of a light pulse. After the time , the PD phase is the same as at the beginning. is the pulse repetition time. ${\displaystyle \,\phi _{0}}$ ${\displaystyle T_{\mathrm {CEO} }}$ ${\displaystyle T_{\mathrm {rep} }}$

The TE phase is the phase difference between the carrier wave and the intensity envelope of a single light pulse (see figure in the time domain). In a pulse train of several light pulses, it often changes from pulse to pulse, since the phase velocity and group velocity are usually different (the only exception is the vacuum). The TE phase increases from pulse to pulse, for example, until it is greater than 2π. From here the process is repeated. After the time the TE phase has changed by 2π and has the same value as at the beginning due to the 2π periodicity of the trigonometric functions . ${\displaystyle \,\phi _{0}}$ ${\displaystyle T_{\mathrm {CEO} }}$

PD phase in the frequency domain: The PD frequency

The carrier envelope phase in the frequency domain: The frequency spectrum of the above pulse train is shown. If you continue the frequency comb in your mind up to frequency zero, there is a small offset there, the PD frequency . is the pulse repetition frequency. ${\displaystyle f_{\mathrm {CEO} }}$ ${\displaystyle f_{\mathrm {rep} }=1/T_{\mathrm {rep} }}$

The change in the PD phase over time is described by the PD frequency . The following therefore applies to these: ${\displaystyle f_{\mathrm {CEO} }}$

${\displaystyle f_{\mathrm {CEO} }={\frac {d\phi _{0}}{dt}}={\frac {1}{T_{\mathrm {CEO} }}}}$.

In the frequency spectrum of a pulse train (see Fourier transformation ), the so-called frequency comb , this PD frequency is expressed as the common offset of all frequency needles (see figure frequency range).

See also

• High harmonics
• Attosecond laser