Carrier-envelope phase (CEP)
Light can be described as an electromagnetic field that oscillates with a particular wavelength. Mathematically this can be described by, for example:
\(\cos(2\pi t c / \lambda)\)
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(carrier wave)
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In the case of a laser pulse, this oscillation exists only for a limited amount of time. To take this into account, we can multiply the carrier by an envelope, for example:
\( e^{-t^2/{2\tau^2}} \)
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(Gaussian envelope)
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In the graph on the right I have plotted the product of the carrier and envelope equations, in blue. The envelope is plotted in red. I have taken the pulse length τ to be very small, so that the pulse lasts just a few femtoseconds (a femtosecond is one millionth of one billionth of a second).
The maximum of the electric field (blue) coincides with the maximum of the envelope (red). We say that the phase between the two, the so-called Carrier-Envelope Phase, is equal to zero. |
In green I plotted the electric field in case the carrier is shifted by π/2 :
\(\cos(2\pi t c / \lambda + \pi/2)\)
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(carrier wave shifted by π/2)
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The Carrier-Envelope Phase is now π/2. The envelope stays the same, and therefore also the intensity profile of the laser pulse stays the same. But inside the pulse, the electric field is different, its maximum value is lower. The shorter the pulse is, the stronger this effect. This can influence the interaction of the pulse with it's surroundings (for example, the plasma in a Laser Wakefield Accelerator).