Carrier-Envelope Phase Shift Using Linear Media
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A) The Carrier-Envelope Offset Frequency
[0020]The real electric field, E(z,t), of a laser pulse may be decomposed into
E(z,t)=Re{A(z,t)ei(ω0t+k(ω0)zetφ(t)eIφCEO} (1)
with A(z,t) representing the real envelope and the following exponential describing the oscillation with the carrier frequency, ω0, where the time-dependent phase term, φ(t), describes the chirp of the pulse and φCEO describes the phase between the maximum 16 of the carrier-wave 12 and the maximum 18 of the envelope 14 (as shown in FIG. 1)—the so-called carrier-envelope phase. During propagation of the wave-packet, the carrier-wave propagates with the phase velocity, νp, and the envelope 14 propagates with the group velocity, νg. Since all media, and even air, exhibit a wavelength-dependent index of refraction, phase and group velocity through a medium are generally different. As a consequence, φCEO changes continuously over time. The carrier-envelope phase shift, Δφ, caused by passing through a dispersive medium of leng...
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