# Carrier Envelope Phase

An optical pulse can be described as an envelope superimposed on a carrier wave. Although it is often ignored, there can be a relative phase shift between the peak of the envelope and maximum of the carrier. Click on the animation  to watch the phase evolve as the pulse propagates. Because, in general, the group velocity and phase velocity are not the same, this shift will change as the pulse propagates inside a laser cavity. This results in successive pulses emitted from a modelocked laser being different. Click on the animation below to see this.

In collaboration with the groups of Jan Hall and Jun Ye, we developed a technique that allowed us to lock the group and phase velocity together inside a laser cavity. This is important both in the time domain and, interestingly, in the precision measurement of optical frequencies. In the time domain, a very highly nonlinear process is sensitive to the exact phase of the carrier within the envelope (this represents a break down of the slowly varying envelope approximation). An example is x-ray generation, which has been pioneered by JILA faculty members Murnane & Kapetyn.

To understand how this can be used in the frequency domain, the complementary nature of time and frequency must be considered (see diagram above). The short duration of the pulses (τ) means that they have a broad frequency bandwidth. However, the fact that they are repetitive in time (spacing T) means that underlying the broad spectrum is a frequency comb. The spacing of this comb is the repetition rate of the laser, frep. It is this comb that is useful in making frequency measurements. If the comb spacing is locked to a clock, and the frequency position of one comb line is locked to a source with a known frequency, any other optical frequency within the frequency bandwidth of the laser output can be measured by comparing it to the closest comb line and counting the number of intervening comb lines. The pulse-to-pulse evolution of the carrier envelope phase results in a shift of the comb spectrum.

Ultimately, if sufficient bandwidth can be generated so that the red side of the spectrum can be frequency doubled and locked to the blue side, the optical frequency of all of the comb lines will be just an integer multiple of the repetion rate. Hence they will be known absolutely and an intermediate optical frequency standard will not be needed.