...at JILA, which is a joint institute of the University of Colorado and the National Institute for Standards and Technology
Control of the 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 above 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.
Representation of laser pulses in the time domain and frequency domain.
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 (Δt) means that they have a broad frequency bandwidth. However, the fact that they are repetitive in time (spacing τ) means that underlying the broad spectrum is a frequency comb. The spacing of this comb is the repetition rate of the laser. 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. In an audio analog of this you can actually hear the frequency shift. Click on the icon below to hear a demonstration (good low frequency response in the computers speakers make it more noticeable). For the first half of the clip, all the pulses are in phase, for the second half, they alternate in phase by 180 degrees. The transition should be audible.
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.
It can be shown that this locking together of the comb lines in the frequency domain is equivalent in the time domain to making the phase and group velocities the same.
Quantum Interference Control (QIC)
The original technique for locking the carrier-offset frequency was the ν-2ν interferometer. Using self-phase modulation in a microstructure fiber, the laser spectrum is broadened until it spans an octave. Infrared light with frequency ν is doubled and interfered with visible light with frequency 2ν. Up to a constant offset related to the difference in path lengths in the interferometer, the phase between ν and 2ν is the carrier-envelope phase.
We showed that the carrier-envelope phase can be measured by quantum interference between one- and two-photon absorption in a semiconductor rather than optical interference in an interferometer. This can, in turn, be used as feedback to lock the carrier-envelope frequency just like the ν-2ν interferometer. If all the phase offsets can be accounted for, this technique holds promise for measurement of the absolute carrier-envelope phase.
< postdoc Jared Wahlstrand and undergraduate researcher Robert Snider are currently involved in this research >