Optical frequency combs based on femtosecond mode-locked lasers revolutionized optical frequency metrology and enabled optical atomic clocks and the generation of attosecond pulses using high-harmonic generation. In collaboration with Jan Hall, our group demonstrated the method of self-referencing of a frequency comb (Jones, 2000).
Mode-locked lasers generate a train of ultrashort pulses, which in the frequency domain corresponds to a spectrum of regularly spaced sharp lines, known as a “comb”. If all of the pulses are identical, then the comb lines would simply be integer multiples of the repetition rate of the laser. However, the pulses are not all identical because the carrier-envelope phase of the pulses evolves within the pulse train. The evolution of the carrier envelope phase results in a rigid shift of the comb lines by an amount known as the offset frequency. The development of methods to measure the offset frequency, without an external optical reference, and control were the key advances that launched the field of optical frequency combs.
Femtosecond pulse shaping was first demonstrated over 20 years ago and is now a fairly well developed method[Weiner, 2000]. The most common approach is spectral decomposition where the laser spectrum is dispersed and the amplitude and/or phase of the different frequency components are modulated. With the advent of femtosecond frequency combs, it became possible to increase the spectral resolution until it matched the spacing of the comb such that adjacent comb lines are separately modulated. The ultimate limit is achieved when the modulators run at the repetition rate of the laser, thus allowing them to updated for every pulse. This limit is often called “optical arbitrary waveform generation” [Cundiff, 2010].
We have worked on understanding the fundamental limits to arbitrary waveform generation that rise when the modulation rate of the comb lines matches their spacing [Willits, 2008]. We have also achieved line-by-line pulse shaping at the highest resolution reported so far, to the best of our knowledge, of less than 1 GHz [Willits, 2012]. This high resolution allows the comb lines from a ring mode-locked ti:sapphire to be resolved with out need for extra cavity filtering.
Currently we are working on using line-be-line pulse shaping based on a virtual-imaged phased array to demonstrate an optical delay line that can generate delays equal to the time between pulses.
Our group has been very involved in developing and perfecting the ability to control the evolution of the carrier-envelope in the pulse train produced by a mode-locked laser. This problem is largely solved today, however there are a few interesting open questions. One issue is to understand the fundamental (quantum mechanical) limits to how narrow the comb-lines can be. This limit is related to the famous Schawlow-Townes limit for the linewidth of a CW laser due to the incorporation of spontaneously emitted photons in the lasing mode. For a mode-locked laser, the spontaneously emitted photons are incorporated into all the modes, which is better described in the time domain, as developed by Haus and Mecozzi. To apply the Haus-Mecozzi model to ti:sapphire lasers, we developed a method to characterize the pulse dynamics by applying small perturbations to the pump power [Wahlstrand, 2007].Using this characterization, we were able to predict the quantum limited comb linewidth and the performance of an optical atomic clock that used this laser as the gear work that connected optical frequencies to microwaves [Wahlstrand, 2008].
Currently we are working on using this approach to study mode-locked fiber lasers. The exact method cannot be used for fiber lasers using erbium as the gain material because the life time of the erbium atoms is long and thus the perturbations are filtered out. Thus we are developing new methods to perturb the laser based on injecting a counter propagating depletion field to modulate the gain.
This work is a collaboration with Professor Curtis Menyuk at the University of Maryland – Baltimore County.