Frequency Combs and Waveform Synthesis---Toward synthesis of arbitrary optical waveforms

(Please click on the images for a high-resolution one.)

You may be familiar with the function generator, which is available in most of the physics labs and the simplest version of an electronic waveform generator [1]. It is much more difficult to synthesize arbitrary optical waveforms since the optical frequencies are much higher. The electronic synthesis is generally limited to ns time scales while the optical synthesizer is in the femtosecond range.

Synthesizing optical waveforms requires both broadband coherent light and precise control over the phase and amplitudes for the frequency components. Therefore it is natural to combine the frequency comb technology with the pulse shaping technique, which may enable optical arbitrary waveform generation (OAWG), as discussed in a progress article written by Steven Cundiff, the session presider and A. Weiner, one of the invited speakers in the same session and the most famous person in the pulse shaping area [2]. The application, as pointed out by the authors, “are still a matter of speculation,” as "OAWG is still in its infancy." It can be used for coherent control, generation of attosecond pulses etc.

Currently most of the research is focused on only a small number of comb lines. The results, however, are very exciting. For example, Kung’s group recently demonstrated synthesis and measurement of ultrafast waveforms such as square and saw-tooth fields by using 5 frequency harmonics [3]. The result is similar to the following figures. Due to copyright issues I can’t put the original figures here. Kung is giving a talk in this session as well.

Our group also just achieved pulse-shaper-assisted phase control of 5 Raman frequency combs, which is what I am going to present in the conference. The difference of our work from Kung’s is that our comb itself has broad spectrum. So we not only need to correct "local" phase distortions on each spectrum, but also need to "globally" adjust the relative phases of the sidebands. We manage to make the sidebands "dance" in unison, as shown below.

The SHG spectrum of the 5 sidebands after the BBO crystal as we vary the AS 3 phase from 0 to 9 pi, after we adjust the relative phase among all sidebands to be equal.
A: SHG of AS 1; B: SFG of AS 1&2 ;C: SHG of AS 2;D: SFG of AS 1&4, and AS 2&3; E: SHG of AS 3, SFG of AS 1&5, and AS 2&5; F: SFG o AS 3&4;G: SHG of AS 4.

Session presider Steve Cundiff is the 2011 NLO program chair. Many people probably know him through his work and the book “Femtosecond optical frequency comb technology” book, which is edited by him and Jun Ye, who will give an invited talk at this session.

I am not so familiar with C. Fabre’s work. As I Google him I only found his website in French. When I use the Google translation, I get the following----which is almost as funny as if you put an ancient Chinese poem and use the Google translation to get the English version. I love the last sentence---“to measure travel time fine”.



At last, I would like to mention somewhat related work---Multiple independent comb shaping (MICS) by Marcos Dantus. The comb is not “frequency combs” but more strictly speaking “pulse shaper pixels." as explained to me by Dmitry Pestov, who works with Marcos Dantus. The similarity lies in that it does phase shaping of a pulse to generate complex waveforms [4].

Reference:
[1] Toward Synthesis of Arbitrary Optical Waveforms, Deniz D. Yavuz, Science March 2011, Vol. 331.
[2] Optical arbitrary waveform generation, Steven T. Cundiff & Andrew M. Weiner,Nature Photonics, Volume: 4,Pages:760–766, Dec. 2010.
[3] Synthesis and Measurement of Ultrafast Waveforms from Five Discrete Optical Harmonics, H. Chan, Z. Hsieh, W. Liang, A. H. Kung, C. Lee, C. Lai, R. Pan, and L. Peng,Science, vol. 331, 1165-1168 (2011).
[4] Generation of Complex Optical Pulse Sequences by Multiple Comb Shaping, Dmitry Pestov, Vadim V. Lozovoy and Marcos Dantus, OPN, Dec. 2009.