In this small series of posts I want to have a critical look at some of the older articles and put them into the current context. For a start, I picked the review article from 2011 in Science: “Microresonator-based optical frequency combs” by T.J. Kippenberg, R. Holzwarth and S. A. Diddams. In many papers of the field it is still one of the first references for Kerr frequency combs. In other papers, which are only distantly related to Kerr frequency combs, it might be the only reference for Kerr frequency combs. However, if a reader not familiar with the field reads only this review, he or she will have a much skewed view of today’s Kerr frequency combs. The reason is mostly that the review was published only four years after the first paper on Kerr frequency combs and by now it has been another six years in which the field has moved in some respect much beyond the state of the review. I would recommend these readers to also have a look at the much more recent “News & Views” in Nature Photonics by A. Weiner, which gives a brief update on what has been happening over the last years. But let’s go back to the Science review and have a look at some details.
Basics: the basic explanation of the principle behind Kerr frequency combs, how the different frequency components emerge from the single pump laser, are still valid. Although one could argue about the relevance of this explanation in the field today. This is because current research mostly relies on the soliton states explained below and the simple description of degenerate and non-degenerate four wave mixing is only borderline valid in that case. Nevertheless, I would say, it is still a valid approach to explain this also because it is quite intuitive.
Microresonator platforms: the review includes three platforms: the micro-toroid resonators also featured in the first publication from 2007, the crystalline microresonators and the integrated microresonators (made from silicon nitride and Hydex which is silicon oxynitride). While the latter two platforms are still used very actively in the research field, the first is rarely used anymore. Instead, silica disk resonators have reported some quite impressive results over the last few years. Very recently also Fabry-Perot type microresonators have shown to feature Kerr frequency combs. The integrated resonators have by now also spread to other material platforms (aluminum nitride, silicon, aluminum gallium arsenide, diamond) but until today silicon nitride remains the most widely used one. Although the integrated platforms do feature the potential for integration of components such as couplers, filters and so on, this has rarely been used to date.
Bandwidth and coherence: the review shows some spectra with very significant bandwidth, including an octave spanning spectrum from a micro-toroid resonator and a spectrum that spans 75 THz generated in an integrated silicon nitride microresonator. However, both of these optical spectra are spectra from Kerr frequency combs in incoherent states. Three years after the review these states were labeled unstable modulation instability states (uMI state or sometimes also just MI state). The incoherence makes the Kerr frequency combs in these states useless for metrological and most other applications and experiments. This is already noted in the review itself under “Future Outlook: Challenges and Opportunities”. An explanation of this noisy behavior based on experimental observations and theoretical analysis was only given in 2012, about one year after the review. It is related to the dynamics of how Kerr frequency combs evolve. Therefore, the review was correct to point this out as a challenge. Luckily, it was overcome since then as explained below.
Theory and simulations: in the review there is no section covering the simulations or the theory of Kerr frequency combs. In the years after the review the advances of the understanding of these aspects were substantial. This allowed for validating the reason for the incoherence problem and the later discovery of the soliton states (see below). Today, simulations are an important tool for researchers working with Kerr frequency combs. One huge step forward was that, with the theory of (simple) Kerr frequency combs boiled down to the Lugiato-Lefever-Equation (here and here), it was possible to merge parts of the communities around fiber-based nonlinear systems and microresonators. As a result, many of the concepts made their way from the fiber community to the microresonators (dispersive waves and other higher-order dispersion related topics, Raman-related phenomena, soliton interaction, …). This helped the Kerr frequency comb community very significantly. Today, many papers are written solely about the theory and simulations or feature a significant part about simulations. This also helps to identify and understand some features and effects observed in today’s Kerr frequency combs.
Solitons: the currently most promising way to overcome the problem of incoherence mentioned in the review is the use of dissipative cavity soliton states (also sometimes called dissipative Kerr solitons) instead of uMI states. Solitons are pulses of light that form inside the microresonator and which, due to a balance of the nonlinear and dispersive effects inside the microresonator, retain their shape while propagating. This results in extremely similar, stable waveforms over long time scales which results in a high coherence. Using this effect Kerr frequency comb also move much closer to mode-locked lasers in some respect. Only solitons have allowed to rather recently observe coherent optical spectra as broad as the ones in the review. However, because solitons were only discovered in 2013/2014 they are not part of the review. Therefore the review lacks one of the most interesting and promising aspects of the field today.
Wavelength coverage: the results reported in the review are exclusively around 1.5 µm. This is still the wavelength of most recent experiments, but by now Kerr frequency combs have been observed at several other wavelengths. Examples are at 3 µm, at 2.5 µm, at around 1 µm and some fairly small combs at 800 nm.
Applications: this is where in my opinion the review is the strongest. In some sense this is unfortunate, because most of what is projected for the future in the review from 2011 is still a rather distant future now. But significant progress has been made. Many of the proposed applications have been demonstrated in the lab in some form. Yet, no commercial Kerr frequency comb system is available which could be used for any of these applications commercially. One application that is completely missing from the review is the quantum light source, which has seen some impressive results lately.
Summary: although the field is moving rather quickly and publishes quite rapidly, the review is not entirely outdate. The octave spanning bandwidth that was already claimed (with a small footnote) in the review has only been achieved recently with a coherent Kerr frequency comb (and with a very large mode spacing). The applications mentioned remain possible future applications for Kerr frequency combs. But when it comes to the coherent Kerr frequency combs and the theory behind them, the review is outdated. Better starting points in particular on the theory could be these papers:
- For a brief overview of the later developments in particular in the context of solitons: Frequency combs: Cavity solitons come of age, A. Weiner, Nature Photonics
- Featuring a lot of theory, that is completely missing from the Science review and is Open Access: Kerr optical frequency combs: theory, applications and perspectives, Y. Chembo, Nanophotonics
- Concentrating on the dissipative Kerr solitons is chapter 6 of this book: Nonlinear Optical Cavity Dynamics: From Microresonators to Fiber Lasers editor: P. Grelu. Chapter authors: T. Herr et al. The chapter is also available as an Arxiv version.
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