Volume 5, Issue 2 - Special Issue: Frequency Comb Generation

Optical frequency combs have revolutionized optical frequency metrology and are being actively investigated in a number of applications outside of pure optical frequency metrology. For reasons of cost, robustness, performance, and flexibility, the erbium fiber laser frequency comb has emerged as the most commonly used frequency comb system and many different designs of erbium fiber frequency combs have been demonstrated. We review the different approaches taken in the design of erbium fiber frequency combs, including the major building blocks of the underlying mode-locked laser, amplifier, supercontinuum generation and actuators for stabilization of the frequency comb.

The optical frequency comb technology is one of the most important breakthrough in photonics in recent years. This concept has revolutionized the science of ultra-stable lightwave and microwave signal generation. These combs were originally generated using ultrafast mode-locked lasers, but in the past decade, a simple and elegant alternativewas proposed,which consisted in pumping an ultra-high-Q optical resonator with Kerr nonlinearity using a continuous-wave laser. When optimal conditions are met, the intracavity pump photons are redistributed via four-wave mixing to the neighboring cavity modes, thereby creating the so-called Kerr optical frequency comb. Beyond being energy-efficient, conceptually simple, and structurally robust, Kerr comb generators are very compact devices (millimetric down to micrometric size) which can be integrated on a chip. They are, therefore, considered as very promising candidates to replace femtosecond mode-locked lasers for the generation of broadband and coherent optical frequency combs in the spectral domain, or equivalently, narrow optical pulses in the temporal domain. These combs are, moreover, expected to provide breakthroughs in many technological areas, such as integrated photonics, metrology, optical telecommunications, and aerospace engineering. The purpose of this review article is to present a comprehensive survey of the topic of Kerr optical frequency combs.We provide an overview of the main theoretical and experimental results that have been obtained so far. We also highlight the potential of Kerr combs for current or prospective applications, and discuss as well some of the open challenges that are to be met at the fundamental and applied level.

Microresonator frequency combs hold promise for enabling a new class of light sources that are simultaneously both broadband and coherent, and that could allow for a profusion of potential applications. In this article, we review various theoretical models for describing the temporal dynamics and formation of optical frequency combs. These models form the basis for performing numerical simulations that can be used in order to better understand the comb generation process, for example helping to identify the universal combcharacteristics and their different associated physical phenomena. Moreover, models allow for the study, design and optimization of comb properties prior to the fabrication of actual devices. We consider and derive theoretical formalisms based on the Ikeda map, the modal expansion approach, and the Lugiato-Lefever equation. We further discuss the generation of frequency combs in silicon resonators featuring multiphoton absorption and free-carrier effects. Additionally, we review comb stability properties and consider the role of modulational instability as well as of parametric instabilities due to the boundary conditions of the cavity. These instability mechanisms are the basis for comprehending the process of frequency comb formation, for identifying the different dynamical regimes and the associated dependence on the comb parameters. Finally, we also discuss the phenomena of continuous wave bi- and multistability and its relation to the observation of mode-locked cavity solitons.

Optical microresonator-based Kerr frequency comb generation has developed into a hot research area in the past decade. Microresonator combs are promising for portable applications due to their potential for chip-level integration and low power consumption. According to the group velocity dispersion of the microresonator employed, research in this field may be classified into two categories: the anomalous dispersion regime and the normal dispersion regime. In this paper, we discuss the physics of Kerr comb generation in the normal dispersion regime and review recent experimental advances. The potential advantages and future directions of normal dispersion combs are also discussed.

A number of dielectric materials have been employed for on-chip frequency comb generation. Silicon based dielectrics such as silicon dioxide (SiO2) and silicon nitride (SiN) are particularly attractive comb materials due to their low optical loss and maturity in nanofabrication. They offer third-order Kerr nonlinearity (χ (3) ), but little second-order Pockels (χ (2) ) effect. Materials possessing both strong χ (2) and χ (3) are desired to enable selfreferenced frequency combs and active control of comb generation. In this review, we introduce another CMOS-compatible comb material, aluminum nitride (AlN),which offers both second and third order nonlinearities. A review of the advantages of AlN as linear and nonlinear optical material will be provided, and fabrication techniques of low loss AlN waveguides from the visible to infrared (IR) region will be discussed.We will then show the frequency comb generation including IR, red, and green combs in high-Q AlN micro-rings from single CW IR laser input via combination of Kerr and Pockels nonlinearity. Finally, the fast speed on-off switching of frequency comb using the Pockels effect of AlN will be shown,which further enriches the applications of the frequency comb.

It was recently demonstrated that broadband quantum cascade lasers can operate as frequency combs. As such, they operate under direct electrical pumping at both mid-infrared and THz frequencies, making them very attractive for dual-comb spectroscopy. Performance levels are continuously improving, with average powers over 100mW and frequency coverage of 100 cm -1 in the mid-infrared region. In the THz range, 10mW of average power and 600 GHz of frequency coverage are reported. As a result of the very short upper state lifetime of the gain medium, the mode proliferation in these sources arises from four-wave mixing rather than saturable absorption. As a result, their optical output is characterized by the tendency of small intensity modulation of the output power, and the relative phases of the modes to be similar to the ones of a frequency modulated laser. Recent results include the proof of comb operation down to a metrological level, the observation of a Schawlow-Townes broadened linewidth, as well as the first dual-comb spectroscopy measurements. The capability of the structure to integrate monothically nonlinear optical elements as well as to operate as a detector shows great promise for future chip integration of dual-comb systems.

Frequency comb sources have revolutionized metrology and spectroscopy and found applications in many fields. Stable, low-cost, high-quality frequency comb sources are important to these applications. Modeling of the frequency comb sources will help the understanding of the operation mechanism and optimization of the design of such sources. In this paper,we review the theoretical models used and recent progress of the modeling of frequency comb sources.

Quadratic nonlinear processes are currently exploited for frequency comb transfer and extension from the visible and near infrared regions to other spectral ranges where direct comb generation cannot be accomplished. However, frequency comb generation has been directly observed in continuously pumped quadratic nonlinear crystals placed inside an optical cavity. At the same time, an introductory theoretical description of the phenomenon has been provided, showing a remarkable analogy with the dynamics of third-order Kerr microresonators. Here, we give an overview of our recent work on χ (2) frequency comb generation. Furthermore, we generalize the preliminary three-wave spectral model to a many-mode comb and present a stability analysis of different cavity field regimes. Although our work is a very early stage, it lays the groundwork for a novel class of highly efficient and versatile frequency comb synthesizers based on second-order nonlinear materials.

We describe spectral or dynamical methods that can be used to determine the stability and noise performance of modelocked lasers.We first review methods that have been used to date to theoretically and computationally study passively modelocked lasers, contrasting evolutionary and dynamical approaches and their application to full, averaged, and reduced models. We then develop the spectral methods and show how they can be used to determine the stability and to calculate the timing jitter and power spectral density for any averaged model with any equilibrium pulse shape. We review work that has been done on soliton lasers using soliton perturbation theory from this dynamical perspective, and we contrast the simplicity and generality of our methods to prior work. We close with a discussion of how to extend our approach from averaged models to full models.

Recent developments in quantum photonics have initiated the process of bringing photonic-quantumbased systems out-of-the-lab and into real-world applications. As an example, devices to enable the exchange of a cryptographic key secured by the laws of quantum mechanics are already commercially available. In order to further boost this process, the next step is to transfer the results achieved by means of bulky and expensive setups into miniaturized and affordable devices. Integrated quantum photonics is exactly addressing this issue. In this paper, we briefly review the most recent advancements in the generation of quantum states of light on-chip. In particular, we focus on optical microcavities, as they can offer a solution to the problem of low efficiency that is characteristic of the materials typically used in integrated platforms. In addition, we show that specifically designed microcavities can also offer further advantages, such as compatibility with telecom standards (for exploiting existing fibre networks) and quantum memories (necessary to extend the communication distance), as well as giving a longitudinal multimode character for larger information transfer and processing. This last property (i.e., the increased dimensionality of the photon quantum state) is achieved through the ability to generate multiple photon pairs on a frequency comb, corresponding to the microcavity resonances. Further achievements include the possibility of fully exploiting the polarization degree of freedom, even for integrated devices. These results pave the way for the generation of integrated quantum frequency combs that, in turn, may find important applications toward the realization of a compact quantum-computing platform.

Optical frequency combs have become indispensable in astronomical measurements, biological fingerprinting, optical metrology, and radio frequency photonic signal generation. Recently demonstrated microring resonator-based Kerr frequency combs point the way towards chip scale optical frequency comb generator retaining major properties of the lab scale devices. This technique is promising for integrated miniature radiofrequency and microwave sources, atomic clocks, optical references and femtosecond pulse generators. Here we present Kerr frequency comb development in a historical perspective emphasizing its similarities and differences with other physical phenomena. We elucidate fundamental principles and describe practical implementations of Kerr comb oscillators, highlighting associated solved and unsolved problems.