Kerr frequency combs (also known as microresonator frequency combs) are optical frequency combs which are generated from a continuous wave pump

laser A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The firs ...

by the Kerr nonlinearity. This coherent conversion of the pump laser to a frequency comb takes place inside an

optical resonator An optical cavity, resonating cavity or optical resonator is an arrangement of mirrors or other optical elements that forms a cavity resonator for light waves. Optical cavities are a major component of lasers, surrounding the gain medium and prov ...

which is typically of micrometer to millimeter in size and is therefore termed a microresonator. The coherent generation of the frequency comb from a continuous wave laser with the optical nonlinearity as a gain sets Kerr frequency combs apart from today’s most common optical frequency combs. These frequency combs are generated by mode-locked lasers where the dominating gain stems from a conventional laser gain medium, which is pumped incoherently. Because Kerr frequency combs only rely on the nonlinear properties of the medium inside the microresonator and do not require a broadband laser gain medium, broad Kerr frequency combs can in principle be generated around any pump frequency. While the principle of Kerr frequency combs is applicable to any type of optical resonator, the requirement for Kerr frequency comb generation is a pump laser field intensity above the parametric threshold of the nonlinear process. This requirement is easier to fulfill inside a microresonator because of the possible very low losses inside microresonators (and corresponding high

quality factor In physics and engineering, the quality factor or ''Q'' factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is. It is defined as the ratio of the initial energy stored in the resonator to the energy l ...

s) and because of the microresonators’ small mode volumes. These two features combined result in a large field enhancement of the pump laser inside the microresonator which allow the generation of broad Kerr frequency combs for reasonable powers of the pump laser. One important property of Kerr frequency combs, which is a direct consequence of the small dimensions of the microresonators and their resulting large free spectral ranges (FSR), is the large mode spacing of typical Kerr frequency combs. For mode-locked lasers this mode spacing, which defines the distance in between adjacent teeth of the frequency comb, is typically in the range of 10 MHz to 1 GHz. For Kerr frequency combs the typical range is from around 10 GHz to 1 THz. The coherent generation of an optical frequency comb from a continuous wave pump laser is not a unique property of Kerr frequency combs. Optical frequency combs generated with cascaded optical modulators also possess this property. For certain application this property can be advantageous. For example, to stabilize the offset frequency of the Kerr frequency comb one can directly apply feedback to the pump laser frequency. In principle it is also possible to generate a Kerr frequency comb around a particular continuous wave laser in order to use the bandwidth of the frequency comb to determine the exact frequency of the continuous wave laser. Since their first demonstration in silica micro-toroid resonators, Kerr frequency combs have been demonstrated in a variety of microresonator platforms which notably also include crystalline microresonators and integrated photonics platforms such as waveguide resonators made from

silicon nitride Silicon nitride is a chemical compound of the elements silicon and nitrogen. is the most thermodynamically stable and commercially important of the silicon nitrides, and the term "silicon nitride" commonly refers to this specific composition. It ...

. More recent research has expanded the range of available platforms further which now includes

diamond Diamond is a solid form of the element carbon with its atoms arranged in a crystal structure called diamond cubic. Another solid form of carbon known as graphite is the chemically stable form of carbon at room temperature and pressure, ...

, aluminum nitride,

lithium niobate Lithium niobate () is a non-naturally-occurring salt consisting of niobium, lithium, and oxygen. Its single crystals are an important material for optical waveguides, mobile phones, piezoelectric sensors, optical modulators and various other line ...

, and, for mid-infrared pump wavelengths,

silicon Silicon is a chemical element with the symbol Si and atomic number 14. It is a hard, brittle crystalline solid with a blue-grey metallic luster, and is a tetravalent metalloid and semiconductor. It is a member of group 14 in the periodic ...

. Because both use the nonlinear effects of the propagation medium, the physics of Kerr frequency combs and of supercontinuum generation from pulsed lasers is very similar. In addition to the nonlinearity, the

chromatic dispersion In optics, and by analogy other branches of physics dealing with wave propagation, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency; sometimes the term chromatic dispersion is used for specificity t ...

of the medium also plays a crucial role for these systems. As a result of the interplay of nonlinearity and dispersion,

soliton In mathematics and physics, a soliton or solitary wave is a self-reinforcing wave packet that maintains its shape while it propagates at a constant velocity. Solitons are caused by a cancellation of nonlinear and dispersive effects in the mediu ...

s can form. The most relevant type of solitons for Kerr frequency comb generation are bright dissipative cavity solitons, which are sometimes also called dissipative Kerr solitons (DKS). These bright solitons have helped to significantly advance the field of Kerr frequency combs as they provide a way to generate ultra-short pulses which in turn represent a coherent, broadband optical frequency comb, in a more reliable fashion than what was possible before. In its simplest form with only the Kerr nonlinearity and second order dispersion the physics of Kerr frequency combs and dissipative solitons can be described well by the

Lugiato–Lefever equation The model usually designated as Lugiato–Lefever equation (LLE) was formulated in 1987 by Luigi Lugiato and René Lefever as a paradigm for spontaneous pattern formation in nonlinear optical systems. The patterns originate from the interaction ...

. Other effects such as the

Raman effect Raman scattering or the Raman effect () is the inelastic scattering of photons by matter, meaning that there is both an exchange of energy and a change in the light's direction. Typically this effect involves vibrational energy being gained by a ...

and higher order dispersion effects require additional terms in the equation.

References

{{Reflist Nonlinear optics Laser science Spectroscopy Photonics

See also

References