Whispering-gallery mode resonators

Ultra-high Q whispering gallery mode (WGM) optical resonators have been the focus of an increasing amount of scientific research in recent years. This interest has been driven by the essential advantages of monolithic WGM technology: low-cost, conceptual simplicity, and low energetic losses. Effectively, provided that the bulk material is low loss and the resonator has smooth surfaces (subnanometer surface irregularities), the light can be trapped for few microseconds by total internal reflection. Their free-spectral range (FSR) may vary from a few gigahertz to a few terahertz, depending on the resonator’s radius, and their quality factor Q can be exceptionally high, of the order of ten billions at 1550 nm.

WGM resonators are also particularly interesting because they are expected to be central components for a wide variety of applications in optics and in microwave photonics. In the linear regime, for example, WGM resonators can be used as extremely narrow optical filters, useful in optical communications or in optoelectronic oscillators. In the nonlinear regime, these resonators allow full-optical frequency conversion through fundamental bulk nonlinearities such as Kerr, Raman or Brillouin. We have developed research activities in the fabrication of WGM resonators and we have obtained state-of-the art or record values for the Q factor of fluorite resonators (generally of the order of a billion at telecom wavelengths). The crystals we have explored include for example calcium fluoride, magnesium fluoride , strontium fluoride, barium fluoride, and lithium fluoride.

Further reading:
– Lin, Coillet & Chembo (2017)
– Lin & Chembo (2019)

 

Optoelectronic oscillators

High stability and spectral purity microwave and millimeter-wave sources have become increasingly crucial in several areas of applications, including aerospace engineering (satellites, GPS navigation, radars, navigation), communication systems, signal processing, spectroscopy, time-frequency metrology, etc. Optoelectronic oscillators (OEOs) combine a nonlinear modulation of laser light with optical storage to generate ultra-pure microwaves for aerospace and communication engineering applications. Their principal specificity is their extremely low phase noise, which can be as low as -160 dBc/Hz at 10 kHz from a 10 GHz carrier. This exceptional performance is achieved through the use of an unusual energy storage principle based on a long optical fiber delay line instead of the classical concept of resonators. OEOs are therefore candidates for various applications in lightwave and microwave technologies. We have developed a framework of analysis based on delay an stochastic differential equations to investigate the spectral stability and phase noise performance of these oscillators. The typical phase noise level of the microwaves generated with our fiber-based OEOs in the X-band (8-12 GHz) is -140 dBc/Hz at 10 kHz from the carrier.

We are also exploring the effects of various phenomena such as the one of dispersion on the phase noise performance, as well as the possibility to generate ultra-low jitter picosecond pulses, along with their nonlinear dynamics. We investigate as well alternative architectures of fiber-based OEOs, such as multi-loop OEOs, and WGM-resonator based OEOs. Our latest research focuses on the exploration of new architectures where both delay lines and WGM resonators are combined to ensure an improvement of the microwave spectral purity.

Further reading:
– Chembo et al. (2019)

 

Kerr comb microwave oscillators

For more than twenty years, optics has started to prove itself as an elegant and reliable solution for the development of microwave and even millimeter-wave sources featuring very high spectral purity. The advent of optical frequency combs generated by femtosecond lasers in the late 1990s has revolutionized the measurement of time and frequency. These lasers have allowed the establishment of a bridge linking the lightwave and the microwave domains. The principle of optical frequency division of an ultra-pure laser to much lower frequencies (microwave frequency range), using an optical frequency comb featuring a mode spacing of few hundreds of MHz, has been demonstrated, but unfortunately, it remains at this date exclusively a laboratory technology. A novel method to generate ultra-pure microwaves is based on using ultra-high Q WGM resonators. Owing to the strong confinement of pump photons and to their long lifetime, nonlinear effect such as the Kerr interaction are enhanced in the resonator. As a consequence, above a certain threshold, the pump photons populate the neighboring eigenmodes of the WGMR, thereby creating the so-called Kerr optical frequency comb. Microwave generation is achieved via a fast photodetection of the comb, as shown in the simplified scheme presented in the figure above.

A challenge for microwave generation is to achive as well ultra-low phase noise performance. This is only possible when the Kerr combs are highly coherent, that is, when the modes are strongly phase-locked with each other. Such a phase locking actually corresponds to a pulse-train in the phase domain. We are investigating the various ways to monitor or strengthen this phase-locking in order to control and possibly increase the coherence of the comb. We have shown that one of the most coherent comb state corresponds to the so-called primary combs in the spectral domain, or Turing rolls in the temporal domain. The specific advantage of primary combs is that they are characterized by a very strong phase correlation and a variable intermodal frequency depending on the detuning of the laser frequency and the dispersion of the resonator. These two features allow to obtain Kerr combs with a variable spacing frequency, therefore opening the door to a multiplicity of applications in microwave photonics.

Several research works have already proven that Kerr combs can effectively deliver competitive solutions for both oscillators (short-term stability) and clocks (long-term stability). One of the early promise of Kerr optical frequency combs was that they could provide ultra-stable signals both in the lightwave and microwave frequency domains. In particular, the short-term stability of the generated microwave can be estimated using the phase noise spectra. The figure on the left shows that Kerr combs are versatile sources of microwaves able to provide a spectral purity better than -100 dBc/Hz at 10 kHz from a carrier with 12-36 GHz frequency (the phase noise spectra A-F are linked to the Kerr combs displayed above). Our studies show that the intermodal frequency can be tuned from ~5 GHz to up to >1 THz with the very same resonator, thereby providing one of the most versatile micro- and mm-wave source today.

Further reading:
– Chembo (2016)
– Lin, Coillet & Chembo (2017)
– Pasquazi et al. (2018)