(content prepared by Yanne Chembo)
Microwave optoelectronic oscillators
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 dBrad2/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 figure displays the typical architecture of a microwave OEO, after ref. [1], where a detailed phase noise analysis is proposed. We are also exploring the effects of various phenomena such as the one of dispersion on the phase noise performance [2], as well as the possibility to generate ultra-low jitter picosecond pulses [3]. The nonlinear dynamics of these OEOs have also been investigated in refs. [4], [5], and [6]. These investigations are led in partnership with CNES.
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 1010. 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. The figure displays a "mushroom" WGM disk-resonator, whose diameter may practically range from few tens of micrometers to few millimeters. The various WGMs of interest are the torus-like eigenmodes of the resonator, as shown in the enlargement.
At the FEMTO-ST Institute, we have developed research ctivities in the fabrication of WGM resonators. In particular, we are exploring the possibility of unconventional bulk materials, such as magnesium fluoride [7]. We also investigate the possibility to use millimeter-sized WGM resonators in optoelectronic oscillators, in replacement of the bulky fiber delay-line [8]. The objective is to realize compact and transportable OEOs. This research is also led in partnership with CNES.
Optical frequency comb generation
Optical frequency combs are sets of regularly spaced spectral lines in the ultraviolet, visible, or infrared ranges. They have for long been generated with mode-locked ultrafast lasers, as periodic trains of ultrashort laser pulses yield such equidistant lines in the spectral domain. Many applications can benefit from these combs: fundamental physics, time-frequency metrology, navigation systems, spectroscopy, sensing, or ultralow phase noise microwave and terahertz generation. An interesting method has been demonstrated recently for the generation of these combs, and it relies on the hyperparametric excitation of the WGMs of an ultra-high Q monolithic resonator. In these resonators, the small volume of confinement, high photon density, and long photon storage time (proportional to the quality factor Q) induce a very strong light-matter interaction. Depending on the dielectric material, this strong coupling can generate a highly efficient four-wave mixing (FWM), where two pump photons are transformed into two sideband photons through the Kerr nonlinearity. Provided that the pump is powerful enough, an optical-frequency comb, sometimes referred to as a Kerr comb, is generated through a cascaded creation of such sideband photons, resulting from a huge sum of weighted interactions involving any four photons fulfilling energy and angular momentum conservation requirements.
We have developed an original framework based on a modal expansion formalism to investigate the dynamical behavior of these Kerr combs. The figure (after ref. [9]) displays the excellent agreement between the theoretical results and the experimental comb spectra obtained with a calcium fluoride cavity pumped around 1550 nm. The detailed theoretical analysis has been presented in ref. [10], and we have also theoretically shown that octave spanning combs can in principle be generated [11]. This activity is led in collaboration with the NASA Jet Propulsion Lab.