Theory and simulations of frequency combs in micro-resonator devices

Frequency combs are spectra consisting of a series of discrete, equally spaced elements and form the modern standard of optical frequencies and clocks. Frequency combs led to the Nobel Prize in Physics to John Hall and Theodor Hänsch in 2005. Micro-resonator-based frequency combs have attracted a lot of attention for their potential applications in quantum technologies, precision metrology, gas sensing, arbitrary optical waveform generation, telecommunication and integrated photonic circuits. Micro-resonator combs are generated in ultra-high-Q optical resonators that enable the confinement of extremely high optical power levels in tiny mode-volumes. The high optical power densities lead to the conversion of a continuous wave laser into a comb of equidistant optical modes that can be used like a ruler for optical frequency measurements. Dr. Pascal Del'Haye at MPI has developed and optimised micro-resonator frequency combs based on periodic and soliton like waveforms of the light circulating in the optical cavity. These are the temporal counterparts of periodic and cavity-soliton solutions discovered and analysed in the CNQO group at Strathclyde for more than ten years first by Prof. Willie J. Firth and then by Prof. Gian-Luca Oppo. In recent years Dr. Del'Haye and Prof. Oppo have already successfully collaborated on symmetry breaking phenomena in two-polarization and counter-propagating ring-resonators, leading to three joint publications. This project develops, optimises, and strategically compares accurate mathematical modelling at Strathclyde for the generation of frequency combs in micro-resonator devices in a close connection with the experiments performed at MPI in Dr. Del'Haye's laboratory. The objectives of the project are:

1) Theoretical setting of partial differential equations describing frequency comb generation in the ring and Fabry-Perot micro-resonators developed at MPI
2) Numerical integration of the theoretical models on already available state-of-the-art CNQO computers
3) Determination of the periodic pulses and cavity-soliton regimes in comparison with the experiments performed at MPI. Special focus on the physical properties of the frequency combs
4) Symmetry breaking phenomena for short pulses of counter-propagating light in micro-resonators. This effect can act as nonreciprocal devices that transmit light in one direction but not in the other. The symmetry breaking can be used for optical diodes, circulators and for the development of integrated optical gyroscopes
5) Development of a new model for the generation and application of microresonator frequency combs in quantum technologies by using counterpropagation and/or two perpendicular polarisation states

The project will run in a close collaboration between Strathclyde and MPI. The CNQO group at Strathclyde is in a unique and strategic position world-wide being the inventor of the theory and first developer of the simulations associated with cavity-solitons, the key elements of the optimal frequency comb generation using resonators. Dr. Del'Haye will be the external supervisor of the PhD student who will periodically visit MPI and compare the results of the simulations and theoretical models with the experimental data. There is an extraordinary international interest in the development and application of compact and versatile devices for frequency combs. The project is expected to generate research publications in top impact journals, development of key applications in quantum technologies.