Optical frequency comb generation in multidimensional geometries

The objectives of the project are to develop theoretical and numerical methods and study nonlinear effects in multimode optical microresonators, where modes involved in generation of ultrabroad spectra (frequency combs) are characterised not by one but by either two or three modal indexes. Examples include cylindrical, spherical and bottle microresonators.

Photon states in optical microresonators are in general characterised by three quantum numbers, similar to the eigenstates of a hydrogen atom. Geometry of such resonators can be, for example, either spherical, cylindrical, toroidal or can take more exotic shapes. A relatively well-developed theory of frequency comb generation in such microcavities deals with the case, when modal families can be characterised by one modal index only and the other two are assumed fixed. However, in some of the proposed and already implemented experiments, this assumption fails. Developing reliable models describing nonlinear light dynamics in such cases, and understanding novel effects involved here, for example, when curvature of the interfaces starts influencing usual intuition about nonlinear light dynamics, will be addressed in this project. In particular, we will derive two and three dimensional generalisations of the Lugiato-Lefever model and develop numerical codes to model frequency comb generation and formation of multi-dimensional comb solitons. There exists an opportunity with this project to collaborate with other UK and international research groups working on experimental and theoretical studies of frequency combs.

Enquiries: Prof. Dmitry Skryabin, [Email Address Removed]