Theory of Kerr Frequency Combs in Fabry-Perot resonators
Daniel C. Cole, Alessandra Gatti, Scott B. Papp, Franco Prati, Luigi Luigato
We derive a spatiotemporal equation describing nonlinear optical dynamics in Fabry-Perot (FP) cavities filled with a Kerr medium. This equation is an extension of the equation that describes dynamics in Kerr-nonlinear ring resonators, referred to as the Lugiato-Lefever equation (LLE) due to its formulation by Lugiato and Lefever in 1987. We use the new equation to study the generation and properties of Kerr frequency combs in FP resonators. The derivation of the equation starts from the set of Maxwell-Bloch equations that govern the dynamics of the forward and backward propagating envelopes of the electric field coupled to the atomic polarization and population difference variables in a FP cavity. The final equation is formulated in terms of an auxiliary field \psi(z; t) that evolves over a slow time t on the domain -L
, Gatti, A.
, Papp, S.
, Prati, F.
and Luigato, L.
Theory of Kerr Frequency Combs in Fabry-Perot resonators, Physical Review A, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=925715
(Accessed May 29, 2023)