Numerical modeling of the opposite waves spatio-temporal dynamics in a ring fibre nonlinear microcavity

Background and Objectives: Optical frequency combs have a significant impact in the terabit communications area. Kerr frequency comb generation in the nonlinear microcavities is especially promising because it allows for creation of the combs with spacings of tens of gigahertz between the frequencies. However, such combs can also spawn strong phase noises, what, in turn, leads to the problems with the high-speed data transmission. Results of the already conducted experiments show that it is Kerr combs that allow for serious demands of the coherent communications and thus are a very effective way to create microsized transmission receivers that are capable of supporting terabit per second rates of data flow. Thus, it is apparent that the ability to predict electromagnetic field behavior within the microcavities has a huge practical value. Since the operating regime of such cavities corresponds to strong nonlinearity, then proper research of its dynamics is possible right now only based on the numerical methods. It should be noted that the models used ought to give an adequate representation of the occurring process and do not require long calculation times. Materials and Methods: Since the equations used are the transport equation, we use in our numerical model an effective finite differences model of the second order known as “Cabaret”. To check for the algorithm stability, we have calculated full pulse energy during a round trip, and it was shown that there is less than 1% of the numerical losses after two million steps, which is about one thousand of the cavity round trips. Results: We have achieved conclusive results in several modes of the model, getting frequency soliton combs, following each other with a period roughly equal to that of a cavity roundtrip, as well as chaotic modes and overlaps of the combs. Conclusion: Summarizing, we can conclude that using the second order finite differences model “Cabaret” allows to simulate long temporal dynamics of the fibre microcavities, with GVD, crossand self phase modulation taken into consideration, displaying good fit to the theoretical expectations. The proposed scheme and model allow to investigate cavity dynamics with two counter-propagatating pulse trains with second order dispersion and modulation instability, Rayleigh scattering and other effects and linear wave interfaces.