Dispersive Fourier Transformation Method to Investigate the Nonlinear Dynamics of Photonic Crystal Fibre Ring Cavities

Abstract: By means of a conventional spectrum analyser for oserving the real-time spectrum of a pluse train up to 100 megahertz repetition rate, we can only view an average of the spectra because of the low scanning rate of the device. To overcome this limitation, one can use the time-stretching method, also kknown as the Dispersive Fourier Transform (DFT) technique, to map the spectral intensity on the temporal pulse and observe the shot-do-shot spectrum by employing a normal oscilloscope with few gighertz bandwidth.

In this thesis we investigated the nonlinear dynamics of a passive photonic crystal fibre ring cavity, pumped in the fs regime, by analysing the shot-do-shot spectrum obtained by the DFT technique. Afterward, we used the obtained spectral information of the cavity to determine the bifurcation diagrams and pointed out different nonlinear dynamical states such as steady, perodic, and highly complex dynamics.

Furthermore, we presented the concept of the spectral correlation maps and applied it on the ensembles of the different dynamical states. Outstandingly, we observed highly correlated areas on the map that remained persistent even when the number of the considered consecutive pulses increased up to few hundreds.