Probing unconventional performance of fiber resonators: light storage, generation and manipulation

This thesis aims at investigating the performance of figure-9 (figure-of-nine) optical fiber resonators as a practical solution for light storage, light generation and manipulation. The first part of the thesis focuses on a theoretical and experimental study describing the performance of the figure-9 laser as a function of different coupling strengths and output coupling conditions. The study provides new insights on Sagnac interferometer-based fiber lasers, which can be useful also for other types of cavities that include this structure, such as the figure-8 (figure-of-eight) or the theta cavity laser. The work on the figure-9 laser is then followed by a generalized theoretical model, validated by numerical results, to demonstrate that resonant systems with a decoupled input and output energy rates can exhibit an arbitrarily high time-bandwidth performance, thus providing a longer delay/storage time. The developed model shows that the time-bandwidth product (TBP) of such a resonant system is only limited by the cavity finesse. This description fits with the time-bandwidth limit (TBL), which states that the cavity bandwidth $\Delta \omega_{\mathrm{cav}}$ is the inverse of the photon lifetime $\tau$ (i.e. $\Delta \omega_{\mathrm{cav}}\cdot \tau=1$), only when the resonator is reciprocal. The results also show that a longer storage time is accompanied by a significant improvement of the intra-cavity power enhancement, with respect to that provided by a reciprocal resonator, which is strongly desirable in all the applications that demand high efficiency in nonlinear processes. By comparing the total power enhancement in the reciprocal and nonreciprocal case, we prove that the TBP can be used as a figure of merit that characterizes the gain of total power enhancement, attained over one free spectral range (FSR) through nonreciprocal coupling, with respect to the reciprocal case considering the same amount of in-coupled power. The model is then used as a reference for an experimental implementation of such a system, at telecommunication wavelengths (around $1.55\,\mathrm{\mu m}$), using a time-variant figure-9 cavity. The results report a TBP that exceeds by a factor of 30 the TBL and is limited only by experimental constraints of the setup used. Lastly, the Sagnac interferometer in the context of generation of light is explored as to achieve electro-optic comb generation with a flat-topped spectral shape.