| dc.description.abstract | Optical communication using light as the carrier signal has advantages of high-speed transmission because of the low propagation loss and high bandwidth. It has been widely used in datacenters and submarine cables for long distance telecommunications. Recently, the development of silicon photonics technology helps to integrate optical elements, such as light sources, modulators, and receivers, together on a single silicon chip, providing a compact, low-power system for optical communications. Micro-ring resonator (MRR) is one of the most applied optical components in silicon photonics. In linear optics, MRRs can be used for signal modulating, bio-sensing, and optical logical operation. In nonlinear optics, broadband frequency combs delivering from MRR can replace the traditional distributed feedback laser diodes, and this multi-wavelength source can be used in a wavelength division multiplexing system. Moreover, for quantum optics, MRRs can also generate entangled photons when the input power is under threshold, this helps to provide a light source in quantum optical circuits.
In this thesis, the author theoretically discusses the nonlinear dynamics and squeezing effect in silicon nitride based MRRs. Utilizing the silicon nitride waveguide MRRs with high quality factor, it provides strong cavity enhancement and therefore results in significant nonlinear processes, such as four-wave-mixing (FWM) and frequency comb generation. The light field in the MRR is numerically analyzed by the spatiotemporal Lugiato-Lefever equation (LLE) model. The cavity dispersion strongly alters the nonlinear dynamics in MRRs. Here, the dispersion effect will be discussed both in normal and anomalous dispersion. The nonlinear phenomena including dark, bright soliton(s) and Turing rolls are further analyzed by comb conversion efficiency, frequency comb repetition rate, and generation dynamics.
In addition, the mode coupling / interaction will be investigated in the LLE. Experimentally, there are several methods, such as polarization modes interaction, higher order modes interaction, or back scattering, can introduce mode interaction in MRRs. In normal dispersion, mode interaction causes avoid mode crossing and generates anomalous dispersion locally. The effectively anomalous dispersion further induces modulational instability (MI) and the cascaded FWM leads the generation of frequency combs. Since normal dispersion is much more common in silicon photonics, mode interaction provides more flexibility in the designs of waveguide structures and materials. Thresholds of MI and mode gain are then obtained from the eigenvalue analysis by solving the nonlinear equations. The threshold with mode interaction shows that the comb generation has upper and lower boundaries in input pump power, exhibiting significant difference to the MI and comb generation in anomalous dispersion. In comparison with the bright and dark soliton case, comb generation by the aid of mode interaction does not require a specific electric field as the initial condition. Numerical analysis shows comparable conversion efficiency for comb generation in normal dispersion with mode interaction to the conventional comb generation in an anomalous-dispersion MRR. In addition, with large detuning, the comb generation shows hysteresis and the threshold is strongly altered by the bistability of cavity power.
Last, the semi-classical LLE modal was introduced to study the quantum effects in the MRR. When MRR is acting as an entangled photon source, it is important to ensure that the light is produced by spontaneous emission. The spontaneous emission spectra will be investigated under different detunings. On the other hand, when MMR is working above comb generation threshold, squeezed light is studied from the stimulated emission. High degree of squeezing can be achieved in silicon nitride MRRs, especially in the form of Turing rolls. | en_US |