Nonlinear Dynamics of Coupled Microring Resonators

• Author / Creator

  Abdollahi,Siamak

• Microring resonators are compact integrated optics resonators which have found a wide range application in optical communication and optical signal processing, including spectral filters, optical delay lines, switches, modulators and wavelength converters. In recent years, there has also been increased interest in studying the dynamical behaviors of nonlinear microresonators, especially in the instability regimes, for applications in all-optical switching, high-frequency optical clock generation, and fast optical pulse generation. In addition to these practical applications, the study of instability phenomena in optical microresonator systems can also provide important contributions to fundamental research on nonlinear dynamical systems. The aim of this thesis is to investigate the nonlinear dynamics in single and coupled microring resonators in the presence of instantaneous and non-instantaneous nonlinearities. Methods based on the energy coupling and power coupling formalisms of microring resonators are developed to analyze and investigate various types of instability in these systems, including bistability, self-pulsation, and period-doubling oscillations. An important objective is to study the influences of various device parameters on the threshold powers for reaching self-pulsation, with the aim of reducing these thresholds to levels that can be realistically achieved in practical integrated optics devices. In particular, in a single microring resonator with free carrier induced nonlinearity, the region of self-pulsation is constrained by a minimum free carrier lifetime. By exploring high-order instability, we show that on higher-order branches of the stability curve, the free carrier lifetime has a less restrictive influence on the nonlinear dynamics, allowing self-pulsation to be achieved over a wider range of free carrier lifetimes and with a wider range of oscillation frequencies. We also study the nonlinear dynamical behaviors of a system of coupled microring resonators – also known as Coupled Resonator Optical Waveguides (CROWs). The aim here is that, by enhancing the spatial complexity of the nonlinear system, we can achieve novel instability effects and further reduce the threshold powers for observing self-pulsation. Using the power coupling formalism developed, we show that period-doubling oscillations can occur in a chain of coupled microring resonators with instantaneous Kerr nonlinearity, although the threshold power required to reach this instability increases with the number of resonators. On the other hand, we found that there exists an optimum CROW waveguide length for which the threshold power for observing self-pulsation is minimized. Finally, we also develop a formalism based on the Coupled Map Lattice for describing nonlinear dynamics of CROW waveguides with long length. The formalism allows us to investigate temporal instability in these structures, and potentially spatiotemporal chaos pattern forming if the gain is introduced in the resonators.

• Subjects / Keywords

  • Microring resonator
  • Nonlinear Optics
  • Silicon Photonics
  • Nonlinear Dynamic

• Graduation date

  Fall 2017

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/R3RF5KV7P

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.