Nonlinear Optical Effects and Their Applications: From Parametric Amplification in Coupled Waveguides to Modulation Instabilities in Fibre Ring Resonators

Abstract

This thesis investigates nonlinear optical phenomena in two coupled waveguides and fibre ring resonators, with a particular emphasis on optical parametric amplification (OPA), modulation instability (MI), and optical frequency comb (OFC) generation. The work is divided into two parts. The first part investigates OPA in dual-core waveguide systems. By exploiting coupling-induced dispersion, we demonstrate flexible dispersion engineering that enables broadband gain, even in normally dispersive waveguides. Analytical and numerical models are developed to assess the impact of pump power and phase fluctuations on system stability. Additionally, we explore intermodal four-wave mixing in dual-core fibres, revealing how frequency-dependent coupling and power imbalance between the waveguides lead to asymmetric gain and signal–idler separation into distinct supermodes. These findings offer design strategies for efficient, robust, and tunable amplifiers in both fibre and integrated photonic platforms. The second part focuses on MI in nonlinear optical resonators. We study filter-induced MI in a fibre ring cavity with an intracavity amplifier, demonstrating enhanced MI and efficient energy transfer to spectral sidebands. In parametrically driven resonators with quadratic nonlinearity, we analyse filter-induced MI and show its role in enabling tunable OFC generation. Furthermore, we uncover a new dynamical regime in Kerr resonators: period-4 MI, characterised by temporal patterns repeating every four cavity round trips. Analytical gain expressions are derived and validated through numerical simulations. Together, these results advance the understanding and control of nonlinear wave dynamics in optical systems, providing novel mechanisms for amplification, frequency conversion, and complex temporal pattern formation, with implications for both fundamental science and practical photonic technologies.