Theory of Parametric Amplification in two Coupled Waveguides: Frequency-Dependent Coupling and Resilience to Pump Fluctuations

Parametric amplification in two coupled nonlinear waveguides has been proposed as a solution for signal amplification in optical communications featuring a broadband and flat gain profile with low noise figure [1], [2]. Here we present a general theory of parametric amplification valid both for dual-core silica fibers and integrated coupled waveguides (e.g. silicon nitride) which takes into account the frequency dependency of the coupling strength and captures both phase-sensitive (PS) and insensitive (PI) regimes. We show that coupling dispersion can compensate for waveguide dispersion enabling a substantial control of the gain spectrum and amplification in the normal dispersion regime too. Our theory is based on the coupled nonlinear Schrödinger equations with frequency dependent coupling $C(\omega)=\Sigma_{n=0}^{\infty}(\omega-\omega_0))^{n}C_{n}/n\!$ , where $C_{n}$ is the n-th coefficient of the Taylor expansion of the coupling strength around the pump frequency $\omega_{0}$ .