Electromagnetic Analysis of Ring-Cavity-Assisted Amplified Spontaneous Emission in Er:SiO$_{2}$/a-Si Horizontal Slot Waveguides

Abstract

In this paper, we present an electromagnetic analysis of ring-cavity-assisted amplified spontaneous emission in Er <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</sup> -doped SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> (Er:SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ). A horizontal slot geometry, consisting of a low-index Er:SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> layer embedded between high-index a-Si layers, allows for a planar ring-cavity design which maintains high optical confinement in the active Er:SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> material. The simulations are performed within the auxiliary differential equation-finite-difference time-domain (ADE-FDTD) scheme which couples the quantum mechanical light emission and amplification behavior of the Er:SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> with the electromagnetic device behavior. We present the enhanced spontaneous emission in waveguide-coupled ring cavities with varying coupling gaps. We provide an analysis of the relationship between cavity quality factor, coupling coefficient, and enhanced spontaneous emission.