Stochastic FDTD Modeling of Propagation Loss due to Random Surface Roughness in Sidewalls of Optical Interconnects

The dielectric waveguide (WG) is an important building block of high-speed and high-bandwidth optical and opto-electronic interconnect networks that operate in the THz frequency regime. At the interface of Si/SiO2 dielectric waveguides with width above $w = 2.5 \mu m$ and anisotropic surface roughness, transverse electric (TE) mode surface wave propagation can experience a loss of approximately $a = 2 dB/cm$; however, propagation losses increase rapidly to near $a = 44 dB/cm$ as the width decreases to $w = 500 nm$, due to increased interaction of surface waves and sidewall surface roughness that exhibits random distribution inherent to the manufacturing process. Previous works have developed analytic expressions for computing propagation loss in a single dielectric waveguide exhibiting random roughness. More recent works report $a = 0.4 dB/cm$ noting the non-trivial estimation errors in previous theoretical formulations which relied on planar approximations, and highlight the discrepancy in planar approximations vs. the 3-D Volume Current Method. A challenge that remains in the path of designing nanoscale optical interconnects is the dearth of efficient 3-D stochastic computational electromagnetic (CEM) models for multiple tightly coupled optical dielectric waveguides that characterize propagation loss due to random surface roughness in waveguide sidewalls. Through a series of theoretical and numerical experiments developed in the method of finite-difference time-domain (FDTD), we aim to develop stochastic CEM models to quantify propagation loss and facilitate signal & power integrity modeling & simulation of arbitrary configurations of multiple tightly-coupled waveguides, and to gain further insights into loss mechanisms due to random surface roughness in optical interconnects.