Extension of Marcatili's analytical approach for rectangular silicon optical waveguides

TL;DR

This paper enhances Marcatili's analytical model for rectangular silicon optical waveguides, making it applicable to high-index-contrast waveguides with improved accuracy and explicit expressions for key optical properties.

Contribution

The authors extend Marcatili's model to high-index-contrast waveguides by adjusting electromagnetic field amplitudes, maintaining eigenvalue validity, and deriving explicit formulas for group index and mode interactions.

Findings

Improved agreement with numerical simulations for HIC waveguides

Derived explicit expressions for effective group index

Observed and analyzed avoided crossing phenomena

Abstract

Marcatili's famous approximate analytical description of light propagating through rectangular dielectric waveguides, published in 1969, gives accurate results for low-index-contrast waveguides. However, photonic integrated circuit technology has advanced to high-index-contrast (HIC) waveguides. In this paper, we improve Marcatili's model by adjusting the amplitudes of the components of the electromagnetic fields in his description. We find that Marcatili's eigenvalue equation for the propagation constant is also valid for HIC waveguides. Our improved method shows much better agreement with rigorous numerical simulations, in particular for the case of HIC waveguides. We also derive explicit expressions for the effective group index and the effects of external forces on the propagation constant. Furthermore, with our method the phenomenon of avoided crossing of modes is observed and studied.