Adaptive resolution of fine scales in modes of microstructured optical fibers

TL;DR

The paper tackles automatic, accurate resolution of fine-scale features in eigenmodes of microstructured optical fibers. It introduces a dual-weighted residual error estimator-based adaptive algorithm to drive mesh refinement for leaky hybrid modes derived from Maxwell's equations with a perfectly matched layer. The method captures intricate transverse features and provides reliable confinement loss estimates on adaptively generated meshes across multiple fiber geometries. This enables robust, expert-free analysis of complex microstructured fibers with practical implications for fiber design and optimization.

Abstract

An adaptive algorithm for computing eigenmodes and propagation constants of optical fibers is proposed. The algorithm is built using a dual-weighted residual error estimator. The residuals are based on the eigensystem for leaky hybrid modes obtained from Maxwell equations truncated to a finite domain after a transformation by a perfectly matched layer. The adaptive algorithm is then applied to compute practically interesting modes for multiple fiber microstructures. Emerging microstructured optical fibers are characterized by complex geometrical features in their transverse cross-section. Their leaky modes, useful for confining and propagating light in their cores, often exhibit fine scale features. The adaptive algorithm automatically captures these features without any expert input. The results also show that confinement losses of these modes are captured accurately on the adaptively found meshes.

Figures (2)

• Figure 1: Example figure using external image files.
• Figure 2: Example PGFPLOTS figure.

Theorems & Definitions (5)

• Theorem 6.1: Mean Value Theorem
• Corollary 6.2
• Proof 1
• Claim 6.3
• Proof 2: Proof of main theorem