Resonant scattering and mode coupling in two-dimensional textured planar waveguides

Area of Science:

• Optics and Photonics
• Computational Electromagnetics
• Materials Science

Background:

• Planar waveguides with 2D textures exhibit complex specular reflectivity spectra.
• Understanding these spectra is crucial for optical device design, particularly filters.
• Existing methods for calculating reflectivity can be computationally intensive.

Purpose of the Study:

• To develop an efficient heuristic formalism for calculating the specular reflectivity spectrum of 2D textured planar waveguides.
• To provide an intuitive explanation for Fano-like features in the reflectivity spectrum.
• To demonstrate the formalism's utility in analyzing polarization-insensitive notch filters.

Main Methods:

• A Green's function approach is employed, assuming minimal electric field variation across the textured region's thickness.
• The formalism's accuracy is validated against exact finite difference solutions of Maxwell's equations for thin textured regions.
• The method analyzes the interaction between Fourier components of the scattered field and bare slab modes.

Main Results:

• The heuristic formalism provides efficient and accurate predictions of specular reflectivity spectra.
• It offers an intuitive explanation for Fano-like features by linking them to leaky electromagnetic modes and photonic eigenmodes.
• The dispersion, polarization properties, and lifetimes of these features are explained through mode renormalization.

Conclusions:

• The developed formalism offers a computationally efficient and insightful tool for analyzing 2D textured waveguides.
• It successfully explains complex spectral features and provides a basis for designing advanced optical filters.
• The approach facilitates a deeper understanding of light-matter interactions in nanostructured optical devices.