Performance analysis of waveguide-mode resonant optical filters with stochastic design parameters

Area of Science:

• Optics and Photonics
• Computational Physics
• Nanophotonics

Background:

• Resonant waveguide gratings are crucial optical filter components.
• Performance analysis often assumes ideal design parameters, neglecting real-world variability.

Purpose of the Study:

• To numerically investigate the performance of resonant waveguide grating optical filters in a stochastic context.
• To assess the impact of random fluctuations in design variables on filter performance.
• To develop a more efficient simulation method compared to standard Monte Carlo techniques.

Main Methods:

• Stochastic modeling using polynomial chaos expansions.
• Sparse-grid quadrature for computing spectral projections.
• Rigorous coupled-wave analysis (RCWA) solver for deterministic simulations.
• Comparison with Monte Carlo (MC) analysis for validation.

Main Results:

• Reliable calculation of statistical moments for the filter's spectral response.
• Identification of key design parameters influencing filter performance via Sobol indices.
• Demonstration that neglecting small geometric variations leads to inaccurate performance predictions.

Conclusions:

• Stochastic analysis is essential for accurate optical filter performance prediction.
• Small geometric variations significantly impact filter performance, affecting real-world applications.
• Polynomial chaos expansion with sparse-grid quadrature offers an efficient alternative to MC methods for stochastic analysis.