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This study introduces a polynomial chaos expansion (PCE) algorithm for efficient uncertainty quantification in grating filters. The method significantly reduces computational cost compared to traditional techniques, enabling faster optimization.

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Area of Science:

Computational electromagnetics
Photonics and optical engineering
Uncertainty quantification

Background:

Grating filters are crucial optical components, but their performance analysis involves complex simulations.
Uncertainty quantification (UQ) is essential for reliable filter design, yet computationally intensive.
Existing methods like Monte Carlo (MC) require extensive simulations, limiting design optimization.

Purpose of the Study:

To develop a computationally efficient algorithm for UQ of grating filters.
To enable faster and more reliable optimization of grating filter performance.
To reduce the reliance on time-consuming full-wave solvers.

Main Methods:

Utilizing polynomial chaos expansions (PCEs) for adaptive anisotropic model construction.
Employing the least angles regression (LARS) sparse solver to compute PCE coefficients.
Designing optimal experiments based on local sample variance for enhanced reliability.
Integrating PCE with Kriging interpolation for improved optimization.

Main Results:

The PCE-based method achieves over 2 orders of magnitude speedup compared to full-wave solvers.
Approximately 25 full-wave solver calls were needed, versus 20,000 for MC.
The PCE model efficiently generates samples for optimization, outperforming direct full-wave solver sampling.
Combined PCE and Kriging yielded improved optimization results.

Conclusions:

The proposed PCE algorithm offers a highly efficient and reliable solution for UQ in grating filters.
This approach significantly accelerates the design and optimization cycle for photonic devices.
The method provides a robust framework for integrating UQ with optimization in optical engineering.