Matched coordinates for the analysis of 1D gratings

Area of Science:

• Optics and Photonics
• Computational Electromagnetics

Background:

• The Fourier modal method (FMM) is widely used for modeling diffraction gratings.
• FMM exhibits poor convergence for non-lamellar gratings, especially metallic ones in TM polarization, due to staircase approximation.

Purpose of the Study:

• To introduce a novel method for accurate modeling of non-lamellar diffraction gratings.
• To overcome the convergence limitations of the FMM for challenging grating profiles.

Main Methods:

• Developed the matched coordinate method (MCM) by introducing a profile-matching coordinate system.
• Solved covariant Maxwell's equations within this new coordinate system.
• Compared MCM results with existing literature data.

Main Results:

• The matched coordinate method (MCM) offers an alternative to FMM for diffraction grating analysis.
• MCM effectively handles non-lamellar profiles without staircase approximation issues.
• Computed efficiencies using MCM show good agreement with literature data, validating the method.

Conclusions:

• The matched coordinate method (MCM) is a validated and accurate technique for modeling diffraction gratings.
• MCM provides a superior alternative to FMM for non-lamellar gratings, particularly in TM polarization.
• This method enhances the modeling capabilities for complex optical structures.