Reciprocity theorem and accuracy evaluation on scattering fields by dielectric gratings

Area of Science:

• Optics and Photonics
• Electromagnetics
• Materials Science

Background:

• Diffraction theory for gratings traditionally requires energy balance and reciprocity.
• Multilayered dielectric gratings, especially those with lossy layers, present challenges to these theoretical constraints.
• Existing methods may not fully account for energy dissipation in complex grating structures.

Purpose of the Study:

• To investigate the validity of reciprocity in multilayered dielectric gratings, including those with lossy components.
• To introduce and evaluate reciprocity errors as a novel accuracy criterion for numerical diffraction calculations.
• To establish practical guidelines for verifying the accuracy of diffraction solutions in complex grating systems.

Main Methods:

• Application of shadow theory in conjunction with the matrix eigenvalues method.
• Derivation of formulae demonstrating the symmetry of scattering factors and diffraction efficiencies.
• Numerical validation of theoretical predictions and analysis of reciprocity errors.

Main Results:

• The study demonstrates the symmetry of scattering factors and diffraction efficiencies in multilayered dielectric gratings.
• Reciprocity errors for both scattering factors and diffraction efficiencies were newly defined and analyzed.
• Numerical calculations indicate that checking reciprocity errors for diffraction efficiencies is sufficient for accuracy assessment.

Conclusions:

• Reciprocity holds for multilayered dielectric gratings, even with lossy layers, when analyzed appropriately.
• Reciprocity errors serve as a valuable criterion for assessing the accuracy of numerical diffraction solutions.
• For practical numerical computations, focusing on diffraction efficiency reciprocity errors simplifies accuracy verification.