Mathematical Framework Developed for Identifying Spurious Modes in Photonic Grating Simulations
Researchers have proven that eigenvalues in the left half-plane of a class of Sturm-Liouville problems with complex coefficients are bounded and finite in number. This result addresses long-standing convergence problems in Fourier modal methods used to simulate light diffraction by metallic gratings. The work provides a rigorous criterion for distinguishing physical from non-physical (spurious) modes in computational photonics.
A new mathematical analysis establishes that for non-selfadjoint indefinite Sturm-Liouville problems with complex-valued coefficients, all eigenvalues in the open left half-plane form a bounded set containing only finitely many values. The study focuses on problems arising from transverse-magnetic diffraction by metallic lamellar gratings, a benchmark problem in computational photonics where Fourier modal methods have historically struggled with convergence. The loss of operator definiteness in these systems leads to the emergence of spurious (non-physical) modes that contaminate numerical solutions. The authors' theoretical result yields a practical criterion for identifying and filtering out these spurious modes in low-loss metallic gratings. Numerical examples demonstrate the utility of the approach for improving simulation accuracy in photonic applications.
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Boundedness of Left Half-Plane Eigenvalues for Non-Selfadjoint Indefinite Sturm--Liouville Problems with Applications to Fourier Modal Methods
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