Driven eigenproblem computation in periodic structures accelerated with Brent's method

Abstract

The driven eigenproblem computation opens up the possibility to solve eigenproblems as excitation problems by utilising the analogy to resonators, especially for periodic structures like substrate integrated waveguides or metamaterials which can be modelled as a unit cell. The eigenvalue (wavevector, resonance frequency) can be efficiently searched by monitoring a field observable, for example, based on the electric field or the transmitted power. Therefore, the eigenvalue searching procedure can be converted to a maximisation of the observable over the complex plane of the wavevector at each frequency. The Brent's and Powell's method are employed to accelerate the maximisation. A grounded corrugated leaky-wave antenna is analysed in both infinite-and finite-width cases to verify the method. As a further example, a doubly periodic mushroom struture is analysed.

Anomalous Dispersion Characteristics of Periodic Substrate Integrated Waveguides From Microwave to Terahertz

“…4] based on boundary integral-resonant mode expansion method (BI-RME) corresponding to the cutoff of the side port modes, 7.9% in [25,Fig. 9] based on nonstandard eigenvalue solutions [26].…”