Matched waves and unexpected resonances: Variety of boundary conditions

This article discusses certain interesting findings about phenomena that take place when electromagnetic fields interact with a surface on which given boundary conditions are enforced. In particular, the concept of matched waves is analyzed and illustrated. Furthermore, observations are made on resonance spectra that may accompany sub-wavelength scatterers with an isotropic impedance boundary condition. This invited article, reviewing some of our studies on boundary conditions during the past decades, is based on the Commission B (Fields and Waves) keynote presentation of the 2019 URSI Asia-Pacific Radio Science Conference held in New Delhi, India, March 9-15, 2019.