Spin Waves and Electromagnetic Waves in Photonic-Magnonic Crystals

Abstract

In this paper, we study a periodic 1-D structure with modulated optical and magnetic properties. The considered system represents a photonic-magnonic crystal, in which electromagnetic and spin waves (SWs) can propagate independently encountering bandgaps in the GHz and PHz ranges, respectively. The system consists of periodically arranged dielectric magnetic slabs of yttrium iron garnet and non-magnetic spacers with an internal structure of alternate TiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> and SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> layers, which form finite-size dielectric photonic crystals (PCs). We analyze independently the magnetic and optical properties of these systems in terms of propagation of spin and electromagnetic waves (EMWs). For SWs, we demonstrate that the dynamic dipolar coupling between infinitely extended slabs arranged in a stack depends on the in-plane component of the SWs. For EMWs, the system is a complex magneto-PC with a double periodicity related to the repetition of magnetic slabs and the periodic internal structure of the PC (TiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ) layers. This structural complexity has an impact on the electromagnetic spectrum. Minigaps are found within the photonic bands of the infinite TiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /SiO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> structure, and modes of frequencies within its photonic bandgaps are observed.