Temporal Coupled-Mode Theory of Electromagnetic Components Described by Magnetic Groups of Symmetry

We consider peculiarities of application of the temporal coupled-mode theory to the electromagnetic components with magnetic symmetry. The coupled-mode theory is widely used for analysis of reciprocal devices described by symmetrical scattering matrices and by unitary elements of symmetry, such as for example, a plane of symmetry. However, nonreciprocity and low symmetry of components described by antiunitary elements lead to a necessity of modification of the method. Using as an example a photonic crystal-based W-circulator described by an antiplane of symmetry, we show applicability of the method to the components with antiunitary elements. The circulator characteristics are calculated and compared with those obtained by a numerical method, demonstrating good agreement between the two methods.