Modeling of the Frozen Mode Phenomenon and its Sensitivity Using Discontinuous Galerkin Methods
S. Chun 1, J. S. Hesthaven 1*1 Division of Applied Mathematics, Brown University, Providence, RI 02912, USA.
Received 19 September 2006; Accepted (in revised version) 28 November 2006
Communicated by Wei Cai
Available online 8 January 2007
We investigate the behavior and sensitivity of the frozen mode phenomenon in finite structures with anisotropic materials, including both magnetic materials and non-normal incidence. The studies are done by using a high-order accurate discontinuous Galerkin method for solving Maxwells equations in the time domain. We confirm the existence of the phenomenon also in the time-domain and study carefully the impact of the finite crystal on the frozen mode. This sets the stage for a thorough study of the robustness of the frozen mode phenomenon, resulting in guidelines for which design parameters are most sensitive and acceptable tolerances.
AMS subject classifications: 65M60, 78A48, 78M10, 93M25
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Key words: Discontinuous Galerkin method, Maxwell equation, photonic crystals, frozen mode.
Email: firstname.lastname@example.org (S. Chun), Jan.Hesthaven@Brown.edu (J. S. Hesthaven)