Bending and twisting of electromagnetic waveguides

Abstract: Consider a reference homogeneous and isotropic electromagnetic waveguide with a simply connected cross-section embedded in a perfect conductor. In this setting, when the waveguide is straight, the spectrum of the associated self-adjoint Maxwell operator with a constant twist (which may be zero) is entirely essential, lies on the real line and is symmetric with respect to zero, exhibiting a gap around the origin. In this talk, we present new results on the effects of the geometric defor- mations of bending and twisting on the spectrum of the Maxwell operator. More precisely, we provide, on the one hand, sufficient conditions on the asymptotic behaviour of the curvature and twist of a perturbed waveguide ensuring the preservation of the essential spectrum. Our approach relies on a Birman-Schwinger-type principle which has an interest of its own. On the other hand, we give sufficient conditions, involving in particular the shape of the cross-section, so that the geometrical deformation creates discrete spec- trum within the gap, and give some insight into its localization. Finally, we show some theoretical and numerical results further investigating the suffi- cient condition involving the geometry of the cross-section. Based on joint work with Philippe Briet, Maxence Cassier and Thomas Ourmieres-Bonafos.

MathematicsPhysics

Audience: researchers in the topic

Nečas Seminar on Continuum Mechanics

Series comments: This seminar was founded on December 14, 1966.

Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 8. If not written otherwise, we will meet on Mondays at 15:40 in lecture hall K3 (2nd floor)