Abstract
The problem of guided TM mode reflection from an abruptly terminated planar metamaterial waveguide is studied using a variational technique. The theory is illustrated by examples of abruptly terminated three-layer waveguides with step profiles of permittivity and permeability. The influence of media losses on reflectivity characteristics is considered.
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Notes
Generally, the set of the functions \(\{ \varPhi _q \}\) includes the set \(\{ \varPhi _m \}\) (see above).
Here we distinguish virtual and leaky modes. Foremost, it should be taken into account that in the substrate and cover the power fluxes of virtual modes are directed along the 0z axis, i.e., the power does not flow out of the LHM slab for this mode. On the contrary, the power of the leaky mode flows out of the slab; the name of leaky modes is associated with this property. Thus, we have \(\mathop {\hbox {Im}}\nolimits h_1 = 0\) for virtual modes and \(\mathop {\hbox {Im}}\nolimits h_1 > 0\) for leaky ones (see Fig. 3).
These conditions differ noticeably from the weak guidance conditions.
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Acknowledgements
The author is grateful to anonymous reviewers for valuable remarks. The work was supported by the Russian Foundation for Basic Researches (Project No. 16-02-00789).
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Manenkov, A.B. Reflection of the transverse magnetic modes from an abruptly ended LHM slab waveguide. Opt Quant Electron 49, 268 (2017). https://doi.org/10.1007/s11082-017-1102-8
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DOI: https://doi.org/10.1007/s11082-017-1102-8