najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМОnajo-1143Research ArticleMATHEMATICSМАТЕМАТИКАPhotonic crystal with negative index material layersPravdinK. V.

Saint Petersburg

construeman@gmail.comPopovI. Yu.

Saint Petersburg

popov1955@gmail.comtITMO UniversityRussian Federation20141808202555626643Copyright © Pravdin K.V., Popov I.Y., 20252025Pravdin K.V., Popov I.Y.Pravdin K.V., Popov I.Y.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/1143

We consider the one-dimensional photonic crystal composed of an infinite number of parallel alternating layers filled with a metamaterial and vacuum. We assume the metamaterial is an isotropic, homogeneous, dispersive and non-absorptive medium. We use a single Lorentz contribution and assume the permittivity and permeability are equal. Using the time and coordinate Fourier transforms and the Floquet-Bloch theorem, we obtain systems of equations for TE and TM modes, which ones are identical. We consider radiative and evanescent regimes for the metamaterial and vacuum layers and find sets of frequencies, where the metamaterial has the positive or negative refractive index. We use a numerical approach. As a result, we obtained the photonic band gap structure for different frequency intervals and ascertain how it changes with modification of the system parameters. We observe the non-reflection effect for any directions for a certain frequency but this fails with the layer width modification.

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The authors declare that there are no conflicts of interest present.