Complete tunneling through three-layered periodic structures with metamaterial in far-infrared region
Introduction
Photonic crystals (PCs) are artificial materials with periodically dielectric modulated function, and they have received considerable attention in recent years because of their property for stopping photons with forbidden frequencies from propagating in the structures [1], [2]. Metamaterial is another type of artificially structured material which has new electromagnetic properties unimaginable in conventional positive index media, such as a negative refractive index [3], in which the Poynting vector of a plane wave is anti-parallel with its phase velocity. It has a large number of potential applications in optics, material science, biology, and biophysics [4], [5]. It can be used to realize special photonic band gaps (PBGs), such as single-negative (SNG) gaps [6], [7] originated from the multilayered periodic structures with isotropic epsilon-negative (ENG) and mu-negative (MNG) materials. However, all the research works above are based on metamaterials with Drude model. As another type of metamaterial, Lorentz types of SNG materials can be fabricated using a mixture of conductive spirals or omega particles on printed circuit boards [8]. In addition, they can be manufactured using split ring resonators and wire strips on a circuit board materials [9].
In this paper, we take into account three multilayered structures with different units, including (ENG–MNG), (ENG–MNG–ENG) and (MNG–ENG–MNG) in which the metamaterials are defined by Lorentz type model. Transfer matrix method is used to analyze these periodic structures in far-infrared region, and the influences of the incident angle, the period number, thickness of every layer and their ratio on the transmittance spectra are discussed based on simulation results.
Section snippets
Principle and theoretical model
We consider a multilayered structure created by alternating layers of Lorentz type ENG and MNG material, and make use of N to denote the period number. Here we suppose a TE wave injected into the multilayered structure along z-axis. For simplicity, we mainly focus on an incident TE wave and the results of TM wave can be obtained by duality theory.
We suppose that relative permittivity and permeability in ENG and MNG layers areand
Simulation results and discussion
In this section, we study the three different periodic structures including (ENG–MNG)N, (ENG–MNG–ENG)N and (MNG–ENG–MNG)N. The influences of the incident angle, the period number, thickness of every layer and their ratio on the transmittance spectra are discussed based on simulation results.
First we assume the thicknesses of ENG and MNG are the same, and both of them are equal to d0. A TE polarized light in injected into the periodic structures with an incident angle of 30°. When d0 is
Conclusion
In this paper, we study the tunneling modes in three different periodic structures including (ENG–MNG)N, (ENG–MNG–ENG)N and (MNG–ENG–MNG)N. Transfer matrix method is used to analyze these periodic structures, and the influences of the incident angle, the period number, thickness of every layer and their ratio on the transmittance spectra are discussed based on simulation results. The tunneling modes can be adjusted by the thickness of every layer, the incident angle and the period number.
Acknowledgement
This work is supported by the project of Sichuan Provincial Department of Education (14ZA0054).
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