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Theoretically, the characteristics matrix method is employed to investigate and compare the properties of the band gaps of the one-dimensional ternary and binary lossy photonic crystals which are composed of double-negative and double-positive materials. This study shows that by varying the angle of incidence, the band gaps for TM and TE waves behave differently in both ternary and binary lossy structures. The results demonstrate that, by increasing the angle of incidence for the TE wave, the width and the depth of zero-

Photonic crystals (PCs) are artificial dielectric or metallic structures in which the refractive index changes periodically. The periodic structure of the PCs contributes to photonic band gap (forbidden range of frequencies). Interference of the Bragg scattering is considered as a cause of these phenomena, the so-called Bragg gap. PCs have attracted much interest due to their novel electromagnetic waves characteristics and important scientific and engineering applications and have received attentions by many researchers in recent decades [

In 1D binary MPC, in addition to the zero-

The novel idea of this research is to include the loss factor which is an unavoidable consequence of double-negative materials to investigate optical properties of 1D binary and ternary MPCs. In this regard, the transmission of electromagnetic waves through a 1D ternary lossy PC consisting of layers with double-negative and double-positive materials is studied. The effects of the incidence angle and polarization on the characteristics of the zero-

The 1D MPC structure under study which is located in air is constituted by alternative layers of DNG and DPS materials, where the DNG material is dispersive and dissipative. We consider the 1D binary MPC with periodic structure of

The permittivity and permeability of the DNG (layer

Real parts of permittivity (dotted line), permeability (dashed line), and refractive index (solid line) of layers

The calculation is based on the characteristic matrix method [

The characteristic matrix for

The transmissivity of the multilayer is given by

The above formulations can be applied to TM wave by simple replacements of

Based on the theoretical model described in the previous section, the transmission spectrum of the presented lossy MPC structures was calculated. In the study of the 1D binary MPC, consisting of DNG (layer

The transmission spectra of TE and TM polarized waves for the binary structure at various angles of incidence and for

Transmission spectra for the 1D binary MPC structure for different angles of incidence with

In the next part, the band gaps of the 1D ternary MPC are investigated. The binary structure used before is modified by introducing a third layer of

Transmission spectra for the 1D ternary MPC structure for different angles of incidence with

In this part, the band gaps in binary and ternary structures are compared. As it is seen from Figures

The lower (

The lower and higher frequencies of the zero-

The lower and the higher frequencies of the zero-

The lower and higher frequencies of the (a) zero-

The

The lower and higher frequencies of the Bragg gap as a function of angle of incidence for both binary and ternary structures: (a) TE and (b) TM waves.

The numerical results show that including the loss factor in the permittivity and permeability of the DNG layer the changes in transmission spectrum of TE wave in 1D ternary and binary MPCs behave similar to different incidence angles. The zero-

The authors declare that there is no conflict of interests regarding the publication of the paper.

Alireza Aghajamali would like to acknowledge his gratitude to Parisa Shams for her help and useful discussion.