Omnidirectional gap and defect mode of one-dimensional photonic crystals with single-negative materials

Li-Gang Wang, Hong Chen, and Shi-Yao Zhu

Phys. Rev. B 70, 245102 – Published 1 December 2004

Abstract

A new type of omnidirectional gaps is theoretically found in one-dimensional photonic crystals (1DPCs) composed of two kinds of single-negative (SNG) (permittivity- or permeability-negative) materials. In contrast to the Bragg gaps, the properties (the central frequency and width of the gap) of such omnidirectional gaps are insensitive to the incident angles and the light polarizations, and are invariant upon the change of scale length. Such omnidirectional gaps result from the interaction of evanescent waves. When a defect layer is introduced, a defect mode appears inside the omnidirectional gap, and the spectral position of the defect mode is almost independent of incident angles and nearly invariant with the scaling.

Received 27 August 2004

DOI:https://doi.org/10.1103/PhysRevB.70.245102

Authors & Affiliations

Li-Gang Wang^1,2, Hong Chen^1,3, and Shi-Yao Zhu^1,2,3

¹Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong
²Department of Physics, Zhejiang University, Hangzhou, 310027, China
³Department of Physics, Tongji University, Shanghai, 200092, China

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Vol. 70, Iss. 24 — 15 December 2004

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Images

Figure 1
(a) Schematic representation of the finite MNG-ENG multilayered periodic structures. (b) Photonic band gaps as a function of the incidence angle for an infinite MNG-ENG multilayered periodic structure; we choose the parameters: $d_{A} = 10 mm$ , $d_{B} = 5 mm$ , $a = 3$ and $b = 1.2$ , and $ω_{mp} = 10 GHz$ and $ω_{ep} = 12 GHz$ . The gray areas correspond to the forbidden gaps, and the white areas are the allowed bands. The SNG frequency ranges for both two materials $A$ and $B$ are $ω < 10 GHz$ and $ω < 12 GHz$ , respectively. Note that the left panel shows TE waves and the right panel shows TM waves in (b).Reuse & Permissions
Figure 2
The dependence of the PBGs on the ratio of the thicknesses of the two materials under two different lattice constants (a) $d_{A} = 10 mm$ and (b) $d_{A} = 20 mm$ for the infinite 1DPC as that of Fig. 1b at normal incidence (that is to say, the PBGs have no difference between TE and TM waves). Here, the parameters are the same as Fig. 1b. Note that the frequency scales in SNG and DPS frequency ranges are different from each other.Reuse & Permissions
Figure 3
The EM fields inside the 1DPC of ${(A B)}^{16}$ at different frequencies: (a) $ω = 1.2 GHz$ inside gap I; (b) $ω = 1.376 GHz$ at the up edge of gap I; (c) $ω = 4.291 GHz$ at the low edge of gap II; (d) $ω = 6.407 GHz$ at the mid of gap II; (e) $ω = 8.422 GHz$ at the up edge of gap II; (f) $ω = 35.108 GHz$ at the low edge of gap IV; (g) $ω = 41.699 GHz$ at the mid of gap IV; and (h) $ω = 48.291 GHz$ at the up edge of gap IV. The parameters of the materials are the same as Fig. 1b. Here, the black line is the electric field $∣ E_{x} ∣$ and the gray line is the magnetic field $∣ H_{y} ∣$ . Periodic layers $A$ and $B$ are denoted by light gray and white areas. Note that (a), (d), and (g) are in the logarithmic scale of $∣ E_{x} ∣$ and $∣ H_{y} ∣$ .Reuse & Permissions
Figure 4
The spectral positions of the defect modes inside the PBGs with the finite 1DPC of ${(A B)}^{8} C {(A B)}^{8}$ under different scales for (a) TE waves and (b) TM waves. Solid line for $d_{A} = 24 mm$ and $d_{B} = 12 mm$ ; dashed line for $d_{A} = 19.2 mm$ and $d_{B} = 9.6 mm$ (scaled by $4 ∕ 5$ ); dot line for $d_{A} = 12 mm$ and $d_{B} = 6 mm$ (scaled by $1 ∕ 2$ ). The other parameters are $a = b = 1.5$ and $ω_{mp} = ω_{ep} = 10 GHz$ . For the defect layer, we take $ε_{C} = 2.0$ , $μ_{C} = 2.0$ , and $d_{C} = 42 mm$ . The spectral positions of different defect modes for the case of the solid line are labeled by “1st,” “2nd,” and “3rd,” respectively.Reuse & Permissions
Figure 5
The dependence of the spectral positions of the defect modes on the incident angle for different polarizations (left panel for TE wave and right panel for TM waves). The parameters are the same as the solid line in Fig. 4.Reuse & Permissions

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