Negative refraction in plasma photonic crystals at below plasma frequency
Introduction
Photonic crystals (PCs), which are artificial materials engineered to have properties that have affect the motion of photons in the same way as ionic lattices affect the electrons in solids, have attracted a great deal attention due to their important prospects of manipulating electromagnetic (EM) waves in unprecedented ways [1], [2], [3]. Since the pioneering works of Yablonovitch [2] and John [3] in this field, many new inquisitive ideas have been developed. In recent years, plasmas have attracted considerable attention in plasma PCs [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17] due to their tunable characteristics offering some advantages that conventional PCs composed of dielectrics or metals do not. Since plasmas can be controlled rapidly by changing the applied voltage and gas pressure and temperature, they enable us to realize the tunable PC devices.
Negative refraction, a strange electromagnetic phenomena in which light rays are refracted at an interface in the reverse sense to that normally expected, has aroused great interest and increasing research activities. At first proposed, such an effect can be obtained using a metamaterial that is not found in nature and not observed in the constituent materials because it has been designed to achieve a negative value for both electric permittivity ɛ and magnetic permeability μ [18], [19], [20], [21]. The negative value of ɛ is a natural property of metals and therefore negative-ɛ metamaterials can be created by simple means such as the addition of metallic rods, in which the negative value of μ is obtained by using a resonance. However, this double-resonance scheme faces limitations because the design and fabrication can be complicated. Fortunately, for homogeneous and isotropic materials, negative refraction requires that both electric permittivity and magnetic permeability are negative. But if some degree of asymmetry is introduced in the system, the required condition for negative refraction may be released [22], [23], [24]. In terms of progress of the studies, it seems that negative refraction can be realized by three different paths: double negative electromagnetic parameters [18], anisotropic permittivity or permeability [25], [26], and band-edge effect in photonic crystals [27], [28], [29]. For example, the uniaxial anisotropic metamaterials where μ is scalar and positive, proposed in Ref. [22], [25], can exhibit negative refraction. For inhomogeneous media such as photonic crystals [27], [28], [29], negative refraction may appear when there is strong modulation of waves because of the band-edge effect. Moreover, a potential alternative route to negative refraction without manipulating these parameters (ɛ and μ) is chiral materials [30], [31]. In our previous work [32], we have explored the negative refraction in plasma PCs through analyzing the dispersion relations. We found that plasma PCs can exhibit negative refraction at some band edges and some special frequencies. And the behavior of negative refraction is different in two different frequency regions, below plasma frequency or beyond. In this paper, we continue to study the negative refraction in one-dimensional plasma PCs and focus on the frequency regions at below plasma freqyency which shows negative refraction not only at the frequency edge of the band gap but also at some other frequencies which do not belong to any band gaps. The negative group and positive indices of refraction in plasma PCs, which can denote the negative refraction behavior, have been rarely reported. Therefore, we investigate the negative refraction behavior of plasma PCs through studying the group and phase indices of the refraction.
The paper is organized as follows. The model and corresponding analytical formulas are introduced in Section 2. Numerical results are presented and discussed in Section 3. Finally, conclusions are given in Section 4.
Section snippets
Theoretical model and formulations
In the proposed case, the schematic of the plasma PCs consisting of alternating layers of plasma layer and dielectric discussed here, is shown in Fig. 1. For simplicity, we take the dielectric as air, which dielectric constant is ɛd = 1. The dielectric function of the plasma PCs can be expressed as:
Using the effective medium approximation [33], [34], one can obtain the expressions of the principal dielectric constant, given as:here, ρ is plasma
Results and discussion
We note that there are five selective parameters: plasma filling factor ρ, lattice constant d, plasma frequency ωp, incident angle θ, and collisional frequency γ in our numerical calculations. For simplicity, we introduce the dimensionless variable ωd/2πc which is normalized to 1 at ω = ωp. We introduced the dimensionless variable ω = ω/ωp. The collisional frequency γ is fixed and also defined as γ = γ/ωp = 0.1 in the numerical calculations.
It is well known that the lattice constant has to be much
Conclusions
In conclusion, we demonstrated the negative refraction in plasma PCs at below plasma frequency. The designed structure provides negative group and positive phase indices of refraction for oblique incidence yielding negative refraction in two frequency regions. The dependence of the plasma filling factor on the effective dielectric constants, and the effects of angle of oblique incidence and plasma filling factor on frequency regions for negative refraction are calculated and discussed. Our
Acknowledgements
This work was supported by the National Natural Science Foundation of China under Grant Nos. 11205119, 11575135 and the Fundamental Research Funds for the Central Universities of China under No. WUT: 2014-Ia-009.
References (36)
- et al.
The Voigt effects in the anisotropic photonic band gaps of three-dimensional magnetized plasma photonic crystals doped by the uniaxial material
Opt. Commun.
(2013) - et al.
Analysis of tunable photonic band structure in an extrinsic plasma photonic crystal
Physica E
(2015) - et al.
Negative refraction in one-dimensional plasma photonic crystals
Optik
(2014) - et al.
Photonic Crystals: Molding the Flow of Light
(2008) Inhibited spontaneous emission in solid-state physics and electrons
Phys. Rev. Lett.
(1987)Strong localization of photons in certain disorder dielectric superlattices
Phys. Rev. Lett.
(1987)- et al.
Dispersion relation of electromagnetic waves in one dimensional plasma photonic crystals
J. Plasma Fusion Res.
(2004) - et al.
Verification of a plasma photonic crystal microplasma
Appl. Phys. Lett.
(2004) Transfer matrix method for obliquely incident electromagnetic waves propagating in one dimension plasma photonic crystal
Plasma Sci. Technol.
(2009)Photonic band gap structures of obliquely incident electromagnetic waves propagation in one-dimension absorptive plasma photonic crystal
Phys. Plasmas
(2009)
Formation of a plasma photonic crystal by self-induced quasi periodic plasma density grating
J. Electromagn. Waves Appl.
Omnidirectional photonic band gap of one-dimensional ternary plasma photonic crystals
J. Opt.
Differential transfer matrix method for photonic band structure of one dimensional non-uniform distribution plasma photonic crystal
Optik
Photonic band structures of 1-D plasma photonic crystal with time-variation plasma density
Phys. Plasmas
Photonic band structures of one-dimensional photonic crystals doped with plasma
Phys. Plasmas
Composite patterns formed by paraxial vortex-beams propagation in one-dimensional multilayer plasma photonic crystals
Eur. Phys. J. D
Nonreciprocal electromagnetic wave propagation in one-dimensional ternary magnetized plasma photonic crystals
J. Opt. Soc. Am. B
Tunable filter using defect in one-dimensional plasma photonic crystals
Int. J. Appl. Electromagn. Mech.
Cited by (2)
Full optical 2-bit analog to digital convertor based on nonlinear material and ring resonators in photonic crystal structure
2020, OptikCitation Excerpt :The main feature of PhC is that PBG can be tuned by breaking the periodicity and introducing defects in the structure. By tuning PBG many types of phenomena like optical memory and light storing [1], negative refraction [2], Kerr-like third-order susceptibility [25], two-photon absorption [3], pulse wave generation [4] and pulse detection [5] have been studied. In addition, there are many optical devices such as Optical filters [6–8], optical decoder [9,10], optical switches [11–13], optical demultiplexer [14–16], logical gates [17–19] and power and polarization beam splitters [20] are proposed based on PhC.