During the last two decades
much attention has been focused on the theoretical and experimental
investigation of photonic crystals (PCs) or photonic band gap (PBG) materials,
due to promising applications of PCs in modern photonics 1,2. PCs are important due to their unique
properties and the existence of a PBG in which an electromagnetic wave with a
frequency inside the PBG is forbidden to propagate through the structure 3, 4. In recent years, one –dimensional photonic
crystals (1DPCs) containing the so-called double- negative (DNG) materials or
left- handed (LH) materials have been of great interest to the scientific
community. DNG materials with simultaneous negative permittivity and negative
permeability in a special frequency range, and they have attracted extensive
attention for some peculiar properties 5–7.
DNG materials are now classified as electromagnetic metamaterials and also PCs
containing metamaterials are known as metamaterial photonic crystals 8, 9.
Most studies of metamaterials are extensively based on the isotropic ones 10-12. However, many metamaterials are intrinsically
fabricated in experiments are strongly anisotropic. So, the permittivity and
permeability should be considered as the second- rank tensors 13-15. Compared with the isotropic ones, the
anisotropic metamaterials exhibit the unique optical properties: the Brewster
angle, negative index of refraction, invisibility cloaks, perfect lenses, and
hyper lenses that enable subwavelength far-?eld resolution are some potential
applications of metamaterials 16–19. Among
the varieties of metamaterials, recently, indefinite materials are a kind of
anisotropic metamaterials in which not all the principal elements of the
permittivity and permeability tensors have the same sign 20. In fact, anisotropic left-handed materials are a
special case of an indefinite medium 21-23.
The optical properties and the Goos– Hänchen (GH) shift of a light wave
structure of 1DPCs containing indefinite metamaterials have been studied
recently 24–26. However, The motivation to
undertake this research resides in the fact that the authors have found no
studies to the influence of the orientation of the optical axis of the
indefinite metamaterials and the incidence
angle on the multichannel ?ltering properties without introduce any defect in
to the PCs.
In order to overcome some problems of the
conventional PCs ?lters, a new kind of unconventional materials, such as
metamaterials, superconductor, semiconductor, and plasma, have been chosen to fabricate
new types of PCs ?lters. Compared with traditional ?lters utilizing the defect
modes, such ?lters containing no defect layer can be simply expressed as and are easier to fabricate.
Here, one of the two constituents, say A, may be superconductor, plasma, or LH
materials 27, 28. Recently, the metamaterials
have been introduced into PCs to realize the ?lters that, can be tuned by the
structure period or the layer thickness 29, 30.
These studies indicate that manipulate of these ?ltering properties can be controlled by
changing the number of period structure or the layer thickness 31, 32. In contrast, only few investigate have been
reported on the multichannel ?lters using the anisotropic metamaterials.
in the present
paper, we are
interested to study
the transmission properties of a 1DPC made of alternate layers of an
isotropic media and a uniaxial indefinite metamaterial. The computations of the
present study were carried out using characteristics matrix method for both TE
and TM polarizations. Duo to the anisotropic metamaterial : hence, the effect
of the orientation
of the optical
axis of the
anisotropic layers and the incidence angle on the modulation of the PBG and the frequency position of the multichannel filter are investigated. It will be shown that by
increasing of the incidence angle blue-shift was observed in the BPGs, and the
frequency positions of the multichannel filter can be tuned by this parameter.
Also ,The tunability of
the PBGs and the possibility
of the designing multichannel filter in the certain frequency
is investigated by analyzing the in?uence of
the optical axis of the uniaxial
indefinite metamaterial on the transmission properties of the
The details will be
explained and clarified in the following sections. In Sec. 2, 1D PC composed of isotropic and anisotropic
metamaterial PC structure and the characteristic transfer matrix method is
presented to calculate the transmittance properties of multichannel filter. The
numerical results and the effect of the optical axis and the incidence angle on
the multichannel filtering properties will be given and discussed in Sec. 3. The conclusion is presented in Sec. 4.