Study of transmission properties in a finite magnetized plasma
photonic crystal
Chien-Jang Wu1,*, Tzu-Chyang King2, and Chih-Chiang Yang2
1
Institute of Electro-Optical Science and Technology, National Taiwan Normal University, Taipei 116, Taiwan
2
‎ Department of Applied Physics, National Pingtung University, Pingtung 900, Taiwan
*
corresponding author: jasperwu@ntnu.edu.tw
Abstract-We study the transmission properties in a one-dimensional finite magnetized plasma
photonic crystal of (1/2)N, where 1 is a dielectric layer, 2 is a plasma layer, and N is the number of
periods. When B = 0, the structure behaves as a multichannel filter with a channel number of N-1.
The positions of channels can be shifted as the static magnetic field is applied. The shift can be
blue-shifted or red-shifted depending on the orientation of the applied magnetic field.
The field of photonic crystals (PCs) has been initialized by the works of Yablonovitch and John [1,2] in
1987. So far, it continues to be one of main fields in photonics and condensed matter physics, partially because
the emergence of metamaterials [3,4]. A PC can be characterized by the existence of photonic band gaps (PBGs)..
A PBG is a frequency region within which electromagnetic waves are prohibitive to propagate through the
structure of PC. One of the familiar applications is the design of PC-based transmission filters [5,6]. It is
achieved by introducing a defect layer into the PC such that the translational symmetry is broken. In such design,
the transmission peaks will be produced within the PBG.
The design of PC filters can alternatively be achievable based on the use of the photonic pass band. In this
design, no defect layer is required. One of the constituents has a frequency-dependent permittivity. The real part
of permittivity function must be negative. Materials with these properties may be metals, plasmas, and
superconductors. The related studies on this kind of filter have been available [7,8]. In [7], a filter with multiple
channels is designed based on the plasma photonic crystal (PPC).
This work is to extend the work of [7] to the case of PPC in the presence of static magnetic field. That is, we
shall consider a magnetized PPC. The analysis of tunable filter will be made from the transmission spectra calculated
by the transfer matrix method (TMM) [9]. The structure of 1D PPC is (1/2)N, where 1 is the dielectric layer and 2 is
the plasma layer, and N is the number of periods. The thicknesses of 1 and 2 are denoted by d1 and d2, respectively.
For plasma layer 2, it is a cold magnetized plasma whose permittivity function is given by [10],

2

 pe
 B  , B    1 


 2 1  i 




12



le 
 
,
(1)
where pe, le, and  are the plasma frequency, the gyrofrequency, and the effective collision frequency, respectively.
Expressions for pe and le are given by
2
 pe
 ne2 m 0 and le  eB m . It is worth noting that the minus sign
prior to le represents the right-hand polarization (RHP), i.e., the static magnetic field B is applied in +z direction.
Conversely, if the static magnetic field B is applied in -z direction, then it is called the left-hand polarization (LHP)
[10].
The calculated results are shown in Fig. 1, in which we plot the transmittance responses for finite PC
structures, (1/2)N, in the normal incidence. For B = 0, the left reveals N-1 channels for a given N.
However, when B is applied, the channel position is blue-shifted as B increases under the RHP.
Conversely, the it will be red-shifted under the LHP.
Acknowledgements, C.-J. Wu acknowledges the financial support from the Ministry of Science and
Technology of Taiwan under contract MOST 103-2112-M-003-007-MY3.
Fig. 1 Calculated normal-incidence transmittance responses for four structures, (1/2)10, (1/2)5(2/1)5, (1/2)5A(2/1)5, and
(1/2)5B(2/1)5, respectively.
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