Physics Letters A 364 (2007) 81–85
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Applications of the expanded basis method to study the behavior of light
in polaritonic photonic crystal slab with losses
Li-Ming Zhao
a,b
,Ben-YuanGu
a,∗
, Guo-Zhen Yang
a
a
Institute of Physics, Chinese Academy of Sciences, PO Box 603, Beijing 100080, China
b
Department of Physics, Capital Normal University, Beijing 100037, China
Received 1 September 2006; received in revised form 22 November 2006; accepted 24 November 2006
Available online 6 December 2006
Communicated by J. Flouquet
Abstract
We apply the expanded basis method (EBM) to investigate the behavior of light in polaritonic photonic crystal (PC) slabs with losses. The
influence of losses on transmissivity is studied. It is found that the transmissivity is significantly lowered with the increase of losses, in particular,
it is abruptly decreased in the vicinity of transverse-optical-phonon frequency. The electromagnetic (EM) dissipation is mainly dominated by the
imaginary part of dielectric constant of PC. The larger the imaginary part of the dielectric constant, the more the EM energy depletion is. The
variation of EM dissipation with the number of period layers in the PC slab is approximately linear or oscillatory increase with the number of
period layers.
©
2006 Elsevier B.V. All rights reserved.
PACS : 42.70.Qs; 42.25.Gy; 42.68.Ay; 42.25.Bs
1. Introduction
The polar media, which exhibit highly dispersive properties,
have brought great attention both experimentally [1] and theo-
retically [2,3]. The strong coupling between transverse-optical
photons and the electromagnetic (EM) waves entirely changes
the character of the propagation of EM waves, and a forbidden
band called polariton gap (PG) is created. The dielectric func-
tion of a polar material with losses based on a simple model can
be expressed as
(1)(ω)=
∞
1+
ω
2
L
− ω
2
T
ω
2
T
− ω
2
− iωγ
,
where ω
T
(ω
L
) is the transverse (longitudinal)-optical-phonon
frequency,
∞
is the dielectric constant at high frequency limit,
and ω
L
is related to
∞
and ω
T
via the well-known Lyddane–
Sachs–Teller relation as ω
L
= ω
T
√
0
/
∞
. γ represents the
*
Corresponding author.
E-mail addresses: me_zlm@sohu.com (L.-M. Zhao),
guby@aphy.iphy.ac.cn (B.-Y. Gu).
width of the absorption peak induced by the imaginary part of .
The material having such dielectric function include GaAs, InP,
NaCl, and KCl, etc.
Recently, a lot of research works have devoted to the studies
of photonic crystals (PCs) composed of polar material [4–8].
This kind of PCs display some fascinating features belong-
ing to the interplay of the strongly dispersive nature of polar
medium and the structural dispersion of the PCs. Some remark-
able phenomena induced by polar material take place near the
transverse-optical-phonon frequency ω
T
, in which the strong
frequency-dependence of dielectric function and large loss ap-
pear. The exquisite behavior of light fields in the PCs becomes
unobservable owing to the losses in an infinite PC. Moreover,
the real sample always possesses a finite size, thus, the detailed
investigations of the EM properties of the PC slab composed
of polar material with losses should be attractive and important
issue.
A variety of theoretical or numerical methods have been pro-
posed to explore the characteristics of light waves in finite-size
PCs [9–15]. Recently, an expanded basis method (EBM) has
been applied to calculate the photonic band gaps (PBGs) of PCs
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doi:10.1016/j.physleta.2006.11.065