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where e 0 r is the imaginary part of relative permittivity. The extinction (total)
cross-section describes the intrinsic losses of a plasmonic system including both
absorption loss and scattering (or leaky) loss. Hence, the sum of the scattering
and the absorption cross-section is the extinction cross-section. Moreover, we
have another mathematical expression for the extinction cross-section by making
use of the optical theorem at the far-field limit [ 80 ]
r e ¼ 4p
k 0
Im ½ e i
F e i
ð 7 : 35 Þ
and
E s ¼ exp ð i 0 k 0 r Þ
r
F E i ;
r !1
ð 7 : 36 Þ
where e i is the polarization unit vector of the incident electric field E i .
To understand the mode hybridization for plasmon coupling, the polarization
charge distribution on the surface of metallic nanostructure is given as follows
q p ¼r e 0 ðÞ¼r P
ð 7 : 37 Þ
where P ¼ e e ð Þ E is the polarization density. Based on the divergence-free
condition, the polarization charge is definitely zero except on the heterogeneous
boundaries.
The Fabry-Pérot mode or quasi-guided mode can be characterized by analyzing
the averaged power density of electromagnetic waves flowing within an active or a
grating layer along the lateral direction of OSC devices, which is expressed in
2 Re E y H z E z H y
P x ¼ 1
ð 7 : 38 Þ
where '' y '' is a notation of complex conjugation and the power density flows along
the x direction.
7.4 Results and Discussions
We will review plasmonic effects of typical metallic nanostructures by involving
their functionalities and performances in manipulating the optical properties of
OSCs. The SPR, LPR, and their hybridization are investigated in the three fol-
lowing cases [ 16 , 30 , 33 ]. In modeling OSCs, the complex refractive indices of
metals (Au, Ag, etc) and organic materials can be expressed by the Brendel-
Bormann model [ 81 ] and measured from ellipsometry [ 82 , 83 ], respectively. It is
worth mentioning that standard solar irradiance spectrum (air mass 1.5 global) is
taken into account in our theoretical models.
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