22
A. Hu et al.
the other. The propagation of the SPP modes are limited by the attenuation due to
the absorption in metal [84, 85].
The propagation length of SPP is given by
δ sp =
1
2k
sp
=
c
ω
ε d + ε
m
ε d ε
m
3
2
ε
m
2
ε
m
(1.2.21)
in which k
sp is the imaginary part of the complex SPP wavevector k sp = k
sp + ik
sp ,
ε
m and ε
m are the real and imaginary parts of the complex dielectric function of the
metal
ε m = ε
m + iε
m .
(1.2.22)
The propagation length of a SPP mode is strictly dominated by the mode size.
For a silver nanowire, the propagation length typically ranges from hundreds of
nanometers to several micrometers (Fig. 1.15). This characteristic sets the upper size
limit for any photonic circuit based on SPPs.
To extend the propagation length, hybrid plasmon mode involve together with
optical waveguide modes and SPP modes, and combine the superiority from both
high index difference and SPPs [86, 87]. Fig. 1.17 demonstrates two configurations
involves hybrid plasmon modes. Figure 1.18 shows subwavelength devices based on
plasmonic circuits: plasmonic route, logic gate and the hybrid nanophononic circuits.
Fig. 1.17 Configurations involves hybrid plasmon modes (a Reprinted with permission from
[87]. Copyright 2009. Springer Nature. b Reprinted with permission from [53]. Copyright 2010.
American Institute of Physics Publishing)