Long-range surface plasmons in dielectric-metal-dielectric structure with highly anisotropic substrates Page: 5
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LONG-RANGE SURFACE PLASMONS IN DIELECTRIC-...
SX=7.5, E =2 - - - E <
0.36 0.38 0.40 0.42 0.44
FIG. 4. (Color online) Propagation length for parallel, perpen-
dicular orientations, and for the equivalent isotropic case with metal
film of thickness d=50 nm. ow=0.36os corresponds to
X=0.961 ,um and w=0.45ws corresponds to X=0.768 pm.
It is to be noted that for the given orientation (ex < Ez), the
propagation length at w=0.2ws is about 700 tum, as com-
pared to the difference L(w) -L(w) of 18 /m only. The plot
in the inset shows the strong agreement between Eqs. (5) and
(7). It is also obvious from Fig. 5 that the critical frequency
,0cr shifts toward lower frequencies as the metal thickness d
decreases. This behavior strongly influences the favorability
of one orientation over the other. In particular, within the
telecommunication bandwidth (between w 0.22ws) and
w 0.25cis, having ez< ex is more preferable for very thin
metal, whereas having ex< Ez is more preferable for a thick
metal (compare Figs. 2 and 6).
In Fig. 6, the propagation length for ex< Ez, Ex=ez, and
ez<ex is plotted. The frequency range from w=0.22mws
20 40 60 80 100 120 140 160 180 200
Thickness dof metal film (nm)
FIG. 5. (Color online) Wocr l as a function of thickness d of the
metal film. The inset shows the difference between propagation
lengths (obtained using Eqs. (5) and (7)) as a function of frequency
for metal thickness d= 200 nm.
I I I I I I I
0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25
FIG. 6. (Color online) Propagation length L(o) for different
orientations of dielectric crystal with metal film of thickness
(X=1.57 ~um) to w=0.25w (X=1.384 ~um) contains the
telecommunications bandwidth. Clearly, the propagation
length is enhanced by more than 50% when the optical axis
of uniaxial dielectric substrate is aligned in the direction per-
pendicular to the interface. In particular, if the substrates are
2D photonic crystals, the preferable orientation of cylinders
is perpendicular to the metal film.
Interestingly, the propagation length of surface plasmons
for symmetric configuration is one order of magnitude higher
than the propagation length of surface plasmons for asym-
metric configuration.13 For instance, L(w) 2.3 mm at
X= 1.57 /m for perpendicular orientation in the case of
symmetric configuration compared to L(w) 100 /um at
X= 1.57 /m for the same orientation for asymmetric con-
figuration. That is an enhancement of propagation length by
more than 20 times. It means that the propagation length (in
the case of symmetric configuration that we considered in
this paper) is on the order of a few millimeters within the
telecommunications bandwidth (see Fig. 6).
Another important characteristic of plasmonic structure is
penetration depth (K21). As the penetration depth determines
the coupling strength of the surface plasmons with other el-
ements of integrated photonic circuitry, an enhancement in
penetration depth is desirable. Indeed in Fig. 7, the penetra-
tion depth for perpendicular orientation is enhanced by more
than 300% compared to the penetration depth for parallel
orientation, reasserting the requirement that the perpendicu-
lar orientation is more preferable for bandwidths correspond-
ing to the telecommunications wavelength.
III. KRONIG-PENNEY MODEL FOR
Homogenization of photonic crystals, which we propose
to use as anisotropic substrate, has been developed for the
bulk modes. Currently there are several approaches, apart
from the one proposed in Ref. 15 to the problem of homog-
E=2, z=7.5 cX< e
X Z X Z
e. =3.873 - . z
IS x z
Ix=7.5,z=2- - - Ez x
18 i Ex=2, Ez=7.5------- ex z
020 0.25 0.30 0.35 0.40
ruuu t t .. . .
PHYSICAL REVIEW B 81, 085426 (2010)
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Nagaraj & Krokhin, Arkadii A. Long-range surface plasmons in dielectric-metal-dielectric structure with highly anisotropic substrates, article, February 22, 2010; [College Park, Maryland]. (digital.library.unt.edu/ark:/67531/metadc103273/m1/5/: accessed January 19, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT College of Arts and Sciences.