Long-range surface plasmons in dielectric-metal-dielectric structure with highly anisotropic substrates Page: 4
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PHYSICAL REVIEW B 81, 085426 (2010)
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FIG. 2. (Color online) The top figure shows propagation length
for parallel (x> sz) and perpendicular (sx< z) orientations for
metal thickness d= 20 nm. The bottom figure shows the same
curves between a)=0.21os and o=0.24.-
L(w) ~ m kd > 1.
The propagation length curves [obtained from Eq. (5)] for
the two orientations (ex < Ez and ez < Ex) and for the equiva-
lent isotropic case (ex= Ez= is) are shown in Fig. 4. It is clear
from Eq. (5) and Fig. 4 that the effect of anisotropy of the
dielectric may be used as an advantage to modulate the
propagation length by changing the orientation of the optical
axis of the dielectric crystal. The decreasing trend of L(w)
toward higher frequencies can be seen in Fig. 4, where aw
=0.36 s corresponds to X=0.961 tum, and w=0.45 s corre-
sponds to X=0.768 u/m. This range is much below the tele-
communications wavelength (1.3-1.6 utm). Though the iso-
tropic case is more favorable for wavelengths between
X=0.768 /um and X-=0.961 utm, it is obvious from Fig. 4
that the perpendicular orientation (ex < Ez) is most preferable
at wavelengths above X=0.961 utm. However, at frequen-
cies higher than ocr (critical frequency at which the favor-
FIG. 3. (Color online) Dispersion curves and light lines (11) for
different orientations for metal thicknesses d= 5 nm and
d= 200 nm. Light lines for equivalent isotropic case (sx= s) are not
included in the figure. The anomalous dispersion curves correspond
to metal thickness d= 5 nm (top figure).
able orientation reverses), the parallel orientation is more
For silver metal film of thickness d= 50 nm, and for the
dielectrics having principal dielectric constants as 2 and 7.5,
this critical frequency ocr occurs at w o0.4ws, which corre-
sponds to Xcr=0.865 jtm, i.e., it is still much below the tele-
In Fig. 5, the critical frequency is plotted as a function of
thickness d of the metal film. The ratio ocr/ ws gradually
increases with d until it saturates at w 0.62t s, which cor-
responds to thickness d= 200 nm. The saturation of curve in
Fig. 5 indicates that for a given anisotropy of dielectric, the
metal thickness of d= 200 nm can be safely considered as
semi-infinite. This fact is clearly demonstrated in the inset of
Fig. 5, where the difference between propagation lengths
[calculated from the "exact" Eq. (5) and it's asymptote
[Lo(w),d=oc] Eq. (7)] as a function of frequency is plotted.
NAGARAJ AND A. A. KROKHIN
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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/m1/4/: accessed April 24, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT College of Arts and Sciences.