Long-range surface plasmons in dielectric-metal-dielectric structure with highly anisotropic substrates Page: 2
The following text was automatically extracted from the image on this page using optical character recognition software:
PHYSICAL REVIEW B 81, 085426 (2010)
however, there are very limited options for variation in the
propagation length. One of them is to affect the level of
dissipation through the dielectric properties of the substrate.
The field in the substrate affects the field in the metal (and
thus the level of dissipation) through the boundary condi-
tions. Surface plasmons on anisotropic lossless substrate
were studied in Ref. 11. It was shown that the in-plane an-
isotropy gives rise to the splitting of surface plasmon by two
ordinarylike and extraordinarylike surface modes, if surface
plasmon propagates at an angle with respect to the optical
axis. The effects of anisotropy of the substrate were studied
for asymmetric plasmonic structures, i.e., for vacuum-metal-
dielectric structures. In Ref. 13, the proposed substrate was
two-dimensional (2D) photonic crystal (a periodic arrange-
ment of parallel cylinders) and in Ref. 12, the metallic film
was deposited on multilayered dielectric heterostructure
[one-dimensional (ID) photonic crystal]. In both cases an
essential increase in the propagation length has been re-
Here we consider a symmetric dielectric-metal-dielectric
plasmonic structure. The advantage of this configuration is
that it supports propagation of the long-range surface plas-
mon. The effects of anisotropy may lead to further increase
in the propagation length. Indeed, we report about 20-fold
increase in the propagation length of long-range surface plas-
mon in the symmetric configuration when compared to that
of the asymmetric (vacuum-metal-dielectric) one13 for the
same given parameters at X=1.57 lam. It is important to
mention at this point that an attempt to study the effects of
anisotropy on the propagation length was made in Ref. 14.
Unfortunately, the reported results are erroneous. The calcu-
lated propagation length turned out to be as short as
10-15 m, i.e., on the order of the classical electron radius.
Apart from this many-orders-of-magnitude error, the re-
ported tendency for the propagation length to grow toward
the resonant frequency is wrong. It is clear from the afore-
mentioned effect of vanishing of the total flux S in Eq. (1)
that even infinitesimally weak dissipation Q leads to zero
propagation length at w= ws. In addition, the authors of Ref.
14 report unreasonably strong sensitivity of the propagation
length to the level of anisotropy, taking into account rela-
tively weak anisotropy they used in their calculations.
II. CALCULATION OF THE PROPAGATION LENGTH
The symmetric configuration that we consider consists of
a metal film of thickness d clad with two identical semi-
infinite anisotropic dielectric substrates as shown in the inset
in Fig. 1. The metal film occupies the space between z= 0
and z=d (region 1). The dielectric on top of the metal film
occupies all space above z=d (region 2) and the dielectric
below the metal film occupies all space below z= 0 (region
3). The dielectrics are assumed to be isotropic in the x-y
plane, i.e., ex= y. The dielectric constant in the perpendicu-
lar to the interface direction (along z axis) is, however, dif-
ferent, ez E x.
The surface plasmon propagating along the metal-
dielectric interface is a p-polarized wave with the compo-
nents of the electric field Ex and Ez and with the only com-
8 Ia Dielectric g
Setal (,,W) d
0 2 4 6 8 10 12 14
FIG. 1. (Color online) Dispersion curves for different orienta-
tions of optical axis of the anisotropic dielectric crystals with metal
film of thickness d= 50 nm. The dotted curve represents dispersion
curve for equivalent isotropic dielectric with dielectric constant
8is= - z
ponent of the magnetic field Hy= H(x, z). The field inside the
metallic film is a superposition of two exponents, H (x, z)
=A exp(ikx+ Kz)+B exp(ikx-K1z), with Kl=k2_=Em2/c2
being the inverse skin depth, K11= . In the substrates, which
are two identical uniaxial dielectric crystals, the magnetic
field is obtained from the Helmholtz equation
1 82H 1 82H (02
8X+ +- H= 0.
ez 8x2 8 xz2 C2
The evanescent solutions of this equation are H2(x,z)
= C exp[ikx-K2(z-d)] and H3(x,z)= C exp(ikx+ K2z), where
K2= Ex( - j) is the inverse decay length of the surface
plasmon field in dielectric, and 8e(w)= 1- w2/ w2. From the
continuity of the magnetic field H(x, z) and electric field
Ex(x,z)=(c/ie6x)dH/dz at the interfaces z=0 and z=d, we
obtain the following dispersion equation for the surface plas-
- tanh Kd
This equation gives the dispersion for the mode with anti-
symmetric distribution of Ex with respect to the plane of
symmetry z=d/2, i.e., for the so-called long-range surface
plasmon. It is easy to see that interchanging the values of ex
and ez, two different dispersion equations are obtained. The
transformation ex Ez means 90 rotation of the optical axis
of the dielectric crystal with respect to the metal surface. In
Fig. 1 the solid and dashed curves are the dispersion Eq. (3)
for two different orientations. Both the curves approach the
same resonant frequency
NAGARAJ AND A. A. KROKHIN
Here’s what’s next.
This article can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Article.
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/m1/2/: accessed July 23, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT College of Arts and Sciences.