Propagation properties of the terahertz waveguide using
a metallic nanoslit narrower than skin depth
Jie Yang (杨 洁)*, Gongwei Lin (林功伟), Yueping Niu (钮月萍), Yihong Qi (祁义红),
Fengxue Zhou (周凤雪), and Shangqing Gong (龚尚庆)
Department of Physics, East China University of Science and Technology, Shanghai 200237, China
*Corresponding author: yangjie7898@ecust.edu.cn
Received March 10, 2016; accepted April 22, 2016; posted online June 1, 2016
A terahertz (THz) waveguide using a metallic nanoslit whose width is much smaller than the skin depth is
analytically investigated. By taking some important physical properties into account, we derive a simple,
yet accurate, expression for the effective index. We also study the changes in modal field and the attenuation
coefficient in the whole THz region, and find some interesting physical properties. Finally, we verify that these
theoretical analyses coincide with the rigorous numerical simulations. This research can be useful for various
applications of THz waveguides made of metallic nanoslits.
OCIS codes: 240.6680, 230.7370, 260.3090, 260.3910.
doi: 10.3788/COL201614.072401.
Rapid advances in laser technology have promoted various
techniques for the detection and generation of terahertz
(THz) radiation, which has shown potential applications
in many fields, e.g., in imaging, sensing, and spectros-
copy
[1–3]
. Among this research, powerful THz waveguides
have attracted more and more interest
[4–21]
. It was first pro-
posed by Wang and Mittleman that THz waves can effec-
tively propagate on a simple metal wire
[4]
.Caoet al. quickly
demonstrated that the waveguide effect mainly comes from
the zeroth-order azimuthally polarized surface plasmon po-
laritons (SPPs)
[5]
. Subsequently, various SPP waveguides
have also been proposed, such as a channel waveguide
[22,23]
,
dielectric-loaded SPP waveguide
[24]
, and hybrid SPP
waveguide
[25–27]
. Most of these SPP waveguides work atsub-
wavelength scales. As we all know, skin depth is a very im-
portant length scale for plasmonics in the THz wave range
and other low-frequency radiation
[28]
. Seo et al. demon-
strated that the enhancement of a THz electric field inside
a slit of width around 30000 times smaller than the wave-
length is about 10
5
[29]
. It was quickly pointe d out that the
highlight of the work of Seo et al. is that they considered a
previously unexplored regime in which the skin depth,
which is a measure of how quickly the fields decay inside
the metal, is larger than both the film thickness and slit
width
[30]
. In spite of that, the results have been applied
to many aspects. Up until now, the topics of a THz plasmon
of a metallic slit waveguide with sub-skin-depth width have
been rarely touched
[31]
. The propagation prop erties of a
THz waveguide using a metallic nanoslit narrower than
the skin depth have not been very clear, to the best of
our knowledge.
In this Letter, we shall derive a simple and explicit ana-
lytical expression to describe the propagation properties of
the THz plasmon of the metallic nanoslit with sub-skin-
depth width. The derivation is based on the property of
the huge relative permittivity of nonmagnetic metals in
the spectral region of the THz wave, and the fact that the
width of a nanoslit is much smaller than the skin depth.
The broad validity range and the high precision of the ana-
lytic expression shall also be tested. It is shown that for all
11 tested nonmagnetic metals mentioned in Ref. [
32], in
the whole THz radiation region, and with the width rang-
ing from 1 to 10 mm, the relative deviation for the effective
index is always smaller than 5%. From the explicit analyti-
cal expression, we shall easily find that the propagation
properties of this kind of THz waveguide are closely re-
lated to the product of the complex wave number of
the metal and the width of the metalli c slit. We shall also
study the changes of modal field and the attenuation co-
efficient in the whole THz region, and get some interesting
physical properties. Specifically, we find that the modal
field permeates the metal in a broad region relative to
the width of a nanoslit when the width of the metal slit
is smaller than the skin depth. Finally, all these analytical
conclusions shall be verified with rigorous numerical
simulations.
For a flat metal-dielectric interface, as we all know,
there is a bound electromagnetic state that is called
SPPs
[33]
. It has two electric field components E
x
and E
z
,
and one magnetic field component H
y
. The only magnetic
field component H
y
denotes the TM polarization. Now we
consider metallic slit is surrounded by air, and the width of
the slit is w, which is shown in Fig.
1.
For the TM polarization of a nonmagnetic metal, we
can obtain the following normalized expressions for the
magnetic field component H
y
for three regions in
Fig.
1,
H
y
¼ expðκ
m
k
0
ðx þ w∕2ÞÞ; x ≤ −
w
2
; (1)
H
y
¼ expð− κ
m
k
0
ðx − w∕2ÞÞ; x ≥
w
2
; (2)
COL 14(7), 072401(2016) CHINESE OPTICS LETTERS July 10, 2016
1671-7694/2016/072401(4) 072401-1 © 2016 Chinese Optics Letters