Effect of metal permittivity on resonant properties
of terahertz metamaterials
Ranjan Singh,1Abul K. Azad,2John F. O’Hara,2Antoinette J. Taylor,2and Weili Zhang1,*
1School of Electrical and Computer Engineering, Oklahoma State University, Stillwater, Oklahoma 74078, USA
2Center for Integrated Nanotechnologies, Materials Physics and Applications Division,
Los Alamos National Laboratory, P.O. Box 1663, MS K771, Los Alamos, New Mexico 87545, USA
* Corresponding author: firstname.lastname@example.org
Received February 15, 2008; accepted May 12, 2008;
posted June 5, 2008 (Doc. ID 92819); published June 27, 2008
We investigate the effect of metal permittivity on resonant transmission of metamaterials by terahertz time-
domain spectroscopy. Our experimental results on double split-ring resonators made from different metals
confirm the recent numerical simulations [Phys. Rev. E 65, 036622 (2002)] that metamaterials exhibit
permittivity-dependent resonant properties. In the terahertz regime, the measured inductive–capacitive
resonance is found to strengthen with a higher ratio of the real to the imaginary parts of metal permittivity,
and this remains consistent at various metal thicknesses. Furthermore, we found that metamaterials made
even from a generally poor metal become highly resonant owing to a drastic increase in the value of the
permittivity at terahertz frequencies. © 2008 Optical Society of America
OCIS codes: 300.6495, 160.3918.
Recently, the unique properties, rich physics, and fas-
cinating potential of metamaterials have inspired
significant research over a broad range of the electro-
magnetic spectrum. Metamaterials are typically
made from arrays of subwavelength resonator struc-
tures embedded in an insulating or dielectric board-
ing medium. They behave as continuous materials
and enable intriguing electromagnetic phenomena,
such as negative refraction, perfect lensing, and
cloaking [1–3]. Recently, metamaterials have at-
tracted increased attention in the terahertz regime,
where they may advance the development of next-
generation terahertz elements, such as integrated fil-
ters, modulators, detectors, and sensors [4–7].
Most metamaterials utilize split-ring resonators
(SRRs) to achieve a desired response. The electric
permittivity ??m=?rm+i?im? of metal SRRs is an im-
portant factor that is closely associated with the es-
tablishment of left-handed resonance in metamateri-
als . In typical SRRs, the fundamental resonance
is inductive capacitive (LC) in nature, where current
circulates in the metallic loops to create inductance
and charge accumulates at ring gaps to provide ca-
pacitance. The complex permittivity, ?m, of the metal
plays a very important role in making the structure
highly resonant . Although the exact values of ?m
were not known in the gigahertz regime, a numerical
study investigating the resonance properties of SRR-
based microwave metamaterials has verified this de-
pendence on ?m. By fixing the real part of permit-
tivity to ?rm=1 and increasing the magnitude of the
imaginary permittivity, the resonance gap of SRRs
was found to become narrower and the left-handed
effect was further enhanced.
At terahertz frequencies the values of metal per-
mittivity are much higher than those at optical fre-
quencies but slightly lower than those in the giga-
hertz regime. Wepresent
simulation results of the effect of metal permittivity
on transmission properties of terahertz metamateri-
als made from double SRRs. At the LC resonance,
0.5 THz, the transmission amplitude and linewidth
are shown to exhibit dependence on the permittivity
of the constituent metals. The resonant transmission
minimum is enhanced in correspondence with an in-
crease in the imaginary part of the permittivity, ?im,
or an increase in the ratio of the real to the imagi-
nary permittivity, −?rm/?im, showing consistency
with recent numerical predictions at microwave fre-
quencies . The optimal transmission minimum and
Q factor are observed in SRRs made from Ag, a
highly conducting metal, though Q is effectively satu-
rated owing to the radiative nature of the SRRs.
More interestingly, metamaterials made from Pb, a
generally poor metal, also exhibit strong LC reso-
nances owing to a large permittivity in the terahertz
regime. It thus indicates that terahertz metamateri-
als operate well over a wide range of constituent met-
als. This is essential in integrated terahertz compo-
nents applications, such as filters and modulators,
when fine control of resonant properties is needed
with a fixed layout design.
Broadband terahertz time-domain spectroscopy
metamaterial transmission properties [6,10]. Planar
SRR metamaterials of three different metals—Pb, Al,
and Ag—were lithographically fabricated on a silicon
substrate (0.64 mm thick, p-type resistivity 20 ? cm).
The inset of Fig. 1(a) shows the diagram of a double
SRR unit. The SRRs made from each metal are pre-
pared with three different thicknesses—0.5?, 1?, and
2?—where ? is the skin depth at 0.5 THz. The calcu-
lated values of the skin depth are 336, 116, and
84 nm for Pb, Al, and Ag, respectively. Figures
1(a)–1(c) show the measured amplitude transmission
of the SRR metamaterials made from different met-
als . When the planar SRRs are 0.5? thick, as
shown in Fig. 1(a), a well-defined LC resonance de-
velops at 0.5 THz. The difference in resonance
strength for different metals is clearly seen, with Ag
OPTICS LETTERS / Vol. 33, No. 13 / July 1, 2008
0146-9592/08/131506-3/$15.00© 2008 Optical Society of America
SRRs featuring the deepest resonant transmission of
53.9%, while Al and Pb SRRs are limited at 60.2%
and 64.4%, respectively.
The resonant behavior of the SRRs is further com-
pared by using metals with different thicknesses. As
shown in Figs. 1(b) and 1(c), by increasing the metal
thickness to 1.0? and 2.0?, the resonance is further
strengthened for all metals. The Ag SRRs consis-
tently reveal the strongest resonance, having a trans-
mission minimum reduced to 18.5% at a thickness of
2.0?. Comparatively, for the 2.0? thick Al and Pb
samples the transmissions are 30.2% and 43.1%, re-
spectively. The measured transmission minima at the
LC resonance are plotted in Fig. 2(a) as a function of
metal thickness. It is worth noting that when the
metal thickness is varied from 1.0? to 2.0?, the LC
transmission for the Pb metamaterials is nearly
saturated, while it is continuously strengthened for
the Ag SRRs.
At 0.5 THz the complex permittivity of the given
constituent metals are ?Pb=−1.80?103+1.65?105i,
+2.15?106i [11,12]. The imaginary part of permittiv-
ity ?imshows a monotonic increase from Pb, Al, to Ag.
By noting the measured results shown in Fig. 1, the
LC resonance for different constituent metals is seen
to strengthen with increasing ?im. Such a trend re-
mains true at various given thicknesses, as shown in
Figs. 1(a)–1(c). This is consistent with the recent nu-
merical predictions using the transfer matrix method
at microwave frequencies . The electric permittiv-
ity of Ag, Al, and Pb can be well described by the
Drude model . At terahertz frequencies the Drude
permittivity can be approximately given as ?m
?−?dc/??0??+i?dc/??0??, where ?dcis the dc conduc-
tivity, ?=1/? is the damping rate with ? being the av-
erage collision time, and ?0is the vacuum permittiv-
ity . Our THz-TDS results agree well with this
simplified Drude expression in that ?imis propor-
tional to the dc conductivity ?dc, suggesting that the
LC resonance is more pronounced with metamateri-
als of higher conductivity [8,9].
Furthermore, when the contribution of ?rmis con-
sidered, the LC resonance is found to be enhanced
with an increasing ratio, −?rm/?im, at terahertz fre-
quencies. It was shown that a better conducting
metal is characterized with a higher ratio −?rm/?im
−?rm/?imfor the constituent metals at each given
metal thickness areplotted
0.1 to 3.0 THz. At 0.5 THz, the ratios are 0.011,
0.025, and 0.116 for Pb, Al, and Ag, respectively
[11,12]. As can be seen in Fig. 1, the measured LC
resonance is indeed strengthened with the increasing
ratio −?rm/?imat each given metal thickness. This
again is consistent with the simplified Drude permit-
tivity, where the ratio −?rm/?imis inversely propor-
tional to the damping rate [11,15].
In addition, the quality ?Q? factor of the LC reso-
nance shows dependence on the permittivity of the
constituent metals . As shown in Fig. 2(b), the ex-
perimentally extracted Q at the LC resonance shows
an increasing trend with higher ?im, as well as
−?rm/?im. This relationship is limited, however, as
the metal conductivity becomes very high. It is
known that the SRR can be treated as an equivalent
plitude transmission of planar double SRR metamaterials
made from Pb, Al, and Ag with various film thicknesses: (a)
0.5?, (b) 1.0?, and (c) 2.0?, near the LC resonance. Inset,
schematic of the double SRR unit with dimensions w
=3 ?m, metal width t=6 ?m, l=36 ?m, effective length of
the SRR unit l?=21 ?m, d=2 ?m, and the periodicity P
(Color online) Measured frequency-dependent am-
sion minima and (b) Q factor at the LC resonance 0.5 THz
for different metal SRRs with various thicknesses in skin
(Color online) (a) Measured amplitude transmis-
−?rm/?imof Pb, Al, and Ag in the terahertz regime [11,12];
the vertical dashed line indicates the LC resonance fre-
quency 0.5 THz.
(Color online) Frequency-dependent Drude ratio,
July 1, 2008 / Vol. 33, No. 13 / OPTICS LETTERS
series resistor–inductor–capacitor (RLC) circuit. The Download full-text
Q of the RLC series circuit is inversely proportional
to the resistance, Q?1/R, where R is an effective re-
sistance of the double SRR unit. However, SRRs are
also radiators, continuously shedding resonant en-
ergy following excitation. Therefore the effective re-
sistance can be expressed in two terms: the ohmic re-
sistance, RL, and the radiation resistance, RR,
representing energy loss by heating and by radiation,
respectively. At terahertz frequencies, the ohmic re-
sistance can be approximately given through the
equivalent model, R=4l?/?th??0?im?, with h?2?, h
being the metal thickness . The ohmic resistance
decreases with increasing ?imor conductivity ?dcof
metals, thus increasing the Q factor. When the metal
thickness approaches 2.0?, the Q of the Ag metama-
terial shows a 19% increase as compared with the Pb
SRRs. The Q does not change as dramatically as ?im
owing to the interplay of RLand RR. As the conduc-
tivity increases, RLbecomes negligible compared to
RR. Further increases in ?imor ?dcdo not affect RR
and should result in very little improvement in Q.
The experimental results were supplemented by
finite-element simulations using CST Microwave
Studio . Figures 4(a) and 4(b) illustrate, respec-
tively, the measured and simulated amplitude trans-
missions of 300 nm thick SRR metamaterials made
from different metals. Both the measured and simu-
lated LC resonances reveal similar permittivity de-
minima for the Pb, Al, and Ag samples are 47.7%,
25.5%, and 14.1%, respectively, showing a good
agreement with the simulation results. The devia-
tions in the simulated resonance frequencies may be
caused by the approximations of defect-free SRRs
with frequency-independent metal properties and
thickness-independent conductivity, which are not
necessarily true .
It is important to note that the simulations enable
an extrapolation of measured results. Figure 4(b)
shows the simulated transmission for SRRs made
from a hypothetical metal having conductivity ten
times greater than that of the regular Ag, here re-
ferred to as super Ag (S. Ag), and SRRs made from a
perfect electric conductor. The resonance strength in-
creases as ?imincreases and RL→0, but the improve-
ment in Q is clearly saturated, verifying that radia-
tion resistance limits Q for SRRs of very low loss.
R. Singh and W. Zhang acknowledge financial sup-
port from the National Science Foundation. This
work was performed, in part, at the Center for Inte-
grated Nanotechnologies, a U.S. Department of En-
ergy, Office of Basic Energy Sciences nanoscale sci-
ence research center jointly operated by Los Alamos
and Sandia National Laboratories.
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element simulations of the LC resonant transmission of
metamaterials made from 300 nm thick Pb, Al, Ag, S. Ag,
and PEC. Inset, blow off of the simulated LC resonance.
(Color online) (a) THz-TDS results and (b) finite-
OPTICS LETTERS / Vol. 33, No. 13 / July 1, 2008