Article
Tuning the Resonance in HighTemperature Superconducting Terahertz Metamaterials
MPACINT, MS K771, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
Physical Review Letters (Impact Factor: 7.51). 12/2010; 105(24):247402. DOI: 10.1103/PhysRevLett.105.247402 Source: arXiv
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Available from: Quanxi Jia, Dec 20, 2013Tuning the Resonance in High Temperature Superconducting Terahertz Metamaterials
HouTong Chen,
∗
Hao Yang, Ranjan Singh, John F. O’Hara, Abul
K. Azad, Stuart A. Trugman, Q. X. Jia, and Antoinette J. Taylor
MPACINT, MS K771, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
(Dated: September 10, 2010)
In this Letter we present resonance properties in terahertz metamaterials consisting of a splitring resonator
array made from high temperature superconducting ﬁlms. By varying the temperature, we observed efﬁcient
metamaterial resonance switching and frequency tuning with some features not revealed before. The results
were well reproduced by numerical simulations of metamaterial resonance using the experimentally measured
complex conductivity of the superconducting ﬁlm. We developed a theoretical model that explains the tun
ing features, which takes into account the resistive resonance damping and additional splitring inductance
contributed from both the real and imaginary parts of the temperaturedependent complex conductivity. The
theoretical model further predicted more efﬁcient resonance switching and frequency shifting in metamaterials
consisting of a thinner superconducting splitring resonator array, which were also veriﬁed in experiments.
PACS numbers: 78.67.Pt, 74.25.q, 74.78.w, 74.25.N
Metamaterials consisting of metallic elements have enabled
a structurally scalable electrical and/or magnetic resonant re
sponse, from which exotic electromagnetic phenomena absent
in natural materials have been observed [1]. Metals provide
high conductivity that is necessary to realize strong electri
cal/magnetic metamaterial response [2, 3]. Metals, however,
play a negligible role in active/dynamical metamaterial reso
nance switching and/or frequency tuning, which has been typ
ically accomplished through the integration of metamaterials
with other natural materials (e.g. semiconductors) or devices,
and by the application of external stimuli [4–12]. It is essen
tially the modiﬁcation of the metamaterial embedded environ
ment that contributes to such previously observed functional
ities.
Recently, there has been increasing interest in supercon
ducting metamaterials towards loss reduction [13–20]. Signif
icant Joule losses have often prevented resonant metal meta
materials from achieving proposed applications, particularly
in the optical frequency range. At low temperatures, su
perconducting materials possess superior conductivity than
metals at frequencies up to terahertz (THz), and therefore
it is expected that superconducting metamaterials will have
a lower loss than metal metamaterials. More interestingly,
superconductors exhibit tunable complex conductivity over a
wide range of values, through variation of temperature and ap
plication of photoexcitation, electrical currents and magnetic
ﬁelds. Therefore, we would expect correspondingly tunable
metamaterials, which originate from the superconducting ma
terials composing the metamaterial, in contrast to tuning the
metamaterial environment.
In fact, superconducting metamaterials have enabled dia
magnetic response at very low frequencies, which may en
able screening of static magnetic ﬁelds [21, 22]. In the mi
crowave frequency range (∼10 GHz), lefthanded supercon
ducting transmission lines have been introduced and their tun
ability has been realized with electrical currents or temper
ature [13, 14]. Negative index metamaterials comprised of
niobium wires and splitring resonators exhibited redshifting
in resonance frequency (∼ 0.6%) when the temperature was
increased approaching the transition temperature T
c
[17]. Fur
ther experimental work has demonstrated tunability through
application of external dc or rf magnetic ﬁelds [16, 20].
At THz frequencies, low temperature superconductors may
be not suitable for metamaterial applications, since with a
smaller superconducting gap, Cooper pairs may be excited
and broken by THz photons, and therefore high temperature
superconductors (HTS) should be employed. In this Letter,
we present THz metamaterials based on electric splitring
resonators (SRRs) made from epitaxial YBa
2
Cu
3
O
7−δ
HTS
ﬁlms. These metameterials exhibit temperaturedependent
resonance strength and frequency, which reveal some inter
esting tuning features not previously observed. Finiteelement
numerical simulations and theoretical modeling are performed
to understand the underlying tuning mechanism.
The epitaxial YBa
2
Cu
3
O
7−δ
(YBCO) ﬁlms with δ = 0.05
were prepared using pulsed laser deposition on 500 µm thick
(100) LaAlO
3
(LAO) substrates. The transition temperature
was measured to be T
c
= 90 K. Square arrays of electric SRRs,
with the unit cell shown in the inset to Fig. 1(a), were fabri
cated using conventional photolithographic methods and wet
chemical etching of the YBCO ﬁlms. The YBCO SRRs have
a thickness of d = 180 nm or 50 nm, outer dimensions of
l = 36 µm, line width of w = 4 µm and gap size of g = 4 µm,
and the arrays have the periodicity of p = 46 µm. Terahertz
timedomain spectroscopy (THzTDS) incorporated with a
continuous ﬂow liquid helium cryostat was used to charac
terize the YBCO ﬁlms and metamaterials. Under normal inci
dence, the THz transmission spectra were measured as a func
tion of temperature, using an LAO substrate as the reference.
We focus our attention on the metamaterial fundamen
tal resonance (the socalled LC resonance) resulting from
the circulating currents excited by the incident THz electric
ﬁeld [23]. In Fig. 1(a) we show the THz transmission ampli
tude spectra for the 180 nm thick YBCO metamaterial sam
ple at various temperatures. At temperatures far below T
c
,
e.g. 10 K, the metamaterial exhibits the strongest resonance,
arXiv:1009.1640v1 [condmat.suprcon] 8 Sep 2010
Page 1
2
Temp (K):
80
78
75
70
60
10
100
84
0.2 0.4 0.6 0.8
Frequency (THz)
1.0
0
0.2
0.4
0.6
0.8
1.0
Transmission
0.0
0.2
0.4
0.6
0.8
Ttransmission minimum
20 40 60 80 100 120 140
0.56
0.58
0.60
Resonance frequency (THz)
Temperature (K)
(a)
Experiment
Simulation
Theory
(c)
(b)
Temperature (K)
σ
re
σ
im
40 80 120
0
2
4
6
×10
6
S/m
FIG. 1: (color online). (a) THz Transmission amplitude spectra of
the 180 nm thick YBCO metamaterial at various temperatures. (b)
Transmission minimum and (c) corresponding resonance frequency
as functions of temperature, from experiments, numerical simula
tions, and theoretical calculations. Inset to (a) illustrates a micro
scopic image of a single YBCO SRR, where the lighter colored area
is YBCO. Inset to (b) shows the real and imaginary parts of the com
plex conductivity at 0.6 THz of an unpatterned 180 nm thick YBCO
ﬁlm.
as indicated by the sharp THz transmission dip with a min
imal transmission amplitude of 0.045 at 0.613 THz. This
strong resonance is almost the same as in a metamaterial sam
ple where the YBCO SRRs was replaced by gold SRRs with
the same thickness and at the same temperature. As the tem
perature increases, the resonance strength decreases, as seen
by the broadening and reduction in amplitude of the transmis
sion dip. The resonance frequency experiences a redshifting,
which reaches the lowest value of 0.564 THz near 80 K, re
sulting in a frequency tuning of 8%. As the temperature fur
ther increases, the resonance strength continues to decrease,
but the resonance frequency, on the other hand, shifts back
to higher frequencies. The temperaturedependent transmis
sion minimum and the corresponding resonance frequency are
plotted in Figs. 1(b) and 1(c), respectively. The results show
that, at temperatures near 80 K, the transition of resonance
strength is fastest and the resonance frequency exhibits a dip,
not observed in previous work [17–20]. We can exclude the
LAO substrate as contributing to the metamaterial resonance
tuning, because the features in the temperaturedependent res
onance in the YBCO metamaterial (see Fig. 1) were not ob
served in a metamaterial sample where the YBCO was re
placed by gold. In that gold SRR metamaterial sample, the
resonance frequency shifting was imperceptible, and the res
onance strength only slightly decreased with increasing tem
peratures. Additionally, through THzTDS measurements, it
turns out that the dielectric constant of the LAO substrate only
exhibits a weak dependence on the temperature. Therefore, it
is the temperaturedependent properties of YBCO ﬁlm that are
responsible for the observed metamaterial resonance tuning.
The complex conductivity of YBCO ﬁlm can be expressed
using the wellknown twoﬂuid model [24]:
˜
σ(ω,T ) =
ne
2
m
∗
f
n
(T )
τ
−1
−iω
+ i
f
s
(T )
ω
, (1)
where f
n
and f
s
are fractions of normal (quasiparticle) and
superconducting (superﬂuid) carriers, respectively, with f
n
+
f
s
= 1, n is the carrier density, m
∗
is the carrier effective mass,
and τ is the quasiparticle relaxation time. The real and imagi
nary parts of the complex conductivity are then:
σ
re
=
ne
2
m
∗
f
n
(T )τ
1 + ω
2
τ
2
, (2)
σ
im
=
ne
2
m
∗
f
n
(T )ωτ
2
1 + ω
2
τ
2
+
f
s
(T )
ω
. (3)
Using THzTDS we experimentally measured the conduc
tivity of an unpatterned 180 nm thick YBCO plain ﬁlm. The
resultant real and imaginary parts of the complex conductivity
at 0.6 THz are plotted as functions of temperature in the inset
to Fig. 1(b). The real conductivity [Eq. (2)], which derives
from the Drude response of quasiparticles in Eq. (1), slowly
increases when temperature decreases across T
c
to about 70 K.
It starts to decrease below 70 K, but not signiﬁcantly, over
the temperatures we measured down to 50 K. In this temper
ature range, ωτ 1 at the resonance frequency (∼ 0.6 THz),
the decreasing f
n
(T ) may be compensated by the increasing
quasiparticle scattering time τ [25]. At temperatures above T
c
,
the imaginary conductivity is derived from the Drude response
and is very small, since f
s
(T > T
c
) = 0. As the temperature
decreases below T
c
, the second term in Eq. (3) from the su
perﬂuid Cooper pair state becomes nonzero and results in the
rapidly increasing imaginary conductivity, exceeding the real
conductivity below 80 K. Using these experimental values of
the YBCO complex conductivity at 0.6 THz, the metamaterial
Page 2
3
resonant response was simulated using commercially avail
able ﬁniteelement simulation codes from COMSOL Multi
physics. The simulated transmission minimum and the corre
sponding frequency are plotted as functions of temperature in
Figs. 1(b) and 1(c), respectively, reproducing the experimental
results.
The measured real conductivity of the YBCO ﬁlm reveals
less than 20% change over the temperature range from 60 K to
90 K, where the resonance strength experiences a fast change
and the resonance shifts its frequency. This variation of real
conductivity cannot solely cause the observed large metama
terial resonance switching and frequency tuning. Both the real
and imaginary parts of the complex conductivity have to be
considered for the metamaterial resonance. The imaginary
conductivity, which is due to the superﬂuid carriers and causes
no loss, becomes dominant at low temperatures, and it is re
sponsible for the enhancement in resonance strength.
The resonance frequency is determined by the effective
capacitance, C, inductance, L, and resistance, R, in the
SRRs [26]:
ω
2
0
=
1
LC
−
R
2
4L
2
. (4)
It has been shown that the kinetic inductance, which repre
sents the kinetic energy storage in free electrons in metals, or
Cooper pairs in superconductors, plays an important role in
determining the metamaterial resonance frequency [17, 27].
This effect underpins the redshifting of the resonance fre
quency in niobium metal superconducting metamaterials op
erating near 10 GHz as the temperature increases and ap
proaches T
c
[17]. However, the back blueshifting, shown in
Fig. 1(c) between ∼80 K and T
c
, was not observed in nio
bium, and the model proposed in that work would not explain
this effect when only the superﬂuid state (i.e. imaginary con
ductivity) was considered [17].
Here we consider a more general situation that the SRRs
are fabricated from a conducting ﬁlm (YBCO ﬁlm in our case)
with a complex conductivity
˜
σ and thickness d. Such an un
patterned plain ﬁlm can be modeled as a lumped impedance
in an equivalent transmission line. By equating the (multi
ple) reﬂections or transmissions from the ﬁlm and the trans
mission line model, this complex surface impedance (or sheet
impedance with units of Ω/square) of the unpatterned ﬁlm can
be derived as:
˜
Z
S
= R
S
−iX
S
= Z
0
n
3
+ i ˜n
2
cot(
˜
βd)
˜n
2
2
−n
2
3
, (5)
where the tildes over the variables indicate complex values,
Z
0
= 377 Ω is the vacuum intrinsic impedance, n
3
=
√
ε
LAO
=
4.8 is the LAO substrate refractive index, ˜n
2
=
p
i
˜
σ/ε
0
ω is the
complex refractive index of the ﬁlm, and
˜
β = ˜n
2
ω/c
0
is the
complex propagation constant where c
0
is the light velocity
in vacuum. Both ˜n
2
and
˜
β can be calculated from the experi
mental complex conductivity near the metamaterial resonance
frequency. When n
3
˜n
2
, which is valid in our case, Eq. (5)
can be further simpliﬁed as:
˜
Z
S
= i
Z
0
˜n
2
cot(
˜
βd). (6)
From Eqs. (5) and (6), it is obvious that both the ﬁnite real
and imaginary parts of the ﬁlm refractive index ˜n
2
, and there
fore the ﬁnite real and imaginary parts of the complex con
ductivity
˜
σ, contribute to the ﬁlm surface resistance R
S
and
reactance X
S
. They are plotted in Fig. 2 for the 180 nm thick
YBCO ﬁlm as functions of temperature, and are also calcu
lated for a 50 nm thick YBCO ﬁlm assuming its complex con
ductivity does not depend on the ﬁlm thickness.
The YBCO SRR array resistance R (SRR reactance X is
zero at resonance) can be obtained by considering the nonuni
form distribution of currents in a unit cell [28]: R
∼
=
[(A −
g)/w]R
S
, where A = 64 µm is the median circumference of
the (small) current loop. When temperature increases, the in
creasing SRR resistance R accounts for the resonance damp
ing and therefore the increasing transmission minimum. If we
model the SRR array as a lumped resistor R in the transmis
sion line [29], we can calculate the resonance transmission as
a function of temperature, which is plotted in Fig. 1(b) and sat
isfyingly reproduces the experimental and simulated results.
In order to correctly interpret the temperaturedependent
resonance frequency shifting, additional inductance in SRRs
has to be taken into account besides the geometric inductance
0
12
Surface impedance (Ω/square)
40 60 80 100 120 140
0
2
4
6
Temperature (K)
(b)
(a)
18
6
50 nm
180 nm
50 nm
180 nm
R
S
X
S
24
FIG. 2: (color online). Complex surface impedance of the 180 nm
thick unpatterned YBCO superconducting ﬁlm calculated using the
experimental complex conductivity at 0.6 THz. (a) Surface resis
tance R
S
, and (b) surface reactance X
S
. The dashed curves are for an
assumed 50 nm thick YBCO ﬁlm.
Page 3
4
L
G
. The geometric inductance represents the conventional in
ductance of the SRR loop and can be estimated [30] to be
L
G
∼
=
4 ×10
−11
H. In contrast, the additional inductance L
S
originates dominantly from the kinetic energy in supercon
ducting carriers in the YBCO SRRs. This additional SRR in
ductance can be calculated using the above derived YBCO
ﬁlm surface reactance X
S
and by considering the geometry
and dimensions of the YBCO SRR: L
S
∼
=
[(A −g)/w](X
S
/ω).
Therefore, the total SRR inductance becomes L = L
G
+ L
S
.
In order to obtain the metamaterial resonance frequency using
Eq. (4), we estimate the SRR capacitance C
∼
=
1.5 ×10
−15
F,
from the above estimated geometric inductance L
G
and the
simulated resonance frequency ω
0
= 2π×0.62 THz assuming
perfect conducting SRRs (i.e. L
S
= 0 and R = 0 ). The cal
culated temperaturedependent metamaterial resonance fre
quency is plotted in Fig. 1(c) along with the experimental and
simulation results. Again, the theoretical result reproduces the
frequency tuning features, though the overall tuning range is
about half of the experimental and simulation data.
The above calculations show that the temperature
dependent SRR resistance and additional inductance, due
to the temperaturedependent complex conductivity of the
YBCO ﬁlm, play an important role in the resonance switching
and frequency tuning. Eqs. (5) and (6) further reveal that, for
a ﬁxed value of the real conductivity, which is approximately
the case in our situation, the YBCO ﬁlm surface reactance,
and therefore the additional SRR inductance, reach the maxi
mum value when the imaginary conductivity is approximately
equal to the real conductivity, and vice versa. This is consis
tent with the experimental observations, where the metamate
rial resonance frequency shifts to the lowest value when the
real and imaginary parts of the YBCO complex conductivity
cross each other.
The results in Fig. 2 suggest that metamaterials made from
thinner YBCO superconducting ﬁlms will have a lower res
onance frequency, and will be more efﬁcient in resonance
switching and frequency tuning. In order to verify this pre
diction, we fabricated and characterized a second metamate
rial sample from 50 nm thick YBCO ﬁlm. The temperature
dependent transmission spectra are shown in Fig. 3. The reso
nance frequency at 20 K is measured to be 0.48 THz, which is
signiﬁcantly lower than that in the metamaterial sample from
180 nm thick YBCO ﬁlm. When temperature increases, the
resonance frequency continuously shifts to lower frequencies.
It becomes 0.31 THz at 78 K, achieving a tuning range of
35%. We did not observe the back shifting of resonance fre
quency due to the high resistance at temperatures above 80 K,
which already completely damps the metamaterial resonance.
In conclusion, we have fabricated and characterized electric
SRRbased metamaterials from high temperature supercon
ducting YBCO ﬁlms. We observed temperature induced meta
material resonance switching and frequency tuning, which
can be reproduced by ﬁniteelement numerical simulations us
ing the experimentally measured complex conductivity of the
YBCO ﬁlm. We found that both the temperaturedependent
real and imaginary parts of the complex conductivity of the
0.2 0.3 0.4 0.5 0.6 0.7
0.0
0.2
0.4
0.6
0.8
1.0
82K
80K
78K
75K
70K
60K
50K
40K
20K
Transmission
Frequency (THz)
FIG. 3: (color online). Temperaturedependent THz Transmission
amplitude spectra of the 50 nm thick YBCO metamaterial.
superconducting ﬁlm have to be consistently considered in or
der to achieve a correct interpretation. A theoretical model
has been developed, taking into account the SRR resistance
and additional inductance. Our modeling calculations were in
good agreement with experimental observations and numeri
cal simulations, and further predicted more efﬁcient resonance
switching and frequency tuning with thinner YBCO metama
terials, which was also veriﬁed in experiments. We expect
that such resonance tuning in superconducting metamaterials
could also be realized dynamically through application of op
tical excitation, electrical currents, and/or magnetic ﬁelds. Al
though high temperature superconducting metamaterials may
not be able to essentially address the loss issue at THz fre
quencies and beyond, they should enable the development of
novel, multifunctional metamaterials.
We acknowledge support from the Los Alamos National
Laboratory LDRD Program. This work was performed,
in part, at the Center for Integrated Nanotechnologies, a
US Department of Energy, Ofﬁce of Basic Energy Sciences
Nanoscale Science Research Center operated jointly by Los
Alamos and Sandia National Laboratories. Los Alamos Na
tional Laboratory, an afﬁrmative action/equal opportunity em
ployer, is operated by Los Alamos National Security, LLC, for
the National Nuclear Security Administration of the US De
partment of Energy under contract DEAC5206NA25396.
∗
Electronic address: chenht@lanl.gov
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Page 5
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 "The numerical results are presented inTable III , indicating the minimum and maximum ON/OFF ratios of ~ 37.66 dB for '0 1'/'0 0' or '1 0'/'0 0'and 40.76 dB for '1 1'/'0 0', respectively. The corresponding modulation depth densities are all greater than 99.9% that are also larger than those reported in2324252627282930. These extremely large ON/OFF ratios have been obtained from the device whose length is ~53% of the incident wavelength. "

 "The numerical results are presented inTable III , indicating the minimum and maximum ON/OFF ratios of ~ 37.66 dB for '0 1'/'0 0' or '1 0'/'0 0'and 40.76 dB for '1 1'/'0 0', respectively. The corresponding modulation depth densities are all greater than 99.9% that are also larger than those reported in2324252627282930. These extremely large ON/OFF ratios have been obtained from the device whose length is ~53% of the incident wavelength. "
Dataset: DataseFinal

 "Since very few materials in nature have suitable properties for effective THz modulation without introducing significant insertion loss, alternative materials and structures have been explored for THz modulation and switching applications . These include metamaterials [6][7][8], photonic crystals [9][10][11], graphene [12][13][14][15], phase transition oxides [16][17][18] , and semiconductors and devices [19]. THz SLMs with different materials and structures have been demonstrated. "
[Show abstract] [Hide abstract] ABSTRACT: We demonstrate largecontrast, lowcrosstalk, lowpower, and broadband spatial light modulators (SLMs) for operation at terahertz (THz) frequencies. The electrothermally activated SLMs rely on the insulator–metalphase transition of two VO2 thin films deposited on opposite sides of a sapphire substrate. We validated the effectiveness of our approach by fabricating and testing 2×2 pixel SLM prototypes. Record high amplitude modulation depth of 96%, −30 dB pixeltopixel crosstalk and precise THz transmission control was determined for the fabricated SLMs over a broad range of THz frequencies. Raster scanning THz transmission revealed excellent pixel uniformity with very large on/off contrast. These attributes are fundamental for highcontrast THz imaging and spectroscopy applications.