Experiments on Superconducting
Metamaterial-Induced Transparency
Cihan Kurter, John Abrahams, Chris Bennett, Tian Lan, Steven M. Anlage,
L. Zhang, T. Koschny, C. Soukoulis (Ames/Iowa State)
Alexander Zhuravel (Kharkov, Ukraine),
Alexey Ustinov (KIT, Karlsruhe, Germany),
Work Funded by NSF and ONR
Metamaterials 2010, Karlsruhe, Germany
14 September, 2010
1
Metamaterial-Induced Transparency
Inspired by:
Electromagnetically-Induced Transparency (EIT)
Probe Absorption
Strong dispersion
with little loss
Probe Frequency
Probe Field
Pump Field
Classical Analog of EIT
Garrido Alzar, et al.,
Am J Phys (2002)
Dissipation g2 << g1
to coherently drive
particle 1
Probe Frequency
N. Papasimakis, et al.
Optics and Photonics
News, Oct. 2009
Atom
g2
g1
Light can be slowed, or even stopped at the EIT frequency
L. V. Hau, Nature (1999)
Fleischhauer, PRL (2000)
2
Classical Analog of EIT
The Importance of Strong Loss Contrast
The “atom” has zero displacement
at the EIT frequency, but large
displacement for small de-tuning
g1
Re[x1(t)]
Atom
g2
Pump Field
Probe Field
g2 = 1 x 10-2
100
50
Absorbed Power
Absorption
150
-3
g2 g=2 1<<x g10
1
g1 = 4.0 x 10-2
g2 = 1.0 x 10-7
g1 = 4 x 10-2
0
0.98
3
0.99
g2 = 1 x 10-7
1.00
Frequency
1.01
1.02
Metamaterial-Induced Transparency
Work with L. Zhang, T. Koschny, and C. Soukoulis (Iowa State Univ.)
Normal metal metamaterials:
Papasimakis, PRL 2008
Tassin, PRL 2009
Superconducting Metamaterials
MIT @ 10 GHz
Nb
Normal metal
s1
ay
w2
g2
g1
w1
g
l3
ax
4
Superconducting
l1
l2
B
Nb (dark)
Nb
X-band waveguide
E
Cu (radiative)
s2
Cu
Simulation Results
Metamaterial-Induced Transparency
L. Zhang, T. Koschny, and C. Soukoulis (Iowa State Univ.)
8
1
(n)
T
R
(n)
0.1
6
T,R
Transmission
n and Reflection
Index of Refraction
10
0.01
4
2
EIT Frequency
0
9.5
5
9
10
11
Frequency (GHz)
10
10.5
Frequency (GHz)
12
11
Adjust coupling to dark resonators
and frequencies of dark resonators
to modify n(w) dispersion
Experimental Setup
Metamaterial-Induced Transparency
Network
Analyzer
1
2
Coaxial
Cable
Cryogenic
Dewar
Sample
6
X-band
Waveguide
Superconductor Electrodynamics
s = s1-is2


J =s E
s1(w)
1.0
s2(w) ~ 1/w
0.8
T=0
ideal s-wave
ns(T)
Normal State
(T > Tc)
s2(w)
0.6
(p nse2/m)(w)
(Drude Model)
0
0.4
s1(w)
0.2
Superfluid density
2 ~ m/ns
0
0.0
0
0.5
1.0
1/t2D / 
1.5
2.0
2.5
3.0
3.5
w
sn
s1(T)
“binding energy” of
Cooper pair (100 GHz ~ few THz)
T
Tc
0
0
0
Tc
T
Surface Impedance (w > 0) Z s = Rs  iX s = iw 0 / s
Normal State
Rs = X s 
w 0
1
=
2s 1 s 1
Superconducting State (w < 2D)
Rs ~ s1 = 0
X s = 0w
Penetration depth
(0) ~ 20 – 200 nm
Finite-temperature: Xs(T) = wL = w0(T) → ∞ as T →Tc
7
Narrow wire or thin film of thickness t : L(T) = 0(T) coth(t/(T)) → 0 2(T)/t
Kinetic Inductance
Experimental Results
Tranmsission |S21|/|S21|
max
5
50
40
0
30
-5
20
-10
10
0
-15
-10
-20
-25
9.70
-20
-30
Pin = -30 dBm
T = 4.6 K
9.75
9.80
9.85
Uncalibrated Group Delay (ns)
(dB)
Metamaterial-Induced Transparency
~
d12
dw
-40
9.90
Frequency (GHz)
8
Nb / Cu MM-EIT sample (first generation) in Cu waveguide
EIT bandwidth (3 dB) = 7.5 MHz (~ 0.1%)
Superconducting Metamaterial-Induced Transparency
Effect of Temperature on Transmission
4.9 K
5K
6K
7K
7.5 K
7.8 K
8K
8.2 K
8.4 K
8.5 K
8.6 K
8.7 K
8.75 K
8.8 K
8.83 K
8.86 K
8.89 K
8.92 K
8.95 K
8.98 K
9K
9.04 K
9.1 K
9.2 K
9.3 K
0
-5
-20
-10
-25
-15
-20
21 peak
0 (peak)
(GHz)
f0 (peak)f (GHz)
-30
9.79
9.78
-35
-25
9.77
-40
9.68
9.70
9.72
9.76
5
6
7
9.74
9.76
9.78
9.80
0
-14
-2
-16
-4
-18
-6
-20
9.82
-8
Frequency
f (GHz)(GHz)-22
8
T(K)
Temperature
(K)
9
|S21| (peak) /|S21
|S|max
|
(dB)
(peak) (dB)
Transmission
| max
(dB)(dB)
|S21
|S21|/|S
Transmission
21
-15
9
9.84
5
9.86
6
9.88
7
T(K)
8
Temperature (K)
9
f0 (peak) (GHz)
9.79
9.78
70
50
40
70
30
20
10
Pin = -30 dBm
9.77
0
9.72
9.76
9.74
9.76
9.78
9.80
65
60
55
50
45
9.82
40
Frequency (GHz)
35
5
6
7
8
Temperature (K)
10
4.9 K_smt
7 K_smt
7.8 K_smt
8.2K_smt
8.4 K_smt
8.6 K_smt
8.7 K_smt
8.75 K_smt
8.8 K_smt
8.83 K_smt
8.86 K_smt
8.89 K_smt
8.92 K_smt
8.95 K_smt
8.98 K_smt
9 K_smt
9.1 K_smt
9.2 K_smt
9.3 K_smt
60
Peak Group delay (ns)
Uncalibrated Group Delay (ns)
Superconducting Metamaterial-Induced Transparency
Effect of Temperature on Group Delay
9
5
9.84
9.86
6
7
Temperature (K)
8
9
Experimental Results
Metamaterial-Induced Transparency
Switching/Limiting Behavior at High Power
T= 4.24 K
0
Transmission |S21|/|S21|
max
(dB)
5
-5
-10
-15
P= -30 dBm
P= -10 dBm
P= 17dBm
P= 18dBm
P= 20dBm
-20 The “transparency
window” switches
-25 off between +17 and
+18 dBm
9.70
9.75
9.80
Frequency (GHz)
11
9.85
9.90
RF Power Dependence of Superconducting EIT Features
To investigate the RF power dependence, we examine the RF current
distributions in the superconducting parts of the sample using
Laser Scanning Microscopy (LSM)
modulated
laser
resonator transmission
laser OFF
|S21(f0
)|2
laser ON
|S21(f0)|2
f
f0
D|S12 ~ [ JRF
|2
Pout
Pin
(x,y)]2
8.5 mm
A 
1 mm
10 V
RF photoresponse
~ Jrf2(x, y)
Scanned Area
STO
LAO Substrate
RF output
See A. P. Zhuravel, et al.,
J. Appl. Phys. 108, 033920 (2010)
12
YBCO Ground Plane
0 V
T = 79.5 K
f = 5.2133 GHz
P = - 6 dBm
RF input
YBCO Ground Plane
240 nm thick film
LSM Image of Superconducting RF
Currents in EIT sample @ 10 GHz
Geometry
2D LSM image
Focus on this corner
Nb split ring
Upper Nb split ring
f = 9.63 GHz; P = 18 dBm; T = 7 K
Cu stripe
Bottom
Current flow numerical simulation,
L. Zhang, et al. (Ames)
13
C. Kurter, et al., arXiv:1008.2020
RF Power Dependence of LSM Photoresponse
in a Corner of the Nb Split Ring
2
~ J RF
Nb film
Quartz
substrate
14
15 dBm
20 dBm
20.6 dBm
20.8 dBm
21 dBm
22 dBm
Future Directions for
Superconducting EIT Metamaterials
Rounded-corner samples for better tunability at high power
Calibrated and de-embedded S21 and group delay measurements
15
Conclusions
Demonstrated Superconducting Metamaterial-Induced Transparency
Tunable with variable Kinetic Inductance and RF magnetic fields
Demonstrated Tunability of EIT features:
Temperature tuning (kinetic inductance → plasmonic regime)
RF Magnetic Field tuning (magnetic Abrikosov vortices, JRF peaks)
Superconducting Metamaterials Review Article (J. of Optics, in press):
arXiv:1004.3226
Work Funded by NSF, ONR.
16
CryoCoolers and CryoPackaging
Small, inexpensive and reliable cryocoolers are available
Stirling cycle cryocooler
+compressor!
MTBF > 106 hours
2.8 kg
92 mm OD x 300 mm
5W cooling power @ 77 K
STI “AmpLink” Filter
1850 – 1910 MHz
PCS band
17
Many companies build
cryo-cooled microwave
and high-speed digital
products
18
Outline
Losses in Metamaterials
Brief Review of Superconductor Electrodynamics
New Features Enabled by Superconductivity
Low loss (+ inductance) enables very compact ‘atoms’
New sources of inductance
New sources of nonlinearity and gain
New ‘Atoms’
Some Novel Applications of Superconducting Metamaterials
Future Prospects + Conclusions
Review article on Superconducting Metamaterials (J. of Optics) arXiv:1004.3226
19
Why Superconducting Metamaterials?
The exciting novel applications of metamaterials:
Flat-slab Imaging
“Perfect” Imaging
RHM
Cloaking Devices
Illusion Optics
Point
source
etc. …
Cloaking
Devices
(Engheta, Leonhardt,
Pendry, Milton)
LHM
RHM
Illusion Optics (Lai)
“perfect image”
… have strict REQUIREMENTS on the metamaterials:
Low Losses
Ultra-small size “atoms” (size << wavelength)
Tunability / Texturing of the index of refraction n
SUPERCONDUCTING METAMATERIALS:
Can achieve these requirements!
20
Flat Lens
Imaging
Outline
Losses in Metamaterials
Brief Review of Superconductor Electrodynamics
New Features Enabled by Superconductivity
Low loss (+ inductance) enables very compact ‘atoms’
New sources of inductance
New sources of nonlinearity and gain
New ‘Atoms’
Some Novel Applications of Superconducting Metamaterials
Future Prospects + Conclusions
21
sn
s1(T)
0
22
0
Tc
T
20 000
15 000
10 000
5000
0
0.99
5000
23
1.00
1.01
1.02
Absorption
150
g2 = 1 x 10-2
100
g2 = 1 x 10-3
50
g1 = 4 x 10-2
0
0.98
0.99
g2 = 1 x 10-7
1.00
Frequency
24
1.01
1.02
10
(n)
(n)
8
n
6
4
2
0
9.5
25
10
10.5
Frequency (GHz)
11
Experimental Results
Metamaterial-Induced Transparency
-6
20.0n
Pinput= -30 dBm,T=4.6K
IFBW=300 Hz
-8
-10
10.0n
This includes
transmission losses
in cold cables and
waveguide
-12
Group Delay (sec)
-14
-16
-10.0n
-18
-20.0n
-20
-22
-30.0n
-24
-40.0n
-26
s21MAG
groupDelay
-50.0n
-28
-30
-32
-60.0n
9.65
9.70
9.75
9.80
9.85
Frequency (GHz)
26
Nb / Cu MM-EIT sample (first generation) in Cu waveguide
9.90
9.95
Transmission |S21| (dB)
0.0
Experimental Results
Metamaterial-Induced Transparency
Switching/Limiting Behavior at High Power
-5
Tbath= 4.24 K
21
(dB)
|S|S21||(dB)
-10
-15
P= -30 dB
P= -10 dB
P= 17dB
P= 18dB
P= 20dB
-20
-25
-30
-35
9.60
The “transparency
window” switches
off between +17 and
+18 dBm
9.65
9.70
9.75
9.80
9.85
Frequency
(GHz)
f(GHz)
27
9.90
9.95
Laser Scanning Microscopy of RF Currents
Principle of the Measurement
Work with A. Zhuravel (Kharkov) and A. Ustinov (Karlsruhe)
modulated
laser
resonator transmission
laser OFF
|S21(f0)|2
laser ON
|S21(f0)|2
f0
Pin
f
D|S12|2 ~ [ JRF(x,y)]2 A 
co-planar resonator f0 ~ 5.2 GHz
Local heating produces a change in
transmission coefficient proportional
to the local value of JRF2
J. C. Culbertson, et al. J.Appl.Phys. 84, 2768 (1998)
A. P. Zhuravel, et al., Appl.Phys.Lett. 81, 4979 (2002)
28
Pout
2-D Response Map for RF Current Distribution
of a Sample
Fundamental resonance mode (5.2 GHz)
8.5 mm
1 mm
10 V
RF photoresponse
~ Jrf2(x, y)
YBCO Ground Plane
Scanned Area
STO
LAO Substrate
RF output
0 V
T = 79.5 K
f = 5.2133 GHz
P = - 6 dBm
29
RF input
YBCO Ground Plane
240 nm thick film
8.5 mm
1 mm
10 V
RF photoresponse
~ Jrf2(x, y)
YBCO Ground Plane
Scanned Area
STO
LAO Substrate
RF output
0 V
T = 79.5 K
f = 5.2133 GHz
P = - 6 dBm
30
RF input
YBCO Ground Plane
240 nm thick film
Standing Wave JRF Pattern at Fundamental Frequency
22
20
DP response, (a.u.)
a.u
Photoresponse
18
T=79.5 K
with 8672 A Generator
P=-6 dBm in scale of 8672A
Fmod=99.99 kHz
f=5.2133 GHz
16
14
12
10
8
6
4
2
0
-2
0
Fit:
PR ~ 16 cos2 (0.39x  4.62)
kfit = 0.39 mm-1
ktheory = 0.42 mm-1
31
1
2
3
4
5
6
7
8
9
X, mm
2D image
Proof that measured PR ~ JRF2 to first order approx.