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Simulation of Split Ring Resonator
(SRR) at Optical Frequencies
October 2007
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Split Ring Resonator (SRR)
Glass substrate: 15nm, =2.25
ITO film: 5nm, =3.8
Gold: Drude model:
p=1.367e16 (rad/sec)
c=6.478e13 (rad/sec)
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Gold
ITO
d
b
h
a
Lx
a
Ly
Glass
Lx = 315nm
Ly = 330nm
a = 200nm
b = 80nm, 90nm
d = 70nm
h = 30nm
The parameters are based on the work of Enkrich et al [1] and Burger et al [2]
October 2007
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Simulation Setup
• Drude model used (via “drude” command, version 4.6) to calculate the complex
permittivity of gold
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 p2
 ( )  1 
 (  ic )
• PML2 command (“pml2”, version 4.6) used to terminate the absorbing
boundaries in z direction
• Enhancements to standard PML command: (1) automatically optimize PML
parameters, (2) run faster in FDTD iterations
• Allowing boundaries to be placed closer to scattering objects to reduce simulation
domain size and, therefore, save memory and run time
• Yee cell size = 5nm
• The following effects are simulated
x

y
• Angle of incidence (theta, phi)
• S-polarization
• Dimension b (80nm, 90nm)
October 2007
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
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Transmission Calculation
• The transmission through SRR is calculated as follows
T
I NoSRR
INoSRR is the e-field intensity of 0-order transmitted planewave w/o gold SRR.
ISRR is the e-field intensity of 0-order transmitted planewave w/ gold SRR.
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I SRR
• The “scat_func” command with “ft=true” option is used to compute
diffraction orders of the transmitted field
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Effects of b
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transmission
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theta = 0 degree, phi = 90 degree
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
700
x
E
y
b=80nm
b=90nm
900
1100
1300
1500
1700
1900
wavelength, nm
Mie resonance [1,2]
October 2007
Magnetic resonance [1,2]
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Effects of Incident Angles
E
phi = 0 degree, b = 90 nm
x
1
0.9
y
0.8
transmission
0.7
0.6
theta = 0 deg
0.5
theta = 60 deg
0.4
Magnetic
resonance [1,2]
0.3
0.1
0
600
800
1000
1200
1400
1600
1800
2000
wavelength, nm
E
phi = 90 degree, b = 90 nm
x
1
0.9
y
0.8
0.7
transmmison
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0.2
0.6
theta = 0 degree
0.5
theta = 60 degree
0.4
0.3
0.2
0.1
0
600
800
1000
1200
1400
1600
1800
2000
wavelength, nm
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References
[1] Enkrich et al, “Magnetic Metamaterials at Telecommunication and Visible Frequencies,”
Physical Review Letters, PRL 95, 203901, 11 Nov. 2005
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[2] Burger et al, “Numerical Investigation of Light Scattering off Split-Ring Resonators,”
Metamaterials, Proc. of SPIE Vol. 5955, 595503, 2005
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