Left Handed Maxwell Systems
PART-5
Basic Theory of Small Resonators
SAMEER
Shantanu Das
RR&PS
Reactor Control Division, B.A.R.C. Mumbai-400085
shantanu@barc.gov.in

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Magnetic Activity
Magnetic activity in most materials tends
to ‘tail-off’ at high frequencies of even
few Giga-Hertz!
It is therefore challenge to get, magnetic
activity let alone negative permeability,
at micro-wave frequencies and higher.
Landau and Lifschitz (1984) gave a
general argument that magnetic activity
arising from atomic orbital currents
should be negligible at optical frequency
if one neglects the polarization currents
Here is
J
not usual current density
in units, but is
2
A / m
A / m
r
J
Around the cylinder
H
d
2
e m f =
μ H ( π r )
0
d t
d r o p = J ( 2 π r ) ρ
Per meter

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Diamagnetism
. . . . . . . . (1 )
Diamagnetic effective medium is also
obtained with percolation metallo-dielectric
composites.
In case of nano-metallic structures, the
magnetic moments of induced real &
displacement current distributions can actually
contribute to an effective magnetism at
high and very high frequencies if the electric
polarizabilty of corresponding medium is
. . . . . . . . ( 2 )
small.
d
2
2
e m f =
μ H (π r ) = jω π r μ H
0
0
d t
. . . . . . . . ( 3 )
d r o p = J ( 2 π r ) ρ
ρ : R e s i s t i v i t y
(1 ) ( 2 ) & ( 3 )
In this case of cylinders, the induced current
made it appear as if magnetic monopole were
flowing up down the cylinder. But the problem
was that system only had inductive response
(the monopoles had no inertia). By introducing
capacitive elements into the system (inter-ring
and gap) a ‘rich resonant’ response could be
induced.

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Split Ring Resonator (SRR)
The SRR works on principle of the
magnetic field of EM radiation, can
drive a resonant LC circuit, through
inductance, and this results in
dispersive effect of magnetic
permeability.
The induced currents flow in the same
direction in both the rings , accumulating
charges at the gaps in the rings.
The large gap in each ring prevents the
currents from flowing around in a
single ring, and circuit is completed
across the inter-ring capacitance.
C = ε επ r / 3d
0
Inter-ring C Farads/angle or F/m.
2
2
F = π r / a
F
is ‘filling-factor’, crucial in designing
SRR.

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Magnetic Plasma Frequency
2
2
π r / a
μ = 1 −
2
2
3
1 − (3d / μ ε επ ω r ) + j (2 ρ / μ ω r )
0
0
0
2
F ω
= 1 + 2
2
ω − ω − jΓω
0
= Re(μ ) + j Im(μ )
R e( μ )
M a g n e ti c P la s m a
F
f r e q u e n c y ω
1
m
1 − F
ω
F
F
F

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Dispersion diagram
A magnetic plasma wave!!
Well magnetic surface plasmon polaritons
at the interface of MNG at that band of
frequency
ω
ω = kc
ω m
M a g n e t i c P l a s m a
ω
M N G
0
M a g n e t i c R e s o n a n c e
ω p
E l e c t r i c P l a s m a
E N G
k

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Electric dipole formation in
SRR

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SRR Electric Dipole
( O u t e r )
P x
( I n n e r )
P x
( T o t a l )
P x

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Polarizabilty of SRR

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Bianisotropy

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