Transcript LEFT-HANDED NANOCRYSTALLINE MAGNETIC COMPOSITES

Anisotropic negative refractive
index material (NRM)
S. T. Chui
Bartol Research Institute
University of Delaware
Outline:
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Left handed material, existing material
Magnetic composites: a kind of anisotropic NRM
Inverse total internal reflection.
Anisotropic NRM with positive definite permittivity.
Negative refraction and omidirectional total
transmission.
Photonic Hall effect.
Enhanced localization effect at low frequencies.
Research in collaboration with L. B. Hu
and Z. F. Lin.
Chui was partly supported by the
ARMY research lab through the center
of composite studies at the University
of Delaware, by DARPA and by the
NSF.
Left-Handed Materials
Poynting vector S = E£ H
Convention Materials(RHM):
S¢ k > 0
Wave propagates(phase velocity)
in the same direction of energy
flow(k)
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Left-Handed Materials(LHM):
S ¢ k <0
Wave propagates(phase velocity) in
the opposite direction of energy
flow(k)
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Original Idea:
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Negative dielectric constant.
Negative magnetic susceptibility.
Because the velocity of light is inversly
proportional to the square root of the product of
these two susceptibilities, light propagation is not
damped .
This argument focuses on the real parts of the
susceptibilities.
Some references:
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V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968)
J. B. Pendry, A. J. Holden, W. J. Stewart and I.
Young, Phys. Rev. Lett. 76, 4773 (1996).
D. R. Smith, W. J. Padilla, D. C. Vier, S. C.
Nemet-Nasser, S. Schultz, Phys. Rev. Lett. 67,
3578 (2000).
Unusual Physical
Properties
1.
Reversed Doppler effect – microwave radiation or light shift to lower
frequencies as a source approaches and to higher frequencies as it
recedes.
2.
Reversed Cerenkov effect – light emitted in the backward direction
(forward direction in a right-handed materials) when a charged particle
passes through a medium.
3.
Reversed Snell’s law – light that enters a LHM from a normal material
will undergo reflection, but opposite to that usually observed.
4.
Unusual lens:
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Negative index of refraction
From Material to Air
From Air to Material
nmaterial>1
1>nmaterial>0
nmaterial<0
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Current Material
Since these materials are made by microstructure, they are very difficult
to be used
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Magnetic nanocomposite as lefthanded material
Figure .
Proposed structures with (a) metallic nanowires; (b) metal/insulator multilayer nanowires; (c) metallic nanoparticles; (d)
Negative magnetic susceptibility
comes from a resonance
Magnetic susceptibility: In current material, resonance is from a resonantor. Our material: it is from the intrinsic
Ferromagnetic Resonance due to spin waves:
Dielectric constant of metal is negative: damping
1/τ in metallic phase
  1

LHM
2
p
 ( 
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ώ
ώ0
i

)
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magnetic field b and the
macroscopic field h
i   0   hx 
 bx   
b    i    0   h 
 y 
 y
 bz   0
0 1   hz 
The resonance form of the
susceptibilities
m 0  i 
  1
2
2
0  i   0
m0
 
2
2
0  i   0
Magnetic nanocomposites are examples
of anisotropic LHM’s. Its possible
advantages are:
Easier to manufacture.
 Lower loss.
 Magnetization direction can be locally
tuned.
 Anisotropy offers more degrees of
freedom.
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Effective medium approximation result:
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For left handed circularly polarized radiation
propagating along the direction of the
magnetization.
For metal concentration below the conducting
percolation threshold but above the magnetic
percolation threshold.
The direction of energy flow is opposite the
wavevector above the ferromagnetic resonance.
The damping turns out to be small!
Some references:
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S. T. Chui and L. B. Hu, Phys. Rev. B65, 144407
(2002)
S. T. Chui, L. B. Hu and Z. F. Lin, Phys. Lett.
A319, 85 (2003).
An idea that we have used:
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Imaginary parts of the susceptibilities were
included in our calculation. For a given
frequency  there are two possible wave
vectors §k with k=k’+ik’’. The direction of
energy flow is controlled by the imaginary
part of the wave vector.
E=E0 exp (ik’¢ x –k’’x)
For k’’>0 the wave moves in the direction of increasing x;
for k’’<0 the wave moves in the direction of decreasing x
Imaginary wave vector reamins small
and does not change sign (energy flow
direction is unchanged)
C
C
#
-7
2.0x10
(b)
-7
1.5x10
=0.5
-7
1.0x10
Im(keff)
-8
5.0x10
=1.0
0.0
0
2
4
6
8
10
12
/0
14
16
18
20
Real wave vector becomes
negative
Re(keff)
6.0x10
-4
4.0x10
-4
2.0x10
-4
(a)
=1.0
0.0
=0.5
-4
-2.0x10
0
2
4
6
8
10
12
14
/0
Fig.1(b)
16
18
20
Crucial physics
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At the resonance, the relative sign
between the real and the imaginary part of
the wave vector changes.
Terminology: Positive definite
(indefinite) dielectric constants
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Positive definite: all i are positive.
For anisotropic materials with indefinite
susceptibilities, NRM and LHM conditions are
different:
 E- polarized wave satisfy k . E=0
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For E-polarized wave in materials with uniaxial
anisotropy perpendicular to the plane normal, xy<0
implies LHM; z<0 implies NRM provided additional
constraints on the angles are satisfied.
A similar set of conditions applies for H-polarized
waves.
Similar relationships exist when the axis is parallel to
the interface.
References:
 L. B. Hu, S. T. Chui and Z. F. Lin, Phys. Rev. B66,
085108 (2002).
 V. Lindell et al., Microwave and Opt. Tech. Lett. 31,
129 (2001)
 D. R. Smith and D. Schurig, Phys. Rev. Lett. 90,
077405-1, (2003).
 L. Zhou, C. T. Chan and P. Sheng, Phys. Rev.
B68,115424 (2003).
Inverse total internal reflection
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Under some
conditions, light will
go through only if the
angle of incidence t is
smaller (not larger!)
than some critical
value
Sometimes reentrant
behaviour can also be
exhibited.
t
Anisotropic materials with positive definite
susceptibilities can also exhibit negative
refraction
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Y. Zhang, B.
Fluegel and A.
Mascarenhas,
Phys. Rev. Lett.
91, 157404 (2003)
Twinned
anisotropic YVO4
crystal on both
sides.
Idea behind negative refraction in
anisotropic material
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Geometry of refraction shown on
top, with the direction of the
anisotropy axis as illustrated.
Constant frequency contour in
wavevector space shown in lower
graph. Solid and dashed lines are
for opposite sides
Group velocity is the normal to
this curve.
X component of the wave vector
is conserved.
As illustrated Si and St, the
incident and transmitted energy
flow exhibit negative refraction.
Illustrative results from a
quantitative analysis
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Range of incident angle
(between the solid and the
dashed curves) for negative
refraction.
The anisotropy parameter
u=(1-2)/1; =(1,1,2).
Lower curve is for only one
side anisotropic
Top curve is for both sides
anisotropic
Z. Liu, Z. F. Lin and S. T.
Chui, Phys. Rev. B69,
115402 (2004).
Multilayer structure as negatively
refracting material
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Incoming direction,
surface normal and
anisotropy axis in the
same plane.
Omidirectional total transmission
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When the dielectric
constants on the left and
the right satisfies certain
conditions, all incoming
radiation will be
transmitted, none will be
reflected.
Photonic Hall Effect:
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Mie scattering by magnetic particles:
r£r£(s -1¢BI )- ks2BI=0.
As the magnetization is reversed, ’ changes
sign.
bx    i  0  hx 
b    i   0  h 
 y 
 y
bz   0 0 1   hz 
Mie scattering of magnetic
particles
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BI=n,m dmnMmn(1)(k,r)+ cmnNmn(1)(k,r), not a
function of L because r¢ B=0
r£r£ N(J)mn - k2 N(J)mn =0,
M(J)mn = r £ N(J)mn /k
The usual bais function satisfies the equations:
r¢ M(J)mn=0,
r¢ N(J)mn=0,
r£ L(J)mn=0.
Photonic Hall effect: F(,)=
d(,)/d}|-d(,)/d}|=0.
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Polar plot of magnetotransverse cross section F(,)
at =/2 for two values of .
Solid line (dotted line) denotes
positive (negative) values for
F(,).
The applied magnetic field is in
z direction (normal to the plot)
and incident wave vector in x
direction.
Phys. Rev. E69, 056614
(2004).
Localization of light can be
enhanced by left-handed material
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To enhance localization, the parameter
=kl should be reduced. Here l , the mean
free path is inversely propotional to the
impurity scattering cross section .
For a spherical impurity of radius a,  / x4
when x=ka <<1. Hence / 1/x3 for small x.
It is difficult to localize light in the long
wavelength limit.
Enhanced localization
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For left-handed material,
there are scattering
resonance at low
frequencies.
P/ E/(+2). When =-2, P is
very big
E
Enhanced localization: More
detailed calculation
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(a)  and  of the NIM
(b) The efficiency for
scattering Q_s vs
frequency.
(c) The inverse of the
localization parameter
1/kl vs frequency.
Phys. Rev. E69,
016619 (2004)
Possible LHM Base on
Nanomagnetic composite
Equation of motion:
Wave equation:
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dM
dM
 rM  H eff  dM 
dt
dt
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H eff  H 0  h (t )

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B
 E  
t



B  B 0  b (t )



B  M  0 H
k
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Possible LHM Base on
Nanomagnetic composite
i ' 0  hx 
 bx   
  
 
 by     i '  0  hy 
b   0
 h 
0
1
 z   
 z 

ik  E  ih

k     (   ' )
 m ( 0  i )
2
( 0  i ) 2   0
 m 0
' 
2
( 0  i ) 2   0
  1
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may be negative
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Granular Materials and
Fabrication
• Granular materials (films, and bulk materials)
Insulating:
Teflon
Magnetic:
NiFe
Ferrites
Metallic
• Thin Films: Vapor deposition (magnetron Sputtering)
• Bulk Materials: Ball milling, chemical synthesis, and
microcompounder (arriving in Oct.-Nov.)
• FeNi: Low loss, resonant frequency can be tuned with
composition, and large negative permeability.
• Teflon: Low loss and low dielectric constants
(Bulk materials have been sent out for fabrication a month ago and
will arrive soon. Granular films have been fabricated)