Anisotropic negative refractive index material (NRM)

S. T. Chui

Bartol Research InstituteUniversity of Delaware

Outline:

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.

CMR2UD MAGNETS

Convention Materials(RHM): Left-Handed Materials(LHM):

Wave propagates(phase velocity) in the same direction of energy flow(k)

Wave propagates(phase velocity) in the opposite direction of energy flow(k)

Left-Handed Materials

Poynting vector S = E£ H

S ¢ k <0S¢ k > 0

Original Idea:

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:

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).

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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:

Unusual Physical Properties

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From Material to Air From Air to Material nmaterial>1

1>nmaterial>0

nmaterial<0

Negative index of refraction

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Current Material

Since these materials are made by microstructure, they are very difficult

to be used

Magnetic nanocomposite as left-handed material

Figure . Proposed structures with (a) metallic nanowires; (b) metal/insulator multilayer nanowires; (c) metallic nanoparticles; (d) compacted metallic nanoparticles; and (e) metallic needles embedded in a dielectric matrix.

CMR2UD MAGNETS

)(1

2

ip

Dielectric constant of metal is negative: damping 1/τ in metallic phase

ώ

LHM

ώ0

Magnetic susceptibility: In current material, resonance is from a resonantor. Our material: it is from the intrinsic Ferromagnetic Resonance due to spin waves:

Negative magnetic susceptibilitycomes from a resonance

Relationship between the magnetic field b and the macroscopic field h

0

0

0 0 1

x x

y y

z z

b i h

b i h

b h

The resonance form of the susceptibilities

02 2

0 0

02 2

0 0

1 m

m

i

i

i

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.

Effective medium approximation result:

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:

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:

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 smalland does not change sign (energy flowdirection is unchanged)

0 2 4 6 8 10 12 14 16 18 20

0.0

5.0x10-8

1.0x10-7

1.5x10-7

2.0x10-7

(b)

Fig.1(c)

=0.5

=1.0

C C ###

Im(keff

)

/0

Real wave vector becomes negative

0 2 4 6 8 10 12 14 16 18 20

-2.0x10-4

0.0

2.0x10-4

4.0x10-4

6.0x10-4

Fig.1(b)

Re(keff

)

(a)

=1.0

=0.5

B B ### ###

/0

Crucial physics

At the resonance, the relative sign between the real and the imaginary part of the wave vector changes.

Terminology: Positive definite (indefinite) dielectric constants

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 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

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

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

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

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

Incoming direction, surface normal and anisotropy axis in the same plane.

Omidirectional total transmission

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:

Mie scattering by magnetic particles: r£r£(s -1¢BI )- ks

2BI=0. As the magnetization is reversed, ’ changes

sign.0

0

0 0 1

x x

y y

z z

b i h

b i h

b h

Mie scattering of magnetic particles

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.

Polar plot of magneto-transverse 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

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

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

(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)

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Equation of motion:

)(0 thHH

dt

MdMdHMr

dt

Md

eff

eff

Wave equation:

)(0 tbBB

t

BE

HMB

0

k

Possible LHM Base on Nanomagnetic composite

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z

y

x

z

y

x

h

h

h

i

i

b

b

b

100

0'

0'

)'(

k

hiEki

20

20

0

20

20

0

)('

)(

)(1

i

i

i

m

mmay be negative

Possible LHM Base on Nanomagnetic composite

• Granular materials (films, and bulk materials)

• 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

Magnetic:

NiFe

Insulating:

Teflon

Metallic

Ferrites

Granular Materials and Fabrication

(Bulk materials have been sent out for fabrication a month ago and will arrive soon. Granular films have been fabricated)