three-component gyrotropic metamaterial · 2017. 2. 2. · condensed matter physics-2015...

International Conference and Exhibition on Mesoscopic and

Condensed Matter Physics-2015

Three-component gyrotropic metamaterial

Igor Tralle

22-24 June, 2015 Boston

2015-07-30

Outline

Introduction

The model

Calculation of effective permeability

Calculation of effective permittivity

Results of computer simulations

Conclusions

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According to W. Cai and V. Shalaev, Optical

Metamaterials: Fundamentals and

Applications (Springer-Verlag, Berlin, 2010),

the term “metamaterials” can be used in a

more general,as well as in a more specific

sense. In the more general sense, these are

materials possessing “properties unlike any

naturally occurring substance” or simply “not

observed innature.” More specifically, these are

the materials with a negative refractive index,

whose existence and properties

were discussed for the first time by V. Veselago.

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Wenshan Cai, V. Shalaev, Optical Metamaterials,Springer 2010

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,Wenshan Cai, V. Shalaev, Optical Metamaterials,Springer 2010

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We consider medium whose structural

components sizes are of the order of or

greater than the wavelength λ of waves

propagating in the medium. In an isotropic

medium, the frequency ω depends only on

the absolute value of the wave vector k=|k|,

and therefore the group velocity of the wave

packet is co-directed with

either k or -k, depending on the sign of .

dk

kd

k

k

kd

kdvg

)()(

dk

kd )(

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Dielelctric function of the mixture Ag +

dielectric (silica)

The model

frequency

ferromagnetic resonans

anomalous dielectric dispersion

The model

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We considerthe mixture of the threeingedients:1. Silver2. Hg(1x)Cd(x)Te3. Ferromagnetic

nanoparticles

Effective maganetic permeability of the

composite: Bruggemann theory

Since

where 2112 fff

The model

The total magnetization of a single metallic particle can be define

as:

Hem 00

where:- the magnetic moment of the grain,- the unit vector along the direction of - the magnetic polarizability of the particle,- the external magnetic field.

00e

H

0

The model

"'3/4 3 ia

)2cos()2cosh(

)2sin()2sinh(1

16

9"

)2cos()2cosh(

)2sin()2sinh(1

2

31

8

3'

2 xx

xxx

x

xx

xx

x

where:

here πσωc=δ,δ

a=x 2/ is the skin depth, c is the speed of light in vacuum,

σ is the conductivity of a metallic grain.

The model

nmam 50,10 116

Assuming conductivity of the metallic nano-particles

and for the frequencies up to ω ~ 1014 Hz

we have for the α′ and α′′ the next expressions:

2

2

4

224

10"

105

4'

c

a

c

a


We consider the hypotetical material in an external magnetic field:

),(0 thHH

Where is the time-dependent magnetic field of electromagnetic wave, propagating in the medium.

The equation of motion is of the form:

,HMdt

Md

where is the gyromagnetic constant.

)(th

In the external magnetic field an averaged magnetic moment of the unite volume of such medium is:

0H

The model

The magnetic moments of single-domain nano-particles at room temperature are distributed at random and we can describe their behaviour in the framework of Langevin theory of paramagnetism.

,000 HM

where:

,3/2

00 TkN Bnmg

Nmg-n - the concetration of magnetic nano-particles,kB - Boltzmann constant,T - temperature.


m

hHHkmi

000

hGihm

where:

21

2

00 ~

1~1

2i0

21

0 ~1

~1

2H

iG

here:

is the component of perpendicular to ,h

th

0H

),,0,0( 00 HH

),,0,0( GG

1 ,2~ 22

01 i ,2~ 22

02 i 00 H

-is the component of perpendicular to

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Now we are searhcing for the parameters, T tempe-rature, B magnetic field, r radius of the ferromagnetic nanoparticles, x concentration of Cd in -compound, the volume filling factors, to get

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Effective dielectric permittivity: Briggemann theory:

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321 ,, are the dielectric permittivities of the components

is the dielectric permittivity of the composite

321 ,, fff the percentage of the components in a mixture

Dielectric function of particular components

1. Silver

A silver is a metal, its dielectric function we calculate fromDrude model:

2

1

2

1

i

P

where:

∞ = 5.00 is the permittivity in the limit of very high frequencies,

ωP ~ 14.00 ×1015 Hz is the plasma frequency,

1 ~ 0.032 ×1015 Hz is the damping constant.

Energy gap of mercury cadmium telluride vs

cadmium concentration

-is the conductivity,

- is the damping constant

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Conductivity depends on carrier concentratuon and mobility.

Concentration depends on temperature and energy gap

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Dielectric permittivity of theferromagnetic nanopartilces

Typical values of the dielectric permittivity of

manganese based ferromagnetics :

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Computer simulations

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We are searching for the corresponding values of the next

parameters

T – temperature

B - magnetic field

r – radius of the ferromagnetic nanoparticles

|m| - magnetic moment of the nanoparticle

x – cadmium concentration in the Hg1-xCdxTe – compound

f1, f2 , f3 concentrations of the components in a mixture

with the additional constrains:

0]Im[,0]Im[,0][Re,0)]([Re

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I. Tralle, P. Zięba and W. Paśko, J. Appl Phys 115, 233509 (2014)

Results of the simulations

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Thank you for your attention!

Collaboration: Dr Paweł Zięba and Dr Wioletta Paśko, my former PhD students

three-component gyrotropic metamaterial · 2017. 2. 2. · condensed matter physics-2015...

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