June 9, 2011, Crete, WavePro

Carbon Carbon NanotubeNanotubeCarbon Carbon NanotubeNanotubeas as a Terahertz Delay Line: a Terahertz Delay Line: yy

Manifestations and Potentiality Manifestations and Potentiality in in NanoelectromagneticsNanoelectromagneticsNanoelectromagneticsNanoelectromagnetics

Sergey Maksimenko, G. Ya. Slepyan Institute for Nuclear Problems,

B l St t U i itBelarus State University, Minsk, Belarus

k i k @ ilk i k @ ilsergey.maksimenko@gmail.comsergey.maksimenko@gmail.com

MotivationMotivationMotivation

Milestones in the development of electrodynamics have always been related to practical problems arising from new ideas relating to the transmission and processing of electromagnetic signals.

Advances in quantum electronics led to the development of the theory ofAdvances in quantum electronics led to the development of the theory of open quasi-optical resonators.

The implementation of the fiber optic communication led to the development of the theory of open dielectric waveguides.

Progress in microwave microelectronics stimulated research on the electrodynamics of microstrips and other planar structureselectrodynamics of microstrips and other planar structures.

Metamaterials and plasmonic structures initiate new exciting steps in electrodynamicselectrodynamics. Simulation of electromagnetic processes on nanoscale is one of the main research directions for modern electrodynamics.

— NANOELECTRODYNAMICS —

is currently emerging as a synthesis of macroscopic electrodynamics and microscopic theory of electronic properties of different nanostructures

Diffraction Theory Condensed Matter Physics

microscopic theory of electronic properties of different nanostructures.Electromagnetic field diffraction Confinement of the charge carrier motion

Boundary-value problems Quasi-particle concept:

Diffraction Theory Condensed Matter Physics

for complex-shaped regions: Complex geometry, ordinary electronics

Electrons, phonons, magnons… Complex electronics, ordinary geometry

NANOELECTRODYNAMICS

The present-day challengeis to incorporate into the theory a complex character of the charge carriers is to incorporate into the theory a complex character of the charge–carriers

dispersion and inhomogeneity of electromagnetic field on the nano(subwavelength) scale.

CARBON NANOTUBECARBON NANOTUBECARBON NANOTUBE( 0) i

1τ

3τ

e||

(m,0) - zigzag,(m,m) - armchair

Rc

a

2τ

SWCNT (m,n)

Rc=ma1+na2

a2

a1 e

�

a2

B Ph l PBasic Physical PropertiesLength: 1-10 mkmDiameter: 1 3 nmDiameter: 1-3 nmConductivity type: metallic or semiconductorCurrent-carrying capacity: 109-1010 A/cm2y g p yFree pass length: 0.1-10 mkmThermal conductivity: 2500-6600 W/mK (~1000 for diamond)

nanoelectromagneticsnanoelectromagneticsnanoelectromagnetics

Theoretical modeling of the CNT conductivity is Theoretical modeling of the CNT conductivity is the crucial problem in thethe crucial problem in the electrodynamics of electrodynamics of

CNTCNTCNTsCNTsThis problem is analyzed by the system of kinetic equations for the density matrix:

)( *cccc RReEieE

.])()([

,)(

cvvccvvvccccvvcvzcv

zcv

vccvcvcvzz

z

iRRReEip

eEt

RReEp

eEt

h i th f f th t iti + 1 d i d

zpt

where, is the frequency of the transition, ρυυ + ρcc = 1, and indexes v and c correspond to π-electron in the valence and conduction bands,respectively.

vc

Dynamical conductivity of CNT

The CNT conductivity below the optical transitions bandzigzag amchairW ll k t f i

100 100

zigzag amchairWell-known property of zigzag CNTs to be metallic or semicon-ducting dependently on the radius

1

10

100(m,0) CNs

cond

uctiv

ity

1

(m m) CNTs con

duct

ivity

0,01

0,1

or

mal

ized

axi

al c

21: Metallic CNs (m=3q)2: Semiconducting CNs (m3q)

10(m,m) CNTs

rmal

ized

axi

al

Conductivity of zigzag metallic CNT in the range

0 20 40 60 80 100 120 1401E-3

no

m0 50 100 150 200 250 300

1no

r

m15

20

CN (9,0) 1: Re(zz)2: Im( )tiv

ity

metallic CNT in the range of interband transitions

0

5

10

2

1

2: Im(zz)

ed a

xial

con

duct

The axial conductivity based on

Slepyan et al., PRB 1999

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5-10

-5

norm

aliz

e

The axial conductivity, based on quantum transport theory

Effective boundary conditions for CNTs

2

0 41 l H H E

Spatial

нм142.0,, cn bRb In optical rangeIn optical range

02 2 2 0 0

1 ,(1 / ) zz z RR R

H H Ek i z c

pdispersion parameterl0 ~ 10-5 for

0 0 , 0 , 0| | 0, | | 0z R z R z R z RH H E E metallic CNTs

Solution of the conductivity problem accounting for the spatial confinement Solution of the conductivity problem accounting for the spatial confinement couples classical electrodynamics and physics of nanostructurescouples classical electrodynamics and physics of nanostructures

Nanoelectromagnetics

Complex valued slow wave coefficient Complex-valued slow-wave coefficient for a polar-symmetric surface wave hih

khk

cvph

104 1: Re()2: -Re()/Im()

CN (9,0)

102 2 |Im()| << Re()

100

11 THz 100 THz

|Im()| << Re()

1E-8 1E-7 1E-6 1E-5 1E-4 1E-3 0,0110-2

1

kbb=0.142 nm is the C-C bond length

axial component of the axial component of the timetime--averaged Poynting averaged Poynting vector for surface wavevector for surface wave

What can we learn from the picture?What can we learn from the picture?What can we learn from the picture?

CARBON NANOTUBE as an EM device (mostly in THz range):(mostly in THz range):Electromagnetic Electromagnetic slowslow--wave linewave line:: vvphph//cc~0.02~0.02ppDispersionlessDispersionless surface wavesurface wave nanowaveguidenanowaveguide

Monomolecular traveling wave tubeMonomolecular traveling wave tubeTerahertzTerahertz range antennarange antenna

104 1: Re()2: -Re()/Im()

CN (9,0)TerahertzTerahertz--range antennarange antenna InterconnectsInterconnects

100

102 2Thermal Thermal antennaantenna

A t d tA t d t1E-8 1E-7 1E-6 1E-5 1E-4 1E-3 0,01

10-2

1A spontaneous decay rateA spontaneous decay ratecontroller controller

Long wavelength limit: geometrical resonancesLong wavelength limit: geometrical resonancesLong wavelength limit: geometrical resonances

A vibrator antenna radiates effectively if its length equals to an integer number i i kof halfwaves; for perfectly conducting wire it is kL=m, m=1,2,3…..

Geometrical resonances: hL=mGeometrical resonances: hL=mBecause of the large slow-wave effect, h/k=c/vph=1/~50, at optical lengths ~ 1 mkm the geometrical resonances are shifted to THz

CNT – terahertz antenna!L=1m

Experimental observations of THz peak Experimental observations of THz peak Experimental observations of THz peak ininin CNTCNTCNT---based compositesbased compositesbased composites

Phys. Rev. B 74, 045431 (2006)

Bommeli F., et al. Synt. Met. 86, 2307 (1997).

(b) Real part of the conductivity together with the Drude and Lorentz contributions to the overall fit (solid line). T K f th h t t l (b)T. Kampfrath, phys. stat. sol. (b) 244, No. 11, 3950–3954 (2007)

Comparison with experiment: THz peak

The predicted amplitudes of resonancelines due to first two optical transitionslines due to first two optical transitionsof the semiconducting SWCNTscoincide reasonably well with theexperimental values.p

12

NANO NANO NANO --- Traveling wave tube, Backward wave oscillator, Free Traveling wave tube, Backward wave oscillator, Free Traveling wave tube, Backward wave oscillator, Free electron laser: basic ideaelectron laser: basic ideaelectron laser: basic idea

300MHz –300GH

zRelativistic electron beam

is the lasing medium

300GHz

Traveling-wave tubesTraveling-wave tubes,R Kompfner 1952 Rep. Prog. Phys. 15 275-327

The main elements of a TWT are

•Large slow-down: 1/b > 100•Ballistic electron motion

The main elements of a TWT are (1) an electron gun, (2) a focusing structure that keeps the electrons

in a linear path, p ,(3) slowing-down system(4) an electron collector

Intrinsic properties of CNTsIntrinsic properties of CNTsIntrinsic properties of CNTs

It is well-known, that electron beam at certain conditions can emit radiation In systems which modify photon states and slow down electro-magnetic wave (Cherenkov, Smith-Purcell, quasi-Cherenkov mechanisms);

In systems which modify electron states (undulator, synchrotron and gyrotron systems)

Combination in CNTs of three key properties,

a strong slowing down of surface electromagnetic waves,a strong slowing down of surface electromagnetic waves, ballisticity of the electron flow over typical CNT length, and extremely high electron current density,

allows proposing them as candidates for the development of nano-sized Chernekov-type emitters – nano-TWT, nano-BWO and nano-FEL.

Threshold current and instability Gain per unit length is t l l increment of generationextremely large compa-

ring with macrodevices

j=1010 A/cm2

L= 10 – 30 m

Radiation generation isRadiation generation isalready possible at the already possible at the already poss ble at the already poss ble at the current stage of the current stage of the nanotechnology developmentnanotechnology development

Thermal radiation from a single-wall CNT

MotivationMotivationMotivationMotivationNoise properties and operational limits of CNT based devices are substantially determined by the thermal fluctuations of electromagnetic field

(a) Thermal radiation spectra of metallic (15,0) CNT in the cross-section z0=0. The CNT polarizability is given on the inset.

(b) Thermal radiation from CNT (solid line) and black--body radiation (dashed line) in the near--

The presence of singled out resonances

field zone.

p gillustrated by Fig. (a) allows us to propose metallic CNTs as far-field and near-field thermal antennas for the terahertz rangethermal antennas for the terahertz range

Where we go?Where we go?Where we go?• Nano scale circuits components

Functionalized, filled, coated and doped CNTs, MWCNTs CNT bundles telescopic junctionsMWCNTs, CNT bundles, telescopic junctions, nanorings, ribbons, etc.

• CNT-based composites and metamaterialsCNT based composites and metamaterialsMaxwell Garnet theory accounting for the length anddiameter dispersion and percolation effect, regularstructuresstructures

• Instabilities in CNTsmonomolecular travelling wave tube, nanoFELmonomolecular travelling wave tube, nanoFEL

• Photothermal effectElectromagnetic heating of CNTs and CNT thermo-g gdynamics, heat transfer on nanoscale

• A theory of quantum circuitsP ll ff t lif tiParcell effect, lifetime,

Acknowledgments

I would like to thankI would like to thank ourour coco--workers from the Institute forworkers from the Institute forI would like to thank I would like to thank ourour coco workers from the Institute for workers from the Institute for

Nuclear Problems, BSU, MinskNuclear Problems, BSU, Minsk

KonstantinKonstantin BatrakovBatrakov PolinaPolina KuzhirKuzhir MikhailMikhail ShubaShubaKonstantin Konstantin BatrakovBatrakov, , PolinaPolina KuzhirKuzhir, Mikhail , Mikhail ShubaShuba

and our international collaboratorsand our international collaborators

AkhleshAkhlesh LakhtakiaLakhtakia Christian Thomsen George HansonChristian Thomsen George Hanson

S f h R h

AkhleshAkhlesh LakhtakiaLakhtakia, Christian Thomsen, George Hanson , Christian Thomsen, George Hanson

Support of the Research:

ISTC ISTC ((Intern. Intern. Science and Technology Center)Science and Technology Center)ISTC ISTC ((Intern. Intern. Science and Technology Center)Science and Technology Center)ВВ--17081708

EU FP7 EU FP7 266529266529 BYBY--NanoERANanoERA

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