# carbon nanotube as a terahertz delay nano nano --- traveling wave tube, backward wave oscillator,...

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June 9, 2011, Crete, WavePro

Carbon Carbon NanotubeNanotubeCarbon Carbon NanotubeNanotube as 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 @ [email protected]@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 challenge is 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

1 τ

3 τ

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

Rc

a

2 τ

SWCNT (m,n)

Rc=ma1+na2 a

2

a 1 e

�

a 2

B Ph l PBasic Physical Properties Length: 1-10 mkm Diameter: 1 3 nmDiameter: 1-3 nm Conductivity type: metallic or semiconductor Current-carrying capacity: 109-1010 A/cm2y g p y Free pass length: 0.1-10 mkm Thermal 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

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

)( *cccc RReEieE

.])()([

,)(

cvvccvvvccccvvcvz cv

z cv

vccvcvcvz z

z

iRRReEi p

eE t

RReE p

eE t

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 band zigzag 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

co nd

uc tiv

ity

1

(m m) CNTs c on

du ct

iv ity

0,01

0,1

or

m al

iz ed

a xi

al c

2 1: Metallic CNs (m=3q) 2: Semiconducting CNs (m3q)

10 (m,m) CNTs

rm al

iz ed

a xi

al

Conductivity of zigzag metallic CNT in the range

0 20 40 60 80 100 120 140 1E-3

no

m 0 50 100 150 200 250 300

1 no

r

m 15

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

xi al

c on

du ct

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

no rm

al iz

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 01 ,(1 / ) zz z RR RH H Ek i z c p

dispersion parameter l0 ~ 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

k h k

c vph

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

CN (9,0)

102 2 |Im()|

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~0.02~0.02pp DispersionlessDispersionless surface wavesurface wave nanowaveguidenanowaveguide

Monomolecular traveling wave tubeMonomolecular traveling wave tube TerahertzTerahertz range antennarange antenna

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

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

100

102 2 Thermal Thermal antennaantenna

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

10-2 1A spontaneous decay rateA spontaneous decay rate

controller 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=m Because 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 resonance lines due to first two optical transitionslines due to first two optical transitions of the semiconducting SWCNTs coincide reasonably well with the experimental 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

z Relativistic 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 modif