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 (m3q)

    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 1A 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=1m

  • 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