Nano-sized electromagnetic source on the principles of Free

Electron Lasers

K.G.Batrakov, P.P.Kuzhir S.A.Maksimenko

The main principle of Free Electron Laser (FEL) operation

The work produced by electromagnetic wave on the electron:

Electron trajectory

Electromagnetic field

Cherenkov synchronism condition:

Slowing down systems (TWT, BWO, Cherenkov Lasers: resonators and waveguides change electromagnetic wave properties and decrease it phase velocity,

Destructive interference diminishes A. So, bunching of electron beam is necessary.

Structure factor:

Pump wave:

Trajectory perturbation by pump wave

Induced by the pump wave perturbation of velocity

CARBON NANOTUBE –quasi-one-dimensional carbon macromolecula

Graphene crystalline lattice SWCNT (m,n)

Rc=ma1+na2(m,0) for zigzag CNT(m,m) for armchair CNT

Unrolled circumferential vectors c for a (4,4) armchair nanotube (blackarrow), a (4,0) zigzag nanotube (blue arrow) and a chiral (4,2) nanotube (red arrow) areshown on a graphene plane. a1 and a2 are the unit cell vectors of graphene. The chiralangle and the translational periodicity vector ` of the (4,2) nanotube (green arrow)are also shown. Dashed lines indicate the area spanned by c and ` which correspondsto the unrolled unit cell of the (4,2) nanotube.

Structural parameters and isogonal point group of nanotubes . d is the tube diameter, n is the greatest common divisor of (n1,n2), and q is the number of carbonhexagons (2 C atoms) per unit cell. a0 is the in-plane lattice constant of graphite.

(8,0), (8,2), (8,4), and (8,8) nanotubes with 32, 56, 112, and 32 atoms in the unit cell (indicated in black), respectively.

Some exceptional properties of nanotubes and conventional materials for comparison.(P. G. Collins and P. Avouris, \Nanotubes for electronics", Sci. Am. 283, 62 (2000))

NanoelectromagneticsComplex-valued slow-wave coefficient for

a polar-symmetric surface wave

1E-8 1E-7 1E-6 1E-5 1E-4 1E-3 0,01

10-2

100

102

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

CN (9,0)

2

1

kb

1 THz 100 THz

b=0.142 nm is the C-C bond length

|Im()| << Re()

k k

h h ih

Dispersionlesssurface wave nanowaveguidein the IR range

Light emission in CNTs

EELECTRIC-FIELD-INDUCED LECTRIC-FIELD-INDUCED HEATING OF THE ELECTRON GASHEATING OF THE ELECTRON GASO. Kibis, M. Portnoi, Carbon nanotubes: A new type of emitter in the terahertz range, Technical Physics Letters. V.31. p. 671 (2005)

IMPACT IONIZATIONIMPACT IONIZATION

J. Chen, V. Perebeinos, M. Freitag, J. Tsang, Q. Fu, Jie Liu, Ph. Avouris, Bright Infrared Emission from Electrically Induced Excitons in Carbon Nanotubes, Science 2005, Vol. 310. no. 5751, pp. 1171 - 1174

CHERENKOV RADIATION CHERENKOV RADIATION MECHANISMMECHANISMK. Batrakov, P. Kuzhir, S. Maksimenko, Radiative instability of electron beams in carbon nanotubes, Proceedings of SPIE, V. 6328 “Nanomodeling II”, p. 63280Z (2006)

Interaction between electron beam and produced electromagnetic wave leads to electron beam modulation. This process can be described by self-consistent system for electromagnetic field:

and for electrons:

Properties of nanotubes useful for generation by electron beam

1) Large length of electrons ballistic transport (~1 – 10 micron);2) Large current density (to 1010 A/cm2) [M. Radosavljevi´c, J. Lefebvre, and A. T. Johnson, “High-field electrical transport and breakdown in bundles of single-wall carbon nanotubes”, Phys. Rev. B 64, 241 307® (2001),S.-B. Lee, K. B. K. Teo, L. A. W. Robinson, A. S. Teh, M. Chhowalla,et al., J. Vac. Sci. Technol. B 20, 2773 (2002)].

Dispersion equation

Emission term

Absorptionterm

electron group velocity in nanotube

If width of emission line exceeds the magnitude ofquantum recoil, then traditional form of second-order Cherenkov resonance is realized:

Otherwise, quantum recoil contributes to resonance condition.

Gain is extremely large as compared with the gain

per unit length for macro-devices

Boundary conditions on nanotube tips and dispersion equations give threshold condition and instability increment

Threshold current and instability increment of generation

Radiation generationis already possible at the current stage of nanotechnologies

development.

Method for the instability control

The points of maximum group velocity and respectively low excitation energy can be advantageous for lasing. In the point of group velocity extremum the negative influence of the beam energy spread is smaller, and therefore more electrons interact with the wave: the radiation effectiveness can be increased. It is also possible to intensify the effect of radiation instability in nanotube due to the generation in the region of small effective mass of quasiparticle.

Compensation of electron beam spread

Extremum of group velocity

Dispersion equation

Then, expansion near this point gives

So, negative influence of beam spread can be reduced.

CONCLUSION:What has been done to the moment?

Thus, the generation of the stimulated radiation by electron beams in nanotubes is predicted.

The dispersion equations of the electron beam instability and threshold conditions for stimulated radiation are derived and studied.

The analysis of the threshold conditions shows realizability

of the CNT-based molecular TWT at the current CNT technology development

THANK YOU

FOR ATTENTION!

TU/eEindhovenJ.Havercort

PENN S TATE

Department of Engineering Science and Mechanics

I N ST I T U T F U R F E ST K O R P E R P H Y SI K

: :Usikov InstituteFor Radiophysics And Electronics Ukraine,Kharkov

A.Lakhtakia

J. Herrmann, I.Hertel

A.Hoffmann,D.Bimberg

O.YevtushenkoN LedentsovI Krestnikov

Universitaires Notre-Dame de la Paix NAMUR, BELGIUMPh. Lambin

Boreskov Institute of Catalysis SB RASNovosibirsk

Ecole Polytechnique Federale de Lausanne Switzerland L. Forro

Chalmers University of Technology, Sweden, E. Campbell

V Kuznetsov

LABORATOIRE DE PHYSIQUE DE LA MATIERE CONDENSEEG. BOSSIS

Laboratory National des Champs Magnetiques PulsesJ. Galibert

Collaboration of the Institute of Nuclear Problems of Belarusian State University in the field of NANOSCIENCE

etceteras