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Properties of Carbon Nanotube AntennaYin Lan, Baoqing Zeng*
School of Physical Electronics
University of Electronic Science and Technology of China
Chengdu, 610054, P. R. China
*E-mail: bqzengguestc.edu.cn
Abstract-Carbon nanotube as microwave antennae have
expansive prospect of application, such as: nano-interconnect
technology, fiber communication, aviation communication,
because of the small size, light weight and good electronic
properties. In this paper, we discuss some of the properties of
carbon nanotube antennae, e.g., current distribution on the single
antenna, re-radiation lobe pattern of single antenna, is shown.
Key Word-Carbon nanotube antenna, current distribution,
re-radiation pattern.
I. INTRODUCTION
Polarization effect and length effect of aligned multi-wallcarbon nanotubes (MWCNTS) were demonstrated by Z.F.Ren
et al. [1]. The polarization effect, which suppress the responseof an antenna when the electric field of the incoming radiationis polarized perpendicular to the antenna axis, and the lengtheffect, which maximizes the antenna response when theantenna length is multiple of the radiation half wavelength in
the medium surrounding the antenna. As optical antennae, thedirectional radiation characteristics also have beendemonstrated by computer simulation and experiment [2].Reference [2] shows that the radiation pattern is cylindricallyabout the axis of symmetry, and is characterized by a
multi-lobe pattern, which is most pronounced in the speculardirection.One of the most fundamental parameters of any antenna is
the current distribution on the antenna. This issue has definedantenna theory for many years. Re-radiation properties shouldbe determined by the current distribution on the antenna,
II. CURRENT DISTRIBUTION ON THE SINGLE ANTENNA
A carbon nanotube antenna has been supposed as a center
fed antenna (Fig. 1), which formed by two patulous
Incoming Radiation
Fig. 1. The relation of incoming radiation and carbon
nanotube antenna. Where E is the electric field, 'P is the
incidence angle, and L is the half length of carbon nanotube
antenna.
transmission line with the end open circuit is shown in Fig.2.Fig.1. shows the relation of incoming radiation and carbonnanotube antenna. From Fig.1, the voltage of correspondingpoint ±+z can be shown as:
U Esinle +jkz cosfU+ z= se
U = Esin ~e -jkz cos +U_z
(1)
(2)
From Fig.2:
-U_z = E sin 4(cos(kz cos X) + j sin(kz cos O)
U+Z = E sin +(- cos(kz cos X) + j sin(kz cos O)
0
(3)
(4)
U-z
z
U+z
z -0
- L >
Fig.2. The parallel transmission line, which equal the two arm of center
fed antenna. Where L is the half length of carbon nanotube antenna
Authorized licensed use limited to: Georgia Institute of Technology. Downloaded on January 12, 2009 at 09:43 from IEEE Xplore. Restrictions apply.
From the (3) and (4), the voltage U(z) between the point +z to
-z is:
U(z) = -U UZ-U +Z = 2E sin + cos(kz cosX (5)
Fig.3. shows the equivalent circuit model for a mini-section of
parallel transmission line. From Fig.3:
U( ) (R + jwL1 )I(z) - 2E sin + cos(kz cos °) (6)az
Supposed the carbon nanotubes' end of output be shorted, z =0,therefore, U=0. For a given z =0 and U=0, from (9), thepending constant A1 =-A2. In addition, because of the end oftransmission line is open circuit, from equation (10), I=0, whenz=L. For a given A1 =-A2 and I=0, z=L, from (9), the pendingconstant A1 can be written as:
A = E cos(kL cos )y sin + cos(kL)
(13)
- ( )=(G + jwC1)U(z) (7)az
Combined (6) and (7), the differential equation of voltage can
be rewritten as:
2U 2
---y U+2Ekcos ~sin ~sin(kzcos ~) =0 (8)
So:
U = Aleyz + A2e - 2E cos + sin(kz cos )ksin
The carbon nanotube possess a very low loss, because ofelectrons in the carbon nanotube has ballistic transportationcharacteristics. Therefore, y2 =-k2, from (13) A1 should be:
A jE cos(kL cos ) (14)k sin + cos(kL)
For a given A1 and A1 =-A2, equation (11) can be evaluated, so:
I(z)= j2EZok sin + cos(kL)
- (cos(kL) cos(kz cosX(9)
- cos(kL cos X) cos(kz)) (15)Where A1 and A2 is the pending constant, v is the propagationconstant, and v is given by:
y = (R + jwL1)(G + jwC1) = cc + jk (10)
From (7) and (9), the current I can be evaluated:
1(z) 1I (2E cos(kzcos O _ AleYz +A2e YZ)ZO y ssin (11)
Where Z0 is:
For a given current distribution I(z), the far-field radiationpattern for re-radiation can be evaluated, reference [3] showsthat:
120i sin(O) e- (z) cos(kz cos(O))dz
From (16):
60E
Zor sin(4 cos(kL)
(16)
(17)
Z =|R+ jwL1G + jwC1
(12)
I jwL
jwCl -
Fig.3. The equivalent circuit model for a nilni-section
of parallel transmission line
Where f(O) is the directional function, it is given by:
f(0) = sin(0)(cos(kL)( sin(kL(cos(Q) + cos(O)))+cos(O) + cos(O)
sin(kL(cos() - cos(O))))cos() - cos(O)
- sin(O) cos(kL cos(X))( sin(kL(I + cos(O)))1±+ cos(O)
+ sin(kL(1 - cos(O))))1 - cos(O)
(18)
Using Mathcad professional map-making software [4], whenthe length L of carbon nanotube antenna is as several times as
wavelength X of incidence radiation, the re-radiation pattern ofcarbon nanotube antenna with different incidence angle 1 can
Authorized licensed use limited to: Georgia Institute of Technology. Downloaded on January 12, 2009 at 09:43 from IEEE Xplore. Restrictions apply.
be obtained. Fig.4 shows the results, carbon nanotubes'diameter and length have be taken as a=50nm and L=7X, Fig.4shows that the main lobe direction of re-radiation patternshould be vary with the incidence angle ID, the radiation patternproduced by the carbon nanotube antenna is rotationally
symmetric about the axis of antenna, the pattern is also
symmetric with the x-y plane.The electric conductivity of multi-walled carbon nanotube
can be taken aslO002000s/cm [5], and the mass density can
be taken as 1.6-1.7g/cm3 [6]. Using CST Microwave Studio,for a given D=400, )=500tm, a=50nm, and L1=3500tm,L2=1000m, the radiation pattern can be obtained by computer (a)simulation [7]. Fig.5 shows the simulation results.
In a long radiation antenna, a periodic pattern of currentdistribution is excited along the antenna, synchronized with thepattern of fields outside. The current pattern consists ofsegments, with current direction alternating from segment to P
segment. Therefore, the resulting radiation pattern, as a xheta
function of the angle with respect to the antenna axis, consistsof lobs of constructive interference, separated by radiationminima due to the destructive interference. Fig.5 and Fig.4shows that the back scattering is suppressed, thus, scattering isdominated by the specular reflection, in a other word, the
strongest radiation at the angle of reflection(1 80'-o).Fig.5 shows that the lobe density of re-radiation pattern
increases with the increase of carbon nanotube antenna arrays'length. (b)
0=90° 93
D=33D
'114 300O//85
YO
(c)Fig.4. The re-radiation pattern of carbon nanotube
antenna with different incidence angle cJ
Authorized licensed use limited to: Georgia Institute of Technology. Downloaded on January 12, 2009 at 09:43 from IEEE Xplore. Restrictions apply.
Ph
Th ta
ed., Beijing: Publishing House of Electronics Industry, pp.139-142,
2005.
[4] Mathcad, www.mathcad.com.
[5] K. Kaneto, M, Tsuruta, G. Sakai, W. Y Cho and Y Ando, "Electrical
conductivities of multi-wall carbon nano tubes," Synthetic Metals,
vol. 103, pp.2543-2546, 1999.
[6] M. Buongiorno Nardelli, J. -L. Fattebert, D. Orlikowski et al,
"Mechanical properties, defects and electronic behavior of carbon
nanotubes," Carbon, vol. 38, pp.1703-1711, 2000.
[7] CST-Computer Simulation Technology, www.cst.com.
(d)
Fig.5. The polar and 3D re-radiation pattern of carbon nanotube
antenna. Where (a) is the polar pattern of L1=35001im, (b) is the
3D pattern of L1=35001im, (c) is the polar pattern of
L2=10Oigm, and (d) is the 3D pattern of L2=1000im,
ACKNOWLEDGMENT
The work is partially supported by the National Laboratoryfor Vacuum Electronics.
III. CONCLUSION
Based on the classic transmission line theory, the function ofcurrent distribution and re-radiation pattern of carbon nanotubewith different incidence angle 1 have been obtained bytheoretic study. The re-radiation pattern with differentincidence angle D has been simulated by CST MicrowaveStudio. When the length of carbon nanotube antenna is as
several times as wavelength of incidence wave, the main lobedirection of re-radiation pattern should be varied with theincidence angle 1, and the strongest radiation should be at the
angle of reflection(180'-0). The lobe density of re-radiation
pattern should be increased with the increase of carbonnanotubes' length.
REFERENCES
[1] Y Wang, K. Kempa, Z. F. Ren, et al, "Receiving and transmitting light
like waves: Antenna effect in arrays of aligned carbon nanotube.,"
Appl.Phys.Lett, vol. 85, No. 13, pp. 2607-2609, 2004.
[2] K. Kempa, J. Rybczynski, Z. P. Huang, et al, "Carbon nanotube as
optical antennae," Advanced Materials, In press.
[3] John D. Kraus, Ronald J. Marhefla, Antennas: For All Applications, 3rd
x
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