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

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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

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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

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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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