William Angerer - Department of Physics and Astronomy - University ...

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parameter symbol value
surface density Ns lAx 1011 cm- 2
effective beam area .-leI I 7 X 10- 11 cm 2
(area of nanotubes)
SHG Signal Sshg 3xlO- 11 ergs
fundamental susceptibility €(w) 3.93 + 3.62i [114]
second-harmonic susceptibility f(2w) 3.57 + 3.07i [114]
Table 7.2: Properties of carbon nanotubes for calculating SHG from carbon nanotubes
polarizability of the nanotubes as Q~;).;:
= 1.1 X 10- 27 esu. Although this number is
extremely large for conventional nonlinear molecules. e.g. 10- 30 esu [6. 115, 116]. a
0.5 J.Lm carbon nanotube is composed of approximately 10.000 atoms. and the length
of the tube suggests that very high hyperpolarizabilities may be achieved .
.-\. second calculation shows that local domains of nonlinear molecules are easily
observable by SHG microscopy. vVe calculated the number of SHG photons emitted
from a domain of aligned p-nitrobenzoic acid (PNBA) with the same area as our
carbon nanotube sample. PNBA is an organic molecule that has a permanent dipole
moment and lacks inversion symmetry. The IT-electrons contribute to the hyperpolarizability
along the molecular axis, Q~;~.
Calculations show that Q~;~ typically exceeds
other hyperpolarizability elements by at least one order of magnitude [115]. Thus.
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