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

201
net alignment of,...., V100 = 10 nanotubes for a nanorope composed of 100 nanotubes.
~ote that equation (7.17) assumes the nanotubes are non-interacting. Since our calculation
yields only an approximate value for the second order hyperpolarizability of
carbon nanotubes, this is a reasonable assumption.
Shen [46] has determined the nonlinear intensity reflected from a surface layer
excited by a normally incident fundamental wave as
(7.18)
where e w = L(w) . e w • Note that e w denotes the unit polarization vector of the field
at frequency ;.V and L(w) is a Fresnel factor dyadic with the relevant element
(7.19)
vVe can recast equation (7.18) as
(2) 2 SshgA2r c 3 1
I XS,xxx I = U2Ae//f 327r 3 W 2 Lix(w)Lxx(2w)
(7.20)
The variables in equation (7.20) are defined with their corresponding values in Tables
7.1 and 7.2. Note that X~ljk
is defined in a coordinate system with z normal
to the substrate while o:~2~o
is defined in a coordinate system with the nanotube axis
aligned along z. Equation (7.20) determines the surface nonlinear susceptibility in
terms of the energy of the SHG photons radiated in one second, SSHG, the Ti:AI 2 0 3
laser parameters, and the sample geometry. Note that our analysis assumes that
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