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

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7.3 Calculated SHG Signal from Carbon Nanoropes
In this section, we present two calculations to estimate the limits or our nonlinear
optical microscope as a probe of molecular systems. The first calculation uses the
SHG signal upper limit from carbon nanotubes to determine the second-order hyperpolarizability
of a single carbon nanotube. The second calculation determines the
SHG signal from a surface film of aligned nonlinear molecules with the same area as
our carbon nanotube sample. We chose p-nitrobenzoic acid (PNBA) as the nonlinear
molecule in our calculation because its nonlinear optical properties have been thoroughly
investigated [6]. This calculation demonstrates that SHG microscopy from a
small collection of molecules is feasible.
vVe calculate the ma.ximum nonlinearity of carbon nanotubes using a simple model
that assumes the carbon nanotubes act as a nonlinear surface layer on the glass
substrate. We assume that the carbon nanorope is composed of 100 nanotubes. We
further assume that each nanotube has C sv symmetry [30] and that the dominant
hyperpolarizability of each nanotube is Q~~~,
i.e. the dominant hyperpolarizability is
along the a.xis of the molecule. The surface second-order nonlinear susceptibility is
related to the second-order hyperpolarizability by
(2) 1 N ": ~ ": ~ ~ ~ (2)
X.S,ijk = 4 L(z' (3)(J . ~()(k· tS)Q8-y6(n),
• n=l
(7.17)
with N nanotubes lying in an area A. If we assume that a nanotube has equal probability
of lying parallel to or anti parallel to the z a.xis, then on average there will be a
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