Cancellation of photoinduced absorption in metal nanoparticle composites through a counterintuitive consequence of local field effects

By applying the Maxwell Garnett model to gold nanoparticles in water we deduce a value of $\mathrm{Im} {\chi }_i^{(3)}=1.1$ $\times {10}^{-7} \mathrm{esu}$ for the imaginary part of the cubic susceptibility for gold corresponding to a Fermi smearing mechanism. We also demonstrate a sign reversal in the nonlinear absorption for gold particles in $1, 1^{\prime }, 3, 3, 3^{\prime }, 3^{\prime }$-hexamethylindotricarbocyanine iodide. Although the imaginary part of ${\chi }^{(3)}$ is positive for each component by itself, remarkably the imaginary part of ${\chi }^{(3)}$ is negative for the colloid as a whole. We show that the nonlinearity of the host must be considered and that the sign reversal in ${\chi }^{(3)}$ is a result of the fact that at the surface plasmon resonance the local field factor has an imaginary component that arises from a phase shift between the applied field and the local field inside the particle.