Non-linear optical properties of randomly oriented non-linear spheroidal metal particles in a dielectric host are investigated. Two different Maxwell-Garnett-type approximations are derived based on whether a self-consistency condition on the net polarization is invoked. These two methods lead to quite different spectral density functions. Moreover, we show that the shape of particles has a large influence on the spectral function through the depolarization effects and thereby has a pronounced

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... ffect on the optical absorption and non-linear optical susceptibility. We suggest that the self-consistent formalism can be used for large volume fractions, as mutual interaction between different polarizations is included in the theory.