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We analyze theoretically the oscillator strength and the third-order optical polarizability ^ (3) due to excitons in semiconductor microcrystallites. The nonlinear optical polarizability is shown to be greatly enhanced for an assembly of such microcrystallites as the exciton is quantized due to the confinement effect and the excitons in a single microcrystallite interact strongly enough to make the excitons deviate from ideal harmonic oscillators.
Eiichi Hanamura (1988) studied this question.