We present a theoretical study of optical second-harmonic generation (SHG)
of symmetric semiconductor quantum dots (QDs) excited by the near field of
the tip in a near-field scanning optical microscope. We show that the usual
optical transition selection rules for the SH nonlinear interaction betwee
n the tip field and the QD are broken when the tip is scanned ever the QD,
because the tip field varies rapidly over the QD domain. It is also demonst
rated that the tip-position dependence of the SH signal essentially maps th
e spatial distribution of the tip field. (C) 1999 Academic Press.