Near-field optical second-harmonic generation in semiconductor quantum dots

In a conventional nonlinear optical experiment such as second-harmonic generation (SHG), the nonlinear materials are usually illuminated by a far field (laser beam) and the second-harmonic (SH) signal is also collected in the far-field region. In such a situation, it is well known that the second-order optical nonlinear effects are absent in the electric dipole approximation in materials exhibiting central inversion symmetry. For a quantum dot (QD) structure with a rectangular potential profile in three dimensions excited by a far field, the SH nonlinear susceptibility arising from interband and intersubband transitions vanishes because of the definite parity of the wave functions. In order to observe the second-order nonlinearity in such a system, one has to break the symmetry by means of the driving field. We show that, if the QD is excited by a near field produced by a fiber tip of a near-field scanning microscope, a second-order nonlinear response is generated in a QD system because the tip field (driving field) varies rapidly over the QD domain. We consider a GaAs/Al_x Ga_1-xAs QD structure