We present studies of second harmonic generation in core/shell ZnTe/Zn1−xMgxTe nanowires (NWs) with a waveguiding geometry. The NWs are excited by a pulsed femtosecond laser over a broad range of excitation wavelengths from 800 to 1140 nm. This allows us to demonstrate a giant increase in the second harmonic light intensity. We attribute the observed effect to the combined action of absorption by the NW, the confinement of light due to the waveguiding geometry, and the bending of the NWs. We show that a multi-photon luminescence (MPL) is generated alongside the second harmonic light. Furthermore, we demonstrate a strong polarization anisotropy of the second harmonic and MPL signals. Unlike in bulk semiconductors and quantum wells, this anisotropy is not due to the underlying symmetries of the crystal structure, but can be attributed solely to the shape anisotropy of the NW.

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