Nonlinear optics (NLO) plays a major role in the modern world: nonlinear optical phenomena have been observed in a wavelength range going from the deep infrared to the extreme ultraviolet, to THz radiation. The optical nonlinearities can be found in crystals, amorphous materials, polymers, liquid crystals, liquids, organic materials, and even gases and plasmas. Nowadays, NLO is relevant for applications in quantum optics, quantum computing, ultra-cold atom physics, plasma physics, and particle accelerators. The work presented in the thesis is limited only to the semiconductors that have a second-order optical nonlinearity and includes two phenomena that use second-order nonlinearity: second-harmonic generation (SHG) and spontaneous parametric down-conversion (SPDC). Among the many options available, the investigation presented concerns gallium phosphide (GaP) and gallium indium phosphide (Ga_0.51In_0.49P), two semiconductors of the group III-V with the ¯43m crystal symmetry.

However, some of the results found can be generalized for other materials with ¯43m crystal symmetry.

In the thesis, the fabrication of GaP nanowaveguides with dimensions from 0.03 μm and an aspect ratio above 20 using focused ion beam (FIB) milling is discussed. The problem of the formation of gallium droplets on the surface is solved by using a pulsed laser to oxidize the excess surface gallium locally on the FIB-milled nanowaveguides. SHG is used to evaluate the optical quality of the fabricated GaP nanowaveguides. Additionally, a theoretical and experimental way to enhance SHG in nanowaveguides is introduced. This process uses the overlap of interacting fields defined by the fundamental mode of the pump and the second-order mode of the SHG, which is enhanced by the longitudinal component of the nonlinear polarization density. Through this method, it was possible to obtain a maximum efficiency of 10⁻⁴, which corresponds to 50 W⁻¹cm⁻². The method can be generalized for any material with a ¯43m crystal symmetry. Furthermore, SHG is used to characterize the nonlinear properties of a nanostructure exposed for a long time to a CW laser at 405 nm to reduce the photoluminescence (PL) of Ga_0.51In_0.49P. The PL was reduced by -34 dB without causing any damage to the nanostructures or modifying the nonlinear properties. The fabrication process for obtaining the nanowaveguide is interesting as well, since the fabricated waveguide in Ga_0.51In_0.49P, whose sizes are 200 nm thick, 11 μm wide and 1.5 mm long, was transferred on silicon dioxide (SiO₂). This type of nanowaveguide is interesting for SPDC, since it satisfies the long interaction length necessary for an efficient SPDC. Finally, a configuration consisting of illuminating the top surface of a nanowaveguide with a pump beam to generate signal and idler by SPDC is presented. These fabricated nanostructures open a way to the generation of counter-propagating idler and signal with orthogonal polarization. By using a different cut of the crystal, i.e. [110], it makes possible to obtain degenerate wavelength generation, and in certain conditions to obtain polarization-entangled photons or squeezed states.