Nonlinear optical properties of materials are useful both for their practical applications, but also as a characterization tool for symmetry in novel systems. However, the nonlinear optical response of a material is often not as one of its fundamental properties, along with band structure, linear conductivity, etc. This has particularly been the case with the recent interest in “quantum materials”: materials such as high-Tc superconductors, topological materials, and exotic magnets. Weyl semimetals are a class of materials where band-touching points have divergent Berry curvature, and are host to a number of unique physical phenomena such as the chiral anomaly and Fermi arc surface states. From the nonlinear optics perspective, Weyl semimetals are interesting since inversion-symmetry breaking Weyl semimetals have been experimentally realized, and breaking of inversion-symmetry is crucial for second order nonlinear optical phenomena.In this dissertation, I present results from a number of studies of the Weyl semimetal TaAs and related compounds using nonlinear optical techniques. As detailed here, TaAs was discovered to have the largest measured nonlinear optical susceptibility of any material, and further, this susceptibility was found to be caused by a resonance in the spectrum of nonlinear optical conductivity. TaAs was also measured to have a photogalvanic effect that has qualitatively different characteristics depending on the direction of measurement. These nonlinear optical properties of the TaAs family of materials may lead to interesting applications in near-field nonlinear optics, and optical pulse shaping below the diffraction limit
