Ultrafast spectroscopy allows us to probe and understand material properties. With it, we can measure phonon-polaritons (optical phonons coupled with light) and the resulting dispersion curve in lithium niobate. Customizing the excitation source in ultrafast measurements can excite phonon modes to large amplitudes, allowing the experimental exploration of the Potential Energy Surface in solids. However, stronger pump fluences and bigger signal isn't always the answer in ultrafast spectroscopy. When sample signals and their nonlinear and mechanisms cannot be distinguished with 1D measurements, simple 2D THz measurements are a great place to start searching for distinct factors as was the case in cadmium tungstate. 2D measurements when paired with modeling and first principles calculations can reveal cutting edge information about exciting materials.

Terahertz (THz) spectroscopy is a powerful tool that uses ultrashort pulses of light to study the properties of materials on picosecond time scales. THz light can be generated through a variety of methods. In our lab, we generate THz through the process of optical rectification in nonlinear optical (NLO) organic crystals. THz light can be used to study several phenomena in materials, such as spin precession, electron acceleration, vibrational and rotational motion. The work presented in this dissertation is divided into two parts: (1) the generation of THz light and (2) applications of THz light. The first portion of this work shows how THz light is generated, with an emphasis on the generation through optical rectification. We also show how to improve the generation of THz light by creating heterogenous multi-layer structures with yellow organic THz generation crystals. Additionally, we show that crystals used for THz generation can also be used to generate second-harmonic light. In the second half of this work, we show that THz light can be used to study the vibrational motion of molecular systems. We model how resonant vibrational modes in a fluorobenzene molecule can be excited with a multi-THz pump to transfer energy anharmonically to non-resonant modes. We also show that we can use two-dimensional (2D) THz spectroscopy to excite infrared-active vibrational modes and probe Raman-active modes in a CdWO4 crystal to obtain a nonlinear response. We show that the nonlinear response is due to anharmonic coupling between vibrational modes and we can quantify the relative strengths of these anharmonic couplings, which previously was only accessible through first-principles calculations.