The purpose of this thesis is to investigate the nonlinear phenomena known as doubly-stimulated, non-degenerate two-photon emission (ND-2PE) in Gallium Arsenide (GaAs). 2PE refers to the simultaneous emission of two-photons as electrons move from the conduction band in a direct gap semiconductor to the valence band. Following the same path for describing one-photon emission (1PE) we describe 2PE as a product of the irradiance, and the negative of the loss which in this case is two-photon absorption, , the negative coming from the population inversion. We attempt to observe 2PE by using a frequency non-degenerate pump-probe experiment in which a third beam optically excites a 4 µm thick GaAs sample. We use nondegenerate beams in hopes of utilizing the 3-orders of magnitude enhancement seen in twophoton absorption (2PA) by going to extreme nondegeneracy (END) to enhance 2PE. GaAs is chosen due to the availability of the appropriate wavelengths, the maturity of the GaAs technology, its use in optoelectronic devices and its ability to be electrically pumped. During the experimental development we learn how to effectively etch and manipulate thin GaAs samples and model the transmission spectrum of these samples using thin film transmission matrices. We are able to match the measured transmission spectrum with the theoretical transmission spectrum. Here we etch the bulk GaAs left on the sample leaving only the 4 µm thickness of molecular beam epitaxial grown GaAs plus additional layers of aluminum gallium arsenide (AlGaAs). These samples were grown for us by Professor Gregory Salamo of the University of Arkansas. iv Using the pump-probe experiment on the 4 µm GaAs sample, we measure the change of the 2PA due to the presence of optically excited carriers. The goal is to reduce the 2PA signal to zero and then invert the 2PA signal indicating an increase in transmission indicative of 2PE when the population is inverted. Our results show that we achieve a 45% reduction in the 2PA signal in a 4 μm thick GaAs sample due to the excited carriers. Unfortunately, we currently cannot experimentally determine whether the reduction is strictly due to free-carrier absorption (FCA) of our pump or possibly due to a change in the two-photon absorption coefficient. We measure the transmission of various wavelengths around the bang gap of GaAs as a function of excitation wavelength and achieve a transmittance of ~80% which we attribute to possibly be one photon gain (1PG) at 880 nm. We also go to cryogenic temperatures to concentrate the carriers near the bottom of the conduction band and improve the theoretical gain coefficient for 2PE. Unfortunately, we do not observe a measurable change in 2PA with the addition of optically excited carriers. Along with FCA of our infrared pump we suspect that the difficulties in this first set of experiments are also a result or radiative recombination due to amplified spontaneous emission reducing our free carrier density along with the fact that 4 m is too thick for uniform excitation. We now have 1 m samples from Professor Gregory Salamo which we hope will give better and more definitive results