Nonlinear optics is an important branch of optics that contributes to the generation of new frequencies. With nonlinear optics, processes such as second harmonic generation, sum-frequency generation and others can be implemented. In most models presented for nonlinear optics, a simple one-dimensional geometry is used. While this simple model captures the main concepts, it often does not provide detailed answers to more specific aspects of the process. For example, the formulation and details of second harmonic generation in a nonlinear medium with a spherical geometry are rarely discussed in the literature. In this paper, we extend the existing nonlinear optics formulations by generalizing the light scattering geometry from a flat one-dimensional model to a spherical one, and we investigate the results through simulations using a code written by us. This code operates based on one-dimensional formulation within the framework of geometric optics. In this simulation, a monochromatic light beam is incident on a χ^((2)) active nonlinear spherical medium with known optical properties. According to the geometric optics, the light refracts within the sphere and eventually exits it. Depending on the path length traveled by each ray inside the sphere, the generated second harmonic is computed using one-dimensional models. Finally, the angular distribution of the output light at the second harmonic frequency is calculated. The results show that this angular distribution is highly sensitive to the dispersion of the medium and refractive index at the second harmonic frequency.
