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Polymer or plastic optical fibers' performance lies somewhere between conventional copper wires and glass optical fibers. Copper wires suffer from electromagnetic interference. By comparison, plastic optical fibers are free from interference. Compared to glass fibers, polymer optical fibers (POFs) are much easier to connect because of their large diameters. Coupling of light from the sun or from a source is also very efficient due to large NA and large core diameter. The most important attribute of POFs is their large core diameters of around 1 mm to 20 mm as compared to glass fibers with cores of 50μm or 62.5μm. Such a large diameter results in easier alignment at joints. Any transverse misalignment between the two cores across a joint between two fibers leads to a loss. Hence, this paper studies on the coupling efficiency of light from the sun as a natural light source to a step-index polymer optical fibers in comparison to glass fibers that results in larger light-gathering power for optical fiber daylighting system and in fiber decorative lighting. MATLAB simulation analysis shows that the coupling efficiency and light gathering power increases steadily with an increase in numerical aperture of the step-index PMMA polymer optical fiber that has higher and better light gathering power than step-index PMMA glass optical fiber.