How does the numerical aperture (NA) of an optical fiber affect its light-gathering ability?

The numerical aperture (NA) of an optical fiber directly determines its light-gathering ability, which is the fiber's capacity to accept and propagate light. The NA is a dimensionless number that quantifies the range of angles over which the fiber can accept light. A higher NA indicates a greater light-gathering ability. The NA is defined as the sine of the maximum acceptance angle, which is the largest angle at which light can enter the fiber and still be guided by total internal reflection. The NA is related to the refractive indices of the fiber core (n_core) and cladding (n_clad) by the formula: NA = sqrt(n_core^2 - n_clad^2). A fiber with a higher NA can accept light from a wider range of angles, making it easier to couple light into the fiber. This is particularly important when coupling light from a light source with a large emission angle, such as an LED. A fiber with a lower NA has a smaller acceptance angle, making it more difficult to couple light into the fiber. This requires more precise alignment and a light source with a narrower emission angle, such as a laser. For example, a multimode fiber typically has a higher NA than a single-mode fiber. This is because multimode fibers are designed to accept light from a wider range of angles, while single-mode fibers are designed to guide only one mode of light, requiring a smaller acceptance angle. The NA is an important parameter to consider when selecting a fiber for a particular application. A fiber with a higher NA may be preferred for applications where it is important to maximize light coupling, while a fiber with a lower NA may be preferred for applications where it is important to minimize modal dispersion. Proper matching of the NA of the fiber to the NA of the light source is crucial for efficient light coupling and optimal system performance.