Low-Loss Many-to-One Fiber Couplers with Few or Single-Moded Inputs and a Multi-Mode Output

The coupling of light from a number of few or single-moded fibers into a single multi-mode fiber is analyzed using geometric optics, and simple results demonstrating mode conservation are derived. Coupling from multiple single-mode fibers into a multi-mode fiber is investigated in detail using the overlap integral to determine coupling into each mode of the output fiber as a function of the light phase in the inputs. As well as results with practical relevance to fiber tapped delay-line filters and optical CDMA, the analysis provides pedagogic insight into light propagation and the light-gathering properties of fiber.