With two multimode fibers in common usage today (50/125 and 62.5/125) and two others which have been used occasionally in the past (100/140 and 85/125) and several types of singlemode fiber in use, it is possible to sometimes have to connect dissimilar fibers or use systems designed for one fiber size on another. If you connect a smaller fiber to a larger one, the coupling losses will be minimal, often only the fresnel loss (about 0.3 dB). But connecting larger fibers to smaller ones results in substantial losses, not only due to the smaller cores size, but also the smaller NA of most small core fibers.
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