I have studied that tolerance decreases when diameter increases. But why does it happen?
Perhaps, you meant tolerance for coupling to the fiber. If this this what you really meant, than the explanation is really simple. Large diameter fibers carry optical modes that also have large diameters. Say, one can have 50, 100, even few hundred micron mode diameters in such multi mode (MM) fibers. Single mode fibers on the other hand have usually smaller diameters because they have to carry a single mode only. Hence, mode diameters in such fibers can be around few microns or so.
Coupling to or from MM fibers is less demanding because one can easily couple from a small diameter to a large fiber just making sure that the small one falls within the large. So, alignment tolerance for coupling from say 50 um to say 100 micron can be few microns or more. Even coupling from 50 um to another 50 um fiber doesn't require sub-micron alignment tolerances Pure geometrical considerations, no worries about mode matching between the fibers. However, when coupling from a large fiber to a small fiber losses will be much higher because one would inevitably lose some light. It's like filling a small basket with water from a larger basket.
SM fibers are a different breed. The mode size tends to be smaller and somewhat approaching the wavelength of operation. Also, to couple to and from SM devices one has to satisfy the mode matching condition: the size and the shape of modes in both devices (or fibers) have to be equal to achieve minimal losses as required by the mode matching integral. This small size imposes very tight alignment tolerances, and sub-micron numbers are very common.
I hope it helps.
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