What is the primary reason for the difference in distance capabilities between single-mode and multi-mode fiber?

The primary reason for the difference in distance capabilities between single-mode and multi-mode fiber is modal dispersion. Modal dispersion is the spreading of a light pulse as it travels through the fiber. This spreading happens because different modes, or paths of light, travel at slightly different speeds. Single-mode fiber has a very small core, typically around 9 micrometers. This small core allows only one mode of light to propagate directly down the center. Because only one mode is traveling, there is virtually no modal dispersion, and the signal can travel much farther without significant degradation. Multi-mode fiber, on the other hand, has a much larger core, typically 50 or 62.5 micrometers. This larger core allows multiple modes of light to propagate. These modes travel different paths, some directly down the center, others bouncing off the cladding (the outer layer of the fiber that confines the light). These different paths result in different travel times. As the signal travels, these modes arrive at the end of the fiber at slightly different times, spreading the pulse and limiting the distance the signal can travel before it becomes unreadable. For example, in a multi-mode fiber system, a pulse might spread so much after a few kilometers that it overlaps with the next pulse, making it impossible for the receiver to distinguish between them. This is not a significant issue in single-mode fiber due to the lack of multiple modes.