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One of your assumptions is incorrect: there is no need to have any "round-trip" phase match. All the photons (or wavefronts) just keep reflecting off the mirror surface. The reflections will always contain a vector component in the longitudinal direction (parallel to the axis of the fiber), so all the light will end up at the far end of the fiber, ...


Niels Nielsen's answer is correct. Just to provide some calculations as to actual propagation speeds (not signal bandwidth): Typical optical fibers have $n\approxeq 1.5$ , so the propagation speed is $\frac{c}{1.5}$ , or roughly 2E8 m/s . This is the field, or photon, speed. Using the formula from Wikipedia, the speed of electromagnetic waves in a good ...


Fiber cables have higher data transfer speed not because light travels faster in a fiber than electromagnetic waves in a copper wire, but because they can be modulated by signals having far higher frequencies than can be managed in the case of copper wires.

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