The fibres are too small (10um) for light to behave like a ray, you need the wave equation.
Ray theory works when: (size of all dimensions in system)*(relative error tolerance) >> (wavelength of light).
For macroscopic objects this is usually true.
In a double slit experiment/demonstration, where ray theory fails, we combine a smallish slit size with a sensitive angle measurement to bring out the wave effects of light.
In a single mode fibre the core diameter is only ~15 times larger than the infrared 1um light (shortened to about 0.75 um due to refraction) that is passing through it. This means that you can't have rays bounce off the sides like you could in a wider fibre. The only way to pass light (of the given wavelength) is to have the wavefront propagate directly down.