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I have read ray-theory cannot be applied to single-mode fibers. Why?

I know rays are kind of an approximation to describe the real behavior of light, and electromagnetic theory and photonics are closer to nature, but are there no "rays" in single-mode fibers?

Thank you.

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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.

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    $\begingroup$ I don't need to tell you this, but also don't feel the following comment deserves its own post, so here goes: it might help in thinking about this to recall that the microscopic origin of the ray theory is wrapped up in Huygen's principle and depends on waves being able to propagate in all directions. The boundary conditions imposed by the confines of the fiber prevent propagation in most direction so Huygen's principle does not apply and you can't recover geometric optics. $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented Jun 18, 2014 at 18:10
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The one reason behind this is Interference! The bouncing light rays interfere constructively or destructively which affect the propagation through the fiber.

If you want to go one step further, at the scale of optical fibers and using lasers, the coherence length of the light allows for these interference to happen between the waves before and after "bouncing" on the fiber.

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