# Zero-dispersion wavelength

I found this wiki-article on the topic. Accordingly: "In a single-mode optical fiber, the zero-dispersion wavelength is the wavelength or wavelengths at which material dispersion and waveguide dispersion cancel one another."

Does the zero-dispersion wavelength only exist in single mode fibers?

Does it depend on the length of the fiber? Will two single mode fibers with identical step-profile, but different length (5o km and 300 km) have the same zero-dispersion wavelength?

Dispersion, $$D$$ is defined as:
$$$$D=\frac{\partial^2k}{\partial \omega^2}$$$$
For the first question, then you can see that for highly multimode fibres, waveguinding will not affect propagation much, and the dispersion relation is that of the core's medium. So if it is made of fused silica, then the zero dispersion wavelength will be at approximately $$1250\:nm$$.