As far as I know, vacuum is the only dispersion free medium for electromagnetic waves. This makes me wonder if there are any other dispersion free media for these waves? (Experimentally established or theoreticaly predicted) If there are none for electromagnetic waves, are there any for other kinds of waves?
Dispersion can be locally nought and effectively nought over quite wide bands in engineered devices.
In an optical fiber, for example, the phase delays of the modal fields depends on two things:
The dispersion of the material making up the fiber and
The frequency dependence of the modal eigenvalue equation, which depends on the refractive index profile and is there even if the fiber could be made out of dispersionless materials.
The second order term in the phase as function of wavelength Taylor series determines, to first order, the total dispersion. In optical fibers, the two mechanisms above contribute exactly mutually cancelling dispersions from effects 1 and 2 in certain wavelength bands. For example, a step index profile fiber typically has quite a wide, low dispersion band at 1300nm wavelength. This band can be shifted by engineering the refractive index profile (the so called depressed cladding index profile) into the 1550nm communications band.
Grating devices can hold a system dispersionless over stunningly wide wavelength bands. For instance, carefully designed "chirped " fiber Bragg gratings are used to exactly oppose the dispersion of optical systems over hundreds of nanometers bandwidth, and thus are useful in setting up femtosecond long pulses.
Vacuum with EM field present is also dispersion-less, since EM fields of different sources do not interact directly. So if you pass an EM wave through charged capacitor, the only influence on the wave is due to the matter of capacitor; no influence due to electrified space should occur.