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Phase Velocity

The phase velocity of light is the velocity with which phase fronts propagate in a medium. It is related to the wavenumber <$k$> and the (angular) optical frequency <$\omega$>:

In vacuum, the phase velocity is <$c$> = 299 792 458 m/s, independent of the optical frequency, and equals the group velocity. In a medium, the phase velocity is typically smaller by a factor <$n$>, called the refractive index, which is frequency-dependent (→ chromatic dispersion). In the visible spectral region, typical transparent crystals and optical glasses have refractive indices between 1.4 and 2.8. Semiconductors usually have higher values.

In the X-ray region, refractive indices are slightly below 1, corresponding to phase velocities slightly above the vacuum velocity of light. Similar effects can be caused e.g. by optical resonances of atoms in the visible spectral region. However, this does not allow for superluminal transmission of information, or for violating causality.

There are even cases where the phase velocity is directed opposite to the direction of the energy flow. Such phenomena occur in negative-index media, which can be realized as photonic metamaterials.

The phase velocity is usually considered for plane waves, where the wavefronts are simply moving in a direction perpendicular to their orientation. It is interesting to look at the wavefronts of focused laser beams. Due to the Gouy phase shift, these move slightly faster near the focus.

The term wave velocity is vague; it may refer to phase velocity or group velocity, or possibly mean something else.

More to Learn

Encyclopedia articles:

• velocity of light
• wavefronts
• refractive index
• group velocity
• dispersion