Coherence of Planar Wavefronts - Spatial & Temporal

[Navid]

Homework Statement

Planar wave coherence

Relevant Equations

Plane wave equation: E(r) = E0exp(±ik·r)

Hi, are planar wavefronts both spatially and temporally coherent? Or, they are only spatially coherent and need not be temopral?

 

[BvU]

Hello Navid, !

E(r) = E₀exp(±ik·r) is more a wave function than a wave equation (that would look like $u_{xx}=u_{tt}$). As you can see, your function does not satisfy the wave equation.

You first have to say something about the time dependence...

 

[Navid]

The main thing I want to get clear is a planar wavefront by definition should be spatially coherent. But, do they need to be equidistant in space as well, meaning do they, by definition, need to be temporally coherent?

 

[BvU]

$\exp\bigl (ik(t)\cdot r\bigr)$ is still planar but not necessarily temporally coherent. But now I've said something about the time dependence.