Plane wave conditions

Question

Which conditions have to be fulfilled in order to approximate a light beam by a plane
wave (i.e. $\phi(x)\approx \phi(0)e^{ikx}$)?

I am looking for both mathematical and experimental conditions. At the moment, the only thing I can think of is to consider that the source is at a very distant point and the use of collimators.

Comments

Is this question maybe more appropriate for physics stackexchange?

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I agree with @JoshBurby.

Voting to close as high-school/UG level. PO is for graduate-level+ questions.

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A spherical wave has an exact expression (with $1/r$ factor). Within certain precision $\varepsilon$ the denominator can be considered constant. Thus, the plane wave approximation has the corresponding limits in the volume.

Answer 1

For the intuition's sake, perhaps it would be useful to visualize the ripples produced by throwing a stone into a pond. Close to where the stone impacted the pond's surface, the wave fronts are strongly curved, and are not approximated well by a plane wave. However, at large distances from the point of impact the curvature of the wavefronts is very small, and a plane wave approximation is more accurate.

Because the wave equation for electromagnetic waves in free space is essentially identical to that governing the surface waves on a pond, the above picture generalizes to give a picture of light waves produced by, say, an oscillating dipole. When you are sufficiently far from the dipole, the radiation field will be approximately plane.