# Uniform Plane Waves vs. Plane Waves

1. Apr 28, 2007

### Swapnil

What is the difference between "uniform plane waves" and "planes waves." Are these terms used interchangeably?

What properties would a "non-uniform" plane wave have?

2. Apr 28, 2007

### Chris Hillman

Uniform plane waves?

Can you give some context for where you saw this term?

3. Apr 28, 2007

### pmb_phy

I seems to me that you're right in that the terms are used interchangeably.

Pete

4. Apr 29, 2007

### lpfr

I think that for a plane wave that propagates in the z direction, you say it is uniform if
$${\partial\ \over \partial x}= 0$$ and $${\partial\ \over \partial y}= 0$$

You can imagine a plane wave where the amplitude varies with x or y. This would be a non uniform plane wave.
Maybe you can generate this wave with a filter with variable absorption, as a diapositive or a negative.

5. Apr 29, 2007

### Swapnil

This makes sense. But then what properties would your good old plane waves have (uniform or non-uniform)? Would it be just the fact that the E & H vectors are mutually perpendicular to the direction of propagation?

6. Apr 29, 2007

### Hurkyl

Staff Emeritus
My guess is that adding "uniform" would impose some translational symmetry; maybe any translation along the wavefront front, maybe of one period along the axis of propagation, maybe both.

7. Apr 29, 2007

### lpfr

Uniform, of course.

Yes, translational symmetry in the x and y directions, and the same translational symmetry with $$\lambda$$ as spatial period, in the direction of propagation z.

8. Apr 29, 2007

### Meir Achuz

If the medium had a variable n, k of the plane wave would change with distance, and the wave might be called non-uniform.

9. Apr 29, 2007

### lpfr

In this case I would rather call it "non-plane". For a wave to be called plane, "isophase" surfaces must be planes. E.g. surfaces where E=0 and B=0, must be plane.

10. Apr 29, 2007

### Staff: Mentor

The "plane" in "plane wave" refers to the surfaces of constant phase $\phi$. For example, in $\psi = A \cos (kz - \omega t)$, the points where the cosine is maximum ($\phi = kz - \omega t = 0, 2\pi, 4\pi,...$) form a set of planes parallel to the xy-plane and perpendicular to the z-axis. These planes of constant phase move in the +z direction at speed $v_{phase} = \omega / k$.

11. Apr 29, 2007

### Chris Hillman

Note that jtbell's example is invariant under translations in x,y.

I repeat that context is essential, since the answer will depend upon how the OP answers my request for clarification.

12. Apr 29, 2007

### Xezlec

Uniform plane waves are the ones that aren't working undercover. :tongue: God I'm funny.

13. Apr 30, 2007

### Swapnil

Here's the exact quote which defines uniform plane waves taken from the website on the bottom::

"A uniform plane wave is an electromagnetic wave in which the electric and magnetic fields and the direction of propagation are mutually orthogonal, and their amplitudes and phases are constant over planes perpendicular to the direction of propagation."

Last edited: Apr 30, 2007
14. Apr 30, 2007

### Swapnil

I think the term uniform means that the plane waves are homogeneous meaning that the planes of constant amplitude are parallel to the planes of constant phase.

15. Apr 30, 2007

### Claude Bile

Uniform plane waves are mathematical idealisations, often chosen because they remove the number of variables in a problem owing to their spatial symmetry, and perhaps more importantly, a uniform plane wave does not diffract.

The term "plane-wave" in my experience typically refers to "real" plane-waves such as the beam waist of a Gaussian beam, or a wave emerging from the output aperture of (some) lasers. Real plane-waves have amplitudes that vary across the wavefront and thus these waves do eventually diffract and lose their plane-wave characteristics, but there will still be a region in space where we can regard the wave as being approximately planar. This region is typically defined as the region with which the phase error across the (planar) wavefront is not too large, typically < pi/8 or < pi/4.

Having said that, I have seen the term "plane-wave" and "infinite plane-wave" in addition to "uniform plane-wave" used to refer to the aforementioned mathematical idealisation. At the very least "plane-wave" is a "looser" definition that can refer to many things, whereas "uniform plane-wave" or "infinite plane-wave" carries a much more precise definition.

Claude.

16. May 1, 2007

### lpfr

I'm annoyed by this phrase. All waves diffract. In a uniform plane wave the diffraction result is the same uniform plane wave. I think that this is what you meant.
But I think that is not a good idea to say that there are waves which diffract and others not. Even common polychromatic incoherent ambient light diffract. Just the result is not a stable, visible, classical, beautiful, diffraction image, but a blurr.

17. May 1, 2007

### Claude Bile

Either view is valid according to the laws of physics, for there is no law that tells us that all waves must diffract, only laws that tell us how one wave evolves into another as it propagates. For a wavefront that does not change as it propagates, whether you choose to say it does not diffract, or does diffract but does not change is simply semantics.
Of course, all real waves diffract because all real waves are finite in extent.

Claude.