How do two light beams combine at a shear angle?

[stedwards]

How do two light beams combine at a shear angle?

Two electromagnetic beams cross at a shear angle. They have equal phase, intensity and polarization.

The angle is shear enough, so that in region in which they intersect, there is less than a quarter wave difference in phase over the cross-sectional area.

 

[Dale]

You can just take the superposition of each individual wave.

 

[stedwards]

The combined energy [if that were so] would nearly double, wouldn't it?

Specifically, how do the electric and magnetic field components combine.

 

[Dale]

The combined energy [if that were so] would nearly double, wouldn't it?

Specifically, how do the electric and magnetic field components combine.

The combined energy would be exactly double. See http://en.wikipedia.org/wiki/Poynting's_theorem

This is actually easiest to think about for a finite duration square wave pulse, IMO. The fields add together, and the energy density increases, but the volume decreases, so the end result is twice the total energy of a single pulse.

 

[nasu]

What is this "shear angle"?
It does not looks like you mean the usual meaning of it.
http://encyclopedia2.thefreedictionary.com/shear+angle

 

[stedwards]

What is this "shear angle"?
It does not looks like you mean the usual meaning of it.
http://encyclopedia2.thefreedictionary.com/shear+angle

Really? It's thefreedictionary. Place two lasers closely together. Adjust the beams so they intersect at the other end of the optical bench or much further.

 

[stedwards]

The combined energy [if that were so] would nearly double, wouldn't it?

Specifically, how do the electric and magnetic field components combine.

The combined energy would be exactly double. See http://en.wikipedia.org/wiki/Poynting's_theorem

This is actually easiest to think about for a finite duration square wave pulse, IMO. The fields add together, and the energy density increases, but the volume decreases, so the end result is twice the total energy of a single pulse.

1. No, I’m asking about combing the E and B fields at the beam intersection, not the intensities. The beam intensity at the intersection is not double the two contributing intensities, creating energy out of nothing, as we both know. So what went wrong?

If we naively add the two field amplitudes, the intensity nearly quadruples--shy of quadrupling due to phase variation across the intersection. I believe the error in this idealized set-up is from failure to consider the source apertures, but its just a guess.2. I post this thread is in sequel to https://www.physicsforums.com/threads/splitting-and-combining-em-waves-amplitude-intensity.815517. I appreciated BvU responses and references, but these did not satisfy the original poster nor I. We seem to have three mutually inconsistant principles.

1) $I_m = {A_m}^2$, $I_\Sigma = {A_\Sigma}^2$ –intensity (energy) is equal to the square of the amplitude

2)$I_{\Sigma} = I_{1} + I_{2}$ –conservation of energy

3)$A_{Sigma} = A_{1} + A^{2}$ –interference or superposition principleCombining, $2A_1 A_2 = 0$, which says that either $A_1$, $A_2$ or both must be zero. What happened?

 

[nasu]

Really? It's thefreedictionary. Place two lasers closely together. Adjust the beams so they intersect at the other end of the optical bench or much further.

I did not give the reference to dictionary as an "authority" about the meaning but just to show the meaning that I was familiar with.
I understand now that you mean "a very small angle" when you mean a shear angle. I suppose it is a common use in your field.

 

[stedwards]

sorry

 

[stedwards]

Anyone?

Taken, in general, this is a broad concern beyond electromagnetic radiation to include: Sound Waves in air, solid material Transverse Waves and Electrical Power, Water Waves... and eventually quantum mechanics. Anything else?

There seems to be some general principle that never came up in school.