# How do two light beams combine at a shear angle?

• stedwards
In summary, the conversation discusses how two light beams combine at a shear angle and the resulting increase in energy density. The participants also bring up the principles of intensity, energy conservation, and interference. They also mention how this concept applies to other types of waves such as sound and water waves.
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.

You can just take the superposition of each individual wave.

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

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

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

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

DaleSpam said:
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?

stedwards said:
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.

sorry

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.

Last edited:

## Question 1: What is a shear angle?

A shear angle is the angle formed between two light beams when they intersect and combine.

## Question 2: How do two light beams combine at a shear angle?

When two light beams intersect at a shear angle, they combine by overlapping and interacting with each other's electric and magnetic fields, resulting in a new combined light beam with a different intensity and polarization.

## Question 3: What factors affect the combination of light beams at a shear angle?

The combination of light beams at a shear angle can be affected by the intensity, wavelength, and polarization of the individual light beams, as well as the angle at which they intersect and the properties of the medium they are passing through.

## Question 4: What is the difference between coherent and incoherent combination of light beams at a shear angle?

In coherent combination, the light beams have the same wavelength, phase, and polarization, resulting in a constructive interference and a stronger combined beam. In incoherent combination, the light beams have different wavelengths, phases, and polarizations, resulting in a less intense and more random combination.

## Question 5: What are the practical applications of combining light beams at a shear angle?

Combining light beams at a shear angle can be used in various applications such as optical communications, holography, and interferometry. It can also be used to manipulate and control the properties of light, leading to advancements in technologies such as lasers and optical sensors.

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