# Two coherent beams crossing each other's path; what will be the effect?

A laser beam is split into two beams. After traveling some distance they cross each other's path. I was just wondering this crossing will have any effect on the beam properties or not. More basically, if two coherent beams one heading north and the other heading east cross each other at origin, what will, if any, effect on the beam properties.

Well if you checked them at a distance away from their meeting point they would look normal but if you put a phosophorous screen right at the point of their intersection you would see an interference pattern. (this assumes you've set it up so that both sources are at a distance such that they have the same phase at the point of intersection.)

mgb_phys
Homework Helper
Except in very unusual circumstances or with very high power beams there is no effect.

Andy Resnick
You have described a Mach-Zender interferometer.

So, I can use a Fresnel Prism as a beam splitter?

Andy Resnick
You can use anything you want as a beamsplitter, so long as it does not destroy the coherence properties of the light.

Since photons are bosons, won't the beams just interact with each other and form a greater intensity of light?

Andy Resnick
I don't understand what you are asking.

I assume if both beams are of the same frequency they will just increase in intensity....that is all.

I've wondered things like that myself. Looking at just one beam, The photons that are "flowing", although moving along parallel paths, I believe would resemble cars on a highway. So when it comes to constructive and destructive interference, it would depend on how the wave form of two intersecting photons line up. However such occurrences would be random within the intersection of the two beams as not every photon would actually collide with another photon. So you would get random interferences of both kinds occurring within the intersection which to a photon would be like two people running into each other within our solar system. Ultimately the reason for the increase in intensity at the intersection (seen by blowing smoke) is simply due to a higher photon density at the intersection.

Or am I way off on this....

Andy Resnick
Actually, if you are careful, it's possible to mix two different frequencies- red and green make yellow, for example.

xArherx, photons do not travel like little bullets- that's a analogy that may be initially helpful but ultimately is internally inconsistent and leads to confusion. A single photon is of infinite extent, for example.

I'm having trouble picturing it. I simply thought of them as the particles moving at 300,000km/s. Where each particle then carries with it, a wave form. What do you mean by "infinite extent"?

Andy Resnick
A photon, strictly speaking, is an elementary excitation of the quantized electromagnetic field. In source-free space, this corresponds to monochromatic plane waves which exist for all time and space. In this sense, an individual photon is a quantum or packet of energy.

Real wavefronts have sptially and temporally limited extent. One way to handle this is to let many electromagnetic excitations form a 'wave packet', which consists of many photons, all with slightly different frequencies (energies), thus allowing spatial and temporal localization (think Fourier transforms).

In this way, detection of a photon is the collapse of the wavefunction.

So the photons are considered dense packets of existing waves? Does the source-free space imply that the waves exist without a source? I'm not clear on what your saying but I'm very interested. Though I have to warn you that my current knowledge is limited, after all I did use cars on a highway as an example.lol

Well cars on a highway collide, but photons can mix into one another. They are bosons after all and have no mass.

Actually, if you are careful, it's possible to mix two different frequencies- red and green make yellow, for example.

xArherx, photons do not travel like little bullets- that's a analogy that may be initially helpful but ultimately is internally inconsistent and leads to confusion. A single photon is of infinite extent, for example.

Is air nonlinear enough for combining frequency? With some very high intensity, thats surely possible (even vacuum has some nonlinear properities)... but with some normal lasers - i though you need some nonlinear material for effective (visible) mixing.

Absolutely, cars will collide. Photons can mix/constructive interference/destructive interference.

I guess what I was thinking was that if you had two highways that intersected each other. Then cars drove through without looking, not every car will collide with another. Some of the cars will make it through the intersection unscathed. Now have many cars and the chance of a collision increases. Now make the cars really small and the chance of collisions decreases.

I'm curious about the mass part. Photons have no rest mass. However do they have a relativistic mass? Thinking of it classically, light is affected by gravity (black holes) but only object having mass is supposed to be affected by gravity.

So do they have a relativistic mass or do they remain massless even at relativistic speeds (meaning gravity affects them by some other reason)?

Cthugha
Absolutely, cars will collide. Photons can mix/constructive interference/destructive interference.

You have to be careful here. It is not the case, that any arbitrary photons show constructive or destructive interference, if you superpose them. They usually have to come from the same coherence volume. If any light produces interference, you would see interferences, if you just pointed two flashlights at any screen, which is not the case.

What is meant by "same coherence volume"? Would a laser be an example of such, where the beam passes through two slots creating an interference pattern on a back screen? I've always wondered about that experiment and the shining of two flashlights is why. As you said, if you shine flashlights at the same spot there should be an interference pattern but there isn't one. How is it that the light coming from the same source shining through two slots produces the pattern while the light coming from two difference sources (kinda representing the light as it comes from each slot) doesn't? Also, I always thought that the intensity (brightness) of a light is proportional to the quantity of photons emanating from the source (or reflection). The interference experiment says that the increase and decrease in intensity is due to constructive and destructive interference. Is it one, or the other, or both?

Although shining two flashlights onto the same spot does cause the spot to be brighter than either individual flashlight, would that mean you are simply getting a constructive interference without the destructive? Or is it simply a larger quantity of photons?

I've always been fascinated and puzzled by light.

Andy Resnick
Is air nonlinear enough for combining frequency? With some very high intensity, thats surely possible (even vacuum has some nonlinear properities)... but with some normal lasers - i though you need some nonlinear material for effective (visible) mixing.

The mixing occurs at the detector- heterodyne detection (the beat frequency).

Cthugha
Although shining two flashlights onto the same spot does cause the spot to be brighter than either individual flashlight, would that mean you are simply getting a constructive interference without the destructive? Or is it simply a larger quantity of photons?

In this case, there is no interference. As you said, there is just an increase in the number of photons due to having two flashlights instead of one.

What is meant by "same coherence volume"? Would a laser be an example of such, where the beam passes through two slots creating an interference pattern on a back screen? I've always wondered about that experiment and the shining of two flashlights is why. As you said, if you shine flashlights at the same spot there should be an interference pattern but there isn't one. How is it that the light coming from the same source shining through two slots produces the pattern while the light coming from two difference sources (kinda representing the light as it comes from each slot) doesn't? Also, I always thought that the intensity (brightness) of a light is proportional to the quantity of photons emanating from the source (or reflection). The interference experiment says that the increase and decrease in intensity is due to constructive and destructive interference. Is it one, or the other, or both?

To explain interference, you have to take the underlying fields into account. From a classical point of view, intensity (corresponding to the number of photons) is roughly speaking the square of the underlying em-field. The field is characterized by amplitude and phase. In order for interference to occur, we need the superposition of several fields with a fixed phase relationship, so the fields can add up (when in phase) or cancel (when in antiphase). Taking any arbitrary fields, the phase relationship will be random, so no interference will occur. You just add the squares of the single fields.
If the origin of the two fields is the same source however - like from two atoms inside the same laser - there might be a fixed phase relationship, which allows the fields to add up or cancel and thereby produces interference. So one can define an area of the light source within which there is a fixed phase relationship (you can imagine, that the fields from atoms next to each other have a fixed phase relationship where atoms, which are e.g. 2 meters apart, do not) and some delay, during which interference will occur (if you split a coherent beam, delay one of the arms and recombine them, you can see interferences for short delay times, where for long delay times the phase relationship is random again). So the distance photons can travel during the maximum delay, which still shows interference, times the area mentioned before gives you some kind of volume, which is a first estimation of what a coherence volume is. Generally speaking, the more monochromatic a source is, the larger the coherence volume will be.

From a more mathematical point of view, there is no interference, if the sum of the squares of the single fields equals the square of the sum of the single fields and interferences occur, if the square of the sum of the single fields shows additional terms.

So would a florescent light be considered a coherent volume? Where light emitted would cause interference patterns if shining through two slits? Does that also mean if you put the light in front of a mirror, that there will be very rapid (short term) constructive/destructive inference cycles between the light and mirror?

Andy Resnick