Question about interference/slits/lasers

[fluidistic]

Why do we use for example a double slit screen in order to get interference on a screen?
My understanding is that a single laser creates coherent waves so that if we put a screen with 2 slits, it's as if we had 2 sources of light that are coherent.
While if I directly use 2 laser to point on a screen, I've heard that the laser doesn't create coherent waves between themselves. I don't know why it is so, but anyway assuming it's true and assuming that they emit light of the same frequency, I could move a laser a bit backward or forward until the waves get coherent, right? So that I'll fall in the case of a double sources of coherent waves hitting a screen and I would see interference on a diffuser screen.

So why exactly a double slit rather than a double different sources placed in such a way as being coherent?

 

[Andy Resnick]

Why do we use for example a double slit screen in order to get interference on a screen?
My understanding is that a single laser creates coherent waves so that if we put a screen with 2 slits, it's as if we had 2 sources of light that are coherent.
While if I directly use 2 laser to point on a screen, I've heard that the laser doesn't create coherent waves between themselves.

That's almost correct- your boldface segment should read "2 sources of light that are *mutually* coherent". Two independent sources are not generally mutually coherent. In the double slit experiment, the slits are not illuminated by mutually incoherent light.

Does that help?

 

[fluidistic]

That's almost correct- your boldface segment should read "2 sources of light that are *mutually* coherent". Two independent sources are not generally mutually coherent. In the double slit experiment, the slits are not illuminated by mutually incoherent light.

Does that help?

Thank you Andy.
Ok that's what I thought.
I'm curious as to know why 2 He-Ne lasers aren't necessarily mutually coherent. I mean I would like to know the reason.
Another little question that I asked in my first post: say I have 2 mutually incoherent lasers and I place them such that both beams are parallel. Further, I move 1 of these lasers until the phase difference of both beams becomes 0. Is that possible? It would allow me to get mutually coherent beams, and I could see interference on a screen. Am I right on this? (I don't have any laser pointer to try).

 

[Andy Resnick]

Thank you Andy.
Ok that's what I thought.
I'm curious as to know why 2 He-Ne lasers aren't necessarily mutually coherent. I mean I would like to know the reason.
Another little question that I asked in my first post: say I have 2 mutually incoherent lasers and I place them such that both beams are parallel. Further, I move 1 of these lasers until the phase difference of both beams becomes 0. Is that possible? It would allow me to get mutually coherent beams, and I could see interference on a screen. Am I right on this? (I don't have any laser pointer to try).

There are ways to couple two independent lasers (or other sources) to make the output mutually coherent:

http://www.ireap.umd.edu/Optical/Publications/pub97-5.pdf

The definition of mutual coherence is something like <E1E2*>, where E1 is the electric field E(r,t) of source 1 and E2 is the electric field of source 2. If they are independent- uncoupled power supplies for example- then by definition <E1E2*> = 0.

 

[Dr Lots-o'watts]

I think the first reason why a slit is used instead of two distinct sources for common demonstrations is that it's cheaper, better, and easier.

It's most likely possible to couple two distinct sources as Andy says, but why would you bother? One has to have a good reason to spend twice as much as necessary, and work at least twice as hard.

Of course, you may have good reasons.

 

[Cthugha]

Another little question that I asked in my first post: say I have 2 mutually incoherent lasers and I place them such that both beams are parallel. Further, I move 1 of these lasers until the phase difference of both beams becomes 0. Is that possible?

No, that is impossible. The phase relationship between the fields emitted from a single light source at different times will become lost on the time scale on the coherence time. That means that already the phase of a single light source (given that you know the phase now) is not predictable on longer timescales. Therefore also the relative phase between the fields emitted by two lasers will become completely random if you average over long time scales and interference patterns will vanish. You could now pick one of 3 solutions:

1) Perform single shot measurements on timescales much shorter than the coherence times of the lasers used. On these short timescales the two lasers will indeed be mutually coherent. However, from an experimental point of view, this is pretty difficult.

2) Actively synchronize the phases. This is pretty expensive.

3) Use two slits and a single light source. Although the predictability of the phase is still impossible for long times, all that matters in this case is the relative phase between the fields at the slits. This is constant. The dephasing will just add some random constant to the phases at both slits, so that the difference remains unaltered. Therefore you can even get a pretty well defined phase relationship for light sources with mediocre coherence length/time.

 

[fluidistic]

Thanks for all the replies.
Ok, I do not understand well either what is a wave or coherence.

No, that is impossible. The phase relationship between the fields emitted from a single light source at different times will become lost on the time scale on the coherence time. That means that already the phase of a single light source (given that you know the phase now) is not predictable on longer timescales. Therefore also the relative phase between the fields emitted by two lasers will become completely random if you average over long time scales and interference patterns will vanish.

Good to know, I wanted to know this.
To me a wave of a laser can be written \vec E = \vec E _0 \cos (\omega t - \vec k _1 \cdot \vec r _1 + \varepsilon _1), while the waves of another laser can be written \vec E = \vec E _0 \cos (\omega t - \vec k _2 \cdot \vec r _2 + \varepsilon _2). Graphing these function for a fixed time, we can see only a phase shift. Thus if I move 1 source, i.e. 1 laser, I could make the functions coincides. Assuming that they are the same kind of lasers. And I wouldn't still get coherent waves, despite they are written exactly the same?! I fail to understand this.

 

[Cthugha]

To me a wave of a laser can be written \vec E = \vec E _0 \cos (\omega t - \vec k _1 \cdot \vec r _1 + \varepsilon _1), while the waves of another laser can be written \vec E = \vec E _0 \cos (\omega t - \vec k _2 \cdot \vec r _2 + \varepsilon _2). Graphing these function for a fixed time, we can see only a phase shift. Thus if I move 1 source, i.e. 1 laser, I could make the functions coincides. Assuming that they are the same kind of lasers. And I wouldn't still get coherent waves, despite they are written exactly the same?! I fail to understand this.

This is just an idealized picture. Assuming this relationship means you can predict the future phase of the wave of interest if you know it at any arbitrary instant. While this is true for a completely ideal laser, no laser existing in reality is that ideal - and this is of course the fact that matters in experiments.

From another point of view you might think about time-energy uncertainty (although it is not a thorough uncertainty as momentum-position). A laser beam with completely well defined energy and phase would need to be infinitely long, which is never the case for real lasers.

 

[Andy Resnick]

Thanks for all the replies.
Ok, I do not understand well either what is a wave or coherence.

Good to know, I wanted to know this.
To me a wave of a laser can be written \vec E = \vec E _0 \cos (\omega t - \vec k _1 \cdot \vec r _1 + \varepsilon _1), while the waves of another laser can be written \vec E = \vec E _0 \cos (\omega t - \vec k _2 \cdot \vec r _2 + \varepsilon _2). Graphing these function for a fixed time, we can see only a phase shift. Thus if I move 1 source, i.e. 1 laser, I could make the functions coincides. Assuming that they are the same kind of lasers. And I wouldn't still get coherent waves, despite they are written exactly the same?! I fail to understand this.

I think I understand what you are asking, and it's a reasonable question.

What you wrote were fields for two monochromatic point sources- analogously to the linewidth of sources, finite-sized sources have a spread of wavevectors. The total field can usually be decomposed into a sum/integral of monochromatic plane waves, and the widths of the frequency and wavevector bands relate to the temporal and spatial coherence.

If you had two monochromatic point sources, you are correct- the sources will be mutually coherent for all time, everywhere. Real sources have a finite coherence time and area.

 

[fluidistic]

Ah, nice guys. I think I understand now. I was taking a monochromatic source of light while in reality no such source exist and this seems to be the problem!