Monochromatic and Coherent light

[doubledouble]

How can the same source of monochromatic light produce 2 waves that are incoherent or coherent for that matter? (Is this even a valid question?)

What does coherence really mean beyond the definition of "waves that have a constant phase difference"

could anyone clarify this? thanks.

 

[Danger]

Welcome to PF, Doubledouble.
You must be a fellow Canuk, since nobody else would have clue about what your name means.
Essentially, the term 'monochromatic' just means that all photons involved are of the same frequency. (In casual useage, it just means the same colour, but includes a range of very similar colours.)
Coherency means that the monochromatic EM waves are synchronized so that all 'crests' and 'troughs' are aligned.
As a visualization, let's assume that you have a vector-based drawing programme similar to Illustrator or Coral Draw. Draw a sine wave that represents a particular colour such as the red produced by a chromium atom 'lasing' in a ruby crystal. Now hold down 'Shift' & 'Option' at the same time and drag the line down a tad. Click on 'Repeat Transform' a few times, and you'll have a representation of a coherent beam (laser).
To compare that to a source that's merely monochromatic, randomly select any of the resulant clone lines and move them around and rotate some of them at ambiguous angles. The colour will still be the same, based upon the shape of the waves, but the orientation won't be coherent.
I know that this is a half-assed explanation, but I hope that it serves as a base for further understanding.

 

[Cthugha]

Truly monochromatic point sources can't produce incoherent light.
True monochromatic light has a delta-peak shaped Fourier transform, which in turn means, that the wave shows the same amplitude and a well known phase over an infinite range. So the phase difference is always known.

In reality, there are no truly monochromatic light sources. They all show a certain line width and are therefore at least composed of a narrow frequency range (and do not show infinite length). Due to the superposition of several waves the phase of the wave train is predictable for short times, if you know the phase at some moment, but not for longer times. So from a classical point of view temporal coherence is a measure for the predictability of the phase information and thus also for the ability of the light to show interference.

In quantum optics coherence time is also the timescale, on which effects like bunching occur.

 

[Danger]

I don't know where the hell you came from, Cthugha, but welcome aboard. Nice post.

 

[P0litik]

Do two waves have to be of the same frequency for them to be coherent as well?

 

[Danger]

Yes—otherwise the crests and troughs can't line up along the length of the beam.

 

[west]

can waves be of a constant phase difference but having a different frequency?

 

[nousername]

Hey guys,

i was confused by this aswell, and no explanation has allowed me to truly understand the difference. I found this image online which showed me the difference and thought i might share it with everyone else:
[PLAIN]http://c683966.r66.cf2.rackcdn.com/wp-content/uploads/multichromatic-sunlight-monochromatic-and-coherent-light-950x968.jpg?cda6c1

 

[alkmini]

Truly monochromatic point sources can't produce incoherent light.


http://agamemnon.cord.org/cm/leot/course01_mod04/m1-4f13.jpg


we can have temporally coherent waves which means monochromatic, but not spatially coherent.
is this what the link says or am i confused?

 

[Cthugha]

That post was 5 years old...

However, indeed the post above focused on temporal coherence. Spatial coherence depends on the angular size of a light source as seen from some point, so it is a bit fishy as the spatial coherence of a light source can depend on how far you are away from it. As a rule of thumb point-like light source have ideal spatial coherence.

 

[alkmini]

.
Thank you for answering a question concerning a 5 year old post
My effort to understand interference and diffraction is 2 months old

As a rule of thumb point-like light source have ideal spatial coherence.

This is why we use the slits in interference, isn't it ?
What do we rally need in order to get the interference pattern, temporal or spatial coherence, or both?
if we use a slit we get the same phase for one instant, the instant the wave exits the slit, but if the light is not monochromatic how is this phase going to be the same at later instants?
How did Young produce an interference pattern since he had no monochromatic light?
How did he obtain a constant phase difference?
I bombarded you with questions , sorry

 

[Cthugha]

Thank you for answering a question concerning a 5 year old post
My effort to understand interference and diffraction is 2 months old

No problem. I just did not know whether you were aware that this thread is already rather old.

As a rule of thumb point-like light source have ideal spatial coherence.
This is why we use the slits in interference, isn't it ?

Yes, exactly. You do not really need a slit if you already have spatially coherent light, but using it will increase spatial coherence.

What do we rally need in order to get the interference pattern, temporal or spatial coherence, or both?

For a double slit interference pattern you need spatial coherence. For a Mach-Zehnder-interferometer pattern you need temporal coherence.

if we use a slit we get the same phase for one instant, the instant the wave exits the slit, but if the light is not monochromatic how is this phase going to be the same at later instants?

For experiments testing spatial coherence (like the double slit), the relative phase at different instants is not that important, but the relative phase at different positions. If you have a point-like light source all the light will come from this point and you can predict the phase of a wavefront that left the source at some time pretty well at any position it can travel to. If you have an extended light source the light can come from different points which are not necessarily synchronized and you cannot predict the phase at some position with the same precision as before as you do not know exactly from which point of the light source the light was emitted.

A good measure of how much spatial coherence you have is the angular size of the source as seen from some point. Just imagine you have an extended light source and draw a line from each point of the light source to your position. Now take the longest and the shortest of these lines. You will find that these lines also correspond to different angles. The smaller this difference in angles is, the higher your spatial coherence will be. Now repeat the same procedure for two different positions: One very close to the sample and one very far from the sample. You will notice that the difference in angles is very large close to the light source and very small far from the light source. That means that seen from a huge distance the same light source seems more point-like and therefore will also have higher spatial coherence.

How did Young produce an interference pattern since he had no monochromatic light?
How did he obtain a constant phase difference?

He used a slit to increase spatial coherence. As I said above, temporal coherence and monochromaticity is not the major factor in the double slit experiment - although it makes things much easier. He could also just have used a huge distance. The major problem in Young's experiment was not (only) getting spatial coherence, but getting spatial coherence and a reasonable brightness at the same time.

 

[alkmini]

thank you so much
you explained it extensively and clearly