How Does Coherence Affect Interference and Diffraction in Light Waves?

[khurram usman]

if i have two in coherent waves then will interference and diffraction be noticeable?
if yes then to what extent and what factors matter?please xplain

 

[Drakkith]

Khurram, do you know what coherence, interference, and diffraction are?

 

[khurram usman]

lol...frankly speaking i do but there are some things i am confused about.
but do u mind answering my question?
also if u can then explain what is coherence other than 'a constant phase difference'?

 

[Drakkith]

Well, first of all, I really don't understand your question very well. I'm assuming English isn't your first language, so just bear with us if we need you to elaborate or re-phrase it.

Are you asking if two waves that are coherent (and by this that they are in phase and the same frequency) will interfere and diffract?

If the waves are the same frequency and phase then they will constuctively interfere. If they are out of phase they will vary between different amounts of interference. If they are exactly opposite phases then they will interfere destructively and cancel themselves completely.

As for diffraction, I don't think that has anything to do with multiple waves and only has to do with each wave by itself. However I am not very familiar with waves so I could be incorrect.

 

[RedX]

if i have two in coherent waves then will interference and diffraction be noticeable?
if yes then to what extent and what factors matter?please xplain

By definition, coherent waves means the waves will produce an interference pattern.

So incoherent waves cannot product an interference pattern.

 

[Cthugha]

So incoherent waves cannot product an interference pattern.

This is not really correct. Any combination of waves will show interference in a double slit or Michelson interferometer under some circumstances. Mainly, this depends on the relative magnitude of coherence time/length to the time delay in the interferometer or the slit distance of the double slit. So you can distinguish between waves having longer or shorter coherence times, but not between coherent and incoherent because in reality there is no light that will never show interference under any circumstances. Even worse there are some kind of coherent light sources like high-beta photonic crystal lasers which are coherent, but have a rather short coherence time, while there are also other light sources like spectral line lamps which have rather long coherence times, but are incoherent.

also if u can then explain what is coherence other than 'a constant phase difference'?

First-order temporal coherence as measured using a Michelson interferometer is basically indeed a measure of how well defined the phase difference is. On the other hand temporal coherence is (for not too nasty lineshapes) the Fourier transform of the spectral density. In other words: The narrower your line is spectrally, the longer your coherence time will be and vice versa. For two waves of different frequency, you can also get interference if the waves are mutually coherent. You will then see some beatings in the signal of the superposed waves. You can picture coherence time as the time over which the relative phase between two light fields randomizes.

In higher orders coherence is (in simple terms) basically a measure of whether photon emission or detection processes are statistically independent of each other or not.

 

[RedX]

So you can distinguish between waves having longer or shorter coherence times, but not between coherent and incoherent because in reality there is no light that will never show interference under any circumstances. Even worse there are some kind of coherent light sources like high-beta photonic crystal lasers which are coherent, but have a rather short coherence time, while there are also other light sources like spectral line lamps which have rather long coherence times, but are incoherent.

I took coherence to mean for a given circumstance, not for all circumstances. So sunlight for example is regarded as spatially incoherent, but technically if the area that it's focusing on is less than 10^-3 mm^2, then it's coherent.

I'm not sure how something can have a short coherence time and yet be coherent, or a long coherence time yet be incoherent?

For two waves of different frequency, you can also get interference if the waves are mutually coherent. You will then see some beatings in the signal of the superposed waves. You can picture coherence time as the time over which the relative phase between two light fields randomizes.

Technically, don't you have to have more than two sources of different frequency for something to be incoherent? I would think you would need as many random sources as it takes to cancel out all interference terms.

 

[Cthugha]

I took coherence to mean for a given circumstance, not for all circumstances. So sunlight for example is regarded as spatially incoherent, but technically if the area that it's focusing on is less than 10^-3 mm^2, then it's coherent.

Sure, but having coherence depend on the circumstances and not solely on the properties of your light source is somewhat dissatisfying, no? To us sunlight is pretty incoherent. Seen from Sirius B, sunlight has rather large spatial coherence just as the light of Sirius B seems rather coherent to us. Also, take some sunlight and pass it through a pinhole and it will become more coherent. For temporal coherence take sunlight and pass it through a very narrow bandwidth spectral filter. The remaining light will have much longer coherence time.

I'm not sure how something can have a short coherence time and yet be coherent, or a long coherence time yet be incoherent?

I have seen QD microdisk laser with coherence times as short as 4 picoseconds and yet they are lasers and coherent.

That is an excellent question that partially led to the development of quantum optics. You can define second and higher-order coherence as a property that is largely independent of the circumstances. It is basically a measure of the underlying photon number distribution and its higher-order factorial moments. The closer it is to a Poissonian distribution and therefore to statistical independence of photon detections, the more coherent it is. For light that is not coherent (for example thermal light), the differences from statistical independence vanish on a timescale on the order of the coherence time which makes it clear why the concept of coherence time is also sensible for incoherent light. For example the HBT-effect utilizes this fact. You can use it to measure star diameters by examining the degree of coherence and coherence time of the light that star emits.

Technically, don't you have to have more than two sources of different frequency for something to be incoherent? I would think you would need as many random sources as it takes to cancel out all interference terms.

Well, technically speaking you need some random phase jumps in your light fields in order to reduce first-order coherence which will automatically broaden all of your lines and include more frequencies. How many you need depends on what you actually consider as incoherent.