How long does a diffraction pattern take to form?

[sophiecentaur]

I was idly musing (as you do) and I was thinking of Fermat's principle which says that light takes the 'shortest route'. That, however, must refer to the classical situation.
Take the simplest diffraction situation of two slits - or forming the really complex diffraction pattern from a large object on a hologram plate. (Or even, now I think about it, forming an image with a lens). You suddenly turn on the illumination. The image that forms in all three cases in made up of light (photons if you insist but I'd really rather not) from many paths of different lengths.

So the diffraction pattern will not be there to start with, as only one contribution will arrive first. The path difference for a large optical system could be several (even tens of) cms, corresponding to time differences of many picoseconds. (c is about one foot per nanosecond).
So this image will form over an extended period - by no means instantaneously - as the various contributions arrive. A bit like a developing photograph.

Obvious, when you think about it, but perhaps not everyone has. Enjoy.

 

[Greg Bernhardt]

@sophiecentaur did you gain more insight on this?

 

[sophiecentaur]

@sophiecentaur did you gain more insight on this?

I was a much younger man at the time I wrote this. I'm sure I must have 'matured' in the intervening time but, apart from adding some actual numbers into this, I don't think I'm much further into it. It's all going to happen pdq because there's no actual resonance involved.

 

[Andy Resnick]

Have you seen this 2004 reference:

https://www.sciencedirect.com/science/article/pii/S0030402605704010

This one is relevant also:

https://www.osapublishing.org/oe/abstract.cfm?uri=OE-11-10-1114

 

[tech99]

I was idly musing (as you do) and I was thinking of Fermat's principle which says that light takes the 'shortest route'. That, however, must refer to the classical situation.
Take the simplest diffraction situation of two slits - or forming the really complex diffraction pattern from a large object on a hologram plate. (Or even, now I think about it, forming an image with a lens). You suddenly turn on the illumination. The image that forms in all three cases in made up of light (photons if you insist but I'd really rather not) from many paths of different lengths.

So the diffraction pattern will not be there to start with, as only one contribution will arrive first. The path difference for a large optical system could be several (even tens of) cms, corresponding to time differences of many picoseconds. (c is about one foot per nanosecond).
So this image will form over an extended period - by no means instantaneously - as the various contributions arrive. A bit like a developing photograph.

Obvious, when you think about it, but perhaps not everyone has. Enjoy.

For the case of the first minimum with Young's Slits, I suppose the time of arrival would result in a flash of half a cycle at switch-on and another flash of half a cycle at switch off. These flashes come from one slit then the other. I can't help feeling this should tell us something about EM waves.
For cases where the delay is large, as for higher order bright fringes, if we try to send a brief flash of light, I suppose we are now trying to send a pulse in multipath environment, so bandwidth will be restricted and the pulse will have distortion and ringing.

 

[Vanadium 50]

Are we discussing diffraction or interference? Diffraction happens immediately at the aperture, Interference has a minimum time of the light transiting the longer path.

 

[tech99]

My suggestion is that for Young's Slits and for waves passing through an aperture, we have diffraction, which causes rays to deviate from their path and then interfere.

 

[sophiecentaur]

Are we discussing diffraction or interference? Diffraction happens immediately at the aperture, Interference has a minimum time of the light transiting the longer path.

That is true when the source is an ideal plane wave, arriving at a normal angle. If not, there will still be a finite settling down time. But, of course, we are talking in terms of a single cycle of the light wave, the minute width of the slit and a small angle. Slit separation will 'talk' much more. (Less "immediate")

People to lose too much sleep in deciding which one describes a situation better. It's another example where classification can cause more aggro than it should.
I would say that it's all Diffraction but that Interference is the approximation when individual, identical sources are involved.

 

[Vanadium 50]

But if we're talking about the "settling down time" of the source, we're talking about the source, not diffraction or interference. (As an aside - ever have to measure a delay 5% as long as the source variation? I have. Not easy.)

I think this is a case where distinguishing helps. (And helps answer your question)

Diffraction - happens at an aperture because light has a wave nature and is immediate.
Interference - happens when two or more waves intersect and takes the difference in light travel time to occur.

As an aside, it is possible to make very short pulses of light by having the light pulse interfere with itself after a delay. The light turns on, interferes with itself, and "shuts off".

 

[sophiecentaur]

But if we're talking about the "settling down time" of the source, we're talking about the source,

I could have used a better phrase than "settling down" but I meant that (off axis) the phase of contributions across the slits may vary a lot less than between slits but there is still a tilt. That finite coherence of the source means that the zeros of the slit pattern will be partly filled in. i.e. there is a time difference at the start and finish of any wave train and that is what I was referring to as "settling down" time.
And. let's face it, a very handy way to calculate the diffraction pattern width of a slit is to consider the interference between elements on two halves of the slit. The arrival of wavelets from across a real slit is not instantaneous.