I was looking for this kind of videos all around, glad to found it, finally. Yet, it's intimidating to see the amount of detail you are getting into this videos.

i like your video so much, it's very clear and physics enriched

this video is a treasure, thank you very much!

Fantastic video! Helped a lot

WOW!! I Can't even demonstrate you how helpful your video is! thank you so much!

Best video on this theme!!! Thanks

Really good work!

Awesome video, thanks

Thank you for this video!

THANK YOU SO MUCH!

Coherence is NOT about the correlation between field-fluctuations (dU), but between field-values (U). The mutual coherence function (18:00) is a function of field-values (U)!

Thanks!

Great video.

This is a stunning video and has helped me more than all the others I've found on youtube. Thank you!. The only issue I still don't understand is how propagation increases the spatial coherence. At 6:39 , how can there be zero spatial correlation near the point sources but increased correlation near the slits? In the video, you state that each individual point source creates a wave which reaches both slits and is highly correlated which I understand. But how come this is not true near the point source as well? Surely each individual point source creates a wave which is highly correlated spatially at any two points (regardless of whether they are near the emitting source or far away from it), provided the 2 points are separated by the same distance?

@SanderKonijnenberg

Жыл бұрын

Thanks for the question, it's quite a subtle one! I think the key point is that when we talk about the spatial degree of coherence, we typically refer to the coherence with in a plane (i.e. flat surface), whereas the field that is emitted by a point source is coherent with itself on a spherical surface (because that's the field which was emitted at the same time). Only very far away from the source can the spherical surface be approximated as a flat surface. For example, if we consider a flat surface that goes through the point source(s), then the field across that surface is not spatially coherent due to the finite temporal coherence of the source (more quantitatively: the coherence *width* in the plane would equal the coherence *length* of the light). But if we consider a flat surface that is very far away from a point source, the field across that surface is spatially coherent, because we're approximately evaluating a spherical wavefront of the point source, which is coherent with itself.

Great video! I’m having some trouble with basics concepts such as a point source. If a laser is a point source, how can it be such a consentrated field of light instead of creating a spherical wave front and shine its red light like an inflating ball. Do the actual generation of the waves (photons?) go in all directions and the some mechanism in the laser just focuses all of that into one direction? My question then becomes, do the light emitted from the laser grow in diameter as the light goes further away? E.g. if the emitted diameter is 1 cm would the diameter on the moon be 2 cm? (I’m aware here that talking about ”diameter” might not make sense since it’s all waves… but what I’m imaginging is that the diameter is defined too be as wide until the field strength becomes too weak). Thanks for a great video. Please point out flaws in my reasoning!

@SanderKonijnenberg

Жыл бұрын

Thanks for your comment. Why would you say a laser is a point source? A laser produces, like a point source, a spatially coherent field. However, not all coherent fields must necessarily come from a point source. As long as you manage to obtain a well-defined phase relation between fields at different points, you have coherence. In lasers, light is generated by stimulated emission (that's what the acronym LASER stands for). This stimulated emission (as opposed to spontaneous emission) ensures the phase relation between photons, and therefore coherence (see en.wikipedia.org/wiki/Stimulated_emission). The phase relation between points defines the propagation direction. For example, if the wave fronts (=planes of constant phase) are spherical, the field propagates radially outward. If the wave fronts are planar, the field propagates in a single direction. Regarding the growing beam diameter: I think you may find this article on beam divergence helpful en.wikipedia.org/wiki/Beam_divergence. For a Gaussian beam, the beam waist ('diameter') determines the angle with which the beam diverges. A smaller waist implies a larger divergence angle, which makes sense if you consider the limit of a point source.

tq

can I ask some questions by your email? I want to attach some pictures to clarify my puzzling idea

fuckin great explanation, thank you!

4:17 could you derive why U(t-tau1) is the field at point 1 in analytically ?

@SanderKonijnenberg

3 жыл бұрын

You could do this using the causal Green's function for the wave equation (see e.g. webhome.phy.duke.edu/~rgb/Class/phy319/phy319/node75.html ). The amplitude of a field that is emitted by a point source does decrease with 1/r, which I've neglected here because it's the phase fluctuations, not the amplitude, that are relevant for coherence.

@DD-cz2ui

3 жыл бұрын

thanks for your speedy answer!!! and... i want to ask some more things.. 1. 12:59 you wrote the monochromatic light as U1*exp(-iwt) Is U1 meaning complex amplitude? Because I studied that monochromatic light can be expressed by (constant amplitude vector)*exp{i(kr-wt)} so i think U1 in your explanation means constant amplitude * exp(ikr) , that is complex amplitude.. am I right? 2. why quasimonochromatic source can be expressed by U1(t)exp(-iwt)?? what is the meaning of U1(t)?? 3. how can i express random light like monochromatic light?? I want to know what’s the wave expression of random light!! thanks for your kindness

@SanderKonijnenberg

3 жыл бұрын

@@DD-cz2ui 1. Yes, U1 denotes the complex amplitude. In my other video ( kzread.info/dash/bejne/ZWVkmZSjhsmvhag.html at 7:40) I introduce complex notation for time-harmonic fields. 2. A fully monochromatic field by definition has a time dependence of exp(-iwt). A quasimonochromatic field isn't fully monochromatic, so it can have a different sort of time dependence. But because it is *almost* monochromatic with frequency w, it is convenient to factorize the field as U(t)exp(-iwt), where U(t) varies slowly in time compared to exp(-iwt). 3. An arbitrary light field (in free space) is any field U(x,y,z,t) that satisfies the wave equation. It can be decomposed in monochromatic fields U(x,y,z,w) (see 9:24 of this video), where each monochromatic field satisfies the Helmholtz equation.

Are these slides available anywhere?

@SanderKonijnenberg

Жыл бұрын

I've uploaded the slides here: drive.google.com/file/d/1qU42xZs8C1nH7yE0njwQDEJBj1PAqqZP/view?usp=sharing

@xboxsucks12

Жыл бұрын

@@SanderKonijnenberg Great, thank you. This lecture is excellent by the way.

good video but.... to fast .... o my god .... why so fast xD

if you have spatial coherence then wont you also have temporal coherence by default and vice versa?

@SanderKonijnenberg

5 жыл бұрын

That's technically correct, hence the remark at 8:07 : the two concepts are interlinked, but for intuitive purposes it can still be useful to interpret them as two separate concepts. This is for example why the term quasi-monochromatic is introduced: if a field has spatial incoherence, then technically it must also have temporal incoherence (i.e. it can't be perfectly monochromatic), but if the field is significantly spatially incoherent while it's only a little temporally incoherent (i.e. it's quasi-monochromatic), then loosely speaking it can still be convenient to think of the field as spatially incoherent and temporally coherent.

@ARCSTREAMS

5 жыл бұрын

@@SanderKonijnenberg ok i have a few q's,,i made a beam of light using an led , a pin hole apperature and a large 6" plano convex spherical lens or instead of that i made a smaller beam using two small 30mm dia aspherical lenses from my binoculars,,now is the beam coming out relatively more spatially coherent because it was shaped into a collimated beam or does that have to do with it becoming more spatially coherent because it went through the pin hole? and if i used a narrow band color filter would this make it more temporally coherent as well? i also noticed that the smaller the pin hole the sharper and better divergent properties the beam was,,,can you explain to me what is happening? if i simply want a tight beam that has a long distance and very low divergence do i have to relly on spatial or temporal coherence?

@SanderKonijnenberg

5 жыл бұрын

@@ARCSTREAMS Spatial coherence is indeed created by using a small pinhole (because you're essentially making a point source, so the smaller the pinhole, the more spatially coherent the light). As a result of increased spatial coherence, a beam can be collimated better. To see why this is the case, imagine a point source in the front focal plane of a lens. The lens then creates a collimated beam. If there are multiple mutually incoherent point sources at different locations in the front focal plane (i.e. you have an extended source), then the different point sources generate collimated beams at different angles, hence the sum of those beams results in a beam with some divergence. The larger the size of the extended source (i.e. the lower the spatial coherence), the larger the divergence of the beam. So if you want a beam with low divergence, it's important to increase the spatial coherence. A narrow band color filter would indeed increase the temporal coherence, but I'm not sure if that would improve the collimation of the beam a lot compared to reducing the pinhole size.

@ARCSTREAMS

5 жыл бұрын

@@SanderKonijnenberg thank you ,good to know that spatial coherence is basically what is important but i think temporal also plays a role as well somehow juts like a laser,,and i understood what you said about the pin hole but is it possible to somehow,,, 1) have a small hole but increase the intensity emanating from this hole by using a brighter led or would this mean you end up having more rays going through the hole thus making it harder work for the lens ? not sure if more rays means more brightness per square area or if the rays themselves can become brighter without necessarily adding more 2)is it possible to find a way to collect more(or most of the) light from the single led and still somehow have a collimated beam that is brighter?maybe by using a fiber optic attachment that can gather all the light from the source and make them all come out from the small point at the end of the fiber acting like a point source?or will this simply mean more rays coming out thus defeating the purpose? 3)is it better to have this hole further away as possible from the source or closer? 4)a larger dia lens means a better decrease of divergence by the same factor correct? 5)an aspheric lens is better because there is no (or much less) chromatic aberration correct? is it also less spherical aberration? i never really understood spherical aberration in comparison to chromatic which i understand means diffraction of color,wonder what is the best lens to use for my project 6)what is the limit of such a device? how far can my beam go without the spot growing? 7)i always notice there is convergence to a small beam waste and then a collimated beam of limited distance before it starts diverging again,,i hate this and wonder if it can be fixed somehow ,,,also is this something to do with coherence lenght or distance or coherence area or one of those lol

@jacobvandijk6525

3 жыл бұрын

@@ARCSTREAMS Is that all??? @ 33:30 Hahaha...

wow i understood every equation,,NOT ,,all i got is that using different colors in the equations is describing different fields and thats it lol took me a while to also figure that out