Why tilting a diffraction grating produces tilted dots

[Daniel Petka]

TL;DR Summary

If I send a gaussian laser beam through a diffraction grating at an angle, the dots are tilted and not straight.

Why does tilting a diffraction grating tilt the dots as well? This doesn't make sense to me because the lines are still lines when tilted. Even when I consider the phase and consider the gaussian beam that comes in as a superposition of plane waves, what comes out are dots in a straight line. Thanks for any insight!

My best attempt to make sense of this is to imagine the light behind the grating as an interference of many beams (plane waves actually). Ultimately, the light "doesn't know" what happens before it, it just propagates. This works great at normal incidence, it's called the angular spectrum, but it absolutely fails when the light comes in at an angle

 

[BvU]

Hi,

You found the picture, so I suppose you also found the article. (Could have saved us the time to locate it by posting the reference !)

The article goes a long way to answer your questions ....

Why does tilting a diffraction grating tilt the dots as well? This doesn't make sense to me because the lines are still lines when tilted. Even when I consider the phase and consider the gaussian beam that comes in as a superposition of plane waves, what comes out are dots in a straight line. Thanks for any insight!

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[Daniel Petka]

Hi,

You found the picture, so I suppose you also found the article. (Could have saved us the time to locate it by posting the reference !)

The article goes a long way to answer your questions ....



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Sorry for not including the article. The reason why I'm asking this is to understand the Ewald sphere. This is not the first article that I looked into that derives this using the Ewald sphere, so I'm kind of stuck. Forgive me, should have included that in the post. I already have the intuition for the Evald sphere and coupled wave theory at normal incidence - you don't have to worry about the continuity condition E,t1 = E,t2. It's not obvious to me why the continuity condition is connected to the Ewald sphere. That's where I'm struggling

 

[BvU]

Theories for almost any conceivable configuration other than the two mentioned above are treated in the literature (see, e.g., [2, 3]), but remain widely unknown to most non-specialists.

And I'm afraid I'm a non-specialist

Interesting topic, though !

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