I Need Help Understanding Echelle Diffraction Gratings

[dartingeyes]

TL;DR Summary

I am looking for help understanding echelle gratings (the math and physical concept)

Hello,

I am attempting to understand and simulate an echelle grating. The thorlabs website has somewhat of an explanation as to how they work...(here). In the echelle section they calculate the spacing in degrees of 600 nm and 605 nm at different orders. They use an example grating of 31.6 lines/mm. For the n=1 case they get 0.009^o and for n=40 they get 0.6^o. I am not sure how they are getting these numbers, I am also confused how the units work out. I assume they are using the equation:

sinθ^' = nλ/d​

but I am not sure. Can I get some help understanding how they get here?


Additionally, if anyone knows of reference on material that explains the physical and mathematical concepts of echelle gratings a little better than this website, i would appreciate it.

Thank you.

 

[dartingeyes]

I realize that d= 1/31.6 * 1e6, so that the units do work out. but still i do not get the right answer

 

[dartingeyes]

I have solved this. the two angular separations are found by:

arcsin( m * 605/[(1/31.6)*1e6]) - arcsin( m * 600/[(1/31.6)*1e6])

where m=1 or 40.

By multiplying the difference by 180/pi, you get the desired result.

 

[berkeman]

Glad we could help!

And Welcome to PF, BTW.

 

[Andy Resnick]

Hello,

I am attempting to understand and simulate an echelle grating. [...]

Additionally, if anyone knows of reference on material that explains the physical and mathematical concepts of echelle gratings a little better than this website, i would appreciate it.

Echelle gratings are quite specialized; other sources of information I recommend are:

Richardson Grating Lab handbook (https://www.gratinglab.com/Information/Handbook/Handbook.aspx)
and a few technical papers etc:
https://opg.optica.org/ao/fulltext.cfm?uri=ao-34-10-1707&id=46029
https://hal.science/hal-01084458/