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Following on from this question, which I found very useful on the topic, I was wondering how you would use the equation $\beta = k sin \theta \pm \nu g$ to fabricate a grating coupler to generate SPPs at a desired wavelength?

The problem I'm having is, for a fixed free-space wavevector ($k$), incident angle ($\theta$), and groove frequency ($g$), how do you know which diffraction order ($\nu$) to use when you want a specific value of $\beta$? Or will all the SPP modes corresponding to $\nu$ = 1,2,3,... be present at the same time with the lowest modes being the most dominant? In which case would you use $\nu = 1 $ when aiming for a specific $\beta$?

Thanks for the help!

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Sean
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  • If you have a specific and unique value of beta (dictated by your material and the frequency of your incoming light), the equality will hold only for one order nu. – EigenDavid Aug 05 '15 at 13:31
  • Thanks for your comment @David! What you've written makes sense... I guess I've made a bit of a mistake in my question. What I would like to know is, are lower order diffraction modes better than higher order modes when generating the same SPP wavelength (obviously in this case you would have to change one of the other terms as well)? – Sean Aug 05 '15 at 15:51
  • For example, if you varied only the free-space wavelength and the diffraction order to produce the same wavelength of SPPs, would the variations using higher mode SPPs have shorter propagation lengths? – Sean Aug 05 '15 at 15:53
  • I don't think you can have the same SPP wavelength if you vary only the freespace wavelength. If you have in mind the dispersion relation of the SPP and freespace you'll see that if you go up/down on the freespace line you'll have a discrete and finite number of possibilities to go from this line to the SPP curve (for different order), each leading to a different SPP wavelength. But if you change the angle at the same freespace wavelength it should "work". Concerning the efficiency of the generation through 1 or several order I search a little but could'nt find an answer. – EigenDavid Aug 06 '15 at 06:56
  • @Sean, How does one design an tunable optical filter for exclusively filtering intense coherent laser light while leaving the incoherent light background untouched? Thank you. – Frank Aug 23 '16 at 05:34

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