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!
