Hello. I've done several experiments where I see the plasmon peak shifting to longer wavelengths with angle (a Bragg effect). This plasmon peak arises from a gold microstructured array.
When looking into literature for a mathematical model to explain this, however, I always find myself with the following equation, where wl is wavelength, a the grating period of my metamaterial, and theta the angle of incidence:
wl=a/m*[n+sin(theta)]
I apply it to my experimtal values (with the grating a and the different angles). I do not obtain values similar to the ones I got or similar shifts between angles.
Does anyone know why that might be? Or if there's another equation I should be using?
Thanks!
Dear Oriol,
Is your grating 1- or 2-dimensional?
I assume m is an integer denoting the order of diffraction. Then n should be the ((-1)*sine of the) angle at which your grating has maximum reflection. So I would write it as:
wl=a/m [sin(theta)-sin(theta_max)]
depending on the shape of your grating (flat top, saw tooth etc.), the second term could take different values.
Usually, I'd read "n" as a refractive index. Indeed, this is what I would still be missing here. Is your grating in vacuum/air or in a glass/polymer matrix or something else?
You have to account for the effective refractive index of your grating and it's surrounding. Though your excitation wavelength might have a fixed value, what arrives at the grating can be modified through any dispersive medium the light goes through wl -> wl/n_eff. If "a" is in the range of mum then putting n_eff = n_surrounding, should be sufficient, but if your gold structure takes a lot of space/volume in the unit cell - because it is wide or deep compared to "a" -, you'll have to calculate an effective n_eff using the relative filling fractions of the different materials.
Hope that helps,
Christin
Hi Christin,
sorry for lack of explanation. My array is 2D, consisting of gold microstructures in air. Substrate is Si.
Thanks for your answer!
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