Just for intellectual satisfaction. It seems that they are closely related. The Smith- Purcell effect requires an electron beam with high energy, passing parallel to a metal with diffraction grating and perpendicular to the direction of the grating period, this creates a "push" to electrons on the metal and the grating creates the dipole like oscillation for such electrons that allows it to radiate in the far field.
These effects seem, in some sense, similar but I would rather say no. SP effect does not require plasmonic properties of conducting media, and having just a conductive gratins is enough, I.e. nature of electromagnetic waves in the case of SP is different than in the plasmon case. Unlike plasmons, SP waves do not necessary have complex frequencies, and SP effect takes place even in the case of perfect conductance.
I understand that they are different. In fact Smith Purcell effect is an example of Cherenkov radiation ; instead of slowing light by entering a medium with high refractive index due to the polarization of its molecules, light propagates by exciting another dipole and its phase velocity is now slower just because gratings reduce the phase velocity of light. What i am really wondering about is whether the electron parallel to grating rulings imparts a tangential momentum on the metal (which is a standard way to excite SPP) and then the gratings out couple it to the far field as light .
Yes, your understanding that SPR arises due to excitation (in general, both tangential and normal) of electrons in a grating is correct. The excitation of plasmons and/or surface waves, however, is a different story: it can be involved into the process of SPR, but not necessarily.
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