I know that SP is an electrostatic case and an asymptotic limit of SPP in which K=0 i.e modes turn out to be longitudinal. But still the geometric picture for it is not clear to me.
Also why can't a em wave excite it if it's asymptotic limit of SPP?
Surface plasmon resonance is the phenomena or event of coupling of EM wave with oscillating conduction electrons of the metal nanofilm.
Surface plasmon polariton is the propagating EM wave generated at the metal-dielctric interface that propagates along the surface of the metal film after surface plasmon resonance.
Is it that first Surface plasmons are formed then it couples with incident light to propagate forming SPP. Then what leads to formation of surface plasmons at the first place.
Also if surface plasmons are electrostatic case(as far as i understand) how can it couple to an electrodynamic field.
SPP is a special point in SP dispersion relation which has same wave number as incident EM wave. In fact, the oscillation of the SP due to the negative and positive permititvity of the two layers at the interface of them but we'ill have SPP when the oscillation couples to an external EM wave in an especial wave number. You can refer to Maier's "Plasmonics fundamentals and applications" book.
If you are not talking about metal nanoparticles interacting with light, then SP waves and SPR waves can be used interchangeably, since everybody will understand you are talking about (propagating) surface plasmon waves at a given metal/semiconductor interface.
Both refer to a propagating EM wave generated at the metal-dielectric interface that propagates along the surface of the metal film when the incident light satisfies the surface plasmon resonance condition.