Can we understand it on field component basis. Let's say in case of TM wave one of the K- component is along the interface which then satisfy K-matching condition to excite Surface Plasmons. But is it possible to give explanation using E-field components.

Thank you Mr. Pascal for correcting me. I have few more doubts, if you can help me out I will highly appreciate it. Now according to your explanation, if there is only perpendicular component present and then how they are propagating after getting excited.

Moreover, there was an article "Surface plasmon subwavelength optics" in nature by Ebbesen et. al, they have given a schematic of the SP mode in terms of charge clusters with field corresponding to each pair of negative and positive charge clusters pointing in the opposite direction. Then first of all, if there is no E-field component along the interface then how the clusters are forming alternatively (positive charge cluster and negative charge cluster) and secondly, how the direction of propagation is decided.

Why we are not considering the effect of magnetic field component present perpendicular to the dielectric interface.

The SPP are intrinsically made of two TM inhomogeneous plane waves.

If the question is "can we have a mode made of two TE inhomogeneous plane waves, one in a dielectric half space, the other in a metallic half space ?", the response is no. Maybe if I say that a TE polarization inside the metal is too simple (its scalar) to create an exponentially decaying field in the dielectric I will satisfy you a little bit. With the TM case, the polarization is a vector rotating inside the plane perpendicular to the interface containing the direction of SPP propagation (plane xz), and this polarization can create the evanescent wave. But the fact that kz1 + kz2 is never 0, and that kz1/eps1 + kz2/eps2 can be zero is not so mathematically complicated. Your question has something to do with the fact that reflectivity at Brewster's angle can be 0 only for TM waves. In fact, there is a continuity between dielectric-dielectric Brewster's angle, Kretschmann critical coupling of SPP and pure SPP on dielectric-metal interface.

If the question is "can I couple a TE wave with a SPP mode ?", you have to take into account that you cannot couple any homogeneous wave (TE or TM) with a SPP mode, unless if  your dielectric or your metal if finite in one direction. Then the coupling problem is a question of symmetry. You need to break the structure symmetry in order to produce a polarisation in the plane xz from a field polarized along y.

Fabrice Pardo Hi Fabrice, your comment is very informative. Could you give a more detailed explanation on how the Brewster's angle is related to the Kretschmann critical coupling of SPP? Or maybe recommend some related reading?