Hi Ananya,

what exactly do you want to calculate? In SPR sensors various methods are being used to determine the minimum position of the intensity dip, which is then converted into the Resonance signal. The sensorgrams / binding curves are fitted by different equations depending on the type of interaction and analysis.

Cheers Markus

Thanks you sir Markus Sack for the query ,actually we are working on multi-channel SPR sensors based on kreatschmann configuration . So as multi channel microfluidic system is there ,we will be designing the multichannel with PDMS .So we know about the SPR equation for resonance condition ,now i am interested in mathematical modelling of the micro-channel sensor chip where we have to take the consideration of PDMS dielectric.So i need to know will there be any change in resonance condition of the component which we are going to analyse in microchannel ?because when we design a single channel sensor chip,we find a particualr resonance dip . I am sorry i went more bit complicted

From Ananya

All mathematical analyses related to the surface plasmon resonance usually start from the Neumann–Poincaré operator of an open connected domain using a set of functions with zero mean value. This can be continued by some boundary integral equation with the help of the single-layer potential for a given density function. It is well-known that the single-layer potential satisfies some jump condition required to follow up such analysis.

Previously, I have used this reference to analysis the spectrum of SPR biosensor. Hopefully it can be useful

https://www.google.com/url?q=http://www.chem.konan-u.ac.jp/applphys/web_material/spr_tutorial/sprtheory_English.pdf&sa=U&ved=2ahUKEwjdvJjmgqLfAhUIU30KHXRVCKEQFjABegQIARAB&usg=AOvVaw2Vqp3dNL4kGnV91rGB67oH