Asymmetric SPR sensor response curve-fitting equation for the accurate determination of SPR resonance angle

An asymmetric surface plasmon resonance sensor response curve (SPR curve) equation derived from the three-layer Fresnel equation regarding p-polarization was proposed that can be used as a more general and appropriate SPR curve equation than Kretschmann’s equation given by R(X)=(1−α)/{(X−β)2+γ2}, where R is the reflectance of the incident light, α, β and γ are real parameters, and X the incident angle. The proposed equation is expressed as R(X)=A[1−{B+C(X−D)}/{(X−D)2+E2}] with a minimum reflectance at a conventional resonance angle of X=D+(−B+B2+C2E2)/C, where A, B, C, D and E are five real parameters that are very useful as fitting functions for a gold-based SPR curve in real-time measurement. In this equation, a modified resonance angle defined as parameter D is more appropriate than the conventional resonance angle as a variable that gives a linear response to changes in the refractive index of the sensing layer.