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.