A General Description of the Performance of Surface Plasmon Sensors Using a Transmission Line Resonant Circuit Model

Abstract

We analyze the response of surface plasmon (SP) sensors using a transmission line model. We illustrate this analysis with particular reference to a layered structure in which plasmon hybridization occurs. By applying the appropriate resonant condition to the system, we derive a circuit model which predicts the responsivity of different modes. This gives new physical insight into the sensing process. We discuss how the change in the sample region may be modeled as a change in the reactance in the equivalent circuit and from this, it follows that a single parameter can determine the change in resonance position with reactance. This approach is used to predict the response of a generic sensor to binding of an analyte and the bulk change of refractive index. This parameter arises naturally from the circuit representation in a way not readily accessible with the transfer matrix approach. The parameters can be expressed in terms of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula> of a resonant circuit and confirms the intuition that a high <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${Q}$ </tex-math></inline-formula> is associated with poor responsivity, however, we demonstrate that there is another circuit parameter, the resistance at resonance, that can mitigate this effect, providing a route for optimization of the sensor properties.