SURFACE-PLASMON-RESONANCE BASED OPTICAL SENSING

Over the past twenty years, surface plasmon resonance has been developed as an effective technique for use in real-time biotechnological measurements of the kinetics of label-free biomolecular interactions with high sensitivity.^1-16 On a fundamental level, it is the dielectric-imaging involvement of the adsorbed biomolecular layer (DNA for example) in shifting the surface plasmon resonance (SPR) frequency by means of electrostatic coupling at the interface with the metal film substrate that facilitates SPR-based optical sensing. Of course, there are various factors that can influence surface plasmon resonance, including plasma nonlocality, phonons, multiplicity of layers, all of which should be carefully examined. Moreover, tunable SPR phenomenology based on the role of a magnetic field (both classically and quantum mechanically) merits consideration in regard to the field's effects on both the substrate¹⁷ and the adsorbed layer(s).¹⁸ This paper is focused on the establishment of the basic equations governing surface plasmon resonance, incorporating all the features cited above. In it, we present the formulation and closed-form analytical solution for the dynamic, nonlocal screening function of a thick substrate material with a thin external adsorbed layer, which can be extended to multiple layers. The result involves solution of the random phase approximation (RPA) integral equation for the spatially inhomogeneous system of the substrate and adsorbed layer,^19-25 given the individual polarizabilities of the thick substrate and the layer. (This is tantamount to the space-time matrix inversion of the inhomogeneous joint dielectric function of the system.) The frequency poles of the resulting screening function determine the shifted surface (and bulk) plasmon resonances and the associated residues at the resonance frequencies provide their relative excitation amplitudes. The latter represent the response strengths of the surface plasmon resonances (oscillator strengths), and will be of interest in optimizing the materials to be employed.