ELSEVIER ADVANCED TECHNOLOGY Biosensors & Bioelectronics Vol. 11, No. 6/7, pp. 677-684, 1996 © 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0956-5663/96/$15.00 Modeling SPR sensors with the finite-difference time-domain method Douglas Christensen & David Fowers Department of Electrical Engineering and Department of Bioengineering, University of Utah, Salt Lake City, UT 84112, USA Tel: [1] (801) 581 7859 Fax: [1] (801) 581 5281 Abstract: In sensors employing surface plasmon resonance (SPR), the uniformity of the metal film and the wavefront structure of the incident beam have an effect on angular sensitivity, yet most modeling methods are not capable of considering inhomogeneous layers or nonplanar excitation beams. We have applied the numerical electromagnetic method of finite-difference time-domain to this problem. To correctly model the time- domain behavior of the metal's electron oscillations, we add a kinetic force equation consistent with the Drude free electron model. We have analyzed an SPR configuration consisting of an illuminating beam of finite size (approximating a focused beam) incident onto a smooth silver film, and have obtained Poynting vector plots and reflectivity data. We find that the angular width of the near-field reflectivity minimum is in reasonable agreement with an extension of planewave theory using an angular spectrum approach. We have also analyzed a model of a rough metal film, and find that the reflectivity curve is broadened and shifted, and that local electric fields are enhanced near the metal edges. Keywords: surface plasmon resonance, sensor modeling, finite-difference time-domain, numerical techniques INTRODUCTION Surface plasmon resonance (SPR) has proven to be a valuable tool for monitoring the properties of thin films and their local environment (Raether, 1988). For example, it has found application as a real-time monitor of surface interactions (e.g., the Pharmacia BIAcore TM system [Liedberg et al., 1993]), and is being increasingly studied for other chemical or biological sensing applications (Wolfbeis, 1991; Liedberg et al., 1983; Attridge et al., 1991; Lukosz, 1991). The phenomenon of SPR can be observed when a polarized light beam is incident through a transparent substrate onto a thin deposited film of metal, such as silver or gold. When the beam is polarized with its electric field in the plane of incidence, the field causes collective oscillations of the electrons in the metal layer and results in bunching of these electrons (plasmons). ff the angle of incidence is above the critical angle for total internal reflection (TIR), the beam is strongly reflected with a small portion of its electric field extending evanescently into the medium beyond the film. However, at a certain angle corresponding to surface plasmon resonance, the parallel wave vectors of the incident light and the surface plasmons match, strongly coupling the two modes together. This results in a noticable decrease in the reflectivity of the film due to increased absorption of the incident light power by the metal film. The angle at which this reflectivity minimum occurs is a function of the raetal optical properties (expressed in the frequency domain as complex permittivity), the film thickness, and--important for its use in surface sensing--the permittivity of the medium within an evanescent distance bordering the film. 677