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.
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