Surface Plasmon Resonance has been established as a powerful method to monitor label-free biomolecular interactions in liquids. However, today with MP-SPR, it can deliver well beyond kinetics and equilibrium constants.
In this page, we summarize the basic theory behind SPR. You can find here information on surface plasmons, different SPR configurations and modelling.
Excitation of surface plasmons is based on total internal reflection when an incident beam of p-polarized light strikes an electrically conducting gold layer at the interface of a glass sensor with high RI (Refractive Index) and an external medium (gas or liquid) with low RI. At a given angle, the excitation of surface plasmons takes place resulting in a reduced intensity of the reflected light. (Fig.1). A slight change at the interface (e.g. a change in refractive index or formation of a nanoscale film thickness) will lead to a change in SPR signal, allowing precise measurements of thin film properties as well as surface molecular interactions in real-time.
SPR Navi: Basic scheme of prism, rotating laser and detector and simplification of the slide sensor layers
A surface plasmon is an electro-magnetic wave propagating along the surface of a thin metal layer. Optical excitation of the surface plasmon can be achieved in the so-called Kretschmann configuration, where p-polarised, collimated light beam undergoes total internal reflection at a glass/thin-metal-film/dielectric interface. The angle at which the resonance occurs is extremely sensitive to any change in the refractive index (RI) of the medium adjacent to the metal surface, and such changes can be monitored by recording intensity of reflected light when the system goes out of resonance.
The concept of surface plasmons originates in the plasma approach of Maxwell's theory: the free electrons of a metal are treated as an electron liquid of high density (plasma) and density fluctuations occurring on the surface of such a liquid are called plasmons, surface plasmons (SP), or surface polaritons[i].
According to Maxswell's theory, surface plasmons can propagate along a metallic surface and have a spectrum of eigen frequencies (ω) related to the wave-vector (k) by a dispersion relation:
ε2= ε 2'+i ε2'' and ε1 are the dielectric constant of the metal and of the medium in contact with it, respectively. Wave vector k1 of light at frequency ω travelling through the medium ε1 is described by:
where c is the speed of light in vacuum, and for vacuum (or air to some approximation) its dispersion relation is a straight line k1=ω/c (line kc in figure above). Since the SP's dispersion relation (curve SP in figure above) never intersects the dispersion relation of light in air, they cannot be excited directly by a freely propagating beam of light incident upon the metal surface. However, it is possible to "turn down" the light line to the point where both lines cross each other.
There are three principal configurations to achieve plasmon excitation by light. All three are shown schematically in figures below.
In the arrangement (a), light excites plasmons via a grating coupler. If the grating constant is b, then light wave vector is increased by an additional term 2Π/b, and the SP´s dispersion relation can be matched by a component of light vector parallel to the surface. For an angle of incidence equaling Θo the resonance condition takes the form:
The resonance can be observed at angle Θo as an intensity minimum of the reflected light[ii]. The disadvantage of grating-based sensors is that the light beam is incident through the sample solution, which may give some inaccuracies if the sample is absorptive.
The two other configurations presented in figure above are based on the fact, that the light line in in dispersion figure can be "lowered" by a factor √εo, if the beam is travelling through an optically denser medium (e.g. glass) whose dielectric constant is εo. If this is the case, then plasmons can be excited by p-polarised light undergoing total internal reflection (TIR) on the glass surface, or more precisely, they are excited by an evanescent wave associated with TIR and penetrating up to the metal/air interface. Exact matching of photons and plasmons happens for the resonance condition:
In the configuration (b), introduced by Otto,[iii] the metal surface (ε2) is separated from the medium εo by an additional dielectric layer (e.g. an air slit) having the dielectric constant ε1< εo. The SP resonance occurs at the metal (ε2) -dielectric (ε1) interface. The air slit should be only about 1 µm wide, and for this reason the Otto geometry has not been widely explored in SPR sensing.
In the third configuration (c), known as the Kretschmann geometry[iv], a thin metallic layer is formed on the substrate εo and acts itself as the spacer. For the correct film thickness, the evanescent field expanding through the metal may couple to the SP on the opposite (ε2/ε1) metal surface.
In all three cases, momentum matching between the plasmon and the incoming photon, i.e. excitation of plasmons is evidenced by a drop in intensity of reflected light when the angle of resonance is approached. Figure below shows an example of the SPR curve measured for silver with the aid of the Kretschmann configuration. Such resonant behavior gives an advantage in biosensor applications, because the value of the resonant angle ΘR is a sensitive function of the dielectric constants of the two contacting media. Due to this property, the surface plasmon resonance can be utilized in monitoring surface reactions, as every new ad-layer formed on the metal surface causes changes in dielectric function of medium ε1, establishing new resonance angle ΘR'. The shape of the whole resonance curve, i.e. its depth and width depends on optical absorption within the metal and on radiation losses resulting from surface roughness.
Goniometric Fixed Angle SPR
In the fixed angle configuration, the angle of incidence of light is fixed and chosen to be in the middle of the slope of the reflectance dip. Any shift in resonance angle ΘR can be detected as a change in intensity of reflected light when the system goes out of resonance.
Typical angle range is 1 degree.
Focused Beam SPR
The "focused beam" arrangement utilizes an idea of forming simultaneously more than one angle of incidence (an obvious property of any focused beam), and thus being able to record the whole SPR curve without the necessity of rotating the prism. The SPR curve and possible changes of its shape can be followed in real-time by a CCD array, as shown in figure below. A commercial model of the focused SPR, combined with multi-channel flow cell system, and applied to immunological studies, has been presented on the market[vi]. Another possibility is to realize the "focused beam SPR" idea in the form of an integrated optics chip for disposable use[vii].
Typical RI range is 1.30-1.40.
Typical angle range is 10 degrees.
allows the performance of two types of measurements:
Our RI range is from 1.00-1.40.
Our angle range is 40 degrees (38-78°)
This is the only configuration that enables the measurements of Multi-Parametric SPR!
Lower figure shows an experimental apparatus based on the Kretschmann geometry (used by SPR Navi™)that allows the performance of two types of measurements: recording of the whole resonance curve by turning the prism against the laser beam, and fixed angle monitoring when the prism is stopped close to the resonance angle. In order to improve sensitivity and accuracy of measurements, noise suppressing equipment, a light fluctuation compensation procedure, and digital data acquisition has been incorporated into the system. Optical sensitivity of this apparatus depends on the metal used ("steepness" of the slope) and is in the range Δn=10-7 for samples exposed to air, and Δn=10-6 for liquid samples[v].
A shape of the SPR curve can be quantitatively described by Fresnel's equations as the reflectivity of a multilayered system for p-polarised light[viii]. This possibility can be utilised for numerical simulation and prediction of sensor performance. For example, it has been found, that the SPR signal in liquids can be improved by introduction of an additional dielectric layer between substrate (εo) and metal (ε2)[ix], or background responses can be suppressed by adding an intermediate layer with high permittivity between metal (ε2) and analyte (ε1)[x].
Modelling of the SPR response by using a computer program which calculates reflection and transmission of polarised light in a stratified structure (stack of parallel layers) sandwiched between semi-infinite substrate (prism) and ambient (sample solution) media is also possible. All media have to be assumed to be linear, homogeneous and isotropic. For each medium the refractive index and for layers also the thicknesses have been used as input data. The calculation can be based e.g. on a 2x2 scattering matrix derived by using the Fresnel complex-amplitude reflection and transmission coefficients. The scattering matrix represents the overall optical properties and is expressed as a product of the interface and layer matrices of the entire structure[xi].
The opposite procedure, i.e. fitting of measured data into a theoretical model is also possible and may lead to identification of species adsorbed to the metal surface. Theoretically, only one set of s describing an adlayer (thickness and the real and imaginary parts of the dielectric constant) can fit the theoretical curve1, but the function describing minimum fitting error has a very shallow bottom[xii], so an unequivocal solution can be easily buried under instrumental noise and measurement errors. Proper fitting procedure should take into account also the roughness associated with every real surface. Fairly good agreement of data obtained from SPR fitting, as compared with those from direct surface observations by means of an atomic force microscope (AFM), have been reported in the literature[xiii].
[i] H. Raether, "Surface Plasmons", Springler-Verlag, Berlin, 1988.
[ii] D.C. Cullen, R. Lowe, Sensors and Actuators, B1, 576-579 (1990).
[iii] A. Otto, Z. Physik, 216, 398 (1968).
[iv] E. Kretschmann, Z. Physik, 241, 313-324 (1971).
[v] J. Lekkala, M. Albers, J.W. Sadowski, "Use of Protein G as an Intermediate Layer in Surface Plasmon Resonance Immunosensor", Proc. of World Congress on Medical Physics and Biomedical Engineering, Kyoto, Japan, 7-12 July, (1991).
[vi] Ivarsson B., U. Jönsson, S. Sjölander, R. Ståhlberg, H. Sjödin, "Optical Biosensor System", International Patent Application, WO90/05295 (1990).
[vii] J. Aarnio, S. Honkanen, Finnish Patent Application, No. 920412 (1992).
[viii] M. Born, E. Wolf, "Principles of Optics", Pergamon Press, Oxford (1980).
[ix] K. Matsubara, S. Kawata, S. Minami, "Multilayer system for a high-precision surface plasmon resonance sensor", Optics Letters, 15, 75-77 (1990).
[x] R.P.H. Kooyman, H. Kolkman, J. Van Gent, J. Greve, "Surface plasmon resonance immunosensors: sensitivity considerations", Analytica Chimica Acta, 213, 35-45 (1988).
[xi] R.M.A. Azzam and N.M. Bashara, “Ellipsometry and Polarized Light”, North-Holland, New York, 1976.
[xii] J.O. Lekkala, J.W. Sadowski, “Surface Plasmon Immunosensors”, in “Chemical Sensor Technology Vol.5” (editor: M. Aizawa), pp. 199-213, Kodansha Ltd., Tokyo, 1994.
[xiii] J.W. Sadowski, I. Korhonen, J. Peltonen, "Characterization of thin films and their structures in surface plasmon resonance measurements," Optical Engineering, 34 (9), pp. 2581-2586, (1995).