DPI Theory

Fig. 12. Schematic of the optical intensity as light passes through a waveguide

CCD array

Fig. 13. Dual waveguide integrated inteferometer (Cross et al. 2004)

CCD array

Fig. 13. Dual waveguide integrated inteferometer (Cross et al. 2004)

The precise measurement of optical path lengths can best be achieved using interferometric techniques. This involves comparing the path length of a measuring arm with that of a reference arm. DPI utilises a simple integrated interferometric configuration, as shown in Fig. 13. Here the optical path length of the upper sensing waveguide (variant) is compared with the optical path length of the lower reference waveguide (invariant). When the light is emitted from the structure and allowed to interfere in the far-field, the classic interference fringes of Young's famous double slits experiment are observed.

A comparison of the optical path lengths of the two waveguide arms is achieved as follows. First, the two waveguides are excited by a single coherent light source. The wavefront entering the interferometer is thus in phase on entering the structure. As molecules adhere to the surface of the sensing waveguide, changes in the refractive index at this boundary occur. This leads to changes in the effective optical path length of the top waveguide only, which leads to changes in the phase between the light in the two waveguides. Thus, when the light now exits the two waveguides of the interferometer, they no longer hold the same phase relationship they did before the molecules were attached to the surface. This change manifests itself as a change in the position of the interference fringes.

Interferometers offer considerable advantages over angular measurements such as those made in SPR (see for comparison for Figs. 11 and 13), providing an exceedingly stable measurement platform with both high sensitivity and broad dynamic range. The stability of the measurement platform is achieved by the provision of a high-fidelity reference signal via the reference waveguide. Any minor deviations in the local environment or the output radiation will be compensated. The sensitivity is provided by measurement of the position of the interference fringes. Using standard algorithms it is possible to determine the fringe position to a very high accuracy, and therefore very subtle differences can be measured in the condition of the top sensing waveguide when compared to the lower reference waveguide.

So far we have described single-polarisation interferometry. This provides, albeit with extremely high sensitivity, very similar information to that provided using commercial SPR devices. Intrinsic to the physics of SPR is the restriction that monochromatic light of only a single polarization (TM) can excite the electromagnetic surface waves (Burrstein et al. 1974). The angular resonance position of excitation, whose measurement of change provides the basic assay data, is a single piece of information that reflects the changes to an optogeometric parameter of an interface layer that includes the average thickness and average density (through the refractive index) of the layer. It is not possible to unambiguously deconvolve these two aspects of the physical layer deposition (or removal) process (Flanagan and Pantell 1984).

At least two measurement parameters are needed to resolve the optoge-ometric parameters of a layer system. In areas of research demanding more detailed structural information, the output provided by such optical sensors may fall short of requirements. The folding and misfolding of proteins, for example, are increasingly topics of study in their connection with the onset of degenerative diseases such as Alzheimer's disease (Radford 2000). In the case of guided waves, no such restrictions to single measurements pertain.

In alternative evanescent wave techniques, an all-dielectric sensor surface is provided and excitation of bound or partially bound optical modes provides the measurement principle (Cush et al. 1993). In these structures, both TE and TM modes are allowed. Measurement of the excitation condition, by grating coupling for example, may be used to allow decon-volution of the thickness and refractive index of deposited layers (Nellen et al. 1988). However, the individual modes are excited at well-separated coupling angles of incidence, which limits the rate and precision at which data collection can be performed and involves mechanical scanning over several degrees of arc.

Returning to DPI, the use of the second polarisation of light provides a second independent measurement of the layer condition. This relies on the fact that plane polarised light behaves differently in waveguide structures depending upon which polarisation is utilised. The differences in behaviour of the two polarisations result from the differences in the evanescent field profiles generated by the two polarisations. These are shown schematically in Fig. 14.

We can determine the expected optical path length for a given polarisation of light by invoking Maxwell's equations. Maxwell's equations describe how the electric and magnetic fields propagate through any medium. They describe how you must have an electric field if you have a magnetic one and vice versa, what the relationship between the two is, and the fact that they can only change in a gradual manner (no steps). They also relate the material properties to the field's propagation by describing two constants,

Fig. 14. Comparison of evanescent field decay in transverse magnetic (TM) and transverse electric (TE) polarisations and the subsequent responses when alayer structure is deposited. RI Refractive index

the dielectric constant for the material (the refractive index) and the magnetic permeability (which, assuming there is no magnetic material, is equal to 1). To solve Maxwell's equations, you start at the boundaries where you know the solution (in our case in the bulk liquid or in the middle of the waveguide stack where the values are zero and assume an arbitrary value in the waveguide itself) and at each interface you force the electric fields to be equal and the magnetic fields to be equal, but allow the field profiles to vary according to their relationships between these interfaces.

Having solved Maxwell's equations for one polarisation for light travelling along the waveguide and interacting with the thin film and whatever is above it (the bulk refractive index), you get a range of possible solutions where the phase could equate the thickness and refractive index of the layer. This is shown by the solid line in Fig. 14. Returning to Maxwell's equations, we can now look at the behaviour of the second polarisation. As can be seen in Fig. 14, the evanescent field profiles demonstrate different exponential decays with distance from the waveguide surface. In the first case the electric field was perpendicular to the waveguide and now, in the second, it will be parallel (and the magnetic field perpendicular). Now when we resolve Maxwell's equations, we get a different range of possible thicknesses and refractive indices for the deposited layer (see dotted line in Fig. 14). In effect, the waveguide appears to have a different refractive index for one polarisation when compared to the other.

The waveguide is obviously made of the same material so, assuming there is no optical or magnetic anisotropy (birefringence) that could cause this effect, the difference in optical properties must be entirely due to the physical geometries of the layer. When the two plots of allowable layer geometries are superimposed, one upon the other (see Fig. 14), a unique solution is obtained at the intersect, which corresponds to the actual op-togeometric properties of the film. Thus, it can be seen that only modest assumptions (principally that the film is uniformly populated) need to be made in order to complete this analysis.

A more complete analysis of DPI can be found elsewhere (Cross et al. 2004).

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