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A sinusoidal silver grating is used to create a six-fold enhancement of the SPR response compared to a flat surface. The grating parameters are chosen to create a surface plasmon bandgap and it is shown that the enhancement of the sensitivity to bulk sample index occurs when operating near the bandgap. The Kretschmann configuration is considered and the Boundary Element Method is used to generate the dispersion curves.
©2007 Optical Society of America
1. Introduction
Surface plasmon resonance (SPR) is widely used for biosensing applications in areas such as the pharmaceutical industry, water safety testing, and in medical diagnostics such as blood testing. The current and future demands of these applications require compact and highly sensitive SPR surfaces. The motivation of this research is to investigate the impact of surface corrugation on SPR sensitivity. For simplicity the corrugation of the surface will be limited to a sinusoidal profile.
SPR is a phenomena whereby light incident on a metal-dielectric interface couples energy to a surface electron density wave [1]. The coupling to the surface plasmon occurs at a specific energy and momentum collectively referred to as the resonance condition. In most SPR applications the energy and momentum are controlled through the wavelength and incidence angle of the excitation light respectively. Incoming light at the resonance condition will couple to the surface plasmon causing a dip in the reflection spectrum. Since the position of the dip is a function of the properties of the dielectric at the interface, monitoring the position can give information about molecules that bind to that surface.
The standard configuration for coupling light into a surface plasmon uses a prism in the Kretschmann configuration, also known as the attenuated total reflection (ATR) configuration. Light directly incident on the metal (i.e. from outside the prism) does not have sufficient momentum to excite a surface plasmon, therefore the prism is used to increase the momentum of the incoming photon and allow coupling to the surface plasmon.
By adding a corrugation (i.e. grating) to the metal two things can be accomplished: firstly, the grating can be used to couple light into the surface plasmon by providing the necessary momentum matching, analogous to the way grating couplers couple light into waveguides [2,3]; and secondly, the grating can be used to perturb the propagation of the surface plasmon [4]. There are two configurations used for grating coupling: direct and indirect (see Fig. 1). In the direct configuration light is incident directly onto the metal-dielectric interface from the dielectric side [5], while for the indirect configuration the light is incident through a prism [6,7]. The indirect configuration is interesting because it allows for both grating coupled and ATR coupled surface plasmons at two distinct angles. Some authors have also used a grating to both couple incident light to a surface plasmon and then perturb the surface plasmon (see [8,9]). However, the focus of our work is to couple light to a surface plasmon with the ATR method and then use a grating to perturb it (see [4,10–12]).
Surface plasmons propagating in a direction perpendicular to a one dimensional grating (i.e. along the grating vector) will experience back reflections. If the period of the grating corresponds to the Bragg condition then a bandgap will form where no surface plasmons are permitted to propagate[9,13]. In the literature, the main use of the surface plasmon bandgap has been to control the direction of propagation of surface plasmons similar to the use of waveguides and photonic crystals in telecommunications[10,14]. Surface plasmon bandgaps are attractive due to the small wavelength of the surface plasmon that allows for very small optical circuits. Many authors have succeeded in controlling the energy flow of the surface plasmons for creating structures such as mirrors, waveguides, beamsplitters and interferometers[10,15]. However the focus of this paper is to use the surface plasmon bandgap for biosensing applications. In particular we show theoretically that the surface plasmons on the edge of the bandgap experience an increased sensitivity to bulk index changes in the dielectric above the grating.
Fig. 1. Three configurations to couple light to surface plasmons: a) Conventional ATR coupled SPR with a prism and a thin flat metal layer, b) Conventional grating coupled SPR where light is directly incident on the corrugated interface, c) Combined ATR and indirect grating coupled SPR. Due to the additional momentum from the grating, the indirect grating coupling requires a shallower incidence angle (yellow arrow).
This paper is organized as follows: The structure and simulation methods are covered in section 2, the features of the dispersion curve with a grating are described in section 3 and the sensitivity results and conclusions are presented in sections 4 and 5 respectively.
2. Structure and simulation
Our proposed structure consists of a thin layer of silver, of minimum thickness t whose upper surface consists of a sinusoidal surface relief grating of depth h (see Fig. 2). The total thickness of the silver film varies from t to t+h at the troughs and peaks respectively. The period is given by P. The structure is designed to be used in the standard Kretschmann configuration where light is incident through the substrate and reflects off the silver/glass interface. An evanescent field penetrates the silver and couples to a surface plasmon on the grating side of the silver layer. The sample is in contact with the grating side of the silver layer and therefore in direct contact with the surface plasmon.
Since the surface plasmon is not propagating on a flat surface the standard equation for the surface plasmon wavevector no longer holds. A rigorous model is needed to accurately predict the effects of the perturbation from the grating. We have chosen to use the boundary element method (BEM) for our simulations because it offers good accuracy while providing for short computation times. We designed the structure so that we could use the convenient laser wavelengths near 850nm; this allows us to achieve the maximum field penetration depth in the sample while still using glass as the substrate. This is due to the fact that the penetration depth of the surface plasmon evanescent tail in the sample is proportional to the wavelength. However, the bandgap concept is feasible in the visible range as well. The control over the position of the bandgap with respect to wavelength and angle can be accomplished through the manipulation of the period and/or grating height. Changing the period is preferable because it causes a simple shift of the Bragg wavelength, whereas the grating height affects the degree of perturbation and can change the dip shape dramatically.
The calculations were performed using the integral equation treatment of D. Maystre [16]. This theory uses a fictitious surface current to reduce the diffraction problem to a single unknown function for each corrugated interface of the grating stack, while plane interfaces are solved analytically. Separate calculations are carried out for each polarization of light, with the relevant polarization here being TM, where the magnetic field vector of the incident wave is oriented along the grooves of the grating. Optical constants for silver are taken from Johnson and Christy, with each frequency being solved separately [17]. A refractive index of n=1.5 for the prism is used for all curves. Calculations were carried out with a sufficient number of integration points on the sinusoidal profile (100) and plane waves (61) to ensure that all results reported are accurate to better than graphical accuracy. The calculations were carried out on a PC, with each curve taking about 40 minutes (for 3000 points).
3. Features of the bandgap
A comparison of Fig. 3 and Fig. 4 clearly shows the difference in the dispersion curves between a flat surface and a grating. If the grating is not too deep then we can gain some qualitative understanding of the features of the bandgap by using the simple formula for the flat surface propagation constant of a surface plasmon given by:
where k o is the free space propagation constant, ε D is the dielectric constant of the dielectric and ε mr is the real part of the dielectric constant of the metal. The Bragg period (ΛB) is related to the surface plasmon wavelength (λsp) and free-space wavelength (λo) as follows:
The surface plasmons that reflect off the grating receive momentum equal to integral multiples of the grating vector. Using this fact along with Eq. (1) we can calculate the position on the dispersion curve of the reflected surface plasmons (i.e. the -1 order grating reflection) along with the substrate mode surface plasmons. This simple calculation helps to elucidate the dispersion curves calculated with BEM; and the correlation is quite good for small grating heights as seen in Fig. 4. The figure represents reflection intensities. The studded blue lines are calculated with Eq. (1) and Eq. (2) and represent the locus for the unperturbed reflection minima. The vertical line (A) represents the standard surface plasmon for a flat surface while the horizontal lines (B and C) represent the backwards propagating surface plasmon and the substrate mode respectively. These simple calculations reveal only the approximate position of the resonance dips, but not how much energy is coupled between them: the rigorous BEM calculation is needed for that determination.
The key feature for biosensing applications is that the bandgap moves when the sample index changes; i.e. when molecules bind to the surface. With reference to Fig. 4 it moves in a diagonal path up and to the right towards larger angles and longer wavelengths when the sample index increases. This can readily be seen in the attached movie in Fig. 5. Analogous with traditional SPR, movement of the bandgap provides two opportunities to measure the change in sample index: both wavelength and angle interrogation. For wavelength interrogation one can track the edge of the bandgap with respect to wavelength; doing this yields a sensitivity of approximately 600nm/RIU which is comparable to localized surface plasmon and nanograting sensitivities (operating away from the bandgap)[18–20]. However, this is still an order of magnitude less than the sensitivity for a flat surface, and so is limited in terms of future development. The second method of tracking the sample index change is with the angular shift (with constant wavelength) of the dip near the bandgap. In the next section we will show that this method yields enhanced sensitivities compared to those for a flat surface.
Fig. 3. Dispersion curve for a flat silver surface with sample index of n=1.3. The colour bar shows reflectance with white representing high reflectivity.
Fig. 4. Dispersion curve for a 20nm grating with sample index of n=1.3 overlapped with the curves calculated from Eq. (1) (blue diamond studded lines). [Media 1]
Tracking the angular shift near the bandgap has the benefit of enhanced sensitivity, but it has the drawback of limited dynamic range. The higher sensitivity only occurs when operated near the bandgap. This is an analogous situation to phase interrogated SPR when it was first described; i.e. it had high sensitivity but low dynamic range [21]. This was subsequently overcome by using 2D phase imaging [22]. Similarly, the obstacle of a short dynamic range needs to be overcome for future development of this bandgap method. One solution might be to use a tunable wavelength source and dynamically tune it to the bandedge wavelength; thus staying in the high sensitivity zone. However, dynamically tuning the wavelength is a challenging proposition and our current work consists of developing a 2-D imaging method to overcome this challenge [23]. The 2-D method is a way of experimentally generating the dispersion curves seen in Fig. 4 by simultaneously using a broadband source and focusing technique in orthogonal axes. This technique was previously used simply to image the dispersion curve diagrams both with and without a bandgap [24,25], but has not yet been applied to biosensing. The advantage of this method is that it will allow the tracking of the bandedge through image processing techniques instead of a tunable source. Also, it will provide a more robust measurement given that the images will contain much more information than standard SPR curves done with either fixed wavelength (angular interrogation) or fixed angle (wavelength interrogation).
4. Sensitivity results
To investigate the sensitivity enhancement we use the fixed wavelength of 850nm and compared the sensitivity of a flat surface to that of several different grating configurations. Specifically, we chose two grating heights of 20nm and 40nm and we used three different metal thicknesses for each: 30nm, 40nm and 50nm. Of course each configuration perturbs the SP differently and therefore moves the bandgap. To keep the bandgap close to 850nm for all the grating configurations it is necessary to adjust the period of each grating as noted in Fig. 7 (in a practical sensor, as outlined in the previous section, a spectroscopic measurement technique would be used). The sensitivity here is calculated by dividing the angular shift in the dip by the refractive index change noted as refractive index units (Δθ/RIU). The reflectivity dips for a flat surface and grating (h=40nm, t=50nm and h=20nm, t=50nm) are shown in Fig. 6 for sample index values ranging from 1.33 to 1.34. The corresponding sensitivity vs. sample index is shown in Fig. 7 for all gratings. When comparing the sensitivity of the flat surface to that of the grating, it is clear that a broad enhancement emerges near the bandgap for all values of the grating parameters t and h. More specifically, there is a peak in the sensitivity at the edge of the bandgap for each combination of t and h, with a maximum enhancement of over a factor of six for h=40nm. While the magnitude of the enhancement is larger for the deeper gratings (h=40nm), the shape and position of the curves make them less appealing when compared to the shallow gratings (h=20nm). First, the deeper grooves couple more of the energy to the unwanted substrate mode. Second, as can be seen from Fig. 6 the dips for the grating are not as deep as those for the flat surface. This is due to the fact that the average thickness of the metal containing the grating is greater than the 50nm thickness needed for optimal coupling; thus slightly less energy is coupled into the SP resulting in shallower dips; this effect is worse for the 40nm gratings. Finally, the deeper gratings provide dips at higher angles of incidence which would make its implementation more difficult. Note that all sensitivity values are given for bulk index changes which is consistent with the approach followed in previous publications [18,26,27]. It is to be expected that when the refractive index changes occur only in a monolayer the sensitivity will be reduced, but the details will depend on the nature of the monolayer, making it simpler to compare the response for bulk index changes.
Fig. 5. (95KB) Movie of the dispersion curve shift with t=50nm and h=40nm as the sample index varies from n=1.3 to n=1.4 with increments of Δn=0.01.
Near the bandgap the dip becomes wider than that observed for a flat surface. Intuitively, this might seem to have the unwanted effect of lowering the resolution due to the decreased sharpness of the dip. Yoon et al. [18] have introduced a figure of merit (FOM) which is based on this concept and which is equal to the ratio of the angular shift to the dip width. Using this metric, the curves near the bandgap for a 40nm grating (t=50nm) have a lower FOM compared to that of a flat surface (120 vs. 500 respectively) but the curves for a 20nm grating (t=50nm) have a larger FOM (600) when considering the local minima. The changing shape of the curves will cause the FOM to vary at different sample index values so that sometimes it is better than the FOM of a flat surface, and sometimes worse. However, other studies suggest that in a real system, other factors may have a much more significant effect on resolution [28]. In practice, the performance of an SPR sensor is dependent on the method by which the SPR curve is recorded and then analyzed; namely recording with a CCD or diode array followed by analysis with a dip-finding algorithm. Both CCDs and diode arrays are spatially discrete recording devices (i.e. they have pixels), and this effects the resolution of the dip-finding algorithms. Although a narrow dip means a higher theoretical resolution for a continuous curve due to its sharpness (with corresponding large FOM), the discreteness of the detector means that it contains fewer points and therefore imparts more error in the dip-finding algorithm (thus lowering its practical resolution). It has been shown that for some of the high-resolution dip-finding algorithms identical resolution was achieved with either a wide dip or a narrow dip due to the discreteness of the detector [28]. In the preceding reference the resolution of the SPR dips for gold and silver are compared using various CCDs and dip-finding algorithms. Although gold has a dip width twice that of silver, they show that the two dips have the same resolution when imaged with a CCD and analyzed with a dip-finding algorithm. It is still true that the ultimate shot noise detection limit would scale with the dip width; however, most practical SPR systems operate well above the shot noise detection limit [29]. It is also well known that different dip-finding algorithms can lead to varying performance when applied to the same experimental data; therefore, a modified algorithm may be required to gain full advantage from these asymmetric dips.
Fig. 6. Reflectivity dips for a flat surface and two gratings (both with t=50nm) with sample index values from 1.33 to 1.34. The asterisks show the curve minima.
Fig. 7. Sensitivity vs. sample index for a flat surface (solid black line) and various gratings. The red curves represent gratings with h=20nm and the blue curves represent h=40nm. The period required to keep the bandedge near λ=850nm is also noted.
5. Conclusion
We have shown theoretically that it is possible to increase the sensitivity of surface plasmon based biosensors with the use of periodic gratings operated near the bandgap. We have achieved a six-fold increase in sensitivity to bulk sample index relative to a flat surface with a sinusoidal shaped grating. We anticipate that other groove profile forms may yield superior sensitivity, and will investigate this in the context of complete plasmon sensor designs.
Acknowledgments
The authors would like to acknowledge the following agencies for funding: Le Fonds Québécois de la Recherche sur la Nature et les Technologies (FQRNT) and the Australian Research Council.
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