It is demonstrated that surface plasmon sensing can be performed in the shot-noise-limited regime to resolve index of refractive changes on the order of 10−10/√Hz at input powers of 1 mW. This improved resolution is achieved by using active electronic noise cancelling to suppress laser intensity noise and a wavelength that maximizes sensitivity to index of refraction changes occurring at an interface. The resolution of the system is experimentally demonstrated by measuring the refractive index change of air in response to pressure changes.
©2010 Optical Society of America
Surface plasmon resonance (SPR) biosensors have rapidly emerged as the technology of choice to monitor biological interactions in physiological environments in real time [1,2]. This paper sets out to determine experimentally the fundamental factors that limit the ability of a surface plasmon sensor to resolve a small change in refractive index. Improvements in the resolution of SPR sensors will allow the detection of low molecular weight analytes or the detection of lower concentration levels.
In the last two decades, a variety of SPR configurations based on angular, spectral or intensity interrogation have been developed to detect the perturbation of the surface plasmon mode which can be achieved . A change in the refractive index due to analyte binding causes the SPR response curve to shift (e.g., from the blue to the red trace in Fig. 1 ), which can be detected as the change ΔR in the intensity of the beam reflected from the SPR interface at a fixed angle of incidence.
Most SPR biosensors track the perturbation of the surface plasmon resonance by operating at or close to reflectance minimum. They operate either at a fixed wavelength , a fixed angle , by measuring the phase change of the TM reflectivity (either at a fixed wavelength, fixed angle [6–8] or by determining the ellipsometric ratio, rp/rs = tanψejΔ [9–11]), or through differential changes produced by dithering angle, wavelength or polarization [9,10,12,13]. Both non-interferometric and interferometric approaches have been used. Any SPR sensor that relies on the properties of the surface plasmon at the reflectance minimum, regardless of whether intensity or phase is measured, will be limited by the same physical constraints imposed by photon statistics. This aspect has been receiving considerable attention recently [8,14], and it was explicitly shown via theory and experiments that the sensitivity is fundamentally the same for intensity and phase detection .
A widely-used SPR sensor configuration captures the reflectance-curve at snapshots in time by using a photodiode array and a focused low-power optical source, such as an LED [15,16]. Curve-fitting algorithms are used to determine changes in the surface plasmon reflectance curve . Even though this configuration does not operate at the shot-noise limit, in practice, the sensitivity is the same as optical configurations that use a laser source in combination with either a high precision rotation stage or the ability to precisely tune the wavelength of the laser.
Dim light measurements are usually limited by additive noise, and so can often be improved by pulsed operation, which lifts the peak power further above the noise floor. Recently such ultra-short pulse systems have been investigated for SPR sensing [18,19]. Continuous-wave (CW) bright field instruments operating at the shot-noise limit can provide ultimate sensitivities higher than those of any competing technique (whether bright or dark field), and are not limited by additive noise. For a linear interaction such as SPR, the fundamental sensitivity limit is set by the number of detected photons, and the required number is independent of whether they arrive in pulses or continuously, so pulses provide no advantage. Pulsed lasers have poorer amplitude stability than CW ones. Also, thermal transients and nonlinear effects such as two-photon absorption and photo ablation increasingly limit the total dose as the pulse width narrows. Both effects reduce the signal-to-noise ratio (SNR) of pulsed measurements compared with CW measurements. Thus, pulsed measurements are most suitable for studies of fast kinetics, where the advantages of time resolution outweigh the disadvantages in sensitivity. In this work we are interested in maximizing the sensitivity, and for that reason we chose to use a CW measurement.
As mentioned previously, a distinct disadvantage of operating at the reflectance minimum point is that only a small percentage of the incident photons are detected by the photodetector, which severely reduces the signal-to-noise ratio, independent of whether the measurement is shot-noise limited. Shot-noise-limited measurements can be performed at the intensity minimum only if an unrealistically high input power is used. The option to increase the input power is not a viable one. Most of the power delivered to the surface plasmon is dissipated as heat, which can create an undesirable increase in temperature . In addition, near the minimum the reflectance varies quadratically with resonance shift, making this technique even less sensitive to small shifts.
The detection limit of current SPR biosensors is on the order of ~10−6 refractive index unit (RIU) [17, 20, 21]. Ref  established that the reflectance curve configuration that uses a 64 pixels and 12-bit ADC is consistent with the 10−6 RIU limit. We have confirmed through simulation that the 10−6 RIU is consistent with SPR sensors working at the reflectance minimum using either the resonance angle (assuming 0.001 degree angular resolution) or the resonance wavelength (assuming 20 pm wavelength resolution) configuration with a 1 mW input power, 5 Hz detection bandwidth. The value 10−6 RIU corresponds to a detection limit of approximately 1 pg/mm2 change in surface protein concentration . The limit of detection is governed by both the sensitivity of the SPR apparatus and the noise in the system: the magnitude of ΔR produced by a given shift in refractive index is governed by the sensitivity of the apparatus, while the noise in the system limits how small a ΔR can be reliably distinguished (see Fig. 1). Techniques have been investigated to obtain detection limits of ~10−7–10−8 RIU [8, 23, 24]. Not only do most of these approaches operate at an intensity minimum, but, in addition, none actively suppresses or eliminates noise to a level such that detection is performed in the shot-noise limited regime, which is the fundamental noise source limit for optical measurements.
In this work, the detection limit of SPR sensing is improved by increasing the sensitivity as well as suppressing the noise in the system. The inflection points in the SPR reflectance curve adjacent to the intensity minimum offer the largest sensitivity to an index change. Our approach to increase sensitivity is based on operating at the largest sensitivity intensity point, where the intensity of light allows the shot-noise regime to be approached with realistic input powers. We performed surface plasmon simulations on a sensor operating at such a large sensitivity point that indicated the sensitivity of a surface plasmon sensor can be increased by at least three orders of magnitude, provided that shot-noise is the only limiting factor.
In interferometric SPR approaches [25, 26], two common-path beams with a frequency difference are used to probe the SPR interface and optically heterodyned at the photodetector. The signal is measured with a lock-in amplifier such that the measurement is not affected by the 1/f noise. However, the optical signal of interest (the reflectance of the p-polarized beam) is still measured at DC and vulnerable to noises such as vibration. In the approach described next, the measurement is performed at higher frequency by physically modulating the surface plasmon and true shot noise detection limit can be achieved.
In this paper we experimentally show that shot-noise limited detection can be achieved with input powers as low as 1 mW and the detection of RIU approaching 10−10/√Hz. In order to achieve shot-noise-limited detection with a laser, we use active electronic noise cancelling to suppress the laser intensity noise.
2. Optimum wavelength of operation
An SPR biosensor detects changes in the optical properties caused by the adsorption of molecules at the interface between the gold and the dielectric (a buffer solution in most cases). The thickness of the adsorption layer is a few to tens of nanometers. The evanescent tail of the SPR mode extends beyond the adsorption layer and into the bulk buffer solution. Therefore, the measured effective refractive index change depends on the properties of both the adsorption layer and the bulk buffer solution. In most biosensor applications, the sensitivity to changes in the optical properties of the adsorption layer must be optimized. It is important to note that the maximum sensitivity to absorption layer changes (dR/dn|ad) does not occur where the sensitivity of an SPR sensor to bulk index of refraction changes (dR/dn|bulk) is the largest as shown in Fig. 2 . At longer wavelengths, the evanescent wave penetrates into the analyte solution to a depth much greater than the thickness of the adsorption layer. So while at longer wavelength the sensor becomes more sensitive to bulk index changes, it becomes less sensitive to the change of adsorption layer itself. Decreasing the wavelength increases the sensitivity to changes in the adlayer, yet if the operating wavelength is made too small, the surface plasmon will not exist.
The tradeoffs in maximizing the various sensitivities are illustrated in a simulation of SPR sensitivity to bulk and interfacial effects for the Kretschmann configuration with an SF11 prism, a gold film and water solution. For a fixed wavelength, the maximum values of dR/dn|bulk and dR/dn|ad, were determined by varying the angle of incidence and the gold layer thickness; this process was repeated for different wavelengths to build up the curves shown in Fig. 2. The simulation accounts for the dispersion of gold , water , and SF11 . Figure 2(a) shows that dR/dn|bulk increases at longer wavelengths; Fig. 2(b) shows that dR/dn|ad has a maximum occurring in the visible to near-IR regime. The adlayer index-of-refraction sensitivity dR/dn|ad is normalized to its overall maximum because the absolute sensitivity is a function of thickness of the layer. The optimum wavelength of operation that maximizes dR/dn|ad occurs around 900nm and it is independent of both refractive index and adlayer thickness. In practice, wavelengths in the 830–850 nm range are good choices because of the availability of good quality single-mode diode lasers, optical components with excellent anti-reflection coatings, and silicon detectors having high efficiencies at these wavelengths.
3. Noise suppression
In order to enhance the resolution, the noise in the system should be eliminated or suppressed. The fundamental limit of the resolution of an SPR sensor system is set by shot-noise, i.e. the statistical fluctuations of the detected photoelectrons; our goal is to approach shot-noise-limited measurement at milliwatt optical power levels, where the fluctuations are of the order of 1 part in 108 in a measurement time of 1 second. Since the SPR sensitivity dR/dn|bulk= 130 in water, the minimum resolvable refractive index change set by shot-noise should be about 10−10 RIU in 1 second. For future reference, the same configuration used in air has a sensitivity of dR/dn|bulk = 200.
The major noise contributor in most SPR sensors is the laser intensity noise. Depending on the type of laser, the intensity noise level could range from 10 to 60 dB above the shot-noise level. In a small-signal measurement such as SPR, the electronic noise associated with state-of-the-art photodetector circuits and the quantization noise of analog-to-digital converters can be made much smaller than the shot-noise associated with an optical power of 1 mW incident on the detector.
Laser intensity noise can be suppressed by the all-electronic laser noise canceller  as shown in Fig. 3 . In this setup, the laser beam is split into a signal beam and a comparison beam. The comparison beam is used as a reference which contains only the noise information. The beams are detected by separate photodiodes (S1223-01, Hamamatsu), producing signal and comparison photocurrents. The noise canceller circuit dumps a portion of the comparison photocurrent via the current splitter (bipolar junction transistor pair Q1-Q2, MAT04) such that the remaining current (iC2 in Fig. 3) equals the signal photocurrent. In order to get the best noise cancelling performance at photocurrents above about 100 μA, it is helpful to bias Q1 and Q2 with similar collector currents. Therefore, the comparison beam power is set to approximately twice that of the signal beam. This prevents unwanted negative feedback due to the extrinsic emitter resistances of the bipolar junction transistors that may reduce the cancellation performance by as much as 20 dB. The feedback servo loop dynamically adjusts the current splitter ratio to force the comparison current to be exactly equal to the signal current, which eliminates the optical intensity drift between the two beams. This allows the detection circuit to actively subtract the signal current iS from iC2 such that the output of the transimpedance amplifier A1 is zero within the bandwidth of the feedback loop. Within that bandwidth, the balanced noise canceller removes the bulk of the laser amplitude noise since the intensity noise fluctuations of the signal beam and the comparison beam are (ideally) perfectly correlated. The output signal of the electronic noise canceller is sensitive to temperature. In order to compensate the circuit output drift due to temperature variations in the electronics, a thermal sensor and thermoelectric cooler (Marlow Industries, RC12-4-01L) are used to actively control the temperature of the current splitter transistor pair above ambient temperature with a PID temperature controller (Lightwave ILX 5910-B).
The noise canceller has two outputs: a linear output and log ratio output, as shown in Fig. 3. Due to the servo action, the linear output produces a high-pass filtered version of the signal photocurrent with the intensity noise removed; the log ratio is a low-pass filtered signal proportional to ln(Icomp/Isig-1). Since both beams contribute full shot-noise, the lowest noise floor one can get with a simple subtractive scheme such as the laser noise canceller is 3 dB above the shot-noise level.
Figure 4 shows the measured noise floor at the linear output. The results with and without noise canceling are compared with shot-noise limit. For this particular diode laser (Innovative Photonics Solutions 830 nm diode laser, I0830SM0050PA, instantaneous spectral linewidth < 100 kHz), the intensity noise is about 40 dB above the shot-noise floor. The noise canceller suppresses the noise to 4 dB above shot-noise floor. The 1~2 dB extra noise above the theoretical limit of the noise canceller (3 dB above shot-noise level) results because the comparison and signal beam are not exactly correlated. This is caused by a combination of etalon fringes, polarization noise, and interference of stray light, effects that become increasingly difficult to eliminate completely as the complexity of the optical system increases. For various ways to minimize these effects see Ref .
The cancellation performance is essentially independent of the feedback loop bandwidth, since it depends on matching and not on feedback to perform the actual noise cancellation. Thus for a small-signal AC measurement such as SPR with a harmonic pressure-modulated gas sample (in contrast to modulation of the probing optical beam), the loop bandwidth fC and signal frequency f can be chosen for convenience. Very strong signals near the loop corner frequency fC, which is about 500 Hz, can degrade the canceller's performance, due to parametric interactions such as the dependence of the loop bandwidth on the signal level. Thus, in order to use the linear output, the signal frequency f should be much greater than the loop corner frequency so that the tails of the feedback transfer function do not affect the signal. In the presence of large amounts of drift and low frequency noise, due e.g. to the combination of etalon fringes and mechanical vibration, it is better to keep the feedback bandwidth high to help control these optical artifacts. Lock-in detection at frequency f can serve to further reduce noise by accepting only a narrow bandwidth near f. The log ratio output gives a normalized extinction measurement directly, and for this use fC should be much greater than the signal frequency. The log ratio output has the advantage of suppressing noise intermodulation as well as additive noise, but for weak-signal measurements this is not as important as it is in spectroscopy.
3. Experimental confirmation
Figure 5 shows the noise canceller’s application in an intensity-interrogated SPR measurement scheme. The signal detector of the noise canceller measures the power of the signal beam reflected by the SPR surface; the reference detector measures the power of the comparison beam which is split from the main beam before the signal beam goes into the SPR cell. The detected signal beam power is about 1.5 mW and the comparison beam power is about 3.0 mW. The SPR substrate is prepared by depositing a 44 nm thick gold layer onto an SF11 substrate wafer. A cylindrical prism is used to couple the beam as in the Kretschmann configuration. If a triangular prism is used, the spot illuminated on the Au film moves as the prism is rotated. Using a cylindrical coupling prism avoids this problem, but causes unwanted focusing of the beam that degrades the sharpness of the SPR dip. A cylindrical lens placed in front of the SPR cell compensates for the focusing effect of the cylindrical prism, producing an SPR dip with a width very close to the theoretical value. The SPR cell is vertically mounted onto a precision θ/2θ rotation stage. The stage consists of one rotator (Daedel) and a detector mounted on a separate rotating table, which is co-axial and driven by the rotator with an intermeshing gear with its speed ratio set exactly 2:1. A separate optical angle encoder (Renishaw, 104 mm RESM angle encoder ring, 20 nm SiGNUM reader) is integrated to the stage, and this provides a closed-loop angular resolution of 0.144 arc second. The angle of incidence is set at the inflection point of the SPR curve, where the sensitivity (the derivative of the reflected power with respect to refractive index in the sample cell) is at its maximum, as shown in Fig. 6 .
The improved ability to resolve index change of the SPR sensor system with the use of noise canceller is experimentally demonstrated by measuring the SPR response to a change in the refractive index of air induced by modulating the air pressure. In order to prevent the complexities of directly measuring dR/dn|ad , instead dR/dn|bulk is measured at a wavelength where the sensitivity to an adlayer in water will be maximized. Furthermore, instead of performing the measurement with water, air is used to calibrate the SPR system for the following reasons. First, SPR sensors have the highest sensitivity measuring air refractive index change since the refractive index of air is the smallest (e.g. dR/dn|bulk= 200 in air and 100 in water at 830 nm). Second, gas is very stable, and is much easier to handle than aqueous solutions, which means a more reliable and repeatable refractive change could be obtained. Third, additional layers typically applied when working with solutions, such as a chromium adhesion layer between the gold film and the SF11 substrate or a protective SiO2 layer deposited on the gold film, are unnecessary when measuring gases. Only a single layer of gold needs to be deposited onto the SF11 substrate and its thickness can be accurately determined from curve-fitting the measured SPR angular response curve. Finally, the refractive index of air has been very well studied. If the change in air pressure p is known, the resulting change in refractive index n can be obtained, given the value of dn/dp, which is 0.00027/atm at static pressures around one atm . Even though the air refractive index change is a bulk change and not an interfacial layer change, the measurement result still can be used to demonstrate the beneficial effect of noise cancellation on the sensitivity and resolution of the sensor as averaged over one decay length of the evanescent field.
In order to ensure that a precise, controllable refractive index change can be achieved by changing the pressure, the air to be measured must be enclosed in a specially-designed airtight chamber, with a piezo-electric membrane (extracted from a piezo buzzer, RadioShack 2730073) to adjust the chamber volume, see Fig. 7 . The deflection of the membrane, which is 120 nm/V, is experimentally calibrated with a surface profiler (Veeco Dektak 3) so that accurate volume changes can be produced by applying the appropriate voltages on the piezo-electric membrane. By applying the ideal gas law, we can convert the volume change to pressure and so further to a change in refractive index. The pressure change can be calculated from volume change by dp/p=-dV/V and the refractive index change can be calculated by ∆n=(dn/dp)∆p. The resulting fine control can reliably produce refractive index changes as small as 10−12 in this way, which is only limited by the precision and resolution of the voltage applied to the membrane.
Using the linear output of the noise canceller requires the signal to be AC with its frequency much larger than the loop bandwidth, so the refractive index of the air in the chamber needs to be modulated by applying an AC voltage (square wave) to the piezo-electric membrane during the measurement. This modulation is not required for the SPR sensing but is necessary to take advantage of the noise canceller and to escape low frequency optical and electrical drift and noise. In this measurement, a 2 kHz AC voltage signal is applied to the membrane, resulting in a 2 kHz periodic change in the air refractive index, ∆n. The deflection of the membrane is modulated with 2 kHz square wave. Corresponding to the static deflection measurements, the index change caused by the deflection amplitude in the air pressure cell is calculated. As shown in Figs. 6 and 8 , there is a very good agreement between the calculated results and the measured values which implies that that the dynamic deflection amplitude in the experiment is similar to the static deflection calibration. Even though the thickness of the gold layer was 44 nm rather than the optimum value at this wavelength of ~54nm, the sensitivity achieved corresponded very well to theoretically predicted value of dR/dn|bulk =200. Because the modulation frequency (2 kHz) is four times higher than the noise canceller’s loop bandwidth (500 Hz), nearly all of the intensity change of the signal beam resulting from the refractive index change of the air will be reflected at the linear output of the noise canceller. The amplitude ∆V of the linear output signal, which is also a 2 kHz AC signal, corresponds to the refractive index change of ∆n (∆V=S∆n, where S is the sensitivity). In this way, the refractive index change of air is measured free of laser intensity noise and only limited by shot-noise. The temperature of the SPR cell is not actively controlled. The measurement is immune to changes in the bulk index caused by temperature variations since the amplitude of modulation is measured. We verified this characteristic by confirming that the individual measurements were repeatable within a 10 minute window. This insensitivity to temperature variations is another distinct advantage of the proposed technique. In conventional SPR sensors, changes to the bulk index cause a shift in the plasmon curve that is measured in the reflected intensity. By introducing modulation, the technique monitors intensity differences only at the specified frequency of interest. Therefore, any bulk refractive index that occurs at a frequency other than the detected modulation frequency is not detected. Temperature drifts and variations are included in this category.
To explore the detection limit, the amplitude of voltage applied to the membrane was gradually decreased until the resulting ∆V could not be distinguished from noise in the output signal (SNR=1). Figure 8 is a plot of the measured and theoretical SNR of the sensor system as a function of the refractive index change of air in the sample cell. From this measurement, it can be concluded that the minimum resolvable refractive index change is about 1.9 × 10−10RIU/√Hz at SNR = 0 dB which is about 6 dB higher (mainly due to etalon fringes) than calculated shot-noise limited detection limit. For comparison, if the laser noise cancellation is turned off but the measurement is otherwise performed under the same conditions, the minimum resolvable refractive index change is about 2×10−7RIU/√Hz.
This work reports the enhanced detection limit on the order of 10−10 RIU/√Hz for an intensity-based SPR system when measuring a gas phase analyte using an active noise canceller and operating in the shot-noise regime, and is within 6 dB of the fundamental shot-noise limit. The value obtained in this work is two to three orders-of-magnitude improvement over than the largest resolution previously reported for a gas phase analyte measurement using an SPR sensor . For aqueous solutions, since the SPR sensitivity is about 2~3 times smaller than with air as determined from a theoretical calculation, we estimate the resolution of this SPR system with aqueous solution to be on the order of 10−9 RIU/√Hz. The resolution to bulk change can be used as a figure-of-merit to determine the resolution to adlayer, yet ultimately we are interested in the resolution of SPR sensor to adsorption layer change. The resolution to bulk change in terms of RIU has been correlated with surface concentration of, for example, protein-hydrogel layers [16, 17]. The detection limit of 10−9 RIU is approximately equal to 1 fg/mm2 in surface concentration change under the same assumptions detailed in Ref . In order for a biosensor to take full advantage of the noise suppression offered by the noise canceller and insensitivity to temperature variations, the measurement requires modulation of the refractive index within the surface plasmon. Work in this regard is ongoing in our group. The improvement in detection by approaching the shot-noise limit will enable biosensors to detect target molecules with extremely low concentration, or molecular binding interactions (e.g. ion channel conductivity changes) with low surface concentrations.
The research was supported by the National Science Foundation through grant ECS 0823827. We thank Jesse Salem for his assistance in implementing the air-pressure cell.
References and links
1. J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B Chem. 54(1-2), 3–15 (1999). [CrossRef]
3. R. B. M. Schasfoort, and A. J. Tudos, eds., Handbook of Surface Plasmon Resonance (The Royal Society of Chemistry, 2008).
4. B. Liedberg, C. Nylander, and I. Lunström, “Surface-Plasmon Resonance for Gas-Detection and Biosensing,” Sens. Actuators 4, 299–304 (1983). [CrossRef]
5. L. M. Zhang and D. Uttamchandani, “Optical Chemical Sensing Employing Surface-Plasmon Resonance,” Electron. Lett. 24(23), 1469–1470 (1988). [CrossRef]
6. A. V. Kabashin, V. E. Kochergin, A. A. Beloglazov, and P. I. Nikitin, “Phase-polarisation contrast for surface plasmon resonance biosensors,” Biosens. Bioelectron. 13(12), 1263–1269 (1998). [CrossRef]
7. S. A. Shen, T. Liu, and J. H. Guo, “Optical phase-shift detection of surface plasmon resonance,” Appl. Opt. 37(10), 1747–1751 (1998). [CrossRef]
8. A. V. Kabashin, S. Patskovsky, and A. N. Grigorenko, “Phase and amplitude sensitivities in surface plasmon resonance bio and chemical sensing,” Opt. Express 17(23), 21191–21204 (2009). [CrossRef] [PubMed]
9. I. R. Hooper and J. R. Sambles, “Sensing using differential surface plasmon ellipsometry,” J. Appl. Phys. 96(5), 3004–3011 (2004). [CrossRef]
11. S. Y. Wu, H. P. Ho, W. C. Law, C. L. Lin, and S. K. Kong, “Highly sensitive differential phase-sensitive surface plasmon resonance biosensor based on the Mach-Zehnder configuration,” Opt. Lett. 29(20), 2378–2380 (2004). [CrossRef] [PubMed]
12. C. E. H. Berger and J. Greve, “Differential surface plasmon resonance immunosensing,” Sens. Actuators B Chem. 63, 103–108 (2000). [CrossRef]
13. M. J. Jory, G. W. Bradberry, P. S. Cann, and J. R. Sambles, “A Surface-Plasmon-Based Optical Sensor Using Acoustooptics,” Meas. Sci. Technol. 6(8), 1193–1200 (1995). [CrossRef]
16. E. Stenberg, B. Persson, H. Roos, and C. Urbaniczky, “Quantitative-Determination of Surface Concentration of Protein with Surface-Plasmon Resonance Using Radiolabeled Proteins,” J. Colloid Interface Sci. 143(2), 513–526 (1991). [CrossRef]
17. K. Johansen, R. Stalberg, I. Lundstrom, and B. Liedberg, “Surface plasmon resonance: instrumental resolution using photo diode arrays,” Meas. Sci. Technol. 11(11), 1630–1638 (2000). [CrossRef]
18. L. Panga, S. Boris, and Y. Fainman, “Spectral sensitivity of two-dimensional nanohole array surface plasmon polariton resonance sensor,” Appl. Phys. Lett. 91, 123112 (2007).
19. K. A. Tetz, L. Pang, and Y. Fainman, “High-resolution surface plasmon resonance sensor based on linewidth-optimized nanohole array transmittance,” Opt. Lett. 31(10), 1528–1530 (2006). [CrossRef] [PubMed]
21. A. A. Kolomenskii, P. D. Gershon, and H. A. Schuessler, “Sensitivity and detection limit of concentration and adsorption measurements by laser-induced surface-plasmon resonance,” Appl. Opt. 36(25), 6539–6547 (1997). [CrossRef]
22. T. M. Davis and W. D. Wilson, “Determination of the refractive index increments of small molecules for correction of surface plasmon resonance data,” Anal. Biochem. 284(2), 348–353 (2000). [CrossRef] [PubMed]
23. X. D. Fan, I. M. White, S. I. Shopova, H. Y. Zhu, J. D. Suter, and Y. Z. Sun, “Sensitive optical biosensors for unlabeled targets: a review,” Anal. Chim. Acta 620(1-2), 8–26 (2008). [CrossRef] [PubMed]
24. G. D. VanWiggeren, M. A. Bynum, J. P. Ertel, S. Jefferson, K. M. Robotti, E. P. Thrush, D. M. Baney, and K. P. Killeen, “A novel optical method providing for high-sensitivity and high-throughput biomolecular interaction analysis,” Sens. Actuators B Chem. 127(2), 341–349 (2007). [CrossRef]
27. P. B. Johnson and R. W. Christy, “Optical-constants of noble-metals,” Phys. Rev. B 6(12), 4370–4379 (1972). [CrossRef]