We consider amplitude and phase characteristics of light reflected under the Surface Plasmon Resonance (SPR) conditions and study their sensitivities to refractive index changes associated with biological and chemical sensing. Our analysis shows that phase can provide at least two orders of magnitude better detection limit due to the following reasons: (i) Maximal phase changes occur in the very dip of the SPR curve where the vector of probing electric field is maximal, whereas maximal amplitude changes are observed on the resonance slopes: this provides a one order of magnitude larger sensitivity of phase to refractive index variations; (ii) Under a proper design of a detection scheme, phase noises can be orders of magnitude lower compared to amplitude ones, which results in a much better signal-to-noise ratio; (iii) Phase offers much better possibilities for signal averaging and filtering, as well as for image treatment. Applying a phase-sensitive SPR polarimetry scheme and using gas calibration model, we experimentally demonstrate the detection limit of 10−8 RIU, which is about two orders of magnitude better compared to amplitude-sensitive schemes. Finally, we show how phase can be employed for filtering and treatment of images in order to improve signal-to-noise ratio even in relatively noisy detection schemes. Combining a much better physical sensitivity and a possibility of imaging and sensing in micro-arrays, phase-sensitive methodologies promise a substantial upgrade of currently available SPR technology.
©2009 Optical Society of America
Over last 15 years Surface Plasmon Resonance (SPR) has become an undisputable leading technology for label-free detection and studies of biological binding events on the surface [1–3]. SPR biosensors take advantage of the phenomenon of surface plasmon polariton (SPP) excitation over metal/liquid interface. P-polarized light is directed through a glass prism and reflected from a gold covered prism facet in contact with liquid ambience, as shown in Fig. 1 . The SPR effect consists in a resonant transfer of energy from an incident photon to a surface plasmon polariton (kspp) over the metal/liquid interface, which is observed as a dip in angular (spectral) dependence of reflected intensity. Biomolecular binding events on gold lead to an increase of the refractive index (thickness) of an ultra-thin organic layer on the metal film (normally, 200-300 nm), resonantly changing conditions of SPR production and thus shifting angular [4,5] or spectral  position of the SPR dip. Such approach enables one to avoid time-consuming and impairing labeling step and thus obtain all reaction kinetics constants within minutes.
The detection limit of SPR technology is estimated as 1 pg∙mm−2 of biomaterial accumulating at the biosensor surface. This sensitivity is sufficient for studies of many interactions involving relatively large molecules such as e.g., antibody-antigen, protein-DNA, DNA-DNA etc [2,3,7]. However, the sensitivity still needs to be greatly improved for the detection of low molecular weight analytes (typically less than 500 Da) such as drugs, vitamins etc., as well as larger low copy number analytes such as e. g., antigens, viruses etc., which are deadly or pathogenic even in ultra-low quantities [3,7]. The main problem of current commercially available SPR technology is associated with the existence of a physical lower detection limit (LOD) of amplitude-sensitive schemes. This limit is conditioned by the level of noises in measurements and normally is estimated as 10−6 −10−5 Refractive Index Units (RIU) for various sensor implementations with angular, spectral or intensity interrogations .
As we showed several years ago, the detection limit problem can be resolved by the involvement of phase properties of light reflected under SPR [8–13]. Our claim was that under optimal thickness of SPR-supporting film phase of light can provide orders of magnitude better sensitivity than amplitude characteristics [8,9]. This expectation was based on the existence of a sharp jump in angular (wavelength) dependence of phase of p-polarized light component under SPR  and a high stability of phase measurements in optics . To control phase response in real-time we introduced SPR interferometry [8,9], in which phase information is extracted from an interference pattern between the “signal” p-polarized beam, reflected from the SPR-supporting film, and the “reference” beam presented by either an additional p-polarized beam or the unaffected s-polarized component of the same beam . Measuring a phase shift when two gases (Ar, N2) with known difference of refractive indices are brought to contact with gold and assuming a rather moderate instrumental resolution for phase (2π⋅10−3 Rad. ~10−2 Deg.), we estimated that the detection limit of the method can be at least of the order of 10−8 RIU  that is about 100 times better than in conventional SPR. We also introduced techniques of interferometric SPR imaging  and dark field SPR imaging , which offer a 10 micron-level spatial resolution and render possible the imaging of ultra-thin objects, not resolvable by conventional amplitude-sensitive SPR . The concept of phase-sensitive SPR was later transformed to a series of designs and schemes, providing much better sensitivities compared to amplitude-sensitive devices. Advantages of SPR interferometry include a simple optical extraction/visualization of ultra-sensitive phase information and, more importantly, the imaging opportunity due to a good lateral resolution over the surface of the SPR-supporting film. The later option, for example, makes possible parallel sensing in multiple micro-arrays, as e.g. in the case of gene chips and high throughput analysis when hundreds of lead components need to be simultaneously tested. In particular, H.-P. Ho and his group implemented a series of advanced SPR Interferometry schemes (differential phase interferometer [17,18,20,26], multi-pass Michelson  and Fabry-Perot interferometers ), which promised the detection limit of the order of 10−8 RIU. Y.-D. Su , Y. Xinglong , and C. L. Wong  implemented novel interferometric 2D imaging designs for simultaneous sensing in several channels and applied them for protein [24,33] and DNA  sensing. Sheridan  and G. Nemova  implemented miniaturized phase-sensitive designs using plasmon coupling from single mode waveguides and waveguide-based Bragg grating structures, respectively. SPR polarimetry is an alternative phase-sensitive approach, which is based on the extraction of phase information from the analysis of ellipse of light polarization when both s- and p-components are present [14,36–47]. Although SPR polarimetry can be implemented in simplified designs such as, e.g., ones with the use of a rotating analyzer  or spatially beam modulator  making possible phase measurements under relatively simple experimental arrangements, most SPR polarimetry tools take advantage of a temporal phase modulation of the pumping beam that can be introduced by a liquid crystal [37,40], piezoelectric , mechanical  or photoelastic (PEM) [41–43,47] modulators. Phase information after the reflection under SPR is then extracted at different harmonics of the modulating frequency to simplify the removal of noises and thus improve the signal-to-noise ratio. Moreover, by a proper mixing of phase and amplitude signal components, one can combine a high phase sensitivity and wide dynamic range of amplitude measurements [42,43]. Due to high measurement stability and easy electronics tools to remove instrumental and environmental noises, temporally phase-modulated SPR polarimetry schemes can provide exceptional resolution of phase measurements (10−2 – 10−3 Deg.) promising the detection limit of the order of 10−8 RIU and lower. However, imaging prospects of such schemes look too expensive and complicated. Another promising phase-sensitive approach is optical heterodyning, which is based on the analysis of the differential frequency between two frequency-shifted orthogonally polarized s- and p- components of light reflected under SPR. Similarly to temporally modulated polarimetry, this approach makes possible efficient noise removal and phase treatment tools, while its imaging prospects look hardly realistic. Using various modifications of optical heterodyning methodology, several groups managed to achieve extremely high phase resolution promising the detection limit of the order of 10−8 RIU [48–52]. Finally, the sharp phase jump under SPR can be employed in many other closely related tasks, e.g., as a polarization tool  or as a resonant point marker to considerably improve the pattern contrast in conventional SPR sensing [54–57].
The authors of a recent paper  disputed the statement on much higher phase sensitivity of SPR based techniques compared to the intensity one. As the main argument, they used the fact that up to the date of writing of their paper the projected LOD of 10−8 RIU has just been estimated and not confirmed by a direct experiment. Moreover, using a particular phase-step 4-detector polarimetry scheme and considering the shot noise of the detector as the main one, they came to a paradoxal conclusion that the intensity interrogation is better than the phase one and could provide the detection limit of the order of 10−9 RIU, which is far from what has been observed to date. This conclusion is in a direct contradiction with a widely accepted knowledge that phase techniques are far superior to intensity techniques for detection of small signals and often used to improve signal-to-noise ratio . Surprisingly, this conclusion contrasts with results of an earlier paper on the same group , in which a better resolution of phase measurements was obtained using Mach-Zehnder Interferometer-based SPR geometry. It seems therefore important to find the reasons for the dramatic conclusion of the Ref . and reclaim the virtues of the phase technique which made it to become one of the most used techniques in radio, television, precision measurements (such as metrology and gravitation wave detection), etc.
The aim of this paper is to elucidate the physical sense of amplitude and phase sensitivities of SPR techniques and compare them based on the analysis of noises. Before going into a detailed discussion, we would like to briefly summarize why the main assertion of  is incorrect. First, in practical schemes of SPR measurements the detector-related shot noise is not the main source of noise as it is overshadowed by other noises (e.g., the noise associated with the light source). It turns out that generally the phase component of the light is much more stable in relation to these other noises than the amplitude component (e.g. light sources normally have much better stability of phase characteristics compared to amplitude ones); Second, the change of electric field is about twice as big in the SPR dip, where the change of the phase and not of the reflected field amplitude takes place, as at the SPR slopes. As we will show below, this yields a more sensitive phase response to tiny changes of the refractive index. Third, phase offers much more efficient and flexible methods for averaging, image treatment etc., which provides additional tools to improve sensor sensitivity. In fact, we do not disagree with authors of  that the phase sensitivity of the phase-step 4-detector polarimetry scheme in the regime discussed might indeed be lower than the amplitude one. However, we would like to stress that this particular scheme is not the one that is employed in the majority of works on phase-sensitive SPR biosensing and therefore should not be used as a basis for generalized conclusions of Ref .
It is also important to note that the discussion on detection limits of phase and amplitude measurements under SPR continued in many recent works, which appeared after , illustrating a persistent (and increasing) interest to this subject from photonics, analytical chemistry and biological communities. Some of the papers report progress in the improvement of the detection limit in both amplitude- and phase-sensitive schemes. We believe that we need to clearly distinguish three different types of works: (i) works, in which the low detection limit (LOD) is determined (and limited) by the level of instrumental and environmental (temperature and inertial drifts etc.) noises in a single amplitude or phase measurement; (ii) works reporting the LOD after the application of additional tools such as differential schemes, averaging, mathematical treatment of noises etc., which can significantly lower the LOD value in both phase- and amplitude-sensitive modalities; (iii) works, declaring unrealistic LOD values, which can only be explained by artificial facts taking into account the anticipated level of environmental noises. To avoid ambiguities in interpretation, in our analysis we will compare LODs in phase and amplitude measurements under the same level of instrumental noises without any additional signal treatment.
2. Phase and amplitude responses under SPR
Amplitude,, and phase, φ, represent two essential features of the vector of electric field of an electromagnetic wave . Amplitude is connected to the vector length, whereas phase describes an angular shift of the beginning of the oscillation cycle. Depending on geometry of light-medium interaction, the propagation or reflection of light from the medium can be accompanied by a change of amplitude, phase or amplitude and phase simultaneously. An example of a pure phase change includes light propagation in a transparent homogeneous media, whereas examples of pure amplitude changes include the light propagation in homogeneous absorbing media. It is important to note that both phase and amplitude of electromagnetic field carry information about the medium in which light propagates. As an example, the employment of phase information for image generation was used by Zernike to develop Nobel-prize winning phase contrast microscopy, while prominent examples of pure amplitude response include absorption-based gas sensing, light filters etc. Introducing a small change of the electric field produced by a tiny change in a medium as, we can write the (relative) amplitude and phase responses as and respectively. Thus, the maximal amplitude changes takes place when is parallel to, while the maximal phase change occurs when is perpendicular to. In other words it means that the maximal amplitude changes are observed at the condition of the absence of phase changes and, vice versa, the maximal phase change is observed at the minimum of the amplitude response.
Under SPR, we have a resonant phenomenon, consisting in a transfer of energy from a pumping photon to a plasmon under some angle of incidence and wavelength of incident light. This phenomenon is accompanied by simultaneous amplitude and phase changes for reflected light: a drastic drop of amplitude and a sharp phase jump considered as functions of either the incident angle or wavelength. Figure 2(a) shows schematics of SPR measurements where a small change of the refractive index of the analyzed medium produces a change of the reflected electromagnetic wave by . It is clear that in the first approximation , where is the electromagnetic field of the surface plasmon acting on the medium under study and α is a constant close to unity.
Due to properties the plasmon excitation, the surface plasmon field is large which guarantees high sensitivity of the SPR techniques. This gives us the following estimate of the relative amplitude and phase responses: and . The maximum of the phase response is observed at the resonance minimum (where ) while the maximum of the amplitude signal is observed at the resonance slope (where ), see Fig. 2(b). Introducing a figure of merit (FOM) as a ratio of the phase response over the relative amplitude response, we get . The physical meaning of FOM is as follows: it describes how much the phase signal will be larger than the amplitude one at the condition of the same intensity of light collected by the photodetector. Taking the formulae for the electric fields  and typical values for gold film of an optimal thickness at the wavelength of ~700nm, we obtain and and hence . Even larger FOM is obtained for SPR based on Ag films. Hence, the sensitivity of phase technique under SPR condition is at least an order of magnitude better than the amplitude sensitivity.
3. Phase and amplitude sensitivities in SPR schemes
We start our analysis by noting that any SPR technique requires three important ingredients: a source of light, SPR detection cell and a photodetector. Each of these elements contributes some noise into the system which ultimately defines the sensitivity and LOD of a SPR scheme. For the purpose of comparing phase and intensity modes of SPR measurements one needs to compare phase and intensity noises of these three elements.
Noises of the detection cell are related to environmental factors, which can cause variations of the refractive index in the controlled liquid volume inside the cell. Here, refractive index drifts related to temperature variations are considered as the most important. The change of temperature of water by 1 Deg. C° is accompanied by a change of refractive index by 10−4 RIU. Therefore, measurements of refractive index changes at the level of 10−8 RIU require the stability of temperature inside the cell of the order of 10−4 Deg. C°. Although it requires the involvement of rather expensive additional equipment, such and even higher level of stabilization is possible. Commercial active thermostats provide the stabilization of the level of 10−3 Deg. Celsius (see, e.g., ), while a combination of passive thermal stabilization with time filtering of thermal drifts can lead to the same level. Furthermore, the application of differential reference schemes provides even better level of thermal stability . In simplest approach, the required level of thermo stabilization (10−4 Deg. C°) can be achieved through a combination of thermo stating and reference channel strategies. Since the detection cell noises are related to the measured parameter (they are “signal” noises), they are identical for amplitude and phase measurements and require tools to stabilize environmental parameters affecting refractive index inside the cell.
Drifts of characteristics of light source and photodetector present instrumental noises. There most common source of light for SPR measurements are lasers. Lasers usually have excellent phase noise characteristics. The phase noise of a common laser can be evaluated as , where λ is the laser wavelength and lc is the coherence length, Δfl is the laser line width and fl is the laser frequency . The coherence length of typical laser is well above 5 m which yields the magnitude of relative phase noise for a laser working at the wavelength of 500nm at the level of about ≈10−6. The single frequency solid state lasers can easily have even larger coherence length at the level of 10 km which makes phase noise of these lasers negligible . At the same time, relative intensity noise of common lasers is significantly higher and is usually at the level of ≈10−2. There are several important factors which contribute to higher intensity noise of laser sources: instability in pumping, spot burning due to spatial distribution of laser modes, photon statistics during photon emission and absorption, beam pointing fluctuations, etc. All these factors result in considerable drift of laser intensity at low frequencies (1/f noise), a peak of the relaxation oscillation noise, quantum noise, etc. Figure 3 shows the frequency dependence of the intensity noise of the most common gas and solid state lasers normalised on shot noise, where P is the laser power.
The Fig. 3 clearly demonstrates that in a large frequency range from 0 to 106 Hz the intensity noise of lasers is much larger than the shot noise and is governed by the factors others than the photon statistics. It is easy to check that a similar situation takes place for other types of lasers. In fact, it means that the fundamentally conditioned shot noise can dominate only in an idealized situation of the absence of “technological” noises arising during the lasing process, which never take place in practice. We can write the laser intensity noise as , where I is average intensity, nm, ns, nb is the constant describing modulation, shot and background noise, respectively. The modulation noise (drift of laser intensity) is proportional to laser intensity I with coefficient where χ is the numerical coefficient χ ≈10−2 and B is the total bandwidth and the shot noise constant is , where A is the size of the laser spot. From here we conclude that the modulation noise overcomes shot noise for a laser without an intensity stabilization scheme at relatively low powers of above 1μW (at a generous bandwidth of 100MHz). Therefore the intensity modulation noise of the common lasers is the most important type of noise which limits operation of the SPR measurement techniques. (One needs to use different smart types of laser intensity stabilization in order to be in the limit of shot noise!).
Noises related to the detector can be divided into three categories: shot noise, connected with the photon statistics, dark current noise, produced in a photodetector even in the absence of photons, and amplifier noise, e.g., Johnson-Nyquist thermal noise . The correlation between these noises depends on the light intensity, bandwidth of measurements, temperature of the photodiode, electrical parameters of photodiode and amplifier, etc. It is worth stressing, however, that noises of a photodetector working at optimal parameters are usually quite small compared to noise induced by laser intensity fluctuations and noise of the detection cell. For example, using the same arguments as above, we find that shot noise of a photodetector become essential (comparable with laser power fluctuations) only when light power at the photodiode is very small, Pph<1nW for a typical amplifier bandwidth of 100 kHz , which is well below the light power at which most of SPR measurements take place. The dark current noise and thermal noise depend on a particular scheme of the detection and are also quite small. They can be decreased even further using different cooling methods and low-noise amplifiers . Notice that the excitation of plasmons leads to the decrease of laser intensity in the plasmon-affected p-polarized beam. In theory, this decrease can be down to zero, but in practice the minimum of intensity is limited by parameters of the SPR-supporting film (roughness, uniformity, thickness optimization) and cannot be lower than 1-4%. Such a drop of intensity may require an increase of laser power to still be in the range of maximal photodetector sensitivity (Pm). Here, the increase of laser power should not exceed the critical value Pcr, which provides refractive index drifts because of heating effects (detection cell noises). Normally, there is a wide gap between Pm and Pcr, which makes possible efficient phase-sensitive control of events in the detection cell.
Thus, if detection cell noises are minimized to a sufficient level through thermo-stabilization of the system, drifts related to laser source normally present main instrumental noise limiting the LOD of measurements. In this case, since amplitude noises of laser sources are orders of magnitude more pronounced compared to the phase ones (see Fig. 4 ), phase characteristics can potentially provide much lower detection limit. Therefore, in the design of phase-sensitive schemes it is important to avoid or subtract the above-stated amplitude noises related to the source. In interferometric schemes, it can be done e.g., through the application of fringe mode when phase information is extracted from the position of interference fringes, while any variation of light intensity can only affect the interference pattern contrast and not this position [10,11]. In contrast, in SPR polarimetry amplitude noises can be subtracted or eliminated through the application of differential or filtering schemes.
Returning to results and conclusions of Ref , the authors of this work used a 4-detector polarimetry scheme to record changes of light phase. In this scheme, light of a mixed polarization is used to excite Surface Plasmons in the Kretschmann-Raether prism arrangement, while an automated polarizator is rotated using a step algorithm to provide four independent measurements of intensity corresponding to different light ellipticity states (0, π/2, π, 3π/2 for the reference wave). Phase is then extracted from these intensity measurements using standard formulae. The authors then compare signal-to-noise ratios for phase and amplitude measurements in such scheme considering the shot noise of the detector as the prime noise in the system. We believe that the authors employed a very ineffective phase scheme and used it in essentially incorrect regime, which could prevent the implementation of much higher phase sensitivity:
1. The authors found themselves in the region of domination of detector-related shot noises. It means that the intensity of the output light on the detector could be so small that the detector was out of the region of its maximum sensitivity. It is clear that this is an absolutely incorrect regime of detector operation. As we showed above, in normal conditions when the detector is adjusted to its maximal sensitivity, the shot noise is not the one that limits the SPR sensitivity for the common sources of lights. Therefore the theoretical considerations described in  cannot be applied to the majority of SPR measurements.
Furthermore, the authors of  compare the sensitivity of the phase technique with sensitivity of intensity measurements at a fixed intensity of the light source, which is obviously wrong. The phase and intensity measurements should be compared at a fixed intensity of light collected by the photodiode, since it is customary to adjust the power of laser source to a level where photodiode will be in the region of its maximal sensitivity (with the aim to avoid saturation). In this case, the shot noise of the phase scheme and the intensity schemes will be approximately the same, whilst the phase mode will have much better sensitivity due to a much stronger dependence of the light phase on the refractive index in the region of the phase jump than the light intensity. Therefore, even in the case of prevailing shot noise it is relatively easy to achieve much better sensitivity by the phase mode of SPR measurements simply by adjusting laser intensity. This conclusion is actually supported by the formulae presented in , provided the measurements are compared at a fixed intensity of light collected by the photodiode.
It is interesting that the authors of  mentioned in the end of their paper that the increase of pumping intensity led to a drastic increase of phase sensitivity and this was presented as a way to improve the resulting sensor sensitivity. This fact confirms our supposition on the non-optimal regime of detector operation in . It is clear that the increase of the pumping intensity moved the system from the region of domination of detector-related shot noises that, according to the stated above, contributed to a higher phase sensitivity compared to the amplitude one.
2. Even if the pumping intensity is increased, the achievement of superior phase sensitivity requires an employment of methodology, which somehow eliminates or subtracts amplitude noises. In contrast, the scheme and measurement procedure did not ensure amplitude noise-independent phase measurements. Recording the intensity of interferograms without any reference to laser intensity drifts, the authors collected all amplitude noises in their phase signal. Furthermore, they did four independent intensity measurements summarizing four intensity noises for the determination of a single phase value.
3. Experimental assessment of detection limit in phase-sensitive SPR schemes
In our previous papers, we demonstrated the possibility of obtaining the detection limit of 10−8 RIU using SPR interferometry schemes [8,9]. Our analysis was based on the experimentally sensitivity of about 1 Deg. of phase change per 10−5 RIU change and a realistic estimation of possible noises in phase-sensitive schemes of 10−2 Deg. To generalize conclusions on advantages of phase-sensitive methodologies to detect tiny changes of RI, in this paper we use an alternative polarimetry-based scheme to control phase of light reflected under SPR. We employ a modification of a recently introduced Photoelastic Modulator (PEM)-based scheme with sinusoidal temporal phase modulation [42,43]. Under a proper adjustment, this scheme offers powerful tools to filter instrumental and detection cell noises and in particular, noises related to the source. A schematic diagram of the proposed method is shown in Fig. 5(a) . A 5mW stabilized He-Ne laser operating at a wavelength of 632.8 nm is used as the light source. The light is passed through a polarizer to obtain a 45 deg. linearly polarized beam. After passing a combination of half and a quarter wave plates, which serve to optimize the initial phase retardation, phase modulated light is directed to a photoelastic modulator (PEM), which is used to sinusoidally modulate p-component with the frequency φ = 50 kHz. The beam is then directed to the SPR block and, after the reflection, is passed through a 45 Deg. polarizer and directed to a photodetector. Information on the phase-polarization state of light reflected under SPR is extracted by the examination of 1nd and 2rd harmonics of the modulated signal, with the help of a lock in amplifier. Thus, for first two harmonics we have:65]. In this case, we have a pure phase response, which is independent of amplitude noises. The phase resolution of the system was estimated by conditioning initial phase retardation using 3-waveplate retarder (Fig. 5(a)). Rotating one of λ/4 plates, we could provide a fine well-controlled retardation of phase of signal light beam in the system. Using this method we estimated the phase resolution of the system to be of the order of 5⋅10−3 Deg., which is not far from best values for phase-sensitive detection methods and better than what declared in our first studies [8,9].
To illustrate a feasibility of extremely low detection limit in practical conditions, we used a standard commercially available Biacore slide with a 50 nm gold film deposited on a glass substrate. The Biacore slide was in immersion contact with a glass prism (F10 glass). Together with a gas/liquid flow cell, they presented the sensing block. Light after the PEM was passed through the prism and reflected from the gold film, which was in contact with sample gas/liquid medium. Figure 5(b) shows experimentally measured angular dependences of reflectivity and phase of light for two pumping frequencies (632.8 and 670 nm) when gold was in contact with air. One can see that the SPR effect is accompanied by a drastic decrease of intensity of the p-polarized component and a sharp jump of its phase, changing the total polarization state of light. It is also visible that the slides were optimized for 670 nm with sharpest phase characteristics for this wavelength. Nevertheless, the characteristics of the SPR-supporting film were good enough even for 632.8 nm, which is the pumping wavelength in our scheme with a highly stabilized laser.
In our tests, we used a well-established gas methodology for tiny refractive index variations Δn [9,40,46]. This method consists in the comparison of the system response while two different inert gases with known refractive indices are brought into a contact with the gold film. In our experiments Ar and N2 were used, for which the refractive indices differ by Δn ≅1.5⋅10−5 RIU under the normal conditions . The gases were passed to the cell through a long spiral copper tube to equalize their temperatures with a room one and then mixed in a mixer to provide a controlled ration of gases in the flow cell. The mixture of gases was then brought in contact with SPR-supporting gold film. The precision of gas mixing was better than 0.01%.
Figure 6 demonstrates the response of the system when 100% of N2 was replaced by a mixture of 2.5% of Ar and 97.5% of N2 (such replacement of gases corresponds to the change of the refractive index by 4.9*10−7 RIU). One can see that such a tiny RI change leads to a significant phase shift (almost 0.1 Deg.). Taking into account that the noise level did not exceed 0.006 Deg. (Fig. 6), we can conclude that the experimental detection limit of the system is better than 4⋅10−8 RIU, which is orders of magnitude better compared to amplitude-sensitive schemes. It is important that this value of the detection limit was obtained under non-optimal pumping wavelength (632.8 nm) for Biacore slides. Based on 4-times sharper phase characteristics, the use of the optimal wavelength (670 nm) is expected to provide the detection limit lower than 10−8 RIU. However, such measurements require highly stabilized source characteristics, which is not the case for laser diodes used in Biacore system. Another approach for a further improvement of the detection limit is based on the optimization of the film thickness for 632.8 nm pumping wavelength.
4. Phase sensitivity for interferometric SPR imaging
As we showed in the last paragraph, a properly designed phase-sensitive scheme enables one to drastically outperform conventional amplitude-sensitive schemes and obtain the detection limit of 10−8 RIU and lower. In this paragraph we will illustrate that the employment of phase sensitivity makes possible the improvement of the LOD even under relatively noisy experimental arrangement, taking advantage of powerful phase-related filtering and spatial signal averaging methods. As an example, we consider thiol reaction with a gold film described in Ref . Figure 7(a-c) shows the obtained interferometric images of the clean gold film (a), the film half-covered by thiol (b) and fully covered gold film (c). These interferometric images were obtained in the fringe mode of a Mach-Zehnder interferometer with a diverging laser beam . Figure 7(d) gives the line scan of light intensity for Fig. 7(c), while Fig. 7(e) provides a radial-averaged light intensity. The phase of light was evaluated by determining positions of interference fringes. We found that image averaging reduce the phase noise by an order of magnitude (compare Fig. 7(d) and Fig. 7(e)) which resulted in averaged phase stability of 0.2 deg. The phase stability was checked by taking several subsequent images and determining time-stability of interference fringe positions. Such phase noise of the image averaging corresponds to the detection limit of = 9 × 10−8 in this particular scheme where laser was not stabilized and nothing else have been used to improve LOD. This means that interferometric phase imaging can improve phase sensitivity of the SPR technique by almost another order of magnitude with the help of a spatial analysis of light phase.
Thus, phase measurements offer additional powerful and flexible tools to improve signal-to-noise ratio even under a relatively high level of instrumental noises. In fact, such options are granted by nature of phase measurements. Indeed, phase control implies inherent relative measurement with respect to a reference beam or an unaffected component of the same beam. This makes possible spatial or temporal mapping, depending of geometry of phase-sensitive setup, and a subsequent filtering/averaging using the chosen map. In fact, similar mapping and subsequent filtering/averaging is possible in amplitude measurements under the involvement of an independent reference channel, unaffected by the SPR, but such arrangement is normally accompanied by an inevitable complication of the measurement system and increase of its cost. Notice that the latter approach has already been used to lower the measured LOD in some papers using amplitude-sensitive SPR systems.
We compared amplitude and phase characteristics of light reflected in conditions of Surface Plasmon Resonance bio- and chemical sensing. We showed that phase can provide at least two orders of magnitude lower LOD due to: (i) a much stronger response to refractive index variations as a result of probing of medium properties in the very dip of SPR dip where electric field is maximum; (ii) possibilities for a much lower level of phase noises compared to intensity ones under a proper design of phase-sensitive schemes; (iii) possibilities for additional filtering/averaging tools taking advantage of essentially relative nature of phase measurement. Providing a better sensitivity and offering imaging tools, phase-sensitive methodologies are expected to improve current SPR-based bio- and chemical sensing technology.
Finally, we are glad to state that the development of phase-sensitive SPR biosensors has recently resulted in the appearance of commercially available units (see, e.g. the system of BIOptics Inc., Ref. ), offering a better sensitivity and sensing in multi-channels.
We acknowledge the financial contribution from French National Research Agency (ANR) and EPSRC, grant EP/E01111X/1.
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