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We report on the investigation on the resolution of optical sensors exploiting Bloch surface waves sustained by one dimensional photonic crystals. A figure of merit is introduced to quantitatively assess the performance of such sensors and its dependency on the geometry and materials of the photonic crystal. We show that the figure of merit and the resolution can be improved by adopting a full ellipsometric phase-sensitive approach. The theoretical predictions are confirmed by experiments in which, for the first time, such type of sensors are operated in the full ellipsometric scheme.
© 2013 Optical Society of America
1. Introduction
Electromagnetic modes propagating at the interface between a finite one-dimensional photonic crystal (1DPC) and a homogeneous external medium [1], also named Bloch Surface Waves (BSW), have been recently proposed as an alternative to surface plasmon polaritons (SPP) for label-free optical biosensing [2–6].
BSW have also demonstrated their potential when coupled with fluorescent emitters [7–9], for signal enhancement in surface enhanced Raman scattering [10,11], for long range guided propagation of surface waves [12,13], and for fluorescence based biosensing [14].
The main advantages of BSW with respect to SPP are in that their dispersion can be almost arbitrarily tuned in wavelength, momentum and polarization by changing the 1DPC materials and geometry. Typically, the resonances they show when used for label-free biosensing are much sharper due to the reduced absorption losses, resulting in an increase of sensor performances [15,16]. Moreover in fluorescence applications the signal intensity is not quenched by the proximity of any metal layer.
In a previous work [15] we introduced a figure of merit (FOM) which can be used to compare the performance of BSW and SPP sensors. Here we report on extended numerical simulations of the characteristics of BSW optical sensors and study the dependence of the FOM on the geometry and on the absorption losses of the 1DPC. To this aim, numerical simulations were carried out for both a single polarization scheme, commonly adopted in optical surface wave biosensors (for example TM for SPP), and for a full ellipsometric scheme, making use of both TE and TM reflectivities and of their phase relationship.
The numerical simulations are complemented by experimental measurements, indicating that the resolution can be indeed enhanced when using the full ellipsometric approach.
To our knowledge the use of a full ellipsometric approach, also named phase sensitive scheme [17], has never been applied to BSW until now. The results presented here should be compared to those recently obtained for phase sensitive SPP sensors, wherein a further decrease of limit of detection has been reported [17–20].
2. Properties of Bloch surface waves and experimental sensing configuration
Similarly to SPP, BSW are localized at the truncation edge of the 1DPC, at the interface with the external medium. In the case of BSW the confinement, and enhancement, of the electromagnetic field close to the truncation interface of the multilayer is obtained by a combination of total internal reflection (external medium side) and Bragg reflection (1DPC side).
As an example, Fig. 1(a) shows the transverse intensity distribution of a TE polarized BSW propagating at the surface of a 1DPC at λ0 = 543nm. The intensity distribution was calculated numerically by means of the transfer matrix method (TMM) [1]. The 1DPC is a multilayer with N = 4 repetition units constituted by a high/low refractive index dielectric bilayer. The high and low refractive index materials used for the numerical calculation are tantalia (Ta2O5) and silica (SiO2), having refractive indices nH = 2.096 and nL = 1.450, respectively. The thicknesses of the high and low index layers are dH = 130nm and dL = 247nm, respectively. The BSW is squeezed at the truncation interface and shows an exponential tail in the external medium that can be used for optical sensing.
Fig. 1 (a) Typical transverse BSW intensity distribution. (b) Experimental setup used to characterize the performance of optical biosensors exploiting the BSW excitation. (c) Typical angular reflectance spectrum measured at λ0 showing the BSW resonance. The external medium is doubly deionized water.
In the following, when discussing both numerical and experimental results, we shall make reference to data obtained at λ0 for the 1DPC described above, based on tantalia/silica dielectrics. However changing the dielectrics used and the 1DPC geometry, allows one to design and to fabricate 1DPC sustaining BSW in any wavelength range where the materials are transparent for any polarizations (TE or TM), as we have previously shown [15,16, 21].
Similarly to SPP, the BSW dispersion is located beyond the light line of the external homogenous medium [1]. Therefore a direct coupling with an external field can occur by using any mechanism providing a suitable momentum matching (diffraction, refraction and evanescent coupling from high index materials). The simplest and most used method is prism coupling in the so-called Kretschmann-Raether configuration [22].
In Fig. 1(b) we show the experimental setup that implements the excitation of BSW on 1DPC. A He-Ne laser emitting at λ0 is used to measure the reflectance of a 1DPC coupled to a BK7 coupling prism by means of a contact oil. The laser beam has a transverse gaussian shape with divergence Δα = 0.06°. The 1DPC is topped with a fluidic cell wherein different solutions can be injected. The laser beam can be prepared in any polarization state by using a combination of a polarizer and a liquid crystal retarder (LCR). The polarization state of the reflected beam is probed by the analyzer. The incident and reflected intensities are independently monitored with a pair of photodiodes (PD1 and PD2), whose signals are analyzed by two lock-in amplifiers locked at the frequency of a mechanical chopper used to modulate the incident laser. For the sake of simplicity in Fig. 1(b) the amplifiers and the chopper are not shown. The sample and the PD2 arm are rotated by a θ-2θ stage.
The excitation of a BSW is revealed by the observation of a sharp resonance dip of the angularly resolved reflectance. The dip is positioned at an angle θBSW(λ0), corresponding to a transverse momentum matching condition.
A typical angularly resolved reflectance profile indicating a BSW coupling is presented in Fig. 1(c), as calculated with TMM assuming extinction in the low index layers with coefficient κL = 10−4. We point out that the extinction coefficient of the high index layers κH affects only slightly the resonance characteristics, as already reported elsewhere [23], because the BSW field is mainly localized in the low index layers (see Fig. 1(a)). Accordingly, in the following we shall always assume that the main contribution to losses of the 1DPC is given by the low index layers. Calculations do not take into account Fresnel losses at the coupling prism facets.
As for all mode coupling phenomena [24] the characteristics of the resonance, e.g. the depth (D) and the full width at half maximum (W), are determined by the losses, i.e. by κL, and by the coupling coefficient between the external radiation and the BSW, which is controlled by N once the bilayer properties are fixed. In Fig. 2 we show the angularly resolved TE reflectance (R), with the BSW resonance, calculated by the TMM at λ0 for the 1DPC described above with four different values of N, from N = 2 to 5. The external medium is doubly deionized water. In each plot the evolution of R vs κL is shown. It is clear that strong coupling (small N) and large κL contribute to increase W and that the maximum D can be achieved by properly tuning κL and N. In particular, for a given N, a minimum value of κL, is needed to maximize the depth (D = 1) of the resonance.
Fig. 2 Numerical calculations of the angularly resolved TE reflectance of a 1DPC illuminated in the Kretschmann configuration. Different numbers of repetition units N, form 2 to 5 are considered. The extinction coefficient κL ranges from 0 to 10−3.
From calculations it is shown that the resonance angle is independent from κL. We point out that all calculations reported here were performed for plane wave incidence and that the experimental implementation with a finite divergence laser beam can lead to a broadening of the resonances. On the other hand the laser line-width is always so small (about 2pm) that it does not give rise to any broadening of the natural BSW resonances calculated at λ0.
The size of the spot that can be probed with BSW on a sensor surface is limited by the leakage length, that we found experimentally to range between 40μm [9] and 400μm [12], depending on the number of periods (coupling coefficient) of the 1DPC used at a given wavelength. This value should be compared to that reported in literature for optimized SPP on gold layers that ranges between 3μm and 24μm, depending on the operation wavelength [22].
2.1 Single polarization optical sensing
Generally, optical biosensors exploiting the sensitivity of surface electromagnetic waves to perturbations of the refractive index of the external medium (ΔnEXT) are operated in a single polarization scheme, e.g. TM for SPP and TE for BSW. According to this approach, both the polarizer and the analyzer in the experimental setup are set for either the TE or the TM polarization and the LCR is removed from the optical path (or aligned to the polarization direction). The setup is sensitive to intensity variations only and does not reveal any phase effect. In some cases the independent, and not interferometric, use of both TE and TM polarizations was previously proposed to clearly distinguish bulk and surface effects in the optical detector operation [25].
In order to maximize the overall intensity variation of reflected light upon a refractive index perturbation of the external medium ΔnEXT, it is desirable to deal with BSW resonances with maximum D and minimum W. We recently introduced a figure of merit (FOM) for characterizing the performance of single-polarization BSW biosensors and comparing them to SPP biosensors [15]. With reference to Fig. 3, which was obtained for a 1DPC with N = 4, in a sensing approach in which the TE reflectance RTE is measured at λ0 and at a fixed working point (angle) θWP (such scheme is generally referred to as intensity measurement [22]), the change ΔRTE due to a variation ΔnEXT is given by:
In the Eq. (1) S = is the sensitivity of the biosensor [22] and is the slope of the resonance at the working point. If the working point is chosen as the flex of the resonance and a Lorentzian shape is assumed, the maximum slope is and the optimum response becomes:Such a result supports our previous definition [15] of the FOM as given by:The resolution of the sensor will then be expressed as:where ΔRTE,MIN is limited by the measurement noise.Fig. 3 Numerically calculated TE reflectance spectrum RTE(θ) of a 1DPC with N = 4. The gray curves were obtained when the external medium is doubly deionized water, the colored curves were calculated for a slight positive perturbation ΔnEXT. The red curve corresponds to κL = 2.4*10−5 and the blue to κL = 2.4*10−4.
From Fig. 3 it is also clear that tuning κL from 2.4*10−5 to 2.4*10−4 leads to an increase of the overall reflectance change from ΔR1 to ΔR2. Of course there is a strong interplay of D and W, connected to N and κL.
In order to clarify the dependency of the FOM on the W and D parameters we analyzed data shown in Fig. 2. From each plot we extracted the dependency of D and W on κL and the value of the sensitivity S, which does not depend on κL. For S we found the values reported in Table 1. As a result we retrieved the dependencies of the FOM defined by the Eq. (3) on N and κL, as shown in Fig. 4.
Table 1. Numerically calculated sensitivity, FOM and optimum extinction coefficient of the low index layers κL,OPT for four different 1DPC with a different number of repetition units N. Single polarization configuration. In case of N = 2 no local extrema have been obtained within the calculation range.
Fig. 4 Numerically calculated FOM for the 1DPC defined in the text and with different values of the number of repetition units N.
For each N the maximum of the figure of merit FOMMAX is achieved for an optimum value, different from zero, of the extinction coefficient κL,OPT (values are reported in Table 1).
The results shown in Fig. 4 can be used to optimize the design of the 1DPC to be used for optical biosensing based on BSW. We note that in the case of surface plasmon resonance (SPR) biosensors, once a metal film sustaining the SPP has been chosen and therefore its extinction coefficient is known, the only tuning parameter (besides the wavelength of operation) is the thickness of the metal layer, which is normally chosen in order to maximize the SPR depth.
However we point out two main issues that limit the single polarization sensing approach. Firstly, the results show that some extinction is needed to obtain a deep resonance, i.e. to increase D up to its upper limit (D = 1). Unfortunately, the extinction makes W to increase as well, leading to a FOM trade-off. It would be much more desirable to increase the resonance depth D without increasing W by adopting any other method. Secondly, the deposition of dielectric layers with a controlled value of the extinction coefficient is not straightforward. Generally thin film deposition experts work out methods and recipes that minimize the extinction coefficient of their layers. We have recently shown that the silica layers in silica/tantalia 1DPC deposited by plasma ion assisted evaporation under high vacuum conditions show an extinction coefficient as low as κL = 3.5*10−6, measurable by monitoring the BSW resonance [23]. Such low value, highly desirable for other applications such as very low loss mirrors, would reduce the FOM for single polarization optical sensing, according to Fig. 4. An increase of extinction could be achieved by depositing additional lossy layers embedded in the 1DPC structure.
2.2 Full ellipsometric optical sensing
One of the possibilities to increase the performance of optical biosensors is the exploitation of the change of the polarization state upon reflection from the 1DPC. Such condition can be achieved by operating the experimental sensing apparatus in a fully ellipsometric configuration. With reference to Fig. 1(b), the polarizer is turned at 45deg with respect to the incidence plane, giving rise to TE and TM components with the same intensity, and the analyzer is crossed at −45deg. The reflectance of the complete system will depend on the phase and amplitude changes of the TE and TM reflected fields. The LCR is used to change the phase shift between the TE and TM components and bias the input field to any state of canonical polarisation.
In Fig. 5 we show the TMM calculation of the reflectance in a crossed polarizers configuration as a function of the angle θ, for the 1DPC described above (N = 4 and κL = 8.2*10−6). RCROSS can be obtained calculating the TE and TM reflectivities as:
and then evaluating:The RCROSS(θ) curve in Fig. 5 is obtained for a phase difference Ψ = 45 deg between the TE and TM components introduced by the LCR. In Fig. 5 we also show the calculated TE and TM reflectances, RTE and RTM respectively. In all calculations we neglected Fresnel losses at the prism facets.Fig. 5 Numerically calculated RTE, RTM, RCROSS reflectance for the 1DPC as defined in the text. The figure on the right is a zoom about the BSW resonance angle.
RCROSS has a steep change around θBSW, where the RTE shows the BSW resonance. We notice that around the resonance RTM is flat and unitary; it just shows a very shallow resonance around θ = 65 deg due to the presence of a guided mode of the 1DPC. From calculations, it is found that the absolute value of the slope of RCROSS at θBSW is maximum for Ψ = 45 deg and Ψ = 225 deg, with opposite sign.
Figure 5 clearly indicates that, despite the fact that κL is very small and the BSW resonance measured in the TE polarization is shallow, RCROSS is characterized by a large contrast and slope around θBSW, that can be very effectively used for sensing.
As in the case of single polarization operation, in the full ellipsometric approach, the change ΔRCROSS due to a change ΔnEXT is given by:
where is the same sensitivity S of the sensor we discussed above and is the slope of the RCROSS(θ) curve at the working point. Again if the working point corresponds to the flex of RCROSS and comparing to Eqs. (2) and (3) we obtain:that can be directly compared to the FOMTE previously consideredIn Fig. 6 we report the results on the numerical calculation of the FOMCROSS as a function of the extinction coefficient κL, for the 1DPC described above for N = 3,4,5. The FOMCROSS is a monothonically decreasing function of κL; such behavior is due to the broadening of the BSW resonance that reduces the slope of RCROSS.
Fig. 6 Numerically calculated FOMCROSS for the 1DPC as defined in the text and for three different values of the number of repetition units N = 3, 4, 5.
Comparing Fig. 6 and Fig. 4 the advantage of using the full ellipsometric approach for sensing can be better appreciated. The figure of merit can be almost twice larger than in the single polarization configuration, and the resolution can be increased accordingly. It is also found that the FOMCROSS for the 1DPC with N = 5 suffers more from the extinction and BSW resonance broadening. Depending on the extinction coefficient of the 1DPC materials it will be convenient to choose N to maximize the FOMCROSS and the resolution.
We recently showed that κL can be as low as 3.5*10−6 in silica/tantalia 1DPC [23], permitting to operate very close to the FOM maximum. For such value of κL the corresponding FOM are reported in Table 2 for N = 3,4,5. In addition, it is meaningful to calculate the ratio between the figures of merit related to full ellipsometric case and the single polarization case. The results show that the gain in resolution decreases for 1DPC for larger N.
Table 2. Numerically calculated figure of merit for the full ellipsometric configuration and the corresponding ratio to the FOM for the single polarization configuration. Three cases with different values of the 1DPC number of repetition units N are considered.
3. Experimental results and discussion
In the present section we report on the sensing experiments carried out with a tantalia/silica 1DPC sustaining BSW at λ0. The results will be compared with the theoretical predictions reported in the previous section.
3.1 1DPC fabrication
1DPC based on silica (SiO2) and tantalia (Ta2O5) were fabricated based on the design reported in Section 2. The case of 1DPC with N = 4 repetition units is considered.
The deposition of the layered structures was carried out on Schott B270 glass wafers by plasma ion assisted evaporation under high vacuum conditions using an APS904 coating system (Leybold Optics). To obtain layers with low stress and minor absorption losses, low-level argon ion assistance with ion energies of about 80 eV was applied [26]. The refractive indices and the thickness calibration factors were determined by means of standard spectroscopic measurements on single layers. The refractive indices at λ = 543 nm for SiO2 and Ta2O5 are nL = 1.450 and nH = 2.097, respectively. No extinction could be measured within the resolution limits of reflection and transmission spectroscopy.
The deposition conditions were tuned in order to obtain high and low index layers with the design thickness dH = 130 nm and dL = 247 nm respectively.
3.2 Single polarization scheme
The experimental setup used for the characterization of the 1DPC has already been sketched in Fig. 1(b). In the case of single polarization measurements the LCR was removed from the laser path and the polarizer and analyzer were set to the TE polarization.
In Fig. 7 we show the measurement of the angularly resolved absolute TE reflectance RTE as a function of the angle θ, when the fluidic cell is filled with doubly deionized water (ddH2O). The measured RTE is affected by the reflectance of the coupling prism facets; for this reason it is less than unity in the total internal reflection region. The simulated curve was obtained by fitting the experimental data by means of a Matlab code based on the TMM and taking into account the finite divergence (Δα = 0.06°) of the laser beam. From the angular position of the total internal reflection edge, we estimated the refractive index of the external medium (nEXT = 1.3348). For a satisfactory fit, it is also necessary to assume that the layers thicknesses are different from the design values: dH = 138nm and dL = 251nm. Moreover the refractive index of the last silica layer in contact with the analyte is nL’ = 1.4555; this increased value is due to water adsorption in the voids of the last silica layer. In the inset of Fig. 7 we show a zoom of the BSW resonance; the blue offset curve is the result of the numerical simulation carried out without assuming the index change in the last layer. From the fit we also obtain the real value of the extinction coefficient of the low index layers κL = 1.2*10−5.In this 1DPC layout, losses are so low that the BSW resonance results to be very shallow. We can nevertheless evaluate the FOM. From Fig. 7 we get D = 0.083 and W = 0.078 deg and from a separate measurement the experimental sensitivity S = dθBSW/dn = 18.0 deg/RIU. By combining such values according to Eq. (3), we obtain an experimental value for the FOMTE = 19.4 RIU−1, as reported in the first column of Table 3. Such a value should be compared to the theoretical value (280 RIU−1) extracted from Fig. 4, related to the ideal 1DPC structure with N = 4 and the κL value estimated experimentally (second row in Table 3). The experimental value is much lower than the theoretical one. This is due mainly to the finite divergence of the laser beam resulting in a larger resonance width and a smaller resonance depth. A minor contribution is also due to the deviation of the actual 1DPC structure from the ideal design, and the increase of the refractive index of the last layer. We can estimate the resolution of the sensor by using the Eq. (4) and considering that in our experimental setup we have a measurement noise for the reflectance ΔRMIN = 0.002Hz-1/2. We obtain the experimental and theoretical values for the resolution reported in the second column of Table 3. The values obtained for such TE BSW sensor should be compared with those expected for a SPP sensor operating in a single polarization and intensity modulation scheme. For a state of the art SPP sensor operating at λ = 804nm in the TM polarization we previously found [15, 16] an experimental value for the FOM of about 38 RIU−1, with a maximum theoretical value of 60 RIU−1. For SPP sensors with gold layers and operating at the optimum λ = 850 nm, we theoretically have ΔnMIN = 1*10−5 [22], that is smaller than the experimental value found but larger than the theoretical prediction for the actual TE BSW case.
Fig. 7 Experimental measurement of RTE as a function of θ for a four periods (N = 4) 1DPC in ddH2O (black solid circles). The red solid line is the numerical fit. Inset: Zoom of the BSW resonance. The blue curve is the numerical simulation without assuming changes of the refractive index of the last layer due to water adsorption.
It is useful to note that the same 1DPC described here has been already used in a single polarization and wavelength interrogation sensing scheme [27]; the authors found a resolution for refractive index changes ΔnTE,MIN = 3*10−6 RIU that is very close to the theoretical resolution for optimized SPP sensors operating is such scheme, i.e. ΔnMIN = 1*10−6 RIU [22]. In addition, such a result confirms the better resolution performance that can be obtained by operating in the wavelength interrogation scheme rather than in the intensity measurement. In our case, resolution could be improved by a factor 27 by switching from one scheme to the other.
We remark that, if losses in the 1DPC would be tuned to the optimal value that maximizes the FOM, i.e. κL = 1.2*10−4, then the optimized TE BSW sensor (Table 3, 3rd and 4th columns) would theoretically outperform SPP by a factor 7 in resolution and the value that one would achieve experimentally, assuming the same degradation of the performance due to the non ideality of the 1DPC, would get very close to the SPP theoretical limit.
3.3 Full ellipsometric scheme
In the case of full ellipsometric measurements, the LCR was carefully aligned along the laser path in order to set its fast axis along the TE direction. The polarizer was turned to 45deg with respect to the TE direction and the analyzer to −45deg. By controlling the LCR driving voltage it was possible to tune the phase shift Ψ between the TE and TM components to any value in the interval Ψ∈[-π, π]. Such ellipsometric approach was already used for the measurement of the electro-optic properties of poled polymers [28].
In Fig. 8(a) we show the experimental measurement of the reflectance in the cross polarization scheme, for different values of the phase shift Ψ. Such measurements include the information on the amplitude and phase contributions to the TE and TM polarized field reflectivities of the 1DPC and also of the contribution of the BS and of the coupling prism. Therefore the curves show a maximum reflectance value less than unity.
Fig. 8 (a) Experimentally measured RCROSS for the fabricated 1DPC described in the text, with N = 4 repetition units. The curves were obtained for several different values of the phase Ψ between the TE and TM components set by controlling the LCR voltage: (black) Ψ = 0 deg, (red) Ψ = 30 deg, (blue) Ψ = 45 deg, (green) Ψ = 60 deg, (grey) Ψ = 90 deg. The solid lines are guide for the eyes. (b) Numerical calculations carried out by the TMM, assuming the design 1DPC structure with values for the complex indices and thicknesses obtained by fitting data in Fig. 7, for different values of Ψ = 0, 30, 45, 60 90 deg. Same color codes as for the experimental data.
Measurements are in very good agreement with the numerical simulations shown in Fig. 8(b), that were obtained assuming the 1DPC structure as described above with values for the complex indices and thicknesses obtained by fitting data in Fig. 7.
3.4 Refractive index sensing in the full ellipsometric scheme
We tested the full ellipsometric configuration by injecting several different solutions in the fluidic cell with an increasing concentration of glucose in water. The experimental setup was biased to work in the Ψ = 45 deg working point, where the slope of the RCROSS is at a maximum.
In the inset of Fig. 9(a) we show the measured RCROSS and the working point at θWP. By analyzing the curve, dRCROSS/dθ|WP = −15.8deg−1 is obtained. From the measurement of the rigid shift of the RCROSS curve at Ψ = 45deg for a given ΔnEXT we evaluated the sensitivity as S = dθBSW/dn = 18.0 deg/RIU. Therefore, according to Eq. (8), we find:
Such last value is more than 8 times lower than what expected from the simulations for the ideal structure shown in Fig. 6 for the κL = 1.2*10−5 found from the fit of Fig. 7 (FOMCROSS,TH = 1790RIU−1). The reduction is essentially due to a reduced value of the slope dRCROSS/dθ|WP and of the sensitivity S. The slope is 65% of the slope predicted for the real 1DPC (slope of the curve at Ψ = 45deg in Fig. 8(b)) and less than 28% of the slope expected for the ideal structure. The reduced performance is mainly due to the finite divergence of the laser beam and, to a minor extent, to the fact that the high index layers are thicker than expected from design.Fig. 9 (a) Experimentally measured reflectance variations at λ = 543nm for different glucose concentrations in the test solutions. Full ellipsometric configuration operating in the working point θWP. Inset: Angularly resolved RCROSS and position of the working point θWP. (b) Experimental values for RCROSS as a function of the refractive index change of the glucose solution collected at Ψ = 45deg (dots). The red solid curve is the fit with a quadratic function and the black dashed curve is the linear fit in the limit of small Δn.
In Fig. 9(a) we show the results of the measurement of RCROSS as a function of time during the injection of the glucose solutions. After each glucose solution injection the cell is rinsed with ddH2O. Increasing the concentration leads to larger and larger changes ΔRCROSS.
From Fig. 9(a) we can obtain Fig. 9(b), where the measured change ΔRCROSS is plotted against the refractive index variations of the solution. The experimental data can be fitted by means of a quadratic curve (red solid curve), indicating that for large refractive index changes a saturation of the response occurs. In the limit of small Δn the dependence is linear (black dashed line) with slope equal to 282RIU−1, corresponding to FOMCROSS,EXP = 217RIU−1. Such a value for the FOM is very close to that obtained right above from the estimation of the slope and the sensitivity, confirming the validity of both measurement procedures.
The FOMCROSS,EXP is about 11 times larger than the value reported in Table 3 for the single polarization TE scheme. Consequently the resolution in such phase sensitive and intensity measurement scheme is:
Such a value is smaller than the predicted theoretical resolution for SPP as cited above [22]. A further decrease of ΔnMIN can be obtained by improving deposition uncertainties, thus resulting in a 1DPC closer to the designed structure. In that case, a 8 times larger FOMCROSS would be expected.
We notice that, if the sensor would be operated in a wavelength interrogation scheme, the resolution would improve [22] due to the lower measurement noise. Assuming the same improvement factor as in the TE BSW sensor case (factor 27) one would get a resolution ΔnMIN = 2.6*10−7 RIU/Hz1/2, in strong competition with the state of the art SPR sensors operating in such configuration [29].
4. Conclusions
The introduction and use of a FOM constitutes a convenient tool to evaluate the performance of BSW and SPP sensors, allowing one to make simple and quick comparisons. Here, for the first time, we carried out a detailed analysis on the relationship of the features of BSW on the geometry and materials of the 1DPC. In particular we focused our attention on the absorption losses in the dielectrics and on the number of repetition units of the 1DPC. Such analysis can be extended by taking into account also other parameters, such as the thicknesses of the dielectric layers for example, and be used to optimize the 1DPC and the sustained BSW for sensing applications.
The numerical results obtained for the FOM of BSW sensors operated in the single polarization (TE) scheme show that there exist values for the absorption losses and number of periods of the photonic crystal that optimize the sensing resolution. The theoretical resolution (1.4*10−6 RIU) calculated for the 1DPC design presented here outperforms that obtained with SPP under the same sensing scheme (1*10−5 RIU).
In the case the BSW sensors are operated in the full ellipsometric scheme, we have shown here that the FOM is optimized for small absorption losses and that the resolution can be improved by a factor 1.84 with respect to optimized BSW sensors operating in a single polarization scheme. Such result paves the way to the fabrication of high resolution sensors based on very low loss 1DPC. We remind that, during the 1DPC fabrication, it is generally much easier to minimize the absorption losses in the dielectric layers rather than tuning them to a precise value.
The experimental results show that, for a real 1DPC based on silica/tantalia layers sustaining BSW, the resolution that can be achieved in the full ellipsometric scheme is 11 times better than that obtained in the single polarization (TE) scheme.
Acknowledgments
This research has received funding from the European Union Seventh Framework Program (FP7/2007–2013) under grant agreement n 318035—Project BILOBA (www.biloba-project.eu) and from the Italian FIRB 2011 NEWTON (grant RBAP11BYNP).
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