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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 20 — Oct. 7, 2013
  • pp: 23331–23344
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A full ellipsometric approach to optical sensing with Bloch surface waves on photonic crystals

Alberto Sinibaldi, Riccardo Rizzo, Giovanni Figliozzi, Emiliano Descrovi, Norbert Danz, Peter Munzert, Aleksei Anopchenko, and Francesco Michelotti  »View Author Affiliations


Optics Express, Vol. 21, Issue 20, pp. 23331-23344 (2013)
http://dx.doi.org/10.1364/OE.21.023331


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Abstract

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 OSA

1. Introduction

Electromagnetic modes propagating at the interface between a finite one-dimensional photonic crystal (1DPC) and a homogeneous external medium [1

1. P. Yeh, A. Yariv, and C.-S. Hong, “Electromagnetic propagation in periodic stratified media. I. General theory,” J. Opt. Soc. Am. 67(4), 423–438 (1977). [CrossRef]

], also named Bloch Surface Waves (BSW), have been recently proposed as an alternative to surface plasmon polaritons (SPP) for label-free optical biosensing [2

2. M. Shinn and W. M. Robertson, “Surface plasmon-like sensor based on surface electromagnetic waves in a photonic band-gap material,” Sens. Acta. B 105(2), 360–364 (2005). [CrossRef]

6

6. P. Rivolo, F. Michelotti, F. Frascella, G. Digregorio, P. Mandracci, L. Dominici, F. Giorgis, and E. Descrovi, “Real time secondary antibody detection by means of silicon-based multilayers sustaining Bloch surface waves,” Sens. Acta. B 161(1), 1046–1052 (2012). [CrossRef]

].

BSW have also demonstrated their potential when coupled with fluorescent emitters [7

7. M. Ballarini, F. Frascella, N. De Leo, S. Ricciardi, P. Rivolo, P. Mandracci, E. Enrico, F. Giorgis, F. Michelotti, and E. Descrovi, “A polymer-based functional pattern on one-dimensional photonic crystals for photon sorting of fluorescence radiation,” Opt. Express 20(6), 6703–6711 (2012). [CrossRef] [PubMed]

9

9. M. Ballarini, F. Frascella, E. Enrico, P. Mandracci, N. De Leo, F. Michelotti, F. Giorgis, and E. Descrovi, “Bloch surface waves-controlled fluorescence emission: coupling into nanometer-sized polymeric waveguides,” Appl. Phys. Lett. 100(6), 063305 (2012). [CrossRef]

], for signal enhancement in surface enhanced Raman scattering [10

10. A. Delfan, M. Liscidini, and J. E. Sipe, “Surface enhanced Raman scattering in the presence of multilayer dielectric structures,” J. Opt. Soc. Am. B 29(8), 1863–1874 (2012). [CrossRef]

,11

11. S. Pirotta, X. G. Xu, A. Delfan, S. Mysore, S. Maiti, G. Dacarro, M. Patrini, M. Galli, G. Guizzetti, D. Bajoni, J. E. Sipe, G. C. Walker, and M. Liscidini, “Surface-enhanced Raman scattering in purely dielectric structures via Bloch surface waves,” J. Phys. Chem. C 117(13), 6821–6825 (2013). [CrossRef]

], for long range guided propagation of surface waves [12

12. T. Sfez, E. Descrovi, L. Yu, D. Brunazzo, M. Quaglio, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, O. Martin, and H. Herzig, “Bloch surface waves in ultrathin waveguides: near-field investigation of mode polarization and propagation,” J. Opt. Soc. Am. B 27(8), 1617–1625 (2010). [CrossRef]

,13

13. M. Liscidini, D. Gerace, D. Sanvitto, and D. Bajoni, “Guided Bloch surface waves polaritons,” Appl. Phys. Lett. 98(12), 121118 (2011). [CrossRef]

], and for fluorescence based biosensing [14

14. K. Toma, E. Descrovi, M. Toma, M. Ballarini, P. Mandracci, F. Giorgis, A. Mateescu, U. Jonas, W. Knoll, and J. Dostálek, “Bloch surface wave-enhanced fluorescence biosensor,” Biosens. Bioelectron. 43, 108–114 (2013). [CrossRef] [PubMed]

].

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

15. A. Sinibaldi, N. Danz, E. Descrovi, P. Munzert, U. Schulz, F. Sonntag, L. Dominici, and F. Michelotti, “Direct comparison of the performance of Bloch surface wave and surface plasmon polariton sensors,” Sens. Acta. B 174, 292–298 (2012). [CrossRef]

,16

16. A. Sinibaldi, E. Descrovi, F. Giorgis, L. Dominici, M. Ballarini, P. Mandracci, N. Danz, and F. Michelotti, “Hydrogenated amorphous silicon nitride photonic crystals for improved-performance surface electromagnetic wave biosensors,” Biomed. Opt. Express 3(10), 2405–2410 (2012). [CrossRef] [PubMed]

]. Moreover in fluorescence applications the signal intensity is not quenched by the proximity of any metal layer.

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

17. 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]

], 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

17. 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]

20

20. Y. Shao, Y. Li, D. Gu, K. Zhang, J. Qu, J. He, X. Li, S.-Y. Wu, H.-P. Ho, M. G. Somekh, and H. Niu, “Wavelength-multiplexing phase-sensitive surface plasmon imaging sensor,” Opt. Lett. 38(9), 1370–1372 (2013). [CrossRef] [PubMed]

].

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)
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.
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

1. P. Yeh, A. Yariv, and C.-S. Hong, “Electromagnetic propagation in periodic stratified media. I. General theory,” J. Opt. Soc. Am. 67(4), 423–438 (1977). [CrossRef]

]. 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.

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

15. A. Sinibaldi, N. Danz, E. Descrovi, P. Munzert, U. Schulz, F. Sonntag, L. Dominici, and F. Michelotti, “Direct comparison of the performance of Bloch surface wave and surface plasmon polariton sensors,” Sens. Acta. B 174, 292–298 (2012). [CrossRef]

,16

16. A. Sinibaldi, E. Descrovi, F. Giorgis, L. Dominici, M. Ballarini, P. Mandracci, N. Danz, and F. Michelotti, “Hydrogenated amorphous silicon nitride photonic crystals for improved-performance surface electromagnetic wave biosensors,” Biomed. Opt. Express 3(10), 2405–2410 (2012). [CrossRef] [PubMed]

, 21

21. F. Michelotti, B. Sciacca, L. Dominici, M. Quaglio, E. Descrovi, F. Giorgis, and F. Geobaldo, “Fast optical vapour sensing by Bloch surface waves on porous silicon membranes,” Phys. Chem. Chem. Phys. 12(2), 502–506 (2009). [CrossRef] [PubMed]

].

Similarly to SPP, the BSW dispersion is located beyond the light line of the external homogenous medium [1

1. P. Yeh, A. Yariv, and C.-S. Hong, “Electromagnetic propagation in periodic stratified media. I. General theory,” J. Opt. Soc. Am. 67(4), 423–438 (1977). [CrossRef]

]. 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

22. J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Act. B 54(1-2), 3–15 (1999). [CrossRef]

].

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 θBSW0), 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

23. F. Michelotti, A. Sinibaldi, P. Munzert, N. Danz, and E. Descrovi, “Probing losses of dielectric multilayers by means of Bloch surface waves,” Opt. Lett. 38(5), 616–618 (2013). [CrossRef] [PubMed]

], 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

24. R. Ulrich, “Theory of the prism-film coupler by plane-wave analysis,” J. Opt. Soc. Am. B 60(10), 1337–1350 (1970). [CrossRef]

] 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
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.
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.

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

9. M. Ballarini, F. Frascella, E. Enrico, P. Mandracci, N. De Leo, F. Michelotti, F. Giorgis, and E. Descrovi, “Bloch surface waves-controlled fluorescence emission: coupling into nanometer-sized polymeric waveguides,” Appl. Phys. Lett. 100(6), 063305 (2012). [CrossRef]

] and 400μm [12

12. T. Sfez, E. Descrovi, L. Yu, D. Brunazzo, M. Quaglio, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, O. Martin, and H. Herzig, “Bloch surface waves in ultrathin waveguides: near-field investigation of mode polarization and propagation,” J. Opt. Soc. Am. B 27(8), 1617–1625 (2010). [CrossRef]

], 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

22. J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Act. B 54(1-2), 3–15 (1999). [CrossRef]

].

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

25. V. N. Konopsky, T. Karakouz, E. V. Alieva, C. Vicario, S. K. Sekatskii, and G. Dietler, Sensors (Basel Switzerland) 13, 2566–2578 (2013).

].

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

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.

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. As a result we retrieved the dependencies of the FOM defined by the Eq. (3) on N and κL, as shown in Fig. 4
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

23. F. Michelotti, A. Sinibaldi, P. Munzert, N. Danz, and E. Descrovi, “Probing losses of dielectric multilayers by means of Bloch surface waves,” Opt. Lett. 38(5), 616–618 (2013). [CrossRef] [PubMed]

]. 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
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.
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:
r˜TE,TM=rTE,TMejφTE,TM
(5)
and then evaluating:
RCROSS==14{rTE2+rTM2+2rTErTMcos(φTEφTM+Ψ)}==14{RTE+RTM+2RTERTMcos(φTEφTM+Ψ)}
(6)
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.

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:
ΔRCROSS=dRCROSSdθ|WPdθBSWdnΔn
(7)
where dθBSW/dnis the same sensitivity S of the sensor we discussed above and dRCROSS/dθis 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:
FOMCROSS=0.77SdRCROSSdθ|WP
(8)
that can be directly compared to the FOMTE previously considered

In Fig. 6
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.
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.

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.

3. Experimental results and discussion

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

26. P. Munzert, U. Schulz, and N. Kaiser, “Transparent thermoplastic polymers in plasma assisted coating processes,” Surf. Coat. Tech. 174–175, 1048–1052 (2003). [CrossRef]

]. 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.

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

27. E. Descrovi, F. Frascella, M. Ballarini, V. Moi, A. Lamberti, F. Michelotti, F. Giorgis, and C. F. Pirri, “Surface label-free sensing by means of a fluorescent multilayered photonic structure,” Appl. Phys. Lett. 101(13), 131105 (2012). [CrossRef]

]; 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

22. J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Act. B 54(1-2), 3–15 (1999). [CrossRef]

]. 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

28. F. Michelotti, V. Taggi, M. Bertolotti, T. Gabler, H. H. Horhold, and A. Brauer, “Reflection electro-optical measurements on electroluminescent polymer films: A good tool for investigating charge injection and space charge effects,” J. Appl. Phys. 83(12), 7886–7895 (1998). [CrossRef]

].

In Fig. 8(a)
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.
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.

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)
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.
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:
FOMCROSS,EXP=0.77SdRCROSSdθ|WP=219RIU1
(9)
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.

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:

ΔnMIN=0.77ΔRMINFOMCROSS,EXP=7106RIU/Hz1/2
(10)

Such a value is smaller than the predicted theoretical resolution for SPP as cited above [22

22. J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Act. B 54(1-2), 3–15 (1999). [CrossRef]

]. 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

22. J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Act. B 54(1-2), 3–15 (1999). [CrossRef]

] 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

29. M. Piliarik and J. Homola, “Surface plasmon resonance (SPR) sensors: approaching their limits?” Opt. Express 17(19), 16505–16517 (2009). [CrossRef] [PubMed]

].

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).

References and links

1.

P. Yeh, A. Yariv, and C.-S. Hong, “Electromagnetic propagation in periodic stratified media. I. General theory,” J. Opt. Soc. Am. 67(4), 423–438 (1977). [CrossRef]

2.

M. Shinn and W. M. Robertson, “Surface plasmon-like sensor based on surface electromagnetic waves in a photonic band-gap material,” Sens. Acta. B 105(2), 360–364 (2005). [CrossRef]

3.

V. N. Konopsky and E. V. Alieva, “Photonic crystal surface waves for optical biosensors,” Anal. Chem. 79(12), 4729–4735 (2007). [CrossRef] [PubMed]

4.

F. Giorgis, E. Descrovi, C. Summonte, L. Dominici, and F. Michelotti, “Experimental determination of the sensitivity of Bloch surface waves based sensors,” Opt. Express 18(8), 8087–8093 (2010). [CrossRef] [PubMed]

5.

Y. Guo, J. Y. Ye, C. Divin, B. Huang, T. P. Thomas, J. R. Baker Jr, and T. B. Norris, “Real-time biomolecular binding detection using a sensitive photonic crystal biosensor,” Anal. Chem. 82(12), 5211–5218 (2010). [CrossRef] [PubMed]

6.

P. Rivolo, F. Michelotti, F. Frascella, G. Digregorio, P. Mandracci, L. Dominici, F. Giorgis, and E. Descrovi, “Real time secondary antibody detection by means of silicon-based multilayers sustaining Bloch surface waves,” Sens. Acta. B 161(1), 1046–1052 (2012). [CrossRef]

7.

M. Ballarini, F. Frascella, N. De Leo, S. Ricciardi, P. Rivolo, P. Mandracci, E. Enrico, F. Giorgis, F. Michelotti, and E. Descrovi, “A polymer-based functional pattern on one-dimensional photonic crystals for photon sorting of fluorescence radiation,” Opt. Express 20(6), 6703–6711 (2012). [CrossRef] [PubMed]

8.

M. Ballarini, F. Frascella, F. Michelotti, G. Digregorio, P. Rivolo, V. Paeder, V. Musi, F. Giorgis, and E. Descrovi, “Bloch surface waves-controlled emission of organic dyes grafted on a one-dimensional photonic crystal,” Appl. Phys. Lett. 99(4), 043302 (2011). [CrossRef]

9.

M. Ballarini, F. Frascella, E. Enrico, P. Mandracci, N. De Leo, F. Michelotti, F. Giorgis, and E. Descrovi, “Bloch surface waves-controlled fluorescence emission: coupling into nanometer-sized polymeric waveguides,” Appl. Phys. Lett. 100(6), 063305 (2012). [CrossRef]

10.

A. Delfan, M. Liscidini, and J. E. Sipe, “Surface enhanced Raman scattering in the presence of multilayer dielectric structures,” J. Opt. Soc. Am. B 29(8), 1863–1874 (2012). [CrossRef]

11.

S. Pirotta, X. G. Xu, A. Delfan, S. Mysore, S. Maiti, G. Dacarro, M. Patrini, M. Galli, G. Guizzetti, D. Bajoni, J. E. Sipe, G. C. Walker, and M. Liscidini, “Surface-enhanced Raman scattering in purely dielectric structures via Bloch surface waves,” J. Phys. Chem. C 117(13), 6821–6825 (2013). [CrossRef]

12.

T. Sfez, E. Descrovi, L. Yu, D. Brunazzo, M. Quaglio, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, O. Martin, and H. Herzig, “Bloch surface waves in ultrathin waveguides: near-field investigation of mode polarization and propagation,” J. Opt. Soc. Am. B 27(8), 1617–1625 (2010). [CrossRef]

13.

M. Liscidini, D. Gerace, D. Sanvitto, and D. Bajoni, “Guided Bloch surface waves polaritons,” Appl. Phys. Lett. 98(12), 121118 (2011). [CrossRef]

14.

K. Toma, E. Descrovi, M. Toma, M. Ballarini, P. Mandracci, F. Giorgis, A. Mateescu, U. Jonas, W. Knoll, and J. Dostálek, “Bloch surface wave-enhanced fluorescence biosensor,” Biosens. Bioelectron. 43, 108–114 (2013). [CrossRef] [PubMed]

15.

A. Sinibaldi, N. Danz, E. Descrovi, P. Munzert, U. Schulz, F. Sonntag, L. Dominici, and F. Michelotti, “Direct comparison of the performance of Bloch surface wave and surface plasmon polariton sensors,” Sens. Acta. B 174, 292–298 (2012). [CrossRef]

16.

A. Sinibaldi, E. Descrovi, F. Giorgis, L. Dominici, M. Ballarini, P. Mandracci, N. Danz, and F. Michelotti, “Hydrogenated amorphous silicon nitride photonic crystals for improved-performance surface electromagnetic wave biosensors,” Biomed. Opt. Express 3(10), 2405–2410 (2012). [CrossRef] [PubMed]

17.

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]

18.

S. P. Ng, C. M. L. Wu, S. Y. Wu, and H. P. Ho, “White-light spectral interferometry for surface plasmon resonance sensing applications,” Opt. Express 19(5), 4521–4527 (2011). [CrossRef] [PubMed]

19.

Y. H. Huang, H. P. Ho, S. Y. Wu, S. K. Kong, W. W. Wong, and P. Shum, “Phase sensitive SPR sensor for wide dynamic range detection,” Opt. Lett. 36(20), 4092–4094 (2011). [CrossRef] [PubMed]

20.

Y. Shao, Y. Li, D. Gu, K. Zhang, J. Qu, J. He, X. Li, S.-Y. Wu, H.-P. Ho, M. G. Somekh, and H. Niu, “Wavelength-multiplexing phase-sensitive surface plasmon imaging sensor,” Opt. Lett. 38(9), 1370–1372 (2013). [CrossRef] [PubMed]

21.

F. Michelotti, B. Sciacca, L. Dominici, M. Quaglio, E. Descrovi, F. Giorgis, and F. Geobaldo, “Fast optical vapour sensing by Bloch surface waves on porous silicon membranes,” Phys. Chem. Chem. Phys. 12(2), 502–506 (2009). [CrossRef] [PubMed]

22.

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Act. B 54(1-2), 3–15 (1999). [CrossRef]

23.

F. Michelotti, A. Sinibaldi, P. Munzert, N. Danz, and E. Descrovi, “Probing losses of dielectric multilayers by means of Bloch surface waves,” Opt. Lett. 38(5), 616–618 (2013). [CrossRef] [PubMed]

24.

R. Ulrich, “Theory of the prism-film coupler by plane-wave analysis,” J. Opt. Soc. Am. B 60(10), 1337–1350 (1970). [CrossRef]

25.

V. N. Konopsky, T. Karakouz, E. V. Alieva, C. Vicario, S. K. Sekatskii, and G. Dietler, Sensors (Basel Switzerland) 13, 2566–2578 (2013).

26.

P. Munzert, U. Schulz, and N. Kaiser, “Transparent thermoplastic polymers in plasma assisted coating processes,” Surf. Coat. Tech. 174–175, 1048–1052 (2003). [CrossRef]

27.

E. Descrovi, F. Frascella, M. Ballarini, V. Moi, A. Lamberti, F. Michelotti, F. Giorgis, and C. F. Pirri, “Surface label-free sensing by means of a fluorescent multilayered photonic structure,” Appl. Phys. Lett. 101(13), 131105 (2012). [CrossRef]

28.

F. Michelotti, V. Taggi, M. Bertolotti, T. Gabler, H. H. Horhold, and A. Brauer, “Reflection electro-optical measurements on electroluminescent polymer films: A good tool for investigating charge injection and space charge effects,” J. Appl. Phys. 83(12), 7886–7895 (1998). [CrossRef]

29.

M. Piliarik and J. Homola, “Surface plasmon resonance (SPR) sensors: approaching their limits?” Opt. Express 17(19), 16505–16517 (2009). [CrossRef] [PubMed]

OCIS Codes
(130.6010) Integrated optics : Sensors
(170.4580) Medical optics and biotechnology : Optical diagnostics for medicine
(240.6690) Optics at surfaces : Surface waves
(160.5293) Materials : Photonic bandgap materials
(050.5298) Diffraction and gratings : Photonic crystals
(230.5298) Optical devices : Photonic crystals
(310.5448) Thin films : Polarization, other optical properties

ToC Category:
Sensors

History
Original Manuscript: May 21, 2013
Revised Manuscript: August 19, 2013
Manuscript Accepted: August 31, 2013
Published: September 25, 2013

Citation
Alberto Sinibaldi, Riccardo Rizzo, Giovanni Figliozzi, Emiliano Descrovi, Norbert Danz, Peter Munzert, Aleksei Anopchenko, and Francesco Michelotti, "A full ellipsometric approach to optical sensing with Bloch surface waves on photonic crystals," Opt. Express 21, 23331-23344 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-20-23331


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References

  1. P. Yeh, A. Yariv, and C.-S. Hong, “Electromagnetic propagation in periodic stratified media. I. General theory,” J. Opt. Soc. Am.67(4), 423–438 (1977). [CrossRef]
  2. M. Shinn and W. M. Robertson, “Surface plasmon-like sensor based on surface electromagnetic waves in a photonic band-gap material,” Sens. Acta. B105(2), 360–364 (2005). [CrossRef]
  3. V. N. Konopsky and E. V. Alieva, “Photonic crystal surface waves for optical biosensors,” Anal. Chem.79(12), 4729–4735 (2007). [CrossRef] [PubMed]
  4. F. Giorgis, E. Descrovi, C. Summonte, L. Dominici, and F. Michelotti, “Experimental determination of the sensitivity of Bloch surface waves based sensors,” Opt. Express18(8), 8087–8093 (2010). [CrossRef] [PubMed]
  5. Y. Guo, J. Y. Ye, C. Divin, B. Huang, T. P. Thomas, J. R. Baker, and T. B. Norris, “Real-time biomolecular binding detection using a sensitive photonic crystal biosensor,” Anal. Chem.82(12), 5211–5218 (2010). [CrossRef] [PubMed]
  6. P. Rivolo, F. Michelotti, F. Frascella, G. Digregorio, P. Mandracci, L. Dominici, F. Giorgis, and E. Descrovi, “Real time secondary antibody detection by means of silicon-based multilayers sustaining Bloch surface waves,” Sens. Acta. B161(1), 1046–1052 (2012). [CrossRef]
  7. M. Ballarini, F. Frascella, N. De Leo, S. Ricciardi, P. Rivolo, P. Mandracci, E. Enrico, F. Giorgis, F. Michelotti, and E. Descrovi, “A polymer-based functional pattern on one-dimensional photonic crystals for photon sorting of fluorescence radiation,” Opt. Express20(6), 6703–6711 (2012). [CrossRef] [PubMed]
  8. M. Ballarini, F. Frascella, F. Michelotti, G. Digregorio, P. Rivolo, V. Paeder, V. Musi, F. Giorgis, and E. Descrovi, “Bloch surface waves-controlled emission of organic dyes grafted on a one-dimensional photonic crystal,” Appl. Phys. Lett.99(4), 043302 (2011). [CrossRef]
  9. M. Ballarini, F. Frascella, E. Enrico, P. Mandracci, N. De Leo, F. Michelotti, F. Giorgis, and E. Descrovi, “Bloch surface waves-controlled fluorescence emission: coupling into nanometer-sized polymeric waveguides,” Appl. Phys. Lett.100(6), 063305 (2012). [CrossRef]
  10. A. Delfan, M. Liscidini, and J. E. Sipe, “Surface enhanced Raman scattering in the presence of multilayer dielectric structures,” J. Opt. Soc. Am. B29(8), 1863–1874 (2012). [CrossRef]
  11. S. Pirotta, X. G. Xu, A. Delfan, S. Mysore, S. Maiti, G. Dacarro, M. Patrini, M. Galli, G. Guizzetti, D. Bajoni, J. E. Sipe, G. C. Walker, and M. Liscidini, “Surface-enhanced Raman scattering in purely dielectric structures via Bloch surface waves,” J. Phys. Chem. C117(13), 6821–6825 (2013). [CrossRef]
  12. T. Sfez, E. Descrovi, L. Yu, D. Brunazzo, M. Quaglio, L. Dominici, W. Nakagawa, F. Michelotti, F. Giorgis, O. Martin, and H. Herzig, “Bloch surface waves in ultrathin waveguides: near-field investigation of mode polarization and propagation,” J. Opt. Soc. Am. B27(8), 1617–1625 (2010). [CrossRef]
  13. M. Liscidini, D. Gerace, D. Sanvitto, and D. Bajoni, “Guided Bloch surface waves polaritons,” Appl. Phys. Lett.98(12), 121118 (2011). [CrossRef]
  14. K. Toma, E. Descrovi, M. Toma, M. Ballarini, P. Mandracci, F. Giorgis, A. Mateescu, U. Jonas, W. Knoll, and J. Dostálek, “Bloch surface wave-enhanced fluorescence biosensor,” Biosens. Bioelectron.43, 108–114 (2013). [CrossRef] [PubMed]
  15. A. Sinibaldi, N. Danz, E. Descrovi, P. Munzert, U. Schulz, F. Sonntag, L. Dominici, and F. Michelotti, “Direct comparison of the performance of Bloch surface wave and surface plasmon polariton sensors,” Sens. Acta. B174, 292–298 (2012). [CrossRef]
  16. A. Sinibaldi, E. Descrovi, F. Giorgis, L. Dominici, M. Ballarini, P. Mandracci, N. Danz, and F. Michelotti, “Hydrogenated amorphous silicon nitride photonic crystals for improved-performance surface electromagnetic wave biosensors,” Biomed. Opt. Express3(10), 2405–2410 (2012). [CrossRef] [PubMed]
  17. A. V. Kabashin, S. Patskovsky, and A. N. Grigorenko, “Phase and amplitude sensitivities in surface plasmon resonance bio and chemical sensing,” Opt. Express17(23), 21191–21204 (2009). [CrossRef] [PubMed]
  18. S. P. Ng, C. M. L. Wu, S. Y. Wu, and H. P. Ho, “White-light spectral interferometry for surface plasmon resonance sensing applications,” Opt. Express19(5), 4521–4527 (2011). [CrossRef] [PubMed]
  19. Y. H. Huang, H. P. Ho, S. Y. Wu, S. K. Kong, W. W. Wong, and P. Shum, “Phase sensitive SPR sensor for wide dynamic range detection,” Opt. Lett.36(20), 4092–4094 (2011). [CrossRef] [PubMed]
  20. Y. Shao, Y. Li, D. Gu, K. Zhang, J. Qu, J. He, X. Li, S.-Y. Wu, H.-P. Ho, M. G. Somekh, and H. Niu, “Wavelength-multiplexing phase-sensitive surface plasmon imaging sensor,” Opt. Lett.38(9), 1370–1372 (2013). [CrossRef] [PubMed]
  21. F. Michelotti, B. Sciacca, L. Dominici, M. Quaglio, E. Descrovi, F. Giorgis, and F. Geobaldo, “Fast optical vapour sensing by Bloch surface waves on porous silicon membranes,” Phys. Chem. Chem. Phys.12(2), 502–506 (2009). [CrossRef] [PubMed]
  22. J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Act. B54(1-2), 3–15 (1999). [CrossRef]
  23. F. Michelotti, A. Sinibaldi, P. Munzert, N. Danz, and E. Descrovi, “Probing losses of dielectric multilayers by means of Bloch surface waves,” Opt. Lett.38(5), 616–618 (2013). [CrossRef] [PubMed]
  24. R. Ulrich, “Theory of the prism-film coupler by plane-wave analysis,” J. Opt. Soc. Am. B60(10), 1337–1350 (1970). [CrossRef]
  25. V. N. Konopsky, T. Karakouz, E. V. Alieva, C. Vicario, S. K. Sekatskii, and G. Dietler, Sensors (Basel Switzerland)13, 2566–2578 (2013).
  26. P. Munzert, U. Schulz, and N. Kaiser, “Transparent thermoplastic polymers in plasma assisted coating processes,” Surf. Coat. Tech.174–175, 1048–1052 (2003). [CrossRef]
  27. E. Descrovi, F. Frascella, M. Ballarini, V. Moi, A. Lamberti, F. Michelotti, F. Giorgis, and C. F. Pirri, “Surface label-free sensing by means of a fluorescent multilayered photonic structure,” Appl. Phys. Lett.101(13), 131105 (2012). [CrossRef]
  28. F. Michelotti, V. Taggi, M. Bertolotti, T. Gabler, H. H. Horhold, and A. Brauer, “Reflection electro-optical measurements on electroluminescent polymer films: A good tool for investigating charge injection and space charge effects,” J. Appl. Phys.83(12), 7886–7895 (1998). [CrossRef]
  29. M. Piliarik and J. Homola, “Surface plasmon resonance (SPR) sensors: approaching their limits?” Opt. Express17(19), 16505–16517 (2009). [CrossRef] [PubMed]

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