## Resonant waveguide sensing made robust by on-chip peak tracking through image correlation |

Biomedical Optics Express, Vol. 3, Issue 10, pp. 2436-2451 (2012)

http://dx.doi.org/10.1364/BOE.3.002436

Acrobat PDF (2423 KB)

### Abstract

We demonstrate a solution to make resonant-waveguide-grating sensing both robust and simpler to optically assess, in the spirit of biochips. Instead of varying wavelength or angle to track the resonant condition, the grating itself has a step-wise variation with typically few tens of neighboring “micropads.” An image capture with incoherent monochromatic light delivers spatial intensity sequences from these micropads. Sensitivity and robustness are discussed using correlation techniques on a realistic model (Fano shapes with noise and local distortion contributions). We confirm through fluid refractive index sensing experiments an improvement over the step-wise maximum position tracking by more than 2 orders of magnitude, demonstrating sensitivity down to 2 × 10^{−5} RIU, giving high potential development for bioarray imaging.

© 2012 OSA

## 1. Introduction

1. K. Bougot-Robin, J.-L. Reverchon, M. Fromant, L. Mugherli, P. Plateau, and H. Benisty, “2D label-free imaging of resonant grating biochips in ultraviolet,” Opt. Express **18**(11), 11472–11482 (2010). [CrossRef] [PubMed]

2. A. M. Ferrie, Q. Wu, and Y. Fang, “Resonant waveguide grating imager for live cell sensing,” Appl. Phys. Lett. **97**(22), 223704 (2010). [CrossRef] [PubMed]

4. R. Magnusson, D. Wawro, S. Zimmerman, Y. Ding, S. Zimmerman, and Y. Ding “Resonant photonic biosensors with polarization-based multiparametric discrimination in each channel,”,” Sensors (Basel Switzerland) **11**(2), 1476–1488 (2011). [CrossRef]

5. E. M. Yeatman, “Resolution and sensitivity in surface plasmon microscopy and sensing,” Biosens. Bioelectron. **11**(6-7), 635–649 (1996). [CrossRef]

^{−4}RIU (Refractive Index Unit) sensitivity for 0.2% noise vs. optical power, for the usual gold layer structure [6

6. A. Shalabney and I. Abdulhalim, “Sensitivity enhancement methods for surface plasmon sensors,” Laser Photonics Rev. **5**(4), 571–606 (2011). [CrossRef]

2. A. M. Ferrie, Q. Wu, and Y. Fang, “Resonant waveguide grating imager for live cell sensing,” Appl. Phys. Lett. **97**(22), 223704 (2010). [CrossRef] [PubMed]

4. R. Magnusson, D. Wawro, S. Zimmerman, Y. Ding, S. Zimmerman, and Y. Ding “Resonant photonic biosensors with polarization-based multiparametric discrimination in each channel,”,” Sensors (Basel Switzerland) **11**(2), 1476–1488 (2011). [CrossRef]

7. S. George, I. D. Block, S. I. Jones, P. C. Mathias, V. Chaudhery, P. Vuttipittayamongkol, H. Y. Wu, L. O. Vodkin, and B. T. Cunningham, “Label-free prehybridization DNA microarray imaging using photonic crystals for quantitative spot quality analysis,” Anal. Chem. **82**(20), 8551–8557 (2010). [CrossRef] [PubMed]

_{0}, θ

_{0}) configuration through imaging [1

1. K. Bougot-Robin, J.-L. Reverchon, M. Fromant, L. Mugherli, P. Plateau, and H. Benisty, “2D label-free imaging of resonant grating biochips in ultraviolet,” Opt. Express **18**(11), 11472–11482 (2010). [CrossRef] [PubMed]

*u*in both continuous and discrete forms. In Fig. 1(b), we report these same profiles in gray intensity level for more intuitive representation of what will be further described. The refractive index variation may be retrieved from the profile’s shift measurement

*Δu*

_{res}, involving some adequate analysis to allow a precise measurement that encompasses the discreteness of the measured curve.

*f*), we will perform index sensing down to ~2 × 10

^{−5}RIU (refractive index unit) sensitivity. We shall also develop a model to justify that, as observed in practice, the sensing resolution shrinks, by more than two orders of magnitudes below the step Δ

*m*= 1 between two micropads. This point is important not only because accuracy is generally welcome, but also because it positively ensures that current lithography techniques can be used in spite of their inability to define subnanometer steps in gratings ridge/groove dimensions. We will further demonstrate the superiority of a correlation treatment over more conventional ones, using a control template (reference image) and the signal image to determine resonance shifts down to Δ

*m*~0.005, thus equivalent to such a subnanometer RWG pattern variation. Robustness of this correlation scheme to variations such as the change of waveguide thickness or grating depth modifying the Fano resonance shape, is another asset. Eventually, robustness to distortions and aberrations that we also observe in some real RWG assays shall also be evidenced.

## 2. Model of stepped duty-cycle peak tracking resonance detection

### 2.1. Resonant waveguide and discretization

8. S. S. Wang, R. Magnusson, J. S. Bagby, and M. G. Moharam, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. A **7**(8), 1470–1474 (1990). [CrossRef]

*θ*

_{inc}is the angle of incidence,

*k*

_{0}= 2

*π*/

*λ*is the vacuum wavevector of incident light at vacuum wavelength

*λ*,

*G*

_{0}= 2

*π*/Λ is the grating wavevector, and

*n*

_{eff}(

*λ*) is the guided mode effective index in the adequate polarization of wavevector

*k*

_{guid}(

*λ*). The reflected intensity

*I*has a singular behavior, often akin to a Fano resonance (Fig. 1(a)) around this exact resonance condition [9

9. U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. **124**(6), 1866–1878 (1961). [CrossRef]

12. B. Gallinet and O. J. F. Martin, “Ab initio theory of Fano resonances in plasmonic nanostructures and metamaterials,” Phys. Rev. B **83**(23), 235427 (2011). [CrossRef]

*u*

_{res}, as shown on Fig. 1(c), and signal-to-noise considerations may be superfluous. Conversely, when a small shift has to be detected, Fig. 1(d), e.g., to get the ultimate sensing sensitivity, refined analysis is needed.

*I*(

*u*−

*u*

_{res}), not by scanning u ≡ θ or u ≡ λ, but by scanning by steps a grating parameter among {Λ, n

_{eff}}, the effective index being itself sensitive to all the optogeometric grating parameters. For a rectangular-profile (lamellar) grating of period Λ, these parameters are waveguide layer thickness t, etch depth h, filling factor f, refractive index n

_{ridge}of the ridges (or of the grooves if they are not void). Curves given in Fig. 1 (a-d) correspond to our structure and fabrication-limited discretization, limited on a technology basis to be step-wise. However, let us remind here that our theory is general and that this present choice is only for presentation purpose. The continuous and discrete intensities correspond to profiles given in Fig. 1(a) but the gray scale image as in Fig. 1(b) is preferred throughout our work to represent the spatial dimension of our chip imaging technique. More details on our structure will be given later. We shall adopt in this paper the choice of a duty-cycle variation along the tracks using a row of M homogeneous micropads to obtain discrete profiles around the resonance, but it is not needed before Section 2. We will simply assume here that the intensity reflected in a relevant order (say, 0 or ±1) is a Fano-shaped resonance parameterized by a full width

*q*as given in Eq. (2).

*u*, the sign of

*q*might be positive or negative. Typical Fano curves are given in Fig. 1(e) for

*q*= 1,

*q*= 1.5,

*q*= 2.5,

*q*= 3.5 and

*q*= 6,

*q*~3.5 profile resembling the one of our fabricated structure. As

*q*increases, the curve symmetry increases.

*S(m) = I*

_{refl}

*(m)/I*

_{inc}.

*S(m)*is a series of M normalized intensities associated to a series of M varying resonance conditions

*u*(

_{res}*m*) obtained for a given analyte and for a fixed (λ

_{0},θ

_{0}) illumination condition, practically a constant incidence collimated beam (nearly normal) and a nearly monochromatic incoherent source.

*u*

_{res}

*(m)*becomes a shifted set

*u’*

_{res}=

*u*

_{res}

*(m-*Δ

*m)*and

*I*(

*u*−

*u*

_{res}) becomes

*I*(

*u*−

*u’*

_{res}) with a linear relation Δ

*m*= Δ

*m*

_{res}=

*A*S

_{RIU}Δn, where

*A*is a constant, S

_{RIU}a sensitivity to a given (sensed) index and Δn is the fluid index variation, or its equivalent for surface binding of monolayers of biomolecules. If the Δ

*m*versus Δn relation is not linear, a simple calibration shall work.

*m*as accurately as possible, by comparing the signal from the same track without [

*u*

_{res}

*(m)*] and with [

*u*

_{res}

*(m-*Δ

*m)*] the fluid index. Alternatively, adjacent tracks with reference and sensed fluids can be used so that pictures are taken simultaneously, cancelling thermal or mechanical drifts such as pressure stress in biochips. This parallel rather than sequential measurement will be our choice in the following. Typical numbers as in Fig. 1(a-d) are a shift by Δ

*m*~30 to 40 micropads of our track profile from the lower fluid index (generally water n

_{min}= 1.333) to the highest index fluids, say glycerol solutions with n

_{max}= 1.474. In this way, as argued from Fig. 1(b) above, a coarse estimate is given by the discretized shift of the locus of maximum signal, amounting to bracket a fractional shift between two consecutive integers [Δ

*m*] <

*A*S

_{RIU}Δ

*n*

_{fluid }< [Δ

*m*] + 1. Clearly, that would limit the accuracy to about (n

_{max}- n

_{min})/Δ

*m*, hence Δn ≈0.004, in our case with Δ

*m*~37, an insufficient sensitivity.

### 2.2. Duty-cycle variation for linear shift in track

13. N. Destouches, B. Sider, A. V. Tishchenko, and O. Parriaux, “Optimization of a waveguide grating for normal TM mode coupling,” Opt. Quantum Electron. **38**(1-3), 123–131 (2006). [CrossRef]

_{m}= d

_{m}/Λ, with d

_{m}the groove width (1 ≤ m ≤ M) while other parameters (period Λ, waveguide layer thickness t, etching depth h) are kept constant. The groove width is varied between 140 nm to 308 nm by step Δd

_{m}= 4 nm, corresponding to filling factor varying from 0.3 to 0.7 by step Δf

_{m}= 0.0089. Such a variation is at technological limits of our e-beam lithography system. Grooves are along the track direction so that the guided mode of one micropad does not travel to its neighbor.

14. L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A **13**(5), 1024–1035 (1996). [CrossRef]

15. A. David, H. Benisty, and C. Weisbuch, “Fast factorization rule and plane-wave expansion method for two-dimensional photonic crystals with arbitrary hole-shape,” Phys. Rev. B **73**(7), 075107 (2006). [CrossRef]

^{−2}–10

^{−3}equivalent RIU change, so on the order of Δ

*m*~ 1 micropad shift. The row alignment of micropads may also be replaced by different spatial arrangement.

### 2.3. Fitting issues with Fano line shapes

*m*~ 0.005, which shall allow our chip-oriented method to serve at Δn ≈ 2 × 10

^{−5}, nearly the same degree of accuracy as bulky Abbe’s refractometers, but with a lot of versatility, and without any of the ambiguities of the Mach-Zehnder methods [16

16. M. C. Estevez, M. Alvarez, and L. M. Lechuga, “Integrated optical devices for lab-on-a-chip biosensing applications,” Laser Photonics Rev. **6**(4), 463–487 (2012). [CrossRef]

11. B. Gallinet and O. J. F. Martin, “Influence of electromagnetic interactions on the line shape of plasmonic Fano resonances,” ACS Nano **5**(11), 8999–9008 (2011). [CrossRef] [PubMed]

12. B. Gallinet and O. J. F. Martin, “Ab initio theory of Fano resonances in plasmonic nanostructures and metamaterials,” Phys. Rev. B **83**(23), 235427 (2011). [CrossRef]

17. T. K. Fang and T. N. Chang, “Determination of profile parameters of a Fano resonance without an ultrahigh-energy resolution,” Phys. Rev. A **57**(6), 4407–4412 (1998). [CrossRef]

19. K. A. Tetz, L. Pang, and Y. Fainman, “High-resolution surface plasmon resonance sensor based on linewidth-optimized nanohole array transmittance,” Opt. Lett. **31**(10), 1528–1530 (2006). [CrossRef] [PubMed]

^{−3}index step. The corresponding data are the gray dots in Fig. 3(b,c). On these data, a naïve Gaussian fit gives very poor results: the fits themselves on Fig. 3(b) make it clear that a Gaussian fit is fooled by the different behavior of the peak and of the tails. Consequently, as seen by the wavy line in Fig. 3(a), such a fit is heavily affected by the discretization. A home-made Lorentzian fit based on fitting the inverse of the signal as a parabola, and restricting the fit to the set of points underlined by the thick dashed line in Fig. 3(c), has a less wavy overall behavior, as is seen on Fig. 3(a), although shifted systematically to lower index as a consequence of the asymmetry of Fano profile being improperly dealt with and with inconstant step between successive points.

*q*) of Fano shape in play, which may vary on a chip between, for instance, extreme refractive indices. Therefore, a more suited approach is welcome. The red line, on Fig. 3(a), is the resonant peak position retrieved by correlation approach that we have devised, and that we believe to overcome most of the cited limitations of fitting. Peak position is also reported with bars in Fig. 3(c) for the selected profiles.

## 3. The correlation approach and its performance estimation

### 3.1. Resonance shift analysis with correlation approach

17. T. K. Fang and T. N. Chang, “Determination of profile parameters of a Fano resonance without an ultrahigh-energy resolution,” Phys. Rev. A **57**(6), 4407–4412 (1998). [CrossRef]

19. K. A. Tetz, L. Pang, and Y. Fainman, “High-resolution surface plasmon resonance sensor based on linewidth-optimized nanohole array transmittance,” Opt. Lett. **31**(10), 1528–1530 (2006). [CrossRef] [PubMed]

11. B. Gallinet and O. J. F. Martin, “Influence of electromagnetic interactions on the line shape of plasmonic Fano resonances,” ACS Nano **5**(11), 8999–9008 (2011). [CrossRef] [PubMed]

12. B. Gallinet and O. J. F. Martin, “Ab initio theory of Fano resonances in plasmonic nanostructures and metamaterials,” Phys. Rev. B **83**(23), 235427 (2011). [CrossRef]

*q*from 1 to 6 and confirmed the wide validity of correlation analysis, we only present Fano parameter

*q*= 2.5 results to illustrate a signal with no particular odd or even symmetry.

_{x}× D

_{y}= 35 × 20 pixels for each micropad. If the track is assembled along

*y*, we get a 35 × 860 pixels array that forms our practical signal

*C*and looking at the centroid of these higher powers. In our case, a function such as

*C*with exponent

^{k}*k*= 10 typically has a width comparable to the model’s resonance width (2 to 4 micropads). We do not further justify the noncritical exponent value

*k*= 10, a general theory of an optimal

*k*amounts in some respect to the logic of matched filtering hinted above, too long to formalize here. Furthermore, if

*q*is low and the shape asymmetrical,

*C*features large flat “noninformative” regions of high signal whose noise blurs the centroid determination.

*q*= 2.5 is shown in the Figs. 4(a) and 4(b) with a shift value of ~60 pixels = 3 micropads, with a plot of their profile in Fig. 4(c). The correlation

_{x}lines is useless here. We see that the correlation peak is bounded by a high and flat plateau. Here no zero-padding was applied (we used fast Fourier-Transform), but even with zero-padding in a correlation there is a similar issue. This plateau does not help determining the shift through the search of the correlation centroid according to

*C*with a power adapted to the width of the signal, here

^{k}*k*= 10, we adequately isolate the correlation peak. And thus the resulting curve lends itself well to a meaningful centroid calculation. The set of possible

*k*values for such better behavior is reasonably large, starting at about

*k*= 4, hence there is no practical constraint in this “adaptation” of k isolating the peak with usual RWG Fano shapes. We checked more precisely conditions for such a good match of centroid and maxima, and we found that for that purpose, removing the average of

*C*helps for a systematic treatment, by minimizing better the tails values and their influence compared to peak values: thus, we eventually deal with

^{2}*C*,

^{k}*C*being normalized to a maximum at unity. Thus, we have our shift counted in pixels determined by Eq. (3):

*C′*in Fig. 4(d) with clear slope changes reveals the segmented nature of

^{10}*C*that was not so apparent in

*C*itself given the involved width of several micropads. Figure 4(e) gives the centroid position depending on resonance position, and eventually shows that the use of

*C*′

*does retrieve a correct value with the adequate slope (Γ*

^{10}_{res}= 3.05 micropads = 61.0 pixels), whereas the naive use of

*C*gives a much lower slope, due to the fact that

*C*does not vanish at the edges of the segment (since the Fano line shape does not vanish), adding “unpredictable” weights in the centroid: such weights have for instance a heavy dependence on

*q*.

### 3.2. Robustness to Gaussian noise

*q*= 2.5, but adding a large contribution of Gaussian noise. Resulting images and profiles are given in Figs. 5(a) –5(c). Noise was added on pixels

_{S}= 0.3 (e.g. readout noise, the model pixel values are here assimilated to reflectivities 0 <

_{N}= 0.3 for

*m*and get the data of Fig. 5(e): a linear determination with a narrow rms deviation of σ = 0.44 pixel = 0.02 micropad is obtained using

*C*′

*with*

^{k}*k*= 10, whereas a larger rms noise of σ = 0.79 pixel = 0.039 micropad is obtained for the direct use of

*C*, in addition to the skewed slope already commented (again Γ

_{res}= 3.05 micropads = 61.0 pixels). Considering the low initial SNRs, this result demonstrates high robustness to noise and thus potential real-time capability.

### 3.3. Robustness to in-homogeneities resulting from imaging

5. E. M. Yeatman, “Resolution and sensitivity in surface plasmon microscopy and sensing,” Biosens. Bioelectron. **11**(6-7), 635–649 (1996). [CrossRef]

*m*= 3.5, as though the duty-cycle had a local value inside a given micropad reaching the designed one for 3.5 micropads away. We made the shape of the distortions qualitatively resembling some of the imperfect images that we obtained experimentally (Section 4). Figures 6(a) –6(d) present the results with essentially the same reference Fano shape as Figs. 4–5, the value

*q*= 2.5 being kept again.

_{s}= 0.06 (still with Gaussian and photon noise contributions) compared to the previous case σ

_{s}= 0.3. Figure 6(c) gives the plot along the y axis of the

*x*-projected signal

_{i}

*C*and

*C*′

*as in Figs. 4-5. Figure 6(d) shows that the correlation still works well, hence we have identified another robust aspect of our method. To check this at a larger level, Fig. 6(f) eventually gives the retrieval of the shift Δ*

^{k}*j*with the same conventions as in Fig. 5. The bias (less than 1 pixel) is only a systematic one following the contribution of the perturbation, but the linearity with a correct slope is fully preserved. The bias is indeed on the order of a couple of standard deviations associated to this noise level, σ = 0.087 pixels = 0.0043 micropad unit.

## 4. Experimental section

### 4.1. Experimental setup and process

20. I. Abdulhalim, M. Auslender, and S. Hava, “Resonant and scatterometric gratings based nano-photonic structures for biosensing,” J. Nanophotonics **1**(1), 011680 (2007). [CrossRef]

*m*~29 to

*m*~10 and be able to cover the whole range of optical index [1.333-1.474] in the same optical configuration (same incidence angle). Adjusting wavelength instead of angle is more reliable considering the influence of mechanical motion in resonant optics experiments. Considering a quasi linear behavior of the resonant structure when varying a parameter on a small interval range, this wavelength adjustment has nearly no influence on the shift values measured in experiments.

^{−5}. To limit data storage and avoid noise from the red and blue channels, we select only the green one. Each grating micropad is imaged on an area of 1000 to 2000 pixels; we average over 10 successive pictures, thus increasing the SNR by a factor of 100 ~ (10 × 1000)

^{1/2}. Considering a typical relative noise of 4 × 10

^{−3}/image on our camera pixels, the noise contribution is decreased to 4 × 10

^{−5}in relative terms, around the digital accuracy for a typical signal with 2.5 × 10

^{4}counts.

### 4.2. Large span Δn sensing

*m*~ 0.015) but the last one is shifted towards the left by Δ

*m*= 0.6. Indeed, higher pressure, needed when injecting the viscous glycerol solution may have resulted in mechanical instability and chip motion, which confirms the advantage of using a reference.

*m*~ 29 micropads being therefore lower than the expectation Δ

*m*~ 37. This might be partly explained by lower dispersion, for instance associated to deeper etching than the 0.15Λ targeted value or scattering loss through porosity in the silicon nitride. Another aspect is the slightly higher Δf step vs. the designed filling factor variation, as seen from our SEM measurements, reducing the discretization by ~3 micropads on the considered interval, leaving thus a reasonable agreement between theory and experiments.

### 4.3. Highly sensitive sensing on reduced Δn span

^{−3}between 1.333 and 1.337 by using water/glycerol solutions in ratio 1:0, 0.993:0.007, 0.986:0.014, 0.979:0.021, 0.972:0.028. The latter solutions are prepared with double dilution to get accurate concentration steps. In Fig. 8 we give (a) the measured images and (b) there profiles. Looking carefully at the pictures, we see that when the refractive index increases, the maximum is shifted towards micropads of higher number. This is clearly confirmed when looking at the reflectivity profiles. In Fig. 8(c) we give the correlation result of the first image for n = 1.333 (reference of sensing track) with images of index between 1.333 and 1.337, the first curve corresponding to reference.

^{−5}RIU can be achieved. The same error analysis conducted with Gaussian fit or Lorentzian fit give much more spread errors. The amplitude of the variations (inaccuracy) in the fit are not on the order seen in Fig. 3(a), but we look at only a small span of less than 1 micropad. Our data also have a ~twice larger full width at half maximum (~6.5 micropads) and are less asymmetric than expected from our simulated reflectivity profiles.

## 5. Conclusion

22. X. Gan, N. Pervez, I. Kymissis, F. Hatami, and D. Englund, “A high-resolution spectrometer based on a compact planar two dimensional photonic crystal cavity array,” Appl. Phys. Lett. **100**(23), 231104 (2012). [CrossRef]

^{−3}RIU/micropad. Therefore, fine data analysis is necessary to attain sensitivity down to ~10

^{−5}RIU range.

*k*≥ 4) of the correlation and extracting the centroid of the result. This correlation approach was compared to usual fitting techniques (Lorentz, Gauss) and demonstrated superior robustness to asymmetry of the profiles, as well as to diverse parasitic contributions influencing measured signals. Such parasitic contributions may have different origins, such as fabrication (electron beam lithography exposure varies at the edge of the pattern), optical aberrations. For instance, to improve the initially poor success of Gaussian and Lorentzian fitting, we had to clip only pixels in the middle of the micropads, while for correlation analysis the whole track could be considered without harm. This is a significant advantage for the analysis as micropad pixel coordinates do not have to be determined.

^{−3}, giving an accuracy of Δn~2 × 10

^{−5}. This sensitivity is typically equivalent to that of a ~20 pg/cm

^{2}density biological layer. This makes our technique a promising candidate for robust and accurate multiplex label-free bio sensing.

2. A. M. Ferrie, Q. Wu, and Y. Fang, “Resonant waveguide grating imager for live cell sensing,” Appl. Phys. Lett. **97**(22), 223704 (2010). [CrossRef] [PubMed]

4. R. Magnusson, D. Wawro, S. Zimmerman, Y. Ding, S. Zimmerman, and Y. Ding “Resonant photonic biosensors with polarization-based multiparametric discrimination in each channel,”,” Sensors (Basel Switzerland) **11**(2), 1476–1488 (2011). [CrossRef]

7. S. George, I. D. Block, S. I. Jones, P. C. Mathias, V. Chaudhery, P. Vuttipittayamongkol, H. Y. Wu, L. O. Vodkin, and B. T. Cunningham, “Label-free prehybridization DNA microarray imaging using photonic crystals for quantitative spot quality analysis,” Anal. Chem. **82**(20), 8551–8557 (2010). [CrossRef] [PubMed]

^{−5}. A correlation analysis was found to be crucial for the obtainment of such accuracy from the discretized micropad data. This ensemble suggests that the peak-tracking chip scheme has a great potential in the field of biodetection.

## Acknowledgments

## References

1. | K. Bougot-Robin, J.-L. Reverchon, M. Fromant, L. Mugherli, P. Plateau, and H. Benisty, “2D label-free imaging of resonant grating biochips in ultraviolet,” Opt. Express |

2. | A. M. Ferrie, Q. Wu, and Y. Fang, “Resonant waveguide grating imager for live cell sensing,” Appl. Phys. Lett. |

3. | P. Y. Li, B. Lin, J. Gerstenmaier, and B. T. Cunningham, “A new method for label-free imaging of biomolecular interactions,” Sens. Actuators B Chem. |

4. | R. Magnusson, D. Wawro, S. Zimmerman, Y. Ding, S. Zimmerman, and Y. Ding “Resonant photonic biosensors with polarization-based multiparametric discrimination in each channel,”,” Sensors (Basel Switzerland) |

5. | E. M. Yeatman, “Resolution and sensitivity in surface plasmon microscopy and sensing,” Biosens. Bioelectron. |

6. | A. Shalabney and I. Abdulhalim, “Sensitivity enhancement methods for surface plasmon sensors,” Laser Photonics Rev. |

7. | S. George, I. D. Block, S. I. Jones, P. C. Mathias, V. Chaudhery, P. Vuttipittayamongkol, H. Y. Wu, L. O. Vodkin, and B. T. Cunningham, “Label-free prehybridization DNA microarray imaging using photonic crystals for quantitative spot quality analysis,” Anal. Chem. |

8. | S. S. Wang, R. Magnusson, J. S. Bagby, and M. G. Moharam, “Guided-mode resonances in planar dielectric-layer diffraction gratings,” J. Opt. Soc. Am. A |

9. | U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Phys. Rev. |

10. | D. Pietroy, A. V. Tishchenko, M. Flury, and O. Parriaux, “Bridging pole and coupled wave formalisms for grating waveguide resonance analysis and design synthesis,” Opt. Express |

11. | B. Gallinet and O. J. F. Martin, “Influence of electromagnetic interactions on the line shape of plasmonic Fano resonances,” ACS Nano |

12. | B. Gallinet and O. J. F. Martin, “Ab initio theory of Fano resonances in plasmonic nanostructures and metamaterials,” Phys. Rev. B |

13. | N. Destouches, B. Sider, A. V. Tishchenko, and O. Parriaux, “Optimization of a waveguide grating for normal TM mode coupling,” Opt. Quantum Electron. |

14. | L. Li, “Formulation and comparison of two recursive matrix algorithms for modeling layered diffraction gratings,” J. Opt. Soc. Am. A |

15. | A. David, H. Benisty, and C. Weisbuch, “Fast factorization rule and plane-wave expansion method for two-dimensional photonic crystals with arbitrary hole-shape,” Phys. Rev. B |

16. | M. C. Estevez, M. Alvarez, and L. M. Lechuga, “Integrated optical devices for lab-on-a-chip biosensing applications,” Laser Photonics Rev. |

17. | T. K. Fang and T. N. Chang, “Determination of profile parameters of a Fano resonance without an ultrahigh-energy resolution,” Phys. Rev. A |

18. | X. Liu, Y. Huang, L. Zhu, Z. Yuan, W. Li, and K.-Z. Xu, “Numerical determination of profile parameters for Fano resonance with definite energy resolution,” Nucl. Instrum. Methods Phys. Res. |

19. | K. A. Tetz, L. Pang, and Y. Fainman, “High-resolution surface plasmon resonance sensor based on linewidth-optimized nanohole array transmittance,” Opt. Lett. |

20. | I. Abdulhalim, M. Auslender, and S. Hava, “Resonant and scatterometric gratings based nano-photonic structures for biosensing,” J. Nanophotonics |

21. | O. Krasnykov, M. Auslander, and I. Abdulhalim, “Optimizing the guided mode resonance structure for optical sensing in water,” Phys. Express |

22. | X. Gan, N. Pervez, I. Kymissis, F. Hatami, and D. Englund, “A high-resolution spectrometer based on a compact planar two dimensional photonic crystal cavity array,” Appl. Phys. Lett. |

**OCIS Codes**

(070.6110) Fourier optics and signal processing : Spatial filtering

(110.2960) Imaging systems : Image analysis

(280.1415) Remote sensing and sensors : Biological sensing and sensors

(310.2785) Thin films : Guided wave applications

(050.5745) Diffraction and gratings : Resonance domain

**ToC Category:**

Biosensors and Molecular Diagnostics

**History**

Original Manuscript: July 13, 2012

Revised Manuscript: August 23, 2012

Manuscript Accepted: September 2, 2012

Published: September 11, 2012

**Citation**

K. Bougot-Robin, W. Wen, and H. Benisty, "Resonant waveguide sensing made robust by on-chip peak tracking through image correlation," Biomed. Opt. Express **3**, 2436-2451 (2012)

http://www.opticsinfobase.org/boe/abstract.cfm?URI=boe-3-10-2436

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