Fano Resonances and Leakage Radiation for High-Resolution

Article pubs.acs.org/JPCC

Fano Resonances and Leakage Radiation for High-Resolution Plasmonic Sensing Benedikt Stein, Jean-Yves Laluet, Eloïse Devaux, Cyriaque Genet,* and Thomas W. Ebbesen ISIS, University of Strasbourg and CNRS, 8 allée Gaspard Monge, 67000 Strasbourg, France

ABSTRACT: We demonstrate that the asymmetric profiles of Fano resonances lead to important figure of merit (FOM) improvements of surface plasmon (SP)-based refractive index sensors. Exploiting the high angular resolution of a leakage radiation microscope, our sensor shows a 75% improvement over the optimal FOM of classic SP-based sensors, reaching a FOM as high as 234 ± 1 RIU−1. We also perform a full noise assessment of the system and achieve a final resolution of O(10−7) RIU.

T

Note that from this description, the sensitivity S is to be identified with the actual figure of merit (FOM) of the sensor.9 As clear from eq 1, a steep intensity profile i(k) will have the potential to improve the global FOM if the detection setup is able to monitor local intensity variations where the profile is the steepest. We have combined in a single detection scheme two key ingredients: exciting a Fano resonant system and introducing, for the first time in a sensing context, an advanced leakage radiation (LR) microscope.10,11 First, as we show below, the asymmetry of the Fano profile iF(k) is associated with higher steepness compared with conventional SP-based sensor profiles.9 Then, the LR microscope allows us to image iF(k) in k-space and to monitor intensity changes on the steepest point of the profile. There, the ultrahigh angular resolution offered by an LR microscope as a detection setup turns out to be crucial. Finally, the full control available over the setup allows for noise managements and controls that are essential in assessing the actual resolution of our sensor and foreseeing its potential. We chose as a Fano resonant system a single nanoslit at the level of which propagating SPs are launched. Such slits display strong Fano resonances in the k-space due to the interference between the illumination light directly transmitted through the slit (the continuum of states) and the launched SP mode (the resonant state).12 Our samples were fabricated by electron-

he concept of Fano resonance is central to many research areas, ranging from atomic and molecular physics1 to quantum electronics.2 It has been recently recognized to play an important role in surface plasmon (SP) optics.3−6 A Fano resonance arises when a scattering process takes place either directly toward a continuum of states or via a resonant state, which is then coupled to this continuum. Two different channels are thus interfering, and this interference phenomenon is associated with typical asymmetric spectral line shapes. As an interference process, a Fano resonance is particularly sensitive to small changes of the local environment. This property has led to the development of chemical and biological sensors built on carefully engineered localized SP resonators (LSPR) able to display spectrally sharp Fano profiles. As shown, in particular, for bulk refractive index changes, small environmental perturbations can induce sensible shifts of the LSPR resonance that could lead to the design of efficient labelfree chemical probes. (For a detailed review, see ref 7.) In this context, however, a fundamental aspect has not yet been fully exploited: the asymmetry of the Fano profile. We demonstrate in this Article that this asymmetry can readily bring an SP-based sensor close to its ultimate limit.8 This can be seen from an input−output description of the sensor where the shift of the in-plane SP wavevector kSP associated with a refractive index change δn is probed with a sensitivity S by measuring a normalized intensity variation of the resonant profile in the reciprocal (wavevector) k-space S=

δi(k) δk δi(k) · = δk δn δn

Received: December 14, 2011 Revised: February 8, 2012 Published: February 10, 2012

(1) © 2012 American Chemical Society

6092

dx.doi.org/10.1021/jp2120675 | J. Phys. Chem. C 2012, 116, 6092−6096

The Journal of Physical Chemistry C

Article

Figure 1. (a) Optical setup: Light from a λ = 782 nm pigtailed laser diode (LD) passing a polarizer (P1), half-wave plate (HW), beam expander (BE) and mirror (MI) is weakly focused by a microscope objective on a nanoslit in a PDMS microfluidic cell. SPs are decoupled by an NA = 1.49 immersion objective and imaged by two lenses (L1, L2) to intermediate direct space (dotted line) and reciprocal k-space (dashed line) planes, respectively. Spatial filtering of direct transmission is conveniently performed in the first intermediate direct space plane. The reciprocal space can be scanned with high magnification by a third objective and recorded with a charge-coupled device (CCD) after an imaging lens (L5). In parallel, a beam splitter (BS2) allows imaging both the full reciprocal and direct spaces on a CMOS camera, the latter by removing lens L4. Alternatively, by withdrawing MI and introducing a beam splitter (BS1), the illumination beam can be sent through the immersion objective, and SPs can thus be observed on the planar film just like in an ATR configuration. A rotating diffuser (RD) inserted in the illumination path reduces spatial coherence to suppress interference artifacts in the image. (b) Scanning electron micrograph of a w = 300 nm slit in an h = 80 nm thick gold film. The scale bar corresponds to 5 μm. (c) Leakage radiation image in the reciprocal space of SPs launched by this nanoslit. The scale bar corresponds to 5 μm−1, as determined by referencing experimental to theoretical SP peak positions in ethanol and water environments. Linearity over the whole k-space is ensured by using a flat-field microscope objective corrected to fulfill Abbe’s sine condition. (d−f) Zooms around the SP resonance as marked in panel c -white arrow- for Fano (d) and Lorentz (e) profiles compared with an ATR configuration (f). Scale bars correspond to 0.1 μm−1. (g) Theoretical ATR (black), Lorentz (red), and Fano (blue) profiles for an h = 80 nm thick gold film.

classic attenuated total reflection (ATR) profile iATR characteristic of the most commonly used SP-based sensing method,9 we integrate an additional ATR path in the optical setup. (See Figure 1a). As a control experiment, we also consider a symmetric (Lorentzian) SP profile iL generated by spatially filtering in an intermediate image plane the light directly transmitted through the slit. This cancels the Fano interference effect, and we therefore image in k-space the Lorentzian profile of the sole SP resonance. All three experimental profiles are gathered and displayed in Figure 1c−g. Maximal slopes Max(|∂i(k)/∂k|) have been extracted from crosscuts on the experimental k-space images for all three profiles and for all metal film thicknesses. In parallel, maximal slopes have also been evaluated numerically for all profiles and thicknesses. For the ATR profiles, the evaluations of the maximal theoretical slopes are done from the well-known ATR reflectivities Max(|∂R(k)/∂k|), assuming uniform illumination and using standard tabulated data for gold permittivity. For the Lorentzian profiles, slopes were determined from the poles of

beam evaporation of thin layers of gold on glass coverslips. Slits of w = 300 nm width have been milled through the films by focused ion beam lithography. The simplicity of the system has the great advantage to make it truly integrable in a microfluidic context with repeatable access to controlled index variations. To this aim, each nanoslit is enclosed in a microfluidic polydimethylsiloxane (PDMS) cell. SPs are excited by focusing weakly a laser beam at λ = 782 nm on the nanoslit through the cell. SPs are then decoupled on the sample backside by LR using a high numerical aperture immersion objective. Subsequent optical Fourier transform gives access to the reciprocal k-space, which we magnify again to reach higher angular resolution. (See Figure 1a for details.) The effect of refractive index changes is detected on an LR microscope k-space image from local variations of the normalized intensity i(k0) = I/Max(I) at a specified k0 point of the image, as schematized in Figure 2a. As delocalized SP modes propagating on a smooth metal film are involved, in contrast with LSPR devices, the second factor on the right-hand of eq 1 is fixed by the dispersion relation of an SP at a planar interface and is a constant at the chosen k0. As discussed above, the first factor is related to the actual profile of the SP resonance. To compare the asymmetric Fano profile iF to the 6093

dx.doi.org/10.1021/jp2120675 | J. Phys. Chem. C 2012, 116, 6092−6096

The Journal of Physical Chemistry C

Article

index changes δn = nsol − nH2O from δnmin = 3.4 × 10−6 RIU (corresponding to 5.21 × 10−5 w/w of dissolved ethanol) up to δnmax = 5.4 × 10−3 RIU (corresponding to 8.3 × 10−2 w/w of dissolved ethanol). Reciprocal space images were acquired for ATR (h = 60 nm) and Fano configurations (h = 80 nm) with the LR microscope. The images were then spatially averaged over 960 rows of the CCD chip to extract the resonant profiles. Variations in normalized intensities δi were observed at the steepest point of the profile, that is, the point of largest FOM. Typical sample profiles and measurement curves are shown in Figure 2a. Each ethanol solution was referenced against pure water, defining cycles of solution-water exchange in the cell. For each step of the cycle, the intensity was temporally averaged over N = 100 frames (single frame exposure time ts = 80 ms) for Lorentzian and Fano profiles, and over N = 10 frames for the ATR configuration. We then measured such N-averaged intensity values ij̅ over 11 exchanges, j ranging therefore from 1 to 12. From these values, we evaluated over one exchange cycle (two consecutive steps) the variations in normalized intensity associated with the change in refractive index as δij = (−1)j(ij̅ − 2ij+1 ̅ + ij+2 ̅ )/2. This process compensated both for possible thermal effects, assuming similar temperature rise for both liquids, and for the low-frequency drift of the intensity signal. At the end, it generated an M = 10 data set from which we calculated averaged ⟨δi⟩ values. These are plotted as a function of the change in refractive index δn in Figure 3. In the Figure 2. (a) Detection scheme: the shift of the Fano resonance, imaged in the LR microscope k-space on an h = 80 nm gold film induced by a δn = 4.3 × 10−3 RIU refractive index change, leads to a local variation δi of the normalized intensity i. A sample sensing curve over several liquid exchanges is shown in the inset. (b) Theoretical (solid lines) and experimental (open markers) maximum slopes Max(|∂i(k)/∂k|) of ATR (black), Lorentz (red), and Fano (blue) resonance profiles of SP on gold films of different thicknesses h.

the Fresnel reflection amplitude associated with our immersion microscopy configuration. Fano profiles I(k) = tslit + αei ϕ ·

ik″SP (k − k′SP ) + ik″SP

2 (2)

were calculated using the same kSP = kSP ′ + ikSP ″ values as for the Lorentzian profiles. The amplitudes of the direct transmission tslit of the nanoslit and of the interference coupling term α as well as the relative phase ϕ were determined from fits to experimental data. Theoretical curves are close to the experimental data plotted in Figure 2b for all iATR, iL, and iF profiles. These results clearly show that an ATR configuration setup reaches its best FOM at h ∼ 60 nm. This limiting value is fixed from the competition between SP coupling and decoupling loss processes. The Lorentzian slope saturates at a slightly higher thickness just as the losses reach the metal loss limit above h = 80 nm. The same is true for a Fano profile, but the effect of the asymmetry of iF is clearly seen as an improvement on the maximal slope. Our data show an increase of ca. 70% over the highest achievable ATR slopes, and following eq 1, similarly strong improvements are expected in terms of FOM. To confirm this, we implemented a genuine high-resolution sensing experiment, aiming at probing refractive index changes smaller than 10−5 RIU. Deionized water solutions with varying concentrations of ethanol were prepared, scanning refractive

Figure 3. Double logarithmic plot of the normalized intensity variation ⟨δi⟩ (averaged over 10 measurements) as a function of the refractive index change δn in the fluidic cell. Results for δn ≤ 10−3 RIU are fitted by linear regression, yielding FOM of SF = (∂iF/∂n) = 234 ± 1 RIU−1 and SATR = (∂iATR/∂n) = 134 ± 1 RIU−1, respectively.

linear response regime, at small δn of the experiments, we were able to extract and compare the FOM for Fano and ATR profiles, obtaining SF = (∂iF/∂n) = 234 ± 1 RIU−1 and SATR = (∂iATR/∂n) = 134 ± 1 RIU−1, respectively. This is the central result of the Article, showing that resorting to a Fano profile leads effectively to a FOM improvement of 75% compared with optimal classic ATR-type FOM. This result is in close agreement with the estimates based on the maximal slope analysis presented above. Whereas this FOM improvement is due to the fundamental nature of the Fano process rooted in an interference effect, the actual performance of the sensor is also directly related to the 6094

dx.doi.org/10.1021/jp2120675 | J. Phys. Chem. C 2012, 116, 6092−6096

The Journal of Physical Chemistry C

Article

noise figures of the sensing device and its components.8 A clear estimate for the resolution of our Fano sensor can be reached by performing a baseline noise analysis of our setup.13 To this aim, we evaluated over 5 × 104 frames the standard deviation σδi associated with one normalized intensity variation δij increasing the number N of frames over which the average ij̅ is performed. This evaluation is plotted in Figure 4a. As it

optimization of the noise figure of the whole system. We finally emphasize that the strategy presented in this Article allows for resolutions O(10−7) RIU typically one-order of magnitude better than those recently documented on far-field transmission experiments through nanohole arrays where the SP Fano resonance was filtered out.14,15 To summarize, we have demonstrated that the asymmetry of a Fano resonance can lead to a real improvement of the physical FOM of sensors based on planar interface SP modes. We believe that this result will contribute to the extended efforts aiming at improving SP-based sensors up to their ultimate limits. Straightforward, our demonstration was based on implementing a Fano resonant system on a standard LR microscope setup. Our work clearly shows that this type of simple and compact microscopy represents a highly competitive and promising technique for SP-based refractive index sensing. Contrasting with conventional ATR systems, our setup offers simultaneous high-resolution imaging in both real and reciprocal spaces. This could potentially lead to real-time imaging of biological binding events, for example, while monitoring index evolutions, in particular, when working at a wavelength λ = 782 nm in the near-infrared, which provides, as we demonstrated above, high SP-based sensitivity together with a good SP confinement to the metal surface. Sensing could also be easily parallelized by mechanical scanning of the surface. Offering full access to the reciprocal space, LR microscopy could be applied in multidirectional approaches in a sensing context. Moreover, polarization-sensitive measurement schemes can be easily integrated on an LR microscope. We thus expect the method to have a strong impact on future advances in the field of SP-based sensing technology.

Figure 4. (a) Measured standard deviation σδi as a function of the number N of averaged frames. The standard deviation σδi is calculated for a negligible time-delay between liquid exchanges (i.e., τ = 0, black curve) and for a finite time-delay of τ = 22 s (red). (b) Improvement of the standard deviation ratio σ⟨δi⟩/σδi as a function of the number of averaged measurements M. Calculating the propagation of uncertainty induced by our δij measurement protocol, the ratio is expected to scale as (8/3M − 2/M2)1/2 (black curve). This behavior is indeed observed for either very short-time measurements (N = 1, τ = 0 s) or longer ones (N = 100, τ = 22 s). The intermediate case (N = 22, τ = 0 s) displays systematic noise effects that cause a slightly different scaling.

appears, the standard deviation follows a typical shot noise evolution scaling as 1/√N. This means that averaging over many N frames can help indeed in increasing the signal-to-noise ratio (SNR) of the sensor. For too large N values, however, low-frequency noises start dominating over shot noise, as seen clearly in Figure 4a. This puts a limit at N = 22 on the best SNR attainable. Performing this evaluation, we have not accounted for the actual τ = 22 s necessary to perform manually the liquid exchange through the microfluidic cell. Obviously, such an additional time delay will lead to significantly higher noise levels at small N values, as seen in Figure 4a. Nonetheless, we analyzed in this situation the final improvement of the SNR that can be achieved by an additional averaging over M liquid exchanges. Shot noise limitations are clearly seen in Figure 4b with σ⟨δi⟩ scaling as (8/3M − 2/M2)1/2, in agreement with the propagation of uncertainty induced by the way we measure each variation in normalized intensity δij. For the chosen conditions of the data presented in Figure 3 (τ = 22 s, N = 100 frames, and M = 10 measurements), we determined a standard deviation of σ⟨δi⟩ = 1.7 × 10−4. This leads us to estimate a practical resolution of our sensor as implemented in the laboratory of σ⟨δi⟩/S = 7.4 × 10−7 RIU. Future implementation of standard electronic microfluidic controls would allow negligible liquid exchange times. For this τ = 0 case, assuming optimized N = 22 and reasonable M = 50 values, we could expect σ⟨δi⟩ = 3.28 × 10−5, promising a resolution of σ⟨δi⟩/S = 1.4 × 10−7 RIU. Whereas our LR setup leaves room for optical, electronic, and mechanical improvements, we, however, stress that the resolution reached here is already comparable to the best reported systems up to date.8 Higher resolutions can be expected upon further technical

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; Phone: +33 (0)368 855 196. Fax: +33 (0)368 855 121. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We thank the ERC for support (grant no. 227557). B.S. thanks the Studienstiftung des deutschen Volkes and the Stiftung der deutschen Wirtschaft for support.

■

REFERENCES

(1) Fano, U. Phys. Rev. 1961, 124, 1866. (2) Rau, A. R. P. Phys. Scr. 2004, 69, C10. (3) Sarrazin, M.; Vigneron, J.-P.; Vigoureux, J.-M. Phys. Rev. B 2003, 67, 085415. (4) Genet, C.; van Exter, M. P.; Woerdman, J. P. Opt. Commun. 2003, 225, 331. (5) Hao, F.; Sonnefraud, Y.; Van Dorpe, P.; Maier, S. A.; Halas, N. J.; Nordlander, P. Nano Lett. 2008, 8, 3983. (6) Zhang, S.; Genov, D. A.; Wang, Y.; Liu, M.; Zhang, X. Phys. Rev. Lett. 2008, 101, 047401. (7) Luk’yanchuk, B.; Zheludev, N. I.; Maier, S. A.; Halas, N. J.; Nordlander, P.; Giessen, H.; Chong, C. T. Nat. Mater. 2010, 9, 707 and references therein. (8) Piliarik, M.; Homola, J. Opt. Express 2009, 17, 16505. (9) Homola, J. Surface Plasmon Resonance Based Sensors; SpringerVerlag: Heidelberg, 2006. (10) Kano, H.; Knoll, W. Opt. Commun. 1998, 153, 235. 6095

dx.doi.org/10.1021/jp2120675 | J. Phys. Chem. C 2012, 116, 6092−6096

The Journal of Physical Chemistry C

Article

(11) Drezet, A.; Hohenau, A.; Koller, D.; Stepanov, A.; Ditlbacher, H.; Steinberger, B.; Aussenegg, F. R.; Leitner, A.; Krenn, J. R. Mater. Sci. Eng., B 2008, 149, 220. (12) Laluet, J.-Y.; Drezet, A.; Genet, C.; Ebbesen, T. W. New J. Phys. 2008, 10, 105014. (13) Chinowsky, T. M.; Grow, M. S.; Johnston, K. S.; Nelson, K.; Edwards, T.; Fu, E.; Yager, P. Biosens. Bioelectron. 2007, 22, 2208. (14) Tetz, K. A.; Pang, L.; Fainman, Y. Opt. Lett. 2006, 31, 1528. (15) Hwang, G. M.; Pang, L.; Mullen, E. H.; Fainman, Y. IEEE Sens. J. 2008, 8, 2074.

6096

dx.doi.org/10.1021/jp2120675 | J. Phys. Chem. C 2012, 116, 6092−6096