Rational design of high performance surface plasmon resonance sensors based on two-dimensional metallic hole arrays

doi:10.1364/OE.20.012610

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Rational design of high performance surface plasmon resonance sensors based on two-dimensional metallic hole arrays

Lei Zhang, Chung Y. Chan, Jia Li, and Hock C. Ong »View Author Affiliations

Optics Express, Vol. 20, Issue 11, pp. 12610-12621 (2012)
http://dx.doi.org/10.1364/OE.20.012610

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Abstract

We have rationally designed two-dimensional Au and Ag hole arrays for high performing surface plasmon resonance (SPR) sensing. The figure-of-merit (FOM), which is defined as sensitivity/linewidth, is found to be highly geometry-dependent. For sensitivity, we find it is equal to the period of array when exciting low order surface plasmon modes at low incident angle. Therefore, increasing period improves sensitivity. On the other hand, narrow linewidth can be obtained from small hole size so that the radiative decay loss is minimized. By using a pair of orthogonally oriented polarizer and analyzer, the signal-to-noise ratio (SNR) can be greatly enhanced due to the elimination of the nonresonant reflection background. As a proof of our strategy, we have obtained FOM larger than 100/RIU and SNR higher than 110 from Au arrays. Our results show the importance of understanding the basic properties of surface plasmon polaritons in order to systematically optimize the performance of the plasmonic system for a given application.

Surface plasmon polaritons (SPPs) support strong local field on metal surface and are of great importance in bio- and nano-photonics [1

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]

]. In fact, they are found to be applicable in many areas including single molecule detection [2

E. C. Le Ru and P. Etchegoin, Principles of Surface Enhanced Raman Spectroscopy: and Related Plasmonic Effects (Elsevier Science, 2008).

], light extraction from LEDs [3

K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004). [CrossRef] [PubMed]

], optical and terahertz waveguiding [4

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010). [CrossRef]

], and optical trapping [5

M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics 5(6), 349–356 (2011). [CrossRef]

]. Likewise, surface plasmon resonance (SPR) spectroscopy, which relies on detecting the local change of refractive index in the proximity to the metal surface upon binding of target analytes to receptors, has become one of the leading methods for label-free bio and chemical detection [6

J. Homola, Surface Plasmon Resonance Based Sensors, Springer Series on Chemical Sensors and Biosensors (Springer-Verlag, 2006).

]. By monitoring the spectral shift of SPR reflection dip/transmission peak, it is possible to detect the presence of target analytes at low concentration [6

J. Homola, Surface Plasmon Resonance Based Sensors, Springer Series on Chemical Sensors and Biosensors (Springer-Verlag, 2006).

]. Basically, the current practice of commercial SPR sensors employs attenuated total internal reflection (ATR) geometry in which light is coupled to SPPs on flat metal film by a high refractive index prism [7

J. Homola, “Surface plasmon resonance sensors for detection of chemical and biological species,” Chem. Rev. 108(2), 462–493 (2008). [CrossRef] [PubMed]

]. Although ATR geometry provides good figure-of-merit (FOM ~ 63/RIU at λ = 900 nm) [8

M. A. Otte, B. Sepúlveda, W. H. Ni, J. P. Juste, L. M. Liz-Marzán, and L. M. Lechuga, “Identification of the optimal spectral region for plasmonic and nanoplasmonic sensing,” ACS Nano 4(1), 349–357 (2010). [CrossRef] [PubMed]

], it suffers from a major drawback; the need of a bulky prism coupler makes ATR-based SPR sensors impossible for miniaturization. As the current interest is moving towards the development of chip-scale type biosensor, ATR SPR sensors thus cannot meet this demand.

To overcome this limitation, attention has recently been shifted towards the use of metallic nanoparticles that excite localized surface plasmons (LSPs) [9

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008). [CrossRef] [PubMed]

]. Miniaturization of these nanostructures to chip-scale is now possible because light can be directly coupled to LSPs without the use of prism coupler. Unfortunately, the performance reported from these nanostructures so far are still modest (FOM < 7/RIU at λ = 600 - 800 nm) since LSPs always give broad linewidth (~ 40 nm) [8

]. In addition, nanoparticles also suffer from the fact that it is difficult to control their size and shape precisely and to manipulate them at the right position so that they can produce desirable field pattern. In other words, nanoparticles do not offer good reproducibility that is crucial for device fabrication.

Other than ATR and nanoparticle geometries, a third type of SPR sensors is slowly emerging [10

M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev. 108(2), 494–521 (2008). [CrossRef] [PubMed]

,11

R. Gordon, D. Sinton, K. L. Kavanagh, and A. G. Brolo, “A new generation of sensors based on extraordinary optical transmission,” Acc. Chem. Res. 41(8), 1049–1057 (2008). [CrossRef] [PubMed]

]. Periodic metallic arrays are attractive because they possess properties that are in between to those of ATR and nanoparticle counterparts [12

J. Li, H. Iu, W. C. Luk, J. T. K. Wan, and H. C. Ong, “Studies of the plasmonic properties of two-dimensional metallic nanobottle arrays,” Appl. Phys. Lett. 92(21), 213106 (2008). [CrossRef]

]. In addition, they can be fabricated by using currently available lithographic methods so that both the lattice and basis can be designed and tailored precisely at high throughput. Therefore, array-based SPR sensors may outperform ATR and nanoparticle sensors while at the same time maintaining good miniaturizability and reproducibility.

In fact, it is possible to rationally design two-dimensional (2D) circular hole array sensors with high performance based on our understanding on SPPs. FOM, defined as sensitivity/linewidth, is expected to be a strong function of array geometry. For example, for sensitivity, the phase-matching equation for SPPs in 2D cubic array in Γ-X direction is given as [13

L. Pang, G. M. Hwang, B. Slutsky, and Y. Fainman, “Spectral sensitivity of two-dimensional nanohole array surface plasmon polariton resonance sensor,” Appl. Phys. Lett. 91(12), 123112 (2007). [CrossRef]

{(\frac{2 π}{λ} n_{a}^{} \sin θ + n_{x} \frac{2 π}{p})}^{2} + {(n_{y} \frac{2 π}{p})}^{2} = {(\frac{2 π}{λ} \sqrt{\frac{n_{a}^{2} ε_{m}}{n_{a}^{2} + ε_{m}}})}^{2},

(1)

where λ is the free space wavelength, ε_m and n_a are the dielectric constant and refractive index of metal and dielectric, p is the period, θ is the incident angle, and n_x and n_y are integers that specify the order of SPP mode. The sensitivity S can then be determined by taking the derivative of λ with respect to n_a. We numerically calculate the sensitivity of (1,0), (-1,0), and (-1,1) SPP modes for Au and Ag arrays with different periods and incident angles and the results are plotted in Fig. 1 . One can see from the figure that sensitivity is relatively insensitive to the type of metal and it increases with increasing period. The insensitivity is due to that the fact that when ^{$| ε_{m} | > > n_{a}^{2}$}, the phase-matching equation does not depend on ε_m, leading to the consequence that ε_m is not involved much in determining S. Lower order SPP modes have higher sensitivity than the higher order modes. In addition, at low incident angle, the sensitivity of the lowest order SPP modes (i.e. (1,0) and (-1,0)) is approximately equal to the period. As a result, the sensitivity can be improved simply by increasing the period, decreasing the incident angle and the order of SPPs. On the other hand, studies on SPP lifetime (τ_SPP) have shown that the linewidth of the reflection dip is a function of hole geometry [14

D. Y. Lei, J. Li, A. I. Fernández-Domínguez, H. C. Ong, and S. A. Maier, “Geometry dependence of surface plasmon polariton lifetimes in nanohole arrays,” ACS Nano 4(1), 432–438 (2010). [CrossRef] [PubMed]

,15

J. Li, H. Iu, D. Y. Lei, J. T. K. Wan, J. B. Xu, H. P. Ho, M. Y. Waye, and H. C. Ong, “Dependence of surface plasmon lifetimes on the hole size in two-dimensional metallic arrays,” Appl. Phys. Lett. 94(18), 183112 (2009). [CrossRef]

]. Small radius and shallow depth produce long τ_SPP and thus narrow linewidth. As a result, based on these rationales, we believe it is worthwhile to explore structures that have the right geometry to exhibit desirable sensitivity and lifetime in order to obtain high FOM. However, to date, no systematic studies are found on this aspect although it is of important.

Fig. 1 The plots of numerically calculated sensitivity of different orders (n_x, n_y) of SPP modes against incident angle for 2D arrays with different periods (p). The (-1,0) (closed symbols) and (1,0) (open symbols) SPP modes of (a) Au and (b) Ag arrays. The (-1,1) SPP modes of (c) Au and (d) Ag arrays.

In this article, we attempt to achieve the aforementioned goals by studying the optical properties of 2D Au and Ag circular hole arrays. Hole arrays with different periods, hole radii and depths have been fabricated by interference lithography (IL). We systematically study the linewidth and the depth/height of reflectivity profiles for different geometries by using angle- and polarization-resolved reflectivity spectroscopy. We find while the linewidth decreases with decreasing hole depth and radius, the reflection dip becomes shallow at the same time, thus reducing the contrast of the spectrum. To improve the contrast, we show by orthogonally orienting a pair of polarizer and analyzer to eliminate the non-resonant background, the reflectivity dip can be transformed into a Lorentzian peak with good signal-to-noise ratio (SNR) while keeping the linewidth unchanged. Strong and narrow reflection peaks can then be obtained. To demonstrate good FOM, we show that the linewidth of (-1,0) SPP mode can be narrowed to 5.73 nm at λ = 845 nm by using hole radius and depth = 35 and 70 nm. A FOM value of 105/RIU taken at incident angle = 5^o is obtained and this value outperforms those from ATR and nanoparticle sensors.

2D circular hole metallic arrays are fabricated by using IL and thin film deposition as described earlier [14

,15

]. By changing the incident angle, the exposure time and the thickness of SU8 photoresist, the period and hole size of arrays can be controlled independently. In this study, three series of SU8 templates with period p = 655, 670, and 760 nm and hole depth d ranging from 60 to 510 nm and radius r from 35 to 205 nm have been fabricated. Then, they are coated with 50-100 nm thick Au or Ag film by using sputtering. After fabrication, the samples are mounted on a computer-controlled goniometer for angle- and polarization-dependent reflectivity measurements [14

,15

]. The schematic of the setup is shown in Fig. 2(a) . A collimated white light from a quartz lamp is used for illumination and the specular reflection is captured by a CCD based detection system. The incident angle θ is changed from 5^o to 30^o with a step size of 0.5^o. A pair of polarizer (φ₁) and analyzer (φ₂) is placed in the optical path for performing p-p, s-s, and o-o polarized reflectivity measurements, as shown in Fig. 2(b). In the figure, at any θ, for p-p configuration, both the polarization axes of φ₁ and φ₂ are oriented parallel to the incident plane so that only p-polarized light is illuminated and collected. On the other hand, for s-s configuration, only s-polarized reflection is recorded by setting both axes of φ₁ and φ₂ normal to the incident plane. Finally, for o-o configuration, the polarization axes of φ₁ and φ₂ are oriented at 45^o and -45^o with respect to the incident plane, which makes two axes orthogonal to each other. This configuration allows equal portion of p- and s-polarized lights incident on the sample but only collects reflection that is orthogonal to it. All reflection spectra are calculated by normalizing them with their respective incident light spectra, which can be done by recording the spectra directly output from the incident polarizer.

Fig. 2 (a) The schematic for angle- and polarization-resolved reflectivity spectroscopy. (b) Three polarization configurations. The p-p and s-s configurations have two polarization axes aligned parallel and normal to the incident plane. The o-o configuration has two axes oriented at 45^o and -45^o with respect to the incident plane. The dash lines are incident plane.

As an illustration, Figs. 3 and 4 show the angle-dependent p-p and s-s reflectivity mappings, also known as dispersion relations, of six Au hole arrays with d = 60 nm and 300 nm and different radii in Γ-X direction. The insets show the scanning electron microscope (SEM) images of the hole arrays, displaying the holes are arranged in cubic structure with p = 760 nm, r = 65, 105, and 205 nm for d = 60 nm and 62, 110, and 165 nm for d = 300 nm. From the mappings, we find low reflectivity dispersive bands appear frequently, signifying the excitation of propagating SPP modes [14

,15

]. In addition, Wood’s anomalies are also seen above the SPP modes as high reflectivity bands [16

C. Genet, M. P. van Exter, and J. P. Woerdman, “Fano-type interpretation of red shifts and red tails in hole array transmission spectra,” Opt. Commun. 225(4-6), 331–336 (2003). [CrossRef]

]. The spectral positions of SPPs can be described by using Eq. (1) given above. The dielectric constant of Au is extracted from ref [17

E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).

] and the solid lines deduced from Eq. (1) are overlaid on the figures, revealing the excitation of (1,0), (-1,0) and (-1,±1)_s SPP modes under p-polarization and (0,±1)_a and (-1,±1)_a SPP modes under s-polarization [18

J. Li, H. Iu, J. T. K. Wan, and H. C. Ong, “The plasmonic properties of elliptical metallic hole arrays,” Appl. Phys. Lett. 94(3), 033101 (2009). [CrossRef]

]. The excitation of SPPs by s-polarized light is due to the coupling of degenerate (0,±1) (and also (-1,±1)) SPP modes, yielding (0,±1)_s and (0,±1)_a (and also (-1,±1)_s and (-1,±1)_a) modes that have different electric field symmetries with respect to the incident plane [19

S. Collin, C. Sauvan, C. Billaudeau, F. Pardo, J. C. Rodier, J. L. Pelouard, and P. Lalanne, “Surface modes on nanostructured metallic surfaces,” Phys. Rev. B 79(16), 165405 (2009). [CrossRef]

]. Therefore, p-polarized light can excite the symmetric (0,±1)_s mode while the antisymmetric (0,±1)_a mode is excited by s-polarized light. To examine the spectra closer, we have extracted the (-1,0) reflectivity spectra from Figs. 3 and 4 at θ = 5^o and 15^o and plotted them in Fig. 5 . While it is found the spectral positions of SPP modes from all arrays are primarily dependent on period, one may notice from Fig. 5 that, for a given SPP mode, the reflection dips become broader when hole size increases. As the linewidth is inversely proportional to the decay lifetime (τ_SPP) of SPP, it is implied that larger hole size leads to shorter SPP lifetime [14

,15

]. Therefore, the dependence of SPP lifetime (linewidth) on array geometry deserves further attention since it is closely related to the optimization of FOM for SPR sensor.

Fig. 3 The angle-dependent reflectivity mappings of Au arrays with p = 760 nm, d = 60 nm, and different radii taken under different polarizations. (a) and (d) are p-p and s-s mappings for r = 65 nm. (b) and (e) are p-p and s-s mappings for r = 105 nm. (c) and (f) are p-p and s-s mappings for r = 205 nm. The red solid lines are calculated by using the SPP phase-matching equation, specifying different (n_x, n_y) SPP modes. The corresponding SEM images are shown in the insets.

Fig. 4 The angle-dependent reflectivity mappings of Au arrays with p = 760 nm, d = 300 nm, and different radii taken under different polarizations. (a) and (d) are p-p and s-s mappings for r = 62 nm. (b) and (e) are p-p and s-s mappings for r = 110 nm. (c) and (f) are p-p and s-s mappings for r = 165 nm. The red solid lines are calculated by using the SPP phase-matching equation, specifying different (n_x, n_y) SPP modes. The corresponding SEM images are shown in the insets.

Fig. 5 The corresponding p-p reflectivity spectra taken at θ = 5^o and 15^o for Au arrays with p = 760 nm, d = (a) 60 nm and (b) 300 nm, and different radii. The dash lines are the best fits determined by using Fano-like model.

We have determined the lifetimes of (1,0) and (-1,0) SPP modes of Au and Ag arrays from p-p mappings for different geometries. We only work on nondegenerate SPP modes to avoid coupling, which complicates our analysis. For simplicity, as all arrays are uniform, we assume the inhomogeneous broadening is small compared to the homogeneous counterpart. In addition, we also assume the wavelengths are close to the light line so that the effective refractive index in Eq. (1) is almost equal to n_a and the excited SPP wavelength is the same as the incident wavelength for n_a = 1 in air. Finally, to avoid complication, the (1,0) modes at large hole sizes in thick arrays are avoided due to the presence of cavity mode. Hence, all the modes being considered here are pure SPP resonance with no interaction with cavity mode. To determine τ_SPP, we assume the (1,0) and (-1,0) p-p reflection dips are of Fano-type, which can be expressed by a phenomenological Fano-like model [20

M. J. A. de Dood, E. F. C. Driessen, D. Stolwijk, and M. P. van Exter, “Observation of coupling between surface plasmons in index-matched hole arrays,” Phys. Rev. B 77(11), 115437 (2008). [CrossRef]

R_{p - p} (ω) = {| a + \frac{b Γ_{r a d} e^{i δ}}{(ω - ω_{r e s}) + i Γ_{t o t}} |}^{2} �

(2)

where ω_res is the resonant frequency, a and b are constants that take into account of the direct reflection and SPP amplitude, δ is the phase difference between the SPP mode and the outcoupled field, and Γ_tot is the total decay rate given as the summation of absorption and radiative decay rates (i.e. Γ_tot = Γ_abs + Γ_rad). The decay lifetime of the mode is then given as τ_SPP = 1/Γ_tot. We then best fit all the samples at different incident angles and for different geometries and some of the best fits are shown in Fig. 5 as dash lines to illustrate reasonably good fitting. As an example, the (-1,0) τ_SPP is plotted against resonant wavelength λ_res for Au arrays with p = 760 nm, d = 300 nm, and r = 62, 110, 120, and 165 nm and Ag arrays with p = 670 nm, d = 380 nm, and r = 95, 125, 140, and 160 nm in Fig. 6 . Apparently, by log-log plotting τ_SPP as a function of λ_res, we see all SPP modes follow a quasi-linear relationship indicating τ_SPP ∝ λⁿ with n increases from 2.98 to 6.52 for Au and from 4.22 to 5.47 for Ag when hole radius increases [14

,15

]. We also have plotted the dependence of τ_SPP of Au and Ag samples on hole radius at λ_res = 900 nm in Fig. 7 . It is found that at shallow depth, τ_SPP does not vary much with radius, but then follows r ^-m, where m increases from 0 to higher value, at larger hole depth.

Fig. 6 The plots of (-1,0) SPP decay lifetime against resonant wavelength in log-log scale for (a) Au and (b) Ag arrays with different hole radii. The period and hole depth are 760 and 300 nm for Au and 670 and 380 nm for Ag, respectively. The slopes n deduced by linear fitting are also indicated.

Fig. 7 The plots of SPP decay lifetime against hole radius at resonant wavelength = 900 nm in log-log scale for different hole depths. (a) Au arrays with p = 655 nm, (b) Ag arrays with p = 670 nm, and (c) Au arrays with p = 760 nm.

We also find from Fig. 5 that the reflection dips become shallow when τ_SPP increases, thus reducing the contrast of the spectra and possibly making the detection of them difficult despite the narrow linewidth. In fact, this consequence is implied in Eq. (2) as the depth of the reflection dip is directly related to Γ_rad. Longer τ_SPP arising from smaller Γ_rad could lead to narrow linewidth but also diminishes the depth. To overcome this difficulty, we note from the o-o configuration, the Jones vector for the reflected light before passing through the analyzer can be written as:

\frac{1}{\sqrt{2}} E_{0} [\begin{matrix} a + \frac{b Γ_{r a d} e^{i δ}}{(ω - ω_{r e s}) + i Γ_{t o t}} \\ a \end{matrix}]

, for p- and s-polarizations assuming the direct reflections for p- and s-polarizations are identical. E₀ is the incident field. After passing through the analyzer that has the Jones matrix given as [21

E. Hecht, Optics, 4th ed. (Addison Wesley, San Fransisco, C.A., 2001).

\frac{1}{2} [\begin{matrix} 1 & - 1 \\ - 1 & 1 \end{matrix}]

, the o-o reflectivity can then be given as:

R_{o - o} (ω) = \frac{1}{4} {| \frac{b Γ_{r a d} e^{i δ}}{(ω - ω_{r e s}) + i Γ_{t o t}} |}^{2} �

(3)

due to the elimination of the p- and s-direct reflections. The background now primarily is determined by the orthogonality of the polarizer and analyzer. As a result, the o-o reflectivity profile exhibits a Lorentzian lineshape with good SNR while keeping the linewidth unchanged. The o-o reflectivity mappings of the corresponding Au arrays are shown in Fig. 8 . Remarkably, they bear strong resemblance to the p-p and s-s counterparts but the resonant profiles now appear as peaks instead of dips. One can see the spectral positions of all peaks match very well with those of the dips in p-p and s-s mappings indicating they are of SPP origin. In contrast to the p-p and s-s mappings where the non-resonant reflectivity background is strong, the o-o mappings have negligible background. We have plotted the (-1,0) o-o reflectivity spectra in Fig. 9 so that they can be compared with those in Fig. 5. One sees they all manifest Lorentzian lineshape with high SNR. We estimate the SNR for θ = 5^o and it ranges from 25 to 487, while the corresponding SNR from p-p reflectivity ranges from 17 to 40.

Fig. 8 The angle-dependent o-o reflectivity mappings of Au arrays with p = 760 nm and different hole depths and radii. The upper panel is for d = 60 nm with r = (a) 65, (b) 105, and (c) 205 nm. The lower panel is for d = 300 nm with r = (d) 62, (e) 110, and (f) 165 nm. The white solid lines are calculated by using the SPP phase-matching equation, specifying different (n_x, n_y) SPP modes.

Fig. 9 The corresponding o-o reflectivity spectra taken at θ = 5^o and 15^o for Au arrays with p = 760 nm, d = (a) 60 nm and (b) 300 nm and different radii. The dash lines are best fits determined by using Lorentzian model.

It is noted that R_p-p and R_o-o should yield the same decay lifetime as they both arise from the same origin. We have determined the (-1,0) SPP lifetime τ_SPP of p = 655 nm Au arrays with d = 60 nm and r = 55 and 150 nm, d = 120 nm and r = 90 and 145 nm and d = 300 nm and r = 65 and 120 nm, and d = 510 nm and r = 80 and 125 nm by fitting their p-p and o-o reflectivity spectra with Eqs. (2) and (3) and the results are shown in Fig. 10 for comparison. Apparently, the lifetimes obtained from two functions appear almost identical for different resonant wavelengths, supporting the idea of using o-o configuration to enhance SNR without the expense of the linewidth.

Fig. 10 The plots of (-1,0) SPP decay lifetime against resonant wavelength in log-log scale for p = 655 nm Au arrays with different geometries. d = 60 nm, r = (a) 55 nm and (b) 150 nm, d = 120 nm, r = (c) 90 nm and (d) 145 nm, d = 300 nm, r = (e) 65 nm and (f) 120 nm, and d = 510nm, r = (g) 80 nm and (h) 125 nm.

We attempt to minimize the linewidth Γ_tot (or maximize the lifetime τ_SPP) to optimize FOM. In fact, the dependence of τ_SPP on wavelength and geometry can be accounted by knowing τ_SPP actually is: 1/τ_SPP = 1/τ_abs + 1/τ_rad, where τ_abs and τ_rad are absorption and radiative decay lifetimes, respectively. With the fact that all the hole sizes are smaller than the wavelengths, the absorption lifetime can be qualitatively expressed as [14

,15

τ_{a b s} \propto \frac{λ Re {(ε_{m})}^{2}}{2 π Im (ε_{m})} \propto λ^{2},

(4)

which is independent of geometry. On the other hand, within the framework of Mie scattering, the scattering loss τ_rad is proportional to p²/σ, where σ is the SPP scattering cross-section and is given as [14

,15

σ = 24 π^{5} [\frac{r^{4} d^{2}}{λ^{4}} {(\frac{(n_{a}^{2} - ε_{m})}{(n_{a}^{2} + 2 ε_{m})})}^{2} - 5 π^{4} \frac{r^{\frac{20}{3}} d^{\frac{10}{3}}}{λ^{8}} {(\frac{(n_{a}^{2} - 2 ε_{m}) (n_{a}^{2} - ε_{m})}{{(n_{a}^{2} + 2 ε_{m})}^{2}})}^{2}],

(5)

after the inclusion of the quadrupolar corrections in cylindrical hole. The first component indicates the dipolar, or Rayleigh, scattering whereas the second one represents the quadrupolar counterpart. Therefore,

τ_{rad} \propto p^{2} / (r^{4} d^{2} / λ^{4} - r^{~ 6.7} d^{~ 3.3} / λ^{8})

| ε_{m} | > > n_{a}^{2}

and it shows different wavelength dependence depending on the hole size. We expect from the above formulations that at small radius and depth, τ_SPP should follow between λ² and λ⁴ where absorption loss is dominant, but becomes more λ^4-8 dominant at larger radius and depth when dipolar and quadrupolar become more and more important in governing the decay lifetime. In agreement with our observations, for small hole radius in Fig. 6, n is estimated to be ~ 3-4 indicating absorption loss is dominant over radiative scattering loss due to the weak scattering of SPPs on the weakly corrugated surfaces. However, when radius increases, the radiative loss begins to take charge and n increases gradually to 5-7. As a result, at fixed λ_res, narrow linewidth can be obtained by increasing period and decreasing the hole radius and depth so that the radiative decay rate is suppressed. In addition, long period also provides good sensitivity, which is also advantageous in improving the FOM value. One can also see from Eq. (5) that if ^{$| ε_{m} | > > n_{a}^{2}$}, σ is weakly dependent on the metal type and the τ_SPP dependences on wavelength and geometry are almost identical for Au and Ag.

As a demonstration of high FOM, Figs. 11(a) and 11(b) show the o-o reflectivity spectra of (1,0) SPP mode taken from two Au arrays with p = 760 nm, d = 70 nm and r = 35 and 135 nm at θ = 5^o in different refractive index media (n_a = 1, 1.33 and 1.37). We clearly see the peaks red shift to longer wavelength at higher refractive index. The resonance wavelengths are then plotted as a function of refractive index in Figs. 11(c) and 11(d) displaying a linear relationship, which gives the sensitivities of two arrays to be 754.7 and 751.2 nm/RIU, confirming the relationship between sensitivity and period. The linewidths averaged from different refractive indices are determined to be ~ 7.15 and 8.25 nm, resulting in the FOM values to be 105.57 and 91.05/RIU, which are compatible with or even surpasses that of ATR setup and is much better than that of nanoparticles [8

]. Besides, all the peaks show good SNR when compared with the corresponding p-p reflection spectra given in the insets. For example, for r = 35 nm in n_a = 1.33, the SNR is estimated to 29 from o-o reflectivity spectrum while the p-p counterpart yields 7. In addition, the SNR determined from r =135 nm can reach 112 for o-o spectrum in contrast to 30 for p-p spectrum. Our results show that, by combining high FOM and SNR, array-based SPR sensor could revolutionize a new generation of chip-scale biosensors with supreme performance.

Fig. 11 The o-o reflectivity spectra of (1,0) SPP mode taken from two Au arrays with p = 760 nm, d = 70 nm, and (a) r = 35 and (b) 135 nm at θ = 5^o in different refractive index media (n_a = 1, 1.33 and 1.37). The corresponding p-p reflectivity spectra are given in the insets for reference. (c) and (d) The corresponding plots of resonant wavelength against refractive index. The back solid squares are determined from o-o reflectivity spectra while the red solid circles are determined from p-p reflectivity spectra. The dash lines are linear fits. The sensitivity and FOM are determined to be 754.7 nm/RIU and 105.57/RIU for r = 35 nm and 751.18 nm/RIU and 91.05/RIU for r = 135 nm.

Finally, we have determined the FOM values for a series of Au arrays in Tables 1 and 2 together with their sensitivities and averaged linewidths. Table 1 shows the (1,0) and (-1,0) SPPs extracted from arrays with p = 655 nm and d = 70 nm and different hole radii whereas Table 2 consists of arrays with p = 760 nm and d = 70 nm. Expectedly, for different SPP modes, the arrays that have small hole size exhibit high FOM while those with large size give low FOM. In other words, the variation of FOM correlates well with the corresponding linewidth, or τ_SPP. As our present setup only covers wavelength range up to 1000 nm, we are not able to accurately evaluate the FOM of (-1,0) SPP mode for p = 760 nm. Nevertheless, in Table 2, by assuming the sensitivity = 755 nm/RIU and using the linewidths measured in air (n_a = 1), we have determined the projected FOM values for (-1,0) SPP mode, giving the highest value approaching to 131.76/RIU at small hole size. Moving to near infrared regime, we anticipate an even higher FOM is resulted due to higher sensitivity and longer decay lifetime.

Table 1 The sensitivity, averaged linewidth, and FOM of (-1,0) and (1,0) SPPs from Au arrays with different radii. The period and hole depth are 655 and 70 nm.

p = 655 nm	radius (nm)	sensitivity (nm/RIU)	average linewidth (nm)	FOM (RIU^-1)
(1,0)	70	640.35	9.98	64.14
	80	639.89	9.99	64.03
	135	639.36	10.32	61.96
	155	640.91	10.09	63.51
(-1,0)	70	656.58	7.50	87.55
	80	655.50	7.26	90.29
	135	653.73	8.40	77.79
	155	656.23	8.26	79.42

Table 2 The sensitivity, averaged linewidth, and FOM of (-1,0) and (1,0) SPPs from Au arrays with different radii. The period and hole depth are 760 and 70 nm.

p = 760 nm	radius (nm)	sensitivity(nm/RIU)	average linewidth (nm)	FOM (RIU^-1)
(1,0)	35	754.70	7.15	105.57
	55	761.27	7.14	106.69
	95	755.32	7.82	96.65
	135	751.18	8.25	91.05
(-1,0)	35	755	5.73	131.76
	55	755	5.78	130.62
	95	755	5.93	127.32
	135	755	6.37	118.52

In summary, we have proposed a general scheme to rationally design 2D circular hole array SPR sensors with high FOM and SNR. We have shown that the sensitivity is primarily governed by the period of arrays whereas the linewidth is controlled by the hole size. As a result, it is possible to use long period array with small hole size to obtain high FOM. We have shown from the experimental results that FOM can be as large as 105/RIU at low incident angle of 5^o, which outperform those of ATR and nanoparticle counterparts. Finally, by using orthogonal configuration, the non-resonant background can be completely eliminated, which boosts up the SNR.

Acknowledgments

This research was supported by the Chinese University of Hong Kong through the RGC Competitive Earmarked Research Grants (402908, 402909 and 403310) and the Shun Hing Institute of Advanced Engineering (BME-p3-11) and UGC special equipment grant (SEG_CUHK07).

References and links

1.	W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424(6950), 824–830 (2003). [CrossRef] [PubMed]
2.	E. C. Le Ru and P. Etchegoin, Principles of Surface Enhanced Raman Spectroscopy: and Related Plasmonic Effects (Elsevier Science, 2008).
3.	K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater. 3(9), 601–605 (2004). [CrossRef] [PubMed]
4.	D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics 4(2), 83–91 (2010). [CrossRef]
5.	M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics 5(6), 349–356 (2011). [CrossRef]
6.	J. Homola, Surface Plasmon Resonance Based Sensors, Springer Series on Chemical Sensors and Biosensors (Springer-Verlag, 2006).
7.	J. Homola, “Surface plasmon resonance sensors for detection of chemical and biological species,” Chem. Rev. 108(2), 462–493 (2008). [CrossRef] [PubMed]
8.	M. A. Otte, B. Sepúlveda, W. H. Ni, J. P. Juste, L. M. Liz-Marzán, and L. M. Lechuga, “Identification of the optimal spectral region for plasmonic and nanoplasmonic sensing,” ACS Nano 4(1), 349–357 (2010). [CrossRef] [PubMed]
9.	J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater. 7(6), 442–453 (2008). [CrossRef] [PubMed]
10.	M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev. 108(2), 494–521 (2008). [CrossRef] [PubMed]
11.	R. Gordon, D. Sinton, K. L. Kavanagh, and A. G. Brolo, “A new generation of sensors based on extraordinary optical transmission,” Acc. Chem. Res. 41(8), 1049–1057 (2008). [CrossRef] [PubMed]
12.	J. Li, H. Iu, W. C. Luk, J. T. K. Wan, and H. C. Ong, “Studies of the plasmonic properties of two-dimensional metallic nanobottle arrays,” Appl. Phys. Lett. 92(21), 213106 (2008). [CrossRef]
13.	L. Pang, G. M. Hwang, B. Slutsky, and Y. Fainman, “Spectral sensitivity of two-dimensional nanohole array surface plasmon polariton resonance sensor,” Appl. Phys. Lett. 91(12), 123112 (2007). [CrossRef]
14.	D. Y. Lei, J. Li, A. I. Fernández-Domínguez, H. C. Ong, and S. A. Maier, “Geometry dependence of surface plasmon polariton lifetimes in nanohole arrays,” ACS Nano 4(1), 432–438 (2010). [CrossRef] [PubMed]
15.	J. Li, H. Iu, D. Y. Lei, J. T. K. Wan, J. B. Xu, H. P. Ho, M. Y. Waye, and H. C. Ong, “Dependence of surface plasmon lifetimes on the hole size in two-dimensional metallic arrays,” Appl. Phys. Lett. 94(18), 183112 (2009). [CrossRef]
16.	C. Genet, M. P. van Exter, and J. P. Woerdman, “Fano-type interpretation of red shifts and red tails in hole array transmission spectra,” Opt. Commun. 225(4-6), 331–336 (2003). [CrossRef]
17.	E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).
18.	J. Li, H. Iu, J. T. K. Wan, and H. C. Ong, “The plasmonic properties of elliptical metallic hole arrays,” Appl. Phys. Lett. 94(3), 033101 (2009). [CrossRef]
19.	S. Collin, C. Sauvan, C. Billaudeau, F. Pardo, J. C. Rodier, J. L. Pelouard, and P. Lalanne, “Surface modes on nanostructured metallic surfaces,” Phys. Rev. B 79(16), 165405 (2009). [CrossRef]
20.	M. J. A. de Dood, E. F. C. Driessen, D. Stolwijk, and M. P. van Exter, “Observation of coupling between surface plasmons in index-matched hole arrays,” Phys. Rev. B 77(11), 115437 (2008). [CrossRef]
21.	E. Hecht, Optics, 4th ed. (Addison Wesley, San Fransisco, C.A., 2001).

OCIS Codes
(240.6680) Optics at surfaces : Surface plasmons
(260.5740) Physical optics : Resonance
(280.4788) Remote sensing and sensors : Optical sensing and sensors
(310.6628) Thin films : Subwavelength structures, nanostructures

ToC Category:
Sensors

History
Original Manuscript: February 7, 2012
Revised Manuscript: May 3, 2012
Manuscript Accepted: May 5, 2012
Published: May 18, 2012

Citation
Lei Zhang, Chung Y. Chan, Jia Li, and Hock C. Ong, "Rational design of high performance surface plasmon resonance sensors based on two-dimensional metallic hole arrays," Opt. Express 20, 12610-12621 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-11-12610

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References

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003). [CrossRef] [PubMed]
E. C. Le Ru and P. Etchegoin, Principles of Surface Enhanced Raman Spectroscopy: and Related Plasmonic Effects (Elsevier Science, 2008).
K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater.3(9), 601–605 (2004). [CrossRef] [PubMed]
D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4(2), 83–91 (2010). [CrossRef]
M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics5(6), 349–356 (2011). [CrossRef]
J. Homola, Surface Plasmon Resonance Based Sensors, Springer Series on Chemical Sensors and Biosensors (Springer-Verlag, 2006).
J. Homola, “Surface plasmon resonance sensors for detection of chemical and biological species,” Chem. Rev.108(2), 462–493 (2008). [CrossRef] [PubMed]
M. A. Otte, B. Sepúlveda, W. H. Ni, J. P. Juste, L. M. Liz-Marzán, and L. M. Lechuga, “Identification of the optimal spectral region for plasmonic and nanoplasmonic sensing,” ACS Nano4(1), 349–357 (2010). [CrossRef] [PubMed]
J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater.7(6), 442–453 (2008). [CrossRef] [PubMed]
M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev.108(2), 494–521 (2008). [CrossRef] [PubMed]
R. Gordon, D. Sinton, K. L. Kavanagh, and A. G. Brolo, “A new generation of sensors based on extraordinary optical transmission,” Acc. Chem. Res.41(8), 1049–1057 (2008). [CrossRef] [PubMed]
J. Li, H. Iu, W. C. Luk, J. T. K. Wan, and H. C. Ong, “Studies of the plasmonic properties of two-dimensional metallic nanobottle arrays,” Appl. Phys. Lett.92(21), 213106 (2008). [CrossRef]
L. Pang, G. M. Hwang, B. Slutsky, and Y. Fainman, “Spectral sensitivity of two-dimensional nanohole array surface plasmon polariton resonance sensor,” Appl. Phys. Lett.91(12), 123112 (2007). [CrossRef]
D. Y. Lei, J. Li, A. I. Fernández-Domínguez, H. C. Ong, and S. A. Maier, “Geometry dependence of surface plasmon polariton lifetimes in nanohole arrays,” ACS Nano4(1), 432–438 (2010). [CrossRef] [PubMed]
J. Li, H. Iu, D. Y. Lei, J. T. K. Wan, J. B. Xu, H. P. Ho, M. Y. Waye, and H. C. Ong, “Dependence of surface plasmon lifetimes on the hole size in two-dimensional metallic arrays,” Appl. Phys. Lett.94(18), 183112 (2009). [CrossRef]
C. Genet, M. P. van Exter, and J. P. Woerdman, “Fano-type interpretation of red shifts and red tails in hole array transmission spectra,” Opt. Commun.225(4-6), 331–336 (2003). [CrossRef]
E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).
J. Li, H. Iu, J. T. K. Wan, and H. C. Ong, “The plasmonic properties of elliptical metallic hole arrays,” Appl. Phys. Lett.94(3), 033101 (2009). [CrossRef]
S. Collin, C. Sauvan, C. Billaudeau, F. Pardo, J. C. Rodier, J. L. Pelouard, and P. Lalanne, “Surface modes on nanostructured metallic surfaces,” Phys. Rev. B79(16), 165405 (2009). [CrossRef]
M. J. A. de Dood, E. F. C. Driessen, D. Stolwijk, and M. P. van Exter, “Observation of coupling between surface plasmons in index-matched hole arrays,” Phys. Rev. B77(11), 115437 (2008). [CrossRef]
E. Hecht, Optics, 4th ed. (Addison Wesley, San Fransisco, C.A., 2001).

Anderton, C. R.
Anker, J. N.
Barnes, W. L.
Billaudeau, C.
Bozhevolnyi, S. I.
Brolo, A. G.
Collin, S.
de Dood, M. J. A.
Dereux, A.
Driessen, E. F. C.
Ebbesen, T. W.
Fainman, Y.
Fernández-Domínguez, A. I.
Genet, C.
Gordon, R.
Gramotnev, D. K.
Gray, S. K.
Hall, W. P.
Ho, H. P.
Homola, J.
Hwang, G. M.
Iu, H.
Juan, M. L.
Juste, J. P.
Kavanagh, K. L.
Lalanne, P.
Lechuga, L. M.
Lei, D. Y.
Li, J.
Liz-Marzán, L. M.
Luk, W. C.
Lyandres, O.
Maier, S. A.
Maria, J.
Mukai, T.
Narukawa, Y.
Ni, W. H.
Niki, I.
Nuzzo, R. G.
Okamoto, K.
Ong, H. C.
Otte, M. A.
Pang, L.
Pardo, F.
Pelouard, J. L.
Quidant, R.
Righini, M.
Rodier, J. C.
Rogers, J. A.
Sauvan, C.
Scherer, A.
Sepúlveda, B.
Shah, N. C.
Shvartser, A.
Sinton, D.
Slutsky, B.
Stewart, M. E.
Stolwijk, D.
Thompson, L. B.
Van Duyne, R. P.
van Exter, M. P.
Wan, J. T. K.
Waye, M. Y.
Woerdman, J. P.
Xu, J. B.
Zhao, J.

Acc. Chem. Res.

R. Gordon, D. Sinton, K. L. Kavanagh, and A. G. Brolo, “A new generation of sensors based on extraordinary optical transmission,” Acc. Chem. Res.41(8), 1049–1057 (2008). [CrossRef] [PubMed]

ACS Nano

D. Y. Lei, J. Li, A. I. Fernández-Domínguez, H. C. Ong, and S. A. Maier, “Geometry dependence of surface plasmon polariton lifetimes in nanohole arrays,” ACS Nano4(1), 432–438 (2010). [CrossRef] [PubMed]
M. A. Otte, B. Sepúlveda, W. H. Ni, J. P. Juste, L. M. Liz-Marzán, and L. M. Lechuga, “Identification of the optimal spectral region for plasmonic and nanoplasmonic sensing,” ACS Nano4(1), 349–357 (2010). [CrossRef] [PubMed]

Appl. Phys. Lett.

J. Li, H. Iu, D. Y. Lei, J. T. K. Wan, J. B. Xu, H. P. Ho, M. Y. Waye, and H. C. Ong, “Dependence of surface plasmon lifetimes on the hole size in two-dimensional metallic arrays,” Appl. Phys. Lett.94(18), 183112 (2009). [CrossRef]
J. Li, H. Iu, W. C. Luk, J. T. K. Wan, and H. C. Ong, “Studies of the plasmonic properties of two-dimensional metallic nanobottle arrays,” Appl. Phys. Lett.92(21), 213106 (2008). [CrossRef]
L. Pang, G. M. Hwang, B. Slutsky, and Y. Fainman, “Spectral sensitivity of two-dimensional nanohole array surface plasmon polariton resonance sensor,” Appl. Phys. Lett.91(12), 123112 (2007). [CrossRef]
J. Li, H. Iu, J. T. K. Wan, and H. C. Ong, “The plasmonic properties of elliptical metallic hole arrays,” Appl. Phys. Lett.94(3), 033101 (2009). [CrossRef]

Chem. Rev.

J. Homola, “Surface plasmon resonance sensors for detection of chemical and biological species,” Chem. Rev.108(2), 462–493 (2008). [CrossRef] [PubMed]
M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A. Rogers, and R. G. Nuzzo, “Nanostructured plasmonic sensors,” Chem. Rev.108(2), 494–521 (2008). [CrossRef] [PubMed]

Nat. Mater.

J. N. Anker, W. P. Hall, O. Lyandres, N. C. Shah, J. Zhao, and R. P. Van Duyne, “Biosensing with plasmonic nanosensors,” Nat. Mater.7(6), 442–453 (2008). [CrossRef] [PubMed]
K. Okamoto, I. Niki, A. Shvartser, Y. Narukawa, T. Mukai, and A. Scherer, “Surface-plasmon-enhanced light emitters based on InGaN quantum wells,” Nat. Mater.3(9), 601–605 (2004). [CrossRef] [PubMed]

Nat. Photonics

D. K. Gramotnev and S. I. Bozhevolnyi, “Plasmonics beyond the diffraction limit,” Nat. Photonics4(2), 83–91 (2010). [CrossRef]
M. L. Juan, M. Righini, and R. Quidant, “Plasmon nano-optical tweezers,” Nat. Photonics5(6), 349–356 (2011). [CrossRef]

Nature

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature424(6950), 824–830 (2003). [CrossRef] [PubMed]

Opt. Commun.

C. Genet, M. P. van Exter, and J. P. Woerdman, “Fano-type interpretation of red shifts and red tails in hole array transmission spectra,” Opt. Commun.225(4-6), 331–336 (2003). [CrossRef]

Phys. Rev. B

S. Collin, C. Sauvan, C. Billaudeau, F. Pardo, J. C. Rodier, J. L. Pelouard, and P. Lalanne, “Surface modes on nanostructured metallic surfaces,” Phys. Rev. B79(16), 165405 (2009). [CrossRef]
M. J. A. de Dood, E. F. C. Driessen, D. Stolwijk, and M. P. van Exter, “Observation of coupling between surface plasmons in index-matched hole arrays,” Phys. Rev. B77(11), 115437 (2008). [CrossRef]

Other

E. Hecht, Optics, 4th ed. (Addison Wesley, San Fransisco, C.A., 2001).
E. D. Palik, Handbook of Optical Constants of Solids (Academic, 1985).
E. C. Le Ru and P. Etchegoin, Principles of Surface Enhanced Raman Spectroscopy: and Related Plasmonic Effects (Elsevier Science, 2008).
J. Homola, Surface Plasmon Resonance Based Sensors, Springer Series on Chemical Sensors and Biosensors (Springer-Verlag, 2006).

2011, Juan, Nat. Photonics
2010, Otte, ACS Nano
2010, Lei, ACS Nano
2010, Gramotnev, Nat. Photonics
2009, Li, Appl. Phys. Lett.
2009, Li, Appl. Phys. Lett.
2009, Collin, Phys. Rev. B
2008, de Dood, Phys. Rev. B
2008, Anker, Nat. Mater.
2008, Stewart, Chem. Rev.
2008, Gordon, Acc. Chem. Res.
2008, Li, Appl. Phys. Lett.
2008, Homola, Chem. Rev.
2007, Pang, Appl. Phys. Lett.
2004, Okamoto, Nat. Mater.
2003, Barnes, Nature
2003, Genet, Opt. Commun.

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