Nanowire-based enhancement of localized surface plasmon resonance for highly sensitive detection: a theoretical study

doi:10.1364/OE.14.012419

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Nanowire-based enhancement of localized surface plasmon resonance for highly sensitive detection: a theoretical study

Kyujung Kim, Soon J. Yoon, and Donghyun Kim »View Author Affiliations

Optics Express, Vol. 14, Issue 25, pp. 12419-12431 (2006)
http://dx.doi.org/10.1364/OE.14.012419

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▸ Article Outline
– Abstract
1. Introduction
2. Numerical model
3. Results
4. Discussion
5. Concluding remarks
– References and links

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Abstract

A nanowire-based localized surface plasmon resonance (LSPR) biosensor has been investigated to evaluate the impact of design parameters of nanowires on the excitation of localized surface plasmons (LSPs) and the sensitivity enhancement of a LSPR biosensor. The results based on rigorous coupled wave analysis and finite difference time domain method indicate that significant sensitivity increase is associated with LSP excitation mediated by nanowires and that resonant coupling of LSPs through a nanogroove achieves larger field enhancement and sensitivity improvement than LSP excitation in a single nanowire. A specific optimization provided a nanowire-based structure with sensitivity increase by more than 23 times as well as good linear detection properties.

1. Introduction

Sensitivity enhancement of a surface plasmon resonance (SPR) biosensor is extremely important to monitor tiny biomolecular interactions on a quantitative basis using a SPR-based biosensor. A large number of schemes have been proposed to enhance the sensitivity: for example, by amplifying local electromagnetic fields with antibody-conjugated nanoparticles and nanoshells [1–8

S. Kubitschko, J. Spinke, T. Brückner, S. Pohl, and N. Oranth, “Sensitivity enhancement of optical immunosensors with nanoparticles,” Anal. Biochem. 253, 112–122 (1997). [CrossRef] [PubMed]

], using magneto-optical effects [9

B. Sepúlveda, A. Calle, L. Lechuga, and G. Armelles, “Highly sensitive detection of biomolecules with the magneto-optic surface-plasmon-resonance sensor,” Opt. Lett. 31, 1085–1087 (2006). [CrossRef] [PubMed]

], combining with ellipsometric and phase measurements [10

S. Y. Wu, H. P. Ho, W. C. Law, C. Lin, and S. K. Kong, “Highly sensitive differential phase-sensitive surface plasmon resonance biosensor based on the Mach-Zehnder configuration,” Opt. Lett. 29, 2378–2380 (2004). [CrossRef] [PubMed]

,11

H. M. Cho, W. Chegal, Y. J. Cho, Y. Kim, and H. Kim, “Enhancement of biomolecular detection sensitivity by surface plasmon resonance ellipsometry,” in Nanosensing: Materials and Devices II, M. S. Islam and A. K. Dutta, eds., Proc. SPIE 6008, 293–298 (2005).

], or by means of nanowire-mediated resonance coupling of electromagnetic fields between periodic nanowires [12

K. M. Byun, S. J. Kim, and D. Kim, “Design study of highly sensitive nanowire-enhanced surface plasmon resonance biosensors using rigorous coupled wave analysis,” Opt. Express 13, 3737–3742 (2005). [CrossRef] [PubMed]

,13

W-C. Liu, “High sensitivity of surface plasmon of weakly-distorted metallic surfaces,” Opt. Express 13, 9766–9773 (2005). [CrossRef] [PubMed]

]. Many of these approaches are based on localized surface plasmon resonance (LSPR), which relies on the excitation of localized surface plasmons (LSPs) in a rough surface, as a sensitivity enhancement mechanism for a SPR based biosensor. The creation and maintenance of LSPs employ nanostructures [14

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

,15

D. Crouse and P. Keshavareddy, “Role of optical and surface plasmon modes in enhanced transmission and applications,” Opt. Express 13, 7760–7771 (2005). [CrossRef] [PubMed]

], usually metallic nanoparticles, since nanoparticles conjugated with antibodies can amplify a SPR signal when they are bound with target proteins, thus increasing the sensitivity of the detection. For improved control of LSP excitation over nanoparticles, nanowires have recently been investigated [12

,16

K. M. Byun, D. Kim, and S. J. Kim, “Investigation of the profile effect on the sensitivity enhancement of nanowire-mediated localized surface plasmon resonance biosensors,” Sens. Actuators B 117, 401–407 (2006). [CrossRef]

]. The results report theoretically that the excitation of LSPs is highly sensitive to the nanowire structure and the nature of biomolecular interactions that may occur on the nanowire surface.

One of the issues in implementing a nanowire-based LSPR sensor is that despite the fairly obvious sensitivity improvement, typically by an order of magnitude, obtained LSPR characteristics are far from desired. The purpose of this study, therefore, is first to explore the structural dependence of LSPR on nanowire design parameters on a quantitative basis. In particular, the effect of the fill factor and the nanowire depth on the sensitivity characteristics of a LSPR-based biosensor is emphasized. Secondly, the implications of the structural dependence are investigated in conjunction with the sensitivity of an SPR biosensor to the change incurred by the presence of biomolecular interactions on nanowires. Earlier studies focused on the sensitivity enhancement of LSPR biosensors in the case of relatively weak LSPR despite potentially significant sensitivity enhancement with stronger LSPR, largely because the sensitivity enhancement in the event of strong LSPR is often accompanied by a broad SPR dip in the reflectance curve. The broadening in dispersion relation is associated with LSPR excitation that involves a large number of damping modes and is also explained as owing to the decreased effective mean free path of conduction electrons [17

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, Weinheim, Germany, 1983) Chapter 12.

]. The broadening, reported experimentally in many earlier studies [2

L. A. Lyon, D. J. Pena, and M. J. Natan, “Surface plasmon resonance of Au colloid-modified Au films: Particle size dependence,” J. Phys. Chem. B 103, 5826–5831 (1999). [CrossRef]

, 18–20

L. Genzel, T. P. Martin, and U. Kreibig, “Dielectric function and plasma resonances of small metal particles,” Z. Physik B21, 339–346 (1975).

], is generally undesirable for sensor operation in practical applications. In the current study, we see the changes of the LSPR biosensor behavior as LSPR is increasingly enhanced with changes in nanowire designs. This is an attempt to find an optimum structure that achieves maximal sensitivity enhancement at the expense of minimal broadening in the SPR characteristics. For clarification, LSPR is defined as being enhanced or strengthened when momentum matching between incident photons and excited LSP modes occurs at larger momentum. This definition of LSPR enhancement is approximately commensurate with using the quality factor to describe the nature of LSPR, which is typically defined as the ratio of the resonance position to the resonance width. Thirdly, the possibility of zero sensitivity that was suggested as a result of the phase retardation effect of a target binding layer is more thoroughly explored. The phase retardation shifts the resonance condition for target analytes. This consequently introduces a structure in which the presence of target analytes does not shift the resonance as angles or wavelengths in a SPR sensor are scanned. In other words, the resonance may not respond to the presence of a specific analyte. Moreover, it was computationally shown that a specific design may exhibit a negative shift depending on binding events, i.e., resonance shift to a smaller angle or shorter wavelength with target analytes. Such a negative shift has been confirmed experimentally in LSPR using nanoparticles [2

L. A. Lyon, D. J. Pena, and M. J. Natan, “Surface plasmon resonance of Au colloid-modified Au films: Particle size dependence,” J. Phys. Chem. B 103, 5826–5831 (1999). [CrossRef]

] and in waveguide-coupled SPR studies [21

Z. Salamon, G. Lindblom, L. Rilfors, K. Linde, and G. Tollin, “Interaction of phosphatidylserine synthase from E. coli with lipid bilayers: coupled plasmon-waveguide resonance spectroscopy studies,” Biophys. J. 78, 1400–1412 (2000). [CrossRef] [PubMed]

This paper is organized as follows. In Section 2, a numerical model for the rigorous coupled-wave analysis (RCWA) as well as finite difference time domain (FDTD) method is described. The impact of various design parameters on LSPR is presented in Section 3. Quantitative analysis of sensitivity enhancement to obtain an optimal nanowire structure is discussed in Section 4, which is followed by concluding remarks in Section 5.

2. Numerical model

A nanowire-based LSPR biosensing structure is studied with a model using well-established RCWA [22

M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of metallic surface-relief gratings,” J. Opt. Soc. Am. A 3, 1780–1787 (1986). [CrossRef]

], which has been used successfully to explain experimental results of nanostructures [23–25

Y. Kanamori, K. Hane, H. Sai, and H. Yugami, “100 nm period silicon antireflection structures fabricated using a porous alumina membrane mask,” Appl. Phys. 78, 142–143 (2001).

]. The applicability of such a classical approach to a metallic structure on a nanometer scale has been the topic of other studies [26

J. Lermé, “Introduction of quantum finite-size effects in the Mie’s theory for a multilayered metal sphere in the dipolar approximation: application to free and matrix-embedded noble metal clusters,” Eur. Phys. J. D 10, 265–277 (2000). [CrossRef]

, 27

E. Moreno, D. Erni, C. Hafner, and R. Vahldieck, “Multiple multipole method with automatic multipole setting applied to the simulation of surface plasmons in metallic nanostructures” J. Opt. Soc. Am. A 19, 101–111 (2002). [CrossRef]

]. To ensure the validity of RCWA, we have limited the nanowire dimension such that its minimum feature size exceeds 10λ_F, where λ_F denotes the Fermi wavelength and is approximately 0.5 nm for gold. Convergence in RCWA can be achieved by including a sufficient number of space harmonics for the calculation of metallic surface relief structures even with rapidly varying fields in space. For this study, our RCWA routine employed 20 space harmonic orders unless otherwise noted.

A nanowire-based SPR biosensor is represented as a one-dimensional array of rectangular gold nanowires on top of a gold thin film where bulk surface plasmon polaritons (SPPs) are excited, an attachment layer of chromium, and a BK7 glass substrate (see Fig. 1). The thickness of the gold and chromium films is fixed at 40 nm and 2 nm, respectively. Optical properties of BK7 glass, chromium, and gold were taken from Ref 28

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, Orlando, FL, U. S. A., 1985).

The spatial distribution of the electromagnetic field intensity has been visualized using FDTD. The FDTD calculation was performed with a software package EMXP™ [29

P. Liu, EM Explorer , http://www.emexplorer.net.

]. EMXP™ discretizes Maxwell’s equations for monochromatic plane-wave excitation using rectangular 3-D cells of finite volume and solves them based on a time marching algorithm with absorbing boundary conditions. FDTD results have been successfully validated with standard electromagnetic field calculation using Fresnel coefficients and also with RCWA for thin film and grating structures.

The antibody-analyte binding is modeled with a 1-nm thick self-assembled monolayer (SAM) that is supported by gold nanowires and thin film. In this study, 1,6-hexanedithiol (HDT) is initially assumed for the dielectric SAM by approximating it as a homogeneous layer with n(HDT)=1.52643 for the HDT SAM [30

E. Hutter, S. Cha, J-F. Liu, J. Park, J. Yi, J. H. Fendler, and D. Roy, “Role of substrate metal in gold nanoparticle enhanced surface plasmon resonance imaging,” J. Phys. Chem. B 105, 8–12 (2001). [CrossRef]

]. The extinction coefficient of the HDT SAM, k(HDT), is responsible mainly for the reduction of reflectance, rather than the resonance angle shift. k(HDT) was ignored in this study, since the HDT SAM is extremely thin compared with the wavelength and the layer is essentially a lossless dielectric at the wavelength. Dielectric materials other than HDT, refractive indices of which range from 1.33 to 1.6, are considered in the later part of this paper. A SAM that is experimentally obtained is usually thicker than 1 nm. By assuming a 1-nm thick SAM for our study, we are taking the worst-case sensitivity data in the calculation of the sensitivity enhancement. The light source for the model is assumed to be a TM-polarized monochromatic plane wave at a fixed wavelength λ=632.8 nm as the incidence angle (θ) is scanned with an angular resolution of 0.01°.

Fig. 1. Schematics of a nanowire-based of SPR biosensor (d_f: gold film thickness fixed at 40 nm, d_NW: gold nanowire thickness, Λ: nanowire period, light wavelength λ=632.8 nm)

As a quantitative measure of the sensor performance, we have employed the sensitivity enhancement represented by a sensitivity enhancement factor (SEF) and also the minimum reflectance at resonance (MRR) of the SPR dip characteristics. SEF measures the resonance angle shift due to target analyte binding on a nanowire-based biosensor with respect to that of a conventional SPR structure using a thin gold film with equal thickness d_f=40 nm, i.e., SEF=Δθ_SP(nanowires)/Δθ_SP(no nanowires). SEF can be negative if the resonance angle shifts lower as a result of surface modification by biomolecular interactions or structural changes in a LSPR based biosensor. On the other hand, MRR is a measure of the signal contrast of SPR and positively correlates with the angular width (AW) of SPR characteristics. While AW can be directly calculated in reference to the angle of total internal reflection, it may not properly evaluate the integrity of SPR characteristics and can merely be redundant with resonance angles, since the angle of total internal reflection depends only on the dielectric interface and its refractive index. Instead of AW, MRR has been employed as an indirect measure of the SPR characteristics. This is based on the fact that damping tends to be more evenly distributed among excitation modes as LSPR modes are excited, which in turn induces significant broadening.

3. Results

Figure 2 shows the impact of nanowire period (Λ=50, 100, 150, and 200 nm) and depth (d_NW=10, 15, 20, and 25 nm) on the LSPR characteristics represented by the LSP momentum K_SP=2πsinθ_SP/λ, where θ_SP is the LSPR angle, at various volume factors (VFs) in the absence and presence of target binding. Here, a VF is defined as the ratio of the volume occupied by gold in a nanograting. For one-dimensional nanowires, a VF is equivalent to a fill factor. The dotted line in Fig. 2 represents the resonance angle (θ_SP=45.13°) of a SPR biosensor at d_f=40 nm without nanowires.

First of all, trends of enhanced LSPR with smaller Λ and larger dNW are obvious, because increased isolation of a LSP mode encourages decoupling from a bulk SPP mode, as was observed in earlier studies on surface plasmons created on gold and silver gratings [31

I. Pockrand and H. Raether, “Surface plasma oscillations in silver films with wavy surface profiles: a quantitative experimental study,” Opt. Commun. 18, 395–399 (1976). [CrossRef]

, 32

H. Raether, “Dispersion relation of surface plasmons on gold- and silver gratings,” Opt. Commun. 42, 217–222 (1982). [CrossRef]

]. Potential for large sensitivity increase of a decoupled LSP mode, compared with the one coupled with a bulk SPP mode has been numerically investigated in Ref. 33

K. M. Byun, S. J. Kim, and D. Kim, “Profile effect on the feasibility of extinction-based localized surface plasmon resonance biosensors with metallic nanowires,” Appl. Opt. 45, 3382–3389 (2006). [CrossRef] [PubMed]

Second, the LSPR is associated with two different modes of enhancement at a small or a large value of VF. For convenience, we define the VF at maximum LSPR enhancement as VF_L and VF_H, respectively for the enhancement associated with single-nanowire LSP excitation (low VF) and that associated with the resonant coupling of LSPs through a nanogroove (high VF). Note that the LSP excitation associated with a nanogroove tends to be noticeably stronger than that of a single nanowire. The data in Fig. 2 suggest that the two LSP excitation modes be coupled with effective LSPR enhancement. In other words, LSPR enhancement is reduced if the coupling between the two modes is weakened for a large nanowire period. At a very small period and large depth (see the case of Λ=50 nm and d_NW=25 nm), it is apparent that the two modes of enhancement begin to merge and create significant coupling of LSPs excited in neighboring nanowires.

Third, in the presence of a SAM that models target binding, VF_L becomes smaller and VF_H larger. In Fig. 2, not only does the presence of a SAM shift the resonance condition, it also causes the resonance to occur more easily with a SAM, i.e.,

{VF}_{L} (SAM) > {VF}_{L} (no SAM) and {VF}_{H} (SAM) < {VF}_{H} (no SAM) .

(1)

Fig. 2. Plasmon momentum K_SP (y-axis in unit of µm^-1) for various combinations of nanowire depths (d_NW) and periods (Λ). x-axis is VF. Red and black solid lines represent the characteristics of a nanowire-based SPR biosensor with and without a HDT SAM as target analytes. For comparison, the dotted line shows K_SP(θ_SP=45.13°) of a SPR biosensor at d_f=40 nm without nanowires.

Note that the LSPR enhancement is accompanied by the broadening in dispersion relation due to the decreased mean free path which incurs damping into a large number of LSP modes. The angular width of the dip in SPR characteristics Δθ_SP is given by

Δ θ_{SP} = \frac{Im {K_{SP}}}{n_{s} \frac{w}{c} \cos θ_{SP}} = \frac{(Γ_{i} + Γ_{r})}{n_{s} \frac{w}{c} \cos θ_{SP}},

(2)

with n_s as the refractive index of a BK7 prism substrate [35

R. Bruns and H. Raether, “Plasma resonance radiation from non-radiative plasmons,” Z. Physik 237, 98–106 (1970). [CrossRef]

]. w and c are the angular frequency and the free-space speed of light. KSP is the plasmon momentum. Γ_i and Γ_r denote internal and radiative damping, respectively. Equation (2) indicates that the imaginary part of KSP becomes larger, which increases the damping and the width of the SPR characteristic. If ε₁(=ε₁′+iε₁″) is the complex permittivity of a gold film and ε_2,eff (=ε_2,eff′+iε_2,eff″) is the effective permittivity of the nanowire layer in combination with surrounding dielectric analytes, in the case of |ε₁ ′|>>ε₁ ″,

Im (K_{SP}) \approx \frac{w}{c} {(\frac{{ε_{1}}^{'} {ε_{2, eff}}^{'}}{{ε_{1}}^{'} {+ ε_{2, eff}}^{'}})}^{\frac{3}{2}} \frac{{ε_{1}}^{″}}{2 {({ε_{1}}^{'})}^{2}} .

(3)

ε_2,eff″ is assumed to be negligible [16

, 34

D. Kim, “Effect of resonant localized plasmon coupling on the sensitivity enhancement of nanowire-based surface plasmon resonance biosensors,” J. Opt. Soc. Am. A 23, 2307–2314 (2006). [CrossRef]

], which is consistent with the phenomenologically determined effective permittivity of a metallic grating [36

S. Moon and D. Kim, “Fitting-based determination of an effective medium of a metallic periodic structure and application to photonic crystals,” J. Opt. Soc. Am. A 23, 199–207 (2006). [CrossRef]

]. To the zeroth-order, Eq. (2) becomes at momentum matching

Δ θ_{SP} = \frac{2}{n_{s} \cos θ_{SP}} {(\frac{{ε_{1}}^{'} {ε_{2, eff}}^{'}}{{ε_{1}}^{'} {+ ε_{2, eff}}^{'}})}^{\frac{3}{2}} \frac{{ε_{1}}^{″}}{2 {({ε_{1}}^{'})}^{2}},

(4)

which confirms that the enhancement of LSPR as |ε₁′|~ε_2,eff′ is accompanied by the broadening with cosθ_SP in the denominator of Eq. (4).

Comparison of the resonance at Λ=100 nm and d_NW=20 nm with the one at Λ=50 nm and d_NW=10 nm implies that the impact of depth (d_NW) may be more significant than that of nanowire period (Λ), i.e., deeper nanowires yield larger LSPR enhancement at an identical ratio of Λ/d_NW. This is supported by comparing the resonance of Λ=100 nm and d_NW=10 nm versus Λ=200 nm and d_NW=20 nm. This can be a basis of implementing a highly sensitive LSPR biosensor, since it hints at a possibility of sensitivity enhancement using relatively coarse nanowires so that they can be fabricated based on conventional lithography and simply adjusting the depth for sensitivity control, which is far easier to manipulate than the nanowire period.

Table 1. VF_L+ VF_H for various combinations of d_NW and Λ (a) without a HDT-SAM and (b) with a HDT-SAM. N.A. stands for not available, i.e. neither of VF_L and VF_H exists at Λ=200 nm and d_NW=10 nm.

	Λ=50 nm	Λ=100 nm	Λ=150 nm	Λ=200 nm
d_NW=10 nm	1.001	1.001	1.000	N.A.
d_NW=15 nm	0.992	1.001	1.001	0.999
d_NW=20 nm	0.970	0.993	0.999	1.002
d_NW=25 nm	0.943	0.980	0.987	0.999
(a)

	Λ=50 nm	Λ=100 nm	Λ=150 nm	Λ=200 nm
d_NW=10 nm	1.009	1.009	1.002	N.A.
d_NW=15 nm	0.992	1.000	1.009	1.000
d_NW=20 nm	0.973	0.994	0.995	1.008
d_NW=25 nm	0.947	0.982	0.988	0.994
(b)

Details of the data presented in Fig. 2 are described in Fig. 3. Figure 3(a) presents VF_L and VF_H with d_NW at various periods (Λ) in the absence of binding events. It corroborates eased LSPR enhancement with target binding and reveals quadratic dependence of VF_L and VF_H on d_NW. It is interesting to find that LSPR enhancement occurs approximately at a fixed dimension of nanowires in the sense that VF_L·Λ and VF_H·Λ are almost constant for different Λ, as illustrated in Fig. 3(b), which in fact contrasts VF_L·Λ and (1 - VF_H)·Λ. In addition, LSP excitation in a nanowire and in a nanogroove is highly symmetric such that VF_L+VF_H≈1, as listed in Table 1(a) and (b), respectively for the absence and presence of target binding. While the symmetry suggests fundamental equivalence of the LSP excitation in a grating and in a groove on a nanometer scale, it is apparent that the symmetry starts to break with enhanced LSPR at small Λ and large d_NW. This, in turn, indicates preferentially facilitated LSP excitation through a nanogroove. On the other hand, the impact of target binding on the symmetry is marginal, except that the variance is larger. Note also the variation of the LSPR angle θ_SP at VF_L and VF_H in Fig. 3(c). This shows that LSPR enhancement at small Λ and large d_NW induces momentum matching of LSPs to occur at higher K_SP and stronger LSP excitation associated with a nanogroove, i.e., K_SP(VF_H)>K_SP(VF_L). Overall implication of Fig. 3 and Table 1 is that nanowire structures that produce maximal LSPR enhancement based on single-wire LSP excitation and those of the resonant LSP coupling through a nanogroove are symmetric. Also, the matched LSP momentum is higher in the case of resonant LSP coupling than the case of single nanowire excitation.

Fig. 3. Variations of (a) VF_L and VF_H, (b) VF_L·Λ and (1-VF_H)·Λ, and (c) K_SP(VF=VF_L) and K_SP(VF=VF_H) with respect to d_NW for various nanowire periods (Λ). No binding analytes have been assumed in the calculation.

SEF and MRR for the nanowire structures under consideration have been calculated in Fig. 4. Obviously in Fig. 4(a), maximal sensitivity enhancement is achieved near VF_L and VF_H. A structure with strong LSPR enhancement tends to exhibit high SEF, although the correlation is not 100%. Highest peak SEF appears at Λ=50 nm and reaches 65.11. Also note that the change of LSPR characteristics in response to the target binding gives rise to SEF=0. In other words, a nanowire-based biosensor may not respond to the presence of specific biomolecules in the course of significant LSPR enhancement with VF. Across the zero-sensitivity condition, the sign of the shift reverses, i.e., θ_SP in the presence of target binding shifts to a smaller angle. As shown in Table 2, the VF at which SEF=0 changes negligibly for various target samples of a different refractive index. Namely, a nanowire that incurs SEF=0 is rather fixed regardless of binding events and can thus be easily avoided in the process of optimizing SEF.

Fig. 4. (a) SEF and (b) MRR in the y-axis for various nanowire periods with VF in the x-axis. Red and black solid lines represent the characteristics of a nanowire-based SPR biosensor with and without a HDT SAM as target analytes. For comparison, the dotted line in (b) shows MRR=2.68% of a SPR biosensor without nanowires at d_f=40 nm in the presence of a 1-nm thick HDT-SAM.

MRR shown in Fig. 4(b) measures the energy transfer between incident photons and LSPs through radiative and non-radiative damping processes. Large MRR is associated with the decrease of electron mean free path [17

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, Weinheim, Germany, 1983) Chapter 12.

], which increases the imaginary part of metal permittivity [37

U. Kreibig, “Electronic properties of small silver particles: the optical constants and their temperature dependence,” J. Phys. F 4, 999–1014 (1974). [CrossRef]

]. This results in the increase of the radiation field back-scattered at the metal/air interface through enhanced radiative damping process, such that the incident wave is not compensated by destructive interference [38

H. Raether, Surface Plasmon on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, Germany, 1988) Chapter 2.

, 39

A. A. Maradudin, A. R. McGurn, and E. R. Mendez, “Surface plasmon polariton mechanism for enhanced backscattering of light from one-dimensional randomly rough metal surfaces,” J. Opt. Soc. Am. A 12, 2500–2506 (1995). [CrossRef]

]. The increase of MRR is the most notable near VF=VF_L and VF_H. The MRR patterns shown in Fig. 4(b) represent the degree of radiation damping and its interaction with an incident field by nanowires at various VFs. Total damping determines the width of SPR characteristics, which is inherently attributed to the excitation of and substantial energy redistribution into a large number of LSPR modes, as indicated by Eqs. (2)–(4). Note that LSPs excited in a sphere yields an infinite number of modes [38

H. Raether, Surface Plasmon on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, Germany, 1988) Chapter 2.

]. MRR is thus correlated with the width of SPR characteristics.

Table 2. VF(SEF=0) as a function of nanowire period Λ in the presence of a HDT-SAM. Nanowire depth d_NW is fixed at 25 nm.

	Λ=50 nm		Λ=100 nm		Λ=150 nm		Λ=200 nm
n_SAM=1.33	0.188	0.758	0.104	0.876	0.068	0.921	0.053	0.947
n_SAM=1.4	0.191	0.757	0.104	0.876	0.068	0.920	0.053	0.947
n_SAM=1.45	0.192	0.755	0.104	0.875	0.069	0.920	0.053	0.947
n_SAM=1.52643	0.194	0.755	0.104	0.875	0.069	0.921	0.052	0.947
n_SAM=1.6	0.196	0.753	0.104	0.874	0.070	0.920	0.052	0.946

For practical applications in biosensing, as long as MRR is maintained to be smaller than a reference threshold value, whether it is 0.1% or 0.01% does not make much difference. In Fig. 4(b), the reference is set to be the MRR of a conventional SPR biosensor of d_f=40 nm with a 1-nm thick HDT-SAM (≡MRR_ref), in which case MRR_ref=2.68% shown as a dotted line.

For visualization of fields, the spatial distribution of the electric and magnetic field amplitudes |E_x|, |H_y|, and |E_z| at resonance has been calculated based on FDTD method for a nanowire structure that incurs the most significant LSPR enhancement with d_NW=25 nm and Λ=50 nm, as shown in Fig. 5. The calculation was performed on a conventional thin film based structure (d_f=40 nm), i.e., VF=0, and for nanowire-based structures at VF=VF_L (=0.179), 0.5, and VF_H (=0.764), assuming no SAM on nanowires. For each of |E_x|, |H_y|, and |E_z|, calculated fields have been normalized by the respective maximum value given by 35, 11, and 40. For this reason, fields produced by a thin film without nanowires shown in Fig. 5(a) appear relatively weak. The results confirm that significant field enhancement and coupling between nanowires exists through a nanogroove at VF=VF_H=0.764. This is clearly conveyed in Fig. 5, as the structures at VF=VF_L and VF_H show localized field distribution while fields are less localized at VF=0.5 and completely delocalized for a thin film based structure in Fig. 5(a). In other words, the degree of localization correlates with LSPR enhancement, which is consistent with the trends shown in Fig. 2. Note that the fields, particularly H_y, actually decrease at VF=VF_L, compared with VF=0.5 and VF_H. Small amplitude of H_y relative to the maximum value obtained at VF=VF_H tends to make it less clear in Fig. 5(b) that fields are in fact quite well isolated and thus localized around a single nanowire. The FDTD results, combined with the RCWA data presented in Figs. 2–4, strongly suggest that the field localization introduced by nanowires is intimately connected to the LSPR enhancement and possibly the sensitivity improvement. Also, the intensive localized field enhancement observed in nanogrooves as shown in Fig. 5(d) agrees with the results reported with nanoholes [40

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998). [CrossRef]

Fig. 5. Spatial distribution of the electric and magnetic field amplitude |E_x|, |H_y|, and |E_z| at resonance, calculated by FDTD (a) for a thin film without nanowires (d_f=40 nm), i.e. VF=0, and for a nanowire-based structure with d_NW=25 nm and Λ=50 nm when (b) VF=VF_L (=0.179), (c) VF=0.5, and (d) VF=VF_H (=0.764). Maximum field amplitude for |E_x|, |H_y|, and |E_z| is respectively given by 35, 11, and 40.

4. Discussion

In the previous section, the structural dependence of sensitivity enhancement has been investigated. The understanding lays the basis to design a SPR biosensor of optimized sensitivity. In an earlier study, an optimum nanowire structure was determined based on combinations of various metrics such as the product of VF and resonance contrast [34

]. The results therein indicate the existence of an optimum VF that tends to be either somewhat larger than VF_L or smaller than VF_H. The sensitivity increase obtained for such an optimum structure was found to exceed an order of magnitude. In the current study, we have employed a ratio of SEF to MRR to determine an optimum. In addition, MRR has been modified to be equal to MRR_ref if MRR<MRR_ref. The ratio is a more direct representation for the integrity of SPR characteristics than a measure that employs resonance contrast.

Optimization based on maximizing SEF/MRR gives a structure at VF=0.78 with d_NW=20 nm and Λ=50 nm. Note that the determined VF is in line with the optimum VF (VF=0.8) in Ref. 34 based on a metric using the product of VF and resonance contrast, despite somewhat arbitrary choice of metrics in the optimization process. The consistency emphasizes more effective nanowire-based sensitivity enhancement in nanogroove structures.

Fig. 6. (a) θ_SP of a nanowire-based structure optimized for enhanced sensitivity (VF=0.78, d_NW=20 nm, and Λ=50 nm) as the material index of a SAM (n_SAM) is varied. The slope represents ∂θ_SP/∂n_SAM. (b) SPR characteristics of the structure in comparison with a conventional SPR biosensor without nanowires for a HDT-SAM.

For a structure at VF=0.78, SEF=22.41 and MRR=3.38%. This clearly suggests that a nanowire-based LSPR biosensor achieve sensitivity enhancement by more than an order as the increase of MRR is controlled. The structural impact on the change of analyte refractive index (Δn_SAM) is shown in Fig. 6(a), which compares to that of a conventional SPR structure. Note the ratio of the slopes

\frac{\frac{\partial θ_{SP}}{\partial n_{SAM}} (nanowires)}{\frac{\partial θ_{SP}}{\partial n_{SAM}} (no nanowires)}

is equivalent to a differential quantity of SEF. The result shows the enhancement of ∂θ_SP/∂n_SAM by 23.64 times (=7.29/0.31), while it maintains reasonably good SPR characteristics as shown in Fig. 6(b). The structure also performs excellently in terms of linearity as indicated by the correlation coefficient R²=0.9996, which is better than that of a conventional SPR structure.

Practically, a SAM may not be well formed in the valleys between nanowires in the case of a small period and VF approaching 1. The result in this case is presented in Fig. 6(a). Although the sensitivity enhancement is reduced, ∂θ_SP/∂n_SAM compared with that of a conventional SPR structure increases by 13.33 times (=4.11/0.31) with good linearity (R²=0.9924). In other words, even if valleys of nanowires do not participate in the detection process, sensitivity increment by 13.33 times can be obtained using the optimum structure.

5. Concluding remarks

This work presents a comprehensive optimization analysis whereby one may gain quantitative insights regarding the dependence of sensitivity on structural parameters in a nanowire-based LSPR biosensor. More specifically, we have investigated the impact of nanowire design parameters on LSPR characteristics as well as a few unique features, for instance, structures that would incur zero sensitivity. Nanowires of small period and large depth show strong LSPR enhancement. Also found is that the resonant coupling through a nanogroove induces larger LSPR enhancement than LSP excitation in a single nanowire. An optimum VF is located near VF_H and VF_L. The results strongly indicate the possibility of sensitivity improvement by more than an order of magnitude in comparison with a conventional SPR structure. Although the optimization was performed for a specific target analyte, we believe that the trends of stronger sensitivity enhancement for a nanogroove structure will remain valid for target materials of general interest. While the broadening of SPR characteristics may not be completely avoided, its impact can be suppressed. The difficulty is that in order to excite LSPs through nanowires, extremely fine nanowires should be fabricated with precision to optimally tune both the period and the separation. While we are currently working on the implementation of a nanowire-based LSPR structure using interference lithography, advanced lithographic techniques such as e-beam lithography attain the level of making the required precision possible and sufficient for the extremely sensitive performance of a LSPR biosensor to be reproducible. For high-throughput fabrication of a LSPR biosensor, one may take advantage of molding based nanoimprint technology.

Acknowledgments

This research was sponsored by the KOSEF through National Core Research Center for Nanomedical Technology (R15-2004-024-00000-0). The authors gratefully acknowledge the support from the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) under KRF-2005-205-D00051.

References and links

1.	S. Kubitschko, J. Spinke, T. Brückner, S. Pohl, and N. Oranth, “Sensitivity enhancement of optical immunosensors with nanoparticles,” Anal. Biochem. 253, 112–122 (1997). [CrossRef] [PubMed]
2.	L. A. Lyon, D. J. Pena, and M. J. Natan, “Surface plasmon resonance of Au colloid-modified Au films: Particle size dependence,” J. Phys. Chem. B 103, 5826–5831 (1999). [CrossRef]
3.	L. He, M. D. Musick, S. R. Nicewarner, F. G. Salinas, S. J. Benkovic, M. J. Natan, and C. D. Keating, “Colloidal Au-enhanced surface plasmon resonance for ultrasensitive detection of DNA hybridization,” J. Am. Chem. Soc. 122, 9071–9077 (2000). [CrossRef]
4.	M. D. Malinsky, K. L. Kelly, G. C. Schatz, and R. P. Van Duyne, “Chain length dependence and sensing capabilities of the localized surface plasmon resonance of silver nanoparticles chemically modified with alkanethiol self-assembled monolayers,” J. Am. Chem. Soc. 123, 1471–1482 (2001). [CrossRef]
5.	A. D. McFarland and R. P. Van Duyne, “Single silver nanoparticles as real-time optical sensors with zeptomole sensitivity,” Nano Lett. 3, 1057–1062 (2003). [CrossRef]
6.	Y. Sun and Y. Xia, “Increased sensitivity of surface plasmon resonance of gold nanoshells compared to that of gold solid colloids in response to environmental changes,” Anal. Chem. 74, 5297–5305 (2002). [CrossRef] [PubMed]
7.	E. Hutter and J. H. Fendler, “Exploitation of localized surface plasmon resonance,” Adv. Mater. 16, 1685–1706 (2004). [CrossRef]
8.	K. Aslan, J. R. Lakowicz, and G. D. Geddes, “Plasmon light scattering in biology and medicine: new sensing approaches, vision and perspectives,” Curr. Opin. Chem. Biol. 9, 538–544 (2005). [CrossRef] [PubMed]
9.	B. Sepúlveda, A. Calle, L. Lechuga, and G. Armelles, “Highly sensitive detection of biomolecules with the magneto-optic surface-plasmon-resonance sensor,” Opt. Lett. 31, 1085–1087 (2006). [CrossRef] [PubMed]
10.	S. Y. Wu, H. P. Ho, W. C. Law, C. Lin, and S. K. Kong, “Highly sensitive differential phase-sensitive surface plasmon resonance biosensor based on the Mach-Zehnder configuration,” Opt. Lett. 29, 2378–2380 (2004). [CrossRef] [PubMed]
11.	H. M. Cho, W. Chegal, Y. J. Cho, Y. Kim, and H. Kim, “Enhancement of biomolecular detection sensitivity by surface plasmon resonance ellipsometry,” in Nanosensing: Materials and Devices II, M. S. Islam and A. K. Dutta, eds., Proc. SPIE 6008, 293–298 (2005).
12.	K. M. Byun, S. J. Kim, and D. Kim, “Design study of highly sensitive nanowire-enhanced surface plasmon resonance biosensors using rigorous coupled wave analysis,” Opt. Express 13, 3737–3742 (2005). [CrossRef] [PubMed]
13.	W-C. Liu, “High sensitivity of surface plasmon of weakly-distorted metallic surfaces,” Opt. Express 13, 9766–9773 (2005). [CrossRef] [PubMed]
14.	W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003). [CrossRef] [PubMed]
15.	D. Crouse and P. Keshavareddy, “Role of optical and surface plasmon modes in enhanced transmission and applications,” Opt. Express 13, 7760–7771 (2005). [CrossRef] [PubMed]
16.	K. M. Byun, D. Kim, and S. J. Kim, “Investigation of the profile effect on the sensitivity enhancement of nanowire-mediated localized surface plasmon resonance biosensors,” Sens. Actuators B 117, 401–407 (2006). [CrossRef]
17.	C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, Weinheim, Germany, 1983) Chapter 12.
18.	L. Genzel, T. P. Martin, and U. Kreibig, “Dielectric function and plasma resonances of small metal particles,” Z. Physik B21, 339–346 (1975).
19.	L. A. Lyon, M. D. Musick, and M. J. Natan, “Colloidal Au-enhanced surface plasmon resonance immunosensing,” Anal. Chem. 70, 5177–5183 (1998). [CrossRef] [PubMed]
20.	S.-J. Chen, F. C. Chien, G. Y. Lin, and K. C. Lee, “Enhancement of the resolution of surface plasmon resonance biosensors by control of the size and distribution of nanoparticles,” Opt. Lett. 29, 1390–1392 (2004). [CrossRef] [PubMed]
21.	Z. Salamon, G. Lindblom, L. Rilfors, K. Linde, and G. Tollin, “Interaction of phosphatidylserine synthase from E. coli with lipid bilayers: coupled plasmon-waveguide resonance spectroscopy studies,” Biophys. J. 78, 1400–1412 (2000). [CrossRef] [PubMed]
22.	M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of metallic surface-relief gratings,” J. Opt. Soc. Am. A 3, 1780–1787 (1986). [CrossRef]
23.	Y. Kanamori, K. Hane, H. Sai, and H. Yugami, “100 nm period silicon antireflection structures fabricated using a porous alumina membrane mask,” Appl. Phys. 78, 142–143 (2001).
24.	T. R. Jensen, L. Kelley, A. Lazarides, and G. C. Schatz, “Electrodynamics of noble metal nanoparticles and nanoparticle clusters,” J. Cluster Sci. 10, 295–317 (1999). [CrossRef]
25.	J. Cesario, R. Quidant, G. Badenes, and S. Enoch, “Electromagnetic coupling between a metal nanoparticles grating and a metallic surface,” Opt. Lett. 30, 3404–3406 (2005). [CrossRef]
26.	J. Lermé, “Introduction of quantum finite-size effects in the Mie’s theory for a multilayered metal sphere in the dipolar approximation: application to free and matrix-embedded noble metal clusters,” Eur. Phys. J. D 10, 265–277 (2000). [CrossRef]
27.	E. Moreno, D. Erni, C. Hafner, and R. Vahldieck, “Multiple multipole method with automatic multipole setting applied to the simulation of surface plasmons in metallic nanostructures” J. Opt. Soc. Am. A 19, 101–111 (2002). [CrossRef]
28.	E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, Orlando, FL, U. S. A., 1985).
29.	P. Liu, EM Explorer , http://www.emexplorer.net.
30.	E. Hutter, S. Cha, J-F. Liu, J. Park, J. Yi, J. H. Fendler, and D. Roy, “Role of substrate metal in gold nanoparticle enhanced surface plasmon resonance imaging,” J. Phys. Chem. B 105, 8–12 (2001). [CrossRef]
31.	I. Pockrand and H. Raether, “Surface plasma oscillations in silver films with wavy surface profiles: a quantitative experimental study,” Opt. Commun. 18, 395–399 (1976). [CrossRef]
32.	H. Raether, “Dispersion relation of surface plasmons on gold- and silver gratings,” Opt. Commun. 42, 217–222 (1982). [CrossRef]
33.	K. M. Byun, S. J. Kim, and D. Kim, “Profile effect on the feasibility of extinction-based localized surface plasmon resonance biosensors with metallic nanowires,” Appl. Opt. 45, 3382–3389 (2006). [CrossRef] [PubMed]
34.	D. Kim, “Effect of resonant localized plasmon coupling on the sensitivity enhancement of nanowire-based surface plasmon resonance biosensors,” J. Opt. Soc. Am. A 23, 2307–2314 (2006). [CrossRef]
35.	R. Bruns and H. Raether, “Plasma resonance radiation from non-radiative plasmons,” Z. Physik 237, 98–106 (1970). [CrossRef]
36.	S. Moon and D. Kim, “Fitting-based determination of an effective medium of a metallic periodic structure and application to photonic crystals,” J. Opt. Soc. Am. A 23, 199–207 (2006). [CrossRef]
37.	U. Kreibig, “Electronic properties of small silver particles: the optical constants and their temperature dependence,” J. Phys. F 4, 999–1014 (1974). [CrossRef]
38.	H. Raether, Surface Plasmon on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, Germany, 1988) Chapter 2.
39.	A. A. Maradudin, A. R. McGurn, and E. R. Mendez, “Surface plasmon polariton mechanism for enhanced backscattering of light from one-dimensional randomly rough metal surfaces,” J. Opt. Soc. Am. A 12, 2500–2506 (1995). [CrossRef]
40.	T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998). [CrossRef]

OCIS Codes
(050.2770) Diffraction and gratings : Gratings
(130.6010) Integrated optics : Sensors
(240.0310) Optics at surfaces : Thin films
(240.6680) Optics at surfaces : Surface plasmons

ToC Category:
Optics at Surfaces

History
Original Manuscript: August 14, 2006
Revised Manuscript: October 30, 2006
Manuscript Accepted: November 28, 2006
Published: December 11, 2006

Virtual Issues
Vol. 2, Iss. 1 Virtual Journal for Biomedical Optics

Citation
Kyujung Kim, Soon J. Yoon, and Donghyun Kim, "Nanowire-based enhancement of localized surface plasmon resonance for highly sensitive detection: a theoretical study," Opt. Express 14, 12419-12431 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-25-12419

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References

S. Kubitschko, J. Spinke, T. Brückner, S. Pohl, and N. Oranth, "Sensitivity enhancement of optical immunosensors with nanoparticles," Anal. Biochem. 253, 112-122 (1997). [CrossRef] [PubMed]
L. A. Lyon, D. J. Pena, and M. J. Natan, "Surface plasmon resonance of Au colloid-modified Au films: Particle size dependence," J. Phys. Chem. B 103, 5826-5831 (1999). [CrossRef]
L. He, M. D. Musick, S. R. Nicewarner, F. G. Salinas, S. J. Benkovic, M. J. Natan, and C. D. Keating, "Colloidal Au-enhanced surface plasmon resonance for ultrasensitive detection of DNA hybridization," J. Am. Chem. Soc. 122, 9071-9077 (2000). [CrossRef]
M. D. Malinsky, K. L. Kelly, G. C. Schatz, and R. P. Van Duyne, "Chain length dependence and sensing capabilities of the localized surface plasmon resonance of silver nanoparticles chemically modified with alkanethiol self-assembled monolayers," J. Am. Chem. Soc. 123, 1471-1482 (2001). [CrossRef]
A. D. McFarland and R. P. Van Duyne, "Single silver nanoparticles as real-time optical sensors with zeptomole sensitivity," Nano Lett. 3, 1057-1062 (2003). [CrossRef]
Y. Sun and Y. Xia, "Increased sensitivity of surface plasmon resonance of gold nanoshells compared to that of gold solid colloids in response to environmental changes," Anal. Chem. 74, 5297-5305 (2002). [CrossRef] [PubMed]
E. Hutter and J. H. Fendler, "Exploitation of localized surface plasmon resonance," Adv. Mater. 16, 1685-1706 (2004). [CrossRef]
K. Aslan, J. R. Lakowicz, and G. D. Geddes, "Plasmon light scattering in biology and medicine: new sensing approaches, vision and perspectives," Curr. Opin. Chem. Biol. 9, 538-544 (2005). [CrossRef] [PubMed]
B. Sepúlveda, A. Calle, L. Lechuga, and G. Armelles, "Highly sensitive detection of biomolecules with the magneto-optic surface-plasmon-resonance sensor," Opt. Lett. 31, 1085-1087 (2006). [CrossRef] [PubMed]
S. Y. Wu, H. P. Ho, W. C. Law, C. Lin, and S. K. Kong, "Highly sensitive differential phase-sensitive surface plasmon resonance biosensor based on the Mach-Zehnder configuration," Opt. Lett. 29, 2378-2380 (2004). [CrossRef] [PubMed]
H. M. Cho, W. Chegal, Y. J. Cho, Y. Kim, and H. Kim, "Enhancement of biomolecular detection sensitivity by surface plasmon resonance ellipsometry," Proc. SPIE 6008, 293-298 (2005).
K. M. Byun, S. J. Kim, and D. Kim, "Design study of highly sensitive nanowire-enhanced surface plasmon resonance biosensors using rigorous coupled wave analysis," Opt. Express 13, 3737-3742 (2005). [CrossRef] [PubMed]
W-C. Liu, "High sensitivity of surface plasmon of weakly-distorted metallic surfaces," Opt. Express 13, 9766-9773 (2005). [CrossRef] [PubMed]
W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003). [CrossRef] [PubMed]
D. Crouse and P. Keshavareddy, "Role of optical and surface plasmon modes in enhanced transmission and applications," Opt. Express 13, 7760-7771 (2005). [CrossRef] [PubMed]
K. M. Byun, D. Kim, and S. J. Kim, "Investigation of the profile effect on the sensitivity enhancement of nanowire-mediated localized surface plasmon resonance biosensors," Sens. Actuators B 117, 401-407 (2006). [CrossRef]
C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-VCH, Weinheim, Germany, 1983) Chap. 12.
L. Genzel, T. P. Martin, and U. Kreibig, "Dielectric function and plasma resonances of small metal particles," Z. Physik B21, 339-346 (1975).
L. A. Lyon, M. D. Musick, and M. J. Natan, "Colloidal Au-enhanced surface plasmon resonance immunosensing," Anal. Chem. 70, 5177-5183 (1998). [CrossRef] [PubMed]
S.-J. Chen, F. C. Chien, G. Y. Lin, and K. C. Lee, "Enhancement of the resolution of surface plasmon resonance biosensors by control of the size and distribution of nanoparticles," Opt. Lett. 29, 1390-1392 (2004). [CrossRef] [PubMed]
Z. Salamon, G. Lindblom, L. Rilfors, K. Linde, and G. Tollin, "Interaction of phosphatidylserine synthase from E. coli with lipid bilayers: coupled plasmon-waveguide resonance spectroscopy studies," Biophys. J. 78, 1400-1412 (2000). [CrossRef] [PubMed]
M. G. Moharam and T. K. Gaylord, "Rigorous coupled-wave analysis of metallic surface-relief gratings," J. Opt. Soc. Am. A 3, 1780-1787 (1986). [CrossRef]
Y. Kanamori, K. Hane, H. Sai, and H. Yugami, "100 nm period silicon antireflection structures fabricated using a porous alumina membrane mask," Appl. Phys. 78, 142-143 (2001).
T. R. Jensen, L. Kelley, A. Lazarides, and G. C. Schatz, "Electrodynamics of noble metal nanoparticles and nanoparticle clusters," J. Cluster Sci. 10, 295-317 (1999). [CrossRef]
J. Cesario, R. Quidant, G. Badenes, and S. Enoch, "Electromagnetic coupling between a metal nanoparticles grating and a metallic surface," Opt. Lett. 30, 3404-3406 (2005). [CrossRef]
J. Lermé, "Introduction of quantum finite-size effects in the Mie’s theory for a multilayered metal sphere in the dipolar approximation: application to free and matrix-embedded noble metal clusters," Eur. Phys. J. D 10, 265-277 (2000). [CrossRef]
E. Moreno, D. Erni, C. Hafner, and R. Vahldieck, "Multiple multipole method with automatic multipole setting applied to the simulation of surface plasmons in metallic nanostructures" J. Opt. Soc. Am. A 19, 101-111 (2002). [CrossRef]
E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, Orlando, FL, U. S. A., 1985).
P. Liu, EM Explorer, http://www.emexplorer.net.
E. Hutter, S. Cha, J-F. Liu, J. Park, J. Yi, J. H. Fendler, and D. Roy, "Role of substrate metal in gold nanoparticle enhanced surface plasmon resonance imaging," J. Phys. Chem. B 105, 8-12 (2001). [CrossRef]
I. Pockrand and H. Raether, "Surface plasma oscillations in silver films with wavy surface profiles: a quantitative experimental study," Opt. Commun. 18, 395-399 (1976). [CrossRef]
H. Raether, "Dispersion relation of surface plasmons on gold- and silver gratings," Opt. Commun. 42, 217-222 (1982). [CrossRef]
K. M. Byun, S. J. Kim, and D. Kim, "Profile effect on the feasibility of extinction-based localized surface plasmon resonance biosensors with metallic nanowires," Appl. Opt. 45, 3382-3389 (2006). [CrossRef] [PubMed]
D. Kim, "Effect of resonant localized plasmon coupling on the sensitivity enhancement of nanowire-based surface plasmon resonance biosensors," J. Opt. Soc. Am. A 23, 2307-2314 (2006). [CrossRef]
R. Bruns and H. Raether, "Plasma resonance radiation from non-radiative plasmons," Z. Physik 237, 98-106 (1970). [CrossRef]
S. Moon and D. Kim, "Fitting-based determination of an effective medium of a metallic periodic structure and application to photonic crystals," J. Opt. Soc. Am. A 23, 199-207 (2006). [CrossRef]
U. Kreibig, "Electronic properties of small silver particles: the optical constants and their temperature dependence," J. Phys. F Met. Phys. 4, 999-1014 (1974). [CrossRef]
H. Raether, Surface Plasmon on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, Berlin, Germany, 1988) Chap. 2.
A. A. Maradudin, A. R. McGurn, and E. R. Mendez, "Surface plasmon polariton mechanism for enhanced backscattering of light from one-dimensional randomly rough metal surfaces," J. Opt. Soc. Am. A 12, 2500-2506 (1995). [CrossRef]
T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998). [CrossRef]

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