## Abstract

The adsorption of a self-assembled monolayer of molecules on a metal surface commonly causes a red-shift in its surface plasmon resonance. We report that the anomalous dispersion of surface plasmons in a Au nanoslit array structure can cause a blue-shift of optical transmission upon adsorption of a non-absorbing self-assembled monolayer of molecules. We develop a simple model that explains the blue-shift observed in the transmission spectra with monolayer adsorption in terms of the interplay of anomalous dispersion and the cavity resonance of surface plasmons in the nanoslit array.

©2009 Optical Society of America

## 1. Introduction

Anomalous dispersion (d*n*/d*ω* < 0) of light in dispersive media has drawn particular interest because it causes a number of counter-intuitive phenomena [1,2]. The group velocity ($v{}_{g}=c/[n+\omega (dn/d\omega )]$) of a light pulse, for example, can exceed the speed of light or even be negative if the dispersion is sufficiently steep ($\omega \left|dn/d\omega \right|>n$). Anomalous dispersion usually implies strong absorption of light (evident from the Kramers-Kronig relations), and the opacity of conventional passive media renders the study of such phenomena difficult. By contrast, an atomic resonance can display a steep dispersion even with modest absorption, providing a ‘transparent’ anomalous dispersive medium over narrow frequency ranges. Since the first observation of superluminal propagation based on excitonic absorption in a solid-state medium, most experiments have exploited atomic gaseous media involving gain doublets or electromagnetically induced absorption [3–6].

Surface plasmons (SPs) offer an interesting avenue for studying phenomena that involve anomalous dispersion in the optical frequency range. An example of particular interest is organic monolayer assemblies containing dye molecules [7–10]. The coupling of excitonic states of dye molecules to the surface plasmons is known to cause an anomalous dispersion of the surface-bound waves. While the anomalous dispersion originates from the dye layer’s resonant absorption, we also note that the surface plasmons on a planar interface without any adsorbed layer (i.e., SPs on the metal/air interface) show an anomalous behavior around its intrinsic resonance wavelength. In contrast to these conventional assemblies, this work studies the interaction of light with a metal nanoslit structure that can excite plasmon waves traveling on the metal surface, for which the dispersion can accumulate throughout the propagation.^{11,12} Because surface plasmons can decouple into free-space radiation via nanoscale features on the metal surface, these near-field phenomena of the metal surface can affect the far-field radiation. In addition, the SPs’ dispersion characteristic is affected by altering the dielectric environment near the interface [7–14]. This serves as an important basis for surface plasmon resonance (SPR) spectroscopy, which is commonly used in sensing and monitoring molecular adsorption on a metal surface.

This study investigates how the transmission spectra of nanostructured metal films depend on the interactions of surface plasmons in a dispersive resonant-cavity structure. In these structures (see Fig. 1 ), the surface of individual metal stripes of a nanoslit array is treated as a cavity and the metal stripes periphery is used to define the cavity length, hence the resonance condition. In this work the surface plasmon dispersion characteristics are altered by use of thin dielectric layers that do not have resonant absorption bands in the spectral range of interest but modify the dispersion characteristics of the cavity such that a net negative dispersion occurs in the wavelength range of the cavity resonance. Two different dielectric materials are used for this purpose: 1) a high-index dielectric layer (amorphous Si; ~10 nm thickness) that is used to shift the anomalous dispersion regime to a desired spectral range and to reduce the attenuation loss in the SP resonance band, and 2) a monolayer organic film (thiol-based self-assembled monolayer; ~1.5 nm thickness) that is designed to alter the effective index of surface plasmons without modifying the dispersion profile. The latter material would correspond to an analyte layer when the array operates as a sensor. In this work, we show that the interplay of anomalous dispersion and cavity resonance can cause a blue-shift of the optical transmission with adsorption of a non-absorbing monolayer on the array surface.

The manuscript is structured as follows. First we show that the transmission peak through a nanoslit array corresponds to the quadrupolar resonance of surface plasmons on the periphery of an individual metal stripe. Using this insight, a simple model is developed to predict the wavelength shift and its sign. Next we use this model to predict how a high-index, thin dielectric layer between the metal and substrate can alter the surface-plasmon dispersion characteristic and we compare these predictions with experiments.

Being a surface-bound wave at a metal/dielectric interface, a surface plasmon’s dispersion characteristics are governed by the dielectric response of both the metal and the dielectric *ε _{d}*. The dielectric response of noble metals ${\epsilon}_{m}(\omega )$ in the optical frequency range are mainly determined by two types of transitions, one within the conduction band (as described by the Drude model of free electrons) and the other involving interband transitions (bound-electron contributions, modeled with Lorentzian oscillators) [15,16].

*ω*and

_{pe}*γ*are the characteristic frequency and damping rate for the Drude electron response and

_{e}*ω*and

_{pj}*γ*are the frequency and damping rate for the transition

_{j}*j*. The thresholds for direct excitation of

*d*-band electrons to the conduction band are in the UV/visible range (3.9, 2.4, or 2.1 eV for Ag, Au, or Cu, respectively). The interband transitions have a major influence on plasmon energies, shifting the volume (bulk) plasmon frequency (

*ω*) from 9 eV - 12 eV (the value estimated from the free-electron only model) to 2 eV - 4 eV range (close to the

_{p}*d*-band transition energies). For a metal of finite extent and juxtaposed with a dielectric, another type of plasmon, called a surface plasmon, can be supported at the metal/dielectric interface. Surface plasmons are a divergence-free ($\nabla \cdot D=0$) transverse electromagnetic mode associated with charge density oscillations at the interface. The resonance condition of this surface-bound wave is sensitive to the size and geometry of the metal and its surrounding dielectric. In the case of a planar metal/dielectric interface, SPs experience a medium with an effective dielectric constant,${\epsilon}_{m}{\epsilon}_{d}/({\epsilon}_{m}+{\epsilon}_{d})$, and the surface plasmon resonance frequency

*ω*is determined from the condition, ${\epsilon}_{m}({\omega}_{sp})+{\epsilon}_{d}({\omega}_{sp})=0$ [15]. The presence of the dielectric material causes the SP resonance frequency (

_{sp}*ω*) to be red-shifted from that of the bulk plasmon frequency (

_{sp}*ω*). In general,

_{p}*ε*is a complex quantity and a resonance feature is observed at the frequency where$|{\epsilon}_{m}(\omega )+{\epsilon}_{d}(\omega )|$displays a minimum. The SP resonance gives rise to anomalous dispersion and an accompanying strong absorption, a characteristic signature that can be predicted from the Lorentz oscillator model associated with the interband transitions [Eq. (1)]. This work considers how the SP dispersion characteristic is modified by introducing a high-index, thin dielectric layer between the metal and substrate; the findings show that the attenuation loss is significantly reduced (for longer interaction lengths on the metal surface) and the anomalous dispersion regime is broadened and shifted to longer wavelength.

_{m}## 2. Cavity resonance of surface plasmons in a metal nanoslit array structure

Consider a single, rectangular metallic stripe (of length L and thickness H) within a larger grating structure, that is, a nanoslit array structure (Fig. 1). From the perspective of a surface plasmon wave propagating on the metal surface, sharp discontinuities exist at the corners of the rectangular stripe and they can form the fixed points of standing waves. For example, one could envision a standing wave associated with just the top (or bottom) face of the metal and having zeroes for the charge displacement at the corners. Assuming narrow slits (i.e., L ~grating period), a resonance condition can be derived for such a mode, namely

where*λ*

_{0}is the wavelength of the incident light,

*N*

_{top(bottom}_{)}is the effective index, and

*m*is an integer [17–19]. By approximating the top (bottom) face as an isolated, single interface, we can write the effective index as

*m*, or equivalently when the following phase matching condition is met,The quantity

*N*is the effective index of surface plasmons in the slit region, and it can be calculated from the dispersion relation of a slit waveguide structure [20]. It has been proposed that a quadrupolar (

_{slit}*m*= 2) resonant mode occurs at the peak transmission of light in this type of slit array structure [12]. We note that the phase accumulation over SP propagation on a metal surface plays an essential role for the resonance condition, and this fact is distinctly different from the conventional localized-SP-resonance case; the latter occurs in the quasi-static regime, for which the physical size of metal islands (or particles) is significantly smaller than the wavelength and therefore the phase retardation effect across the island is negligible [15,21].

In order to verify the resonant interaction of surface plasmons with individual metal stripes, we have fabricated a Ag nanoslit array structure whose slit number varies from 1 to 10 [Fig. 2(a) ]. First a 100-nm-thick Ag layer was deposited on a fused silica substrate by thermal evaporation of Ag. Single nanoslit and 2-to-10-slit arrays (90-nm slit width and 500 μm length) were formed in the Ag layer using a focused-ion-beam etching technique (Seiko SMI-3050-SE dual beam system: 30-keV Ga ion beam; 10-pA beam current). The typical etch depth for the nanoslits was 200 nm. The grating period of 2-to-10-slit arrays was 450 nm. The optical transmission through the slit arrays was measured in the spectral range of 350 ~1750 nm. A beam from a multimode fiber (core diameter of 62.5 μm and a numerical aperture of 0.20) that was connected to an unpolarized white light source (Ando AQ-4303B) was normally incident to a slit array from the silica substrate side. The zero-order transmission through a slit array was collected with another multimode fiber placed close to the Ag layer surface (< 1 μm gap), and was characterized with an optical spectrum analyzer (Ando AQ-6315A) [Fig. 2(b)]. The measured optical transmission spectra clearly reveal a passband in the visible range for the case of arrays with two or more slits, whereas the single slit structure does not show any such peak profile [Fig. 2(c)]. Since a metal stripe is physically defined by two slits, the distinctly different transmission spectra from the single slit versus two- or more-slit arrays can be understood to arise from the SP resonance localized on an individual stripe.

The sharpening of the transmission with the number of slits results from the interaction between the metal islands and the period of the slit structure, analogous to that observed for annular aperture arrays [22]. The peak transmission occurs at fixed wavelength (620-640 nm), independent of the number of slits (for 2 or greater). The measured peak position shows good agreement with the resonant wavelength (~610 nm) estimated from the quadrupolar resonance condition [*m* = 2 in Eq. (4)]. Here *N _{top}* and

*N*are calculated to 1.04 and 1.59, respectively, referring to Eq. (3).

_{bottom}*N*is estimated to be 1.35 from Ref [23]. In this calculation, the following values are used:

_{slit}*ε*= −13.3 +

_{Ag}*i*0.2 and

*ε*= 2.1 at 600 nm wavelength [24],

_{SiO2}*L*= 360 nm, and

*t*= 100 nm.

In order to substantiate the correspondence of quadrupolar resonance and peak transmission, a finite-difference time-domain (FDTD) calculation was performed for the nanoslit array structure. Figure 3 shows the SP polarization charge distribution calculated at the peak transmission wavelength. The calculation was performed in a 2 μm x 3 μm region centered on the double-slit (divided up into a mesh with a 2.5-nm square grid spacing), with absorbing perfectly-matched-layer (PML) boundary conditions [25]. A 650-nm wavelength plane wave was excited at the top– the ‘air’/metal interface and propagated through the slits and the silica substrate. After roughly twice the time required for the wave to propagate across the metal stripe of thickness H the polarization charge distribution on the double slit appeared to be in steady state – oscillating with a roughly quadrupolar distribution, as shown. The SP polarization’s charge distribution that is obtained by a finite-difference time-domain (FDTD) calculation for this peak transmission wavelength clearly confirms the quadrupolar nature of the resonance (see Fig. 3). It is interesting to note that the antinodes of the SP charge distribution are located around the slit corners for both the entrance and the exit sides of the structure. The dipolar nature of the resonance’s charge displacement on each side of the metal island likely facilitates both the SP excitation (at the entrance side) and decoupling into free-space radiation (at the exit side). This SP distribution enables maximum transmission of incident light through the nanoslit.

## 3. A model of surface plasmon dispersion and resonance blue-shift

Here we develop a simple model to account for the shift in the resonance wavelength of a metal slit array with a change in the ambient’s dielectric constant. Suppose that a transmission peak of a grating structure is caused by a particular SP resonance and consider the wavelength shift δ*λ*
_{0} that is caused by a small modification of the metal surface, such as adding a self-assembled monolayer (SAM) whose dielectric constant is different from the ambient dielectric on the top surface and/or slit wall surface of the metal islands [26]. To account for the wavelength dependence, *λ*
_{0}, of the metal’s dielectric constant and the dependence on the ambient’s dielectric constant, *ε _{d}*, we write the effective index as a function of

*λ*

_{0}and

*ε*:

_{d}*N*(

*λ*

_{0},

*ε*). A simple variational analysis on Eq. (4) yields:

_{d}*m*= 2), the following expression is obtained for the wavelength shift:

*β*$(=2\pi N\left({\lambda}_{0},{\epsilon}_{d}\right)/{\lambda}_{0})$ rather than the effective index to obtain

*m*= 2 in Eq. (4)]. The eigenvalue equation for SPs in the slit region is also used to find exact expressions for the partial derivatives in Eqs. (6) and (7) [20].

The wavelength shift in Eqs. (6) and (7) can be either positive or negative. If dispersion effects are ignored, the denominator in Eq. (6) becomes unity and we obtain the approximate relation, $\delta {\lambda}_{0}\approx \genfrac{}{}{0.1ex}{}{1}{2}\left(\genfrac{}{}{0.1ex}{}{\partial {N}_{top}}{\partial {\epsilon}_{d,top}^{}}\right)L\cdot \delta {\epsilon}_{d,top}^{}+\left(\genfrac{}{}{0.1ex}{}{\partial {N}_{slit}}{\partial {\epsilon}_{d,slit}^{}}\right)H\cdot \delta {\epsilon}_{d,slit}^{}$. In this limit, the total peak shift should be positive (i.e., a red-shift occurs) after adsorption of a SAM layer. This red-shift arises because the derivative of the effective index with respect to the dielectric constant on the insulator side ($\partial N/\partial {\epsilon}_{d}$) is positive, and the effective change in the dielectric constant on the insulator side ($\delta {\epsilon}_{d}$) is also positive, assuming that the dielectric constant of the adsorbed SAM layer is higher than that of the ambient (e.g., air). In the case that all surfaces have normal dispersion ($\partial N/\partial {\lambda}_{0}<0$), Eq. (6) still predicts a red-shift. If some surface regions show anomalous dispersion ($\partial N/\partial {\lambda}_{0}>0$) and those sections are sufficiently long, then the accumulation of the anomalous dispersion can dominate over the normal dispersion terms so that the denominator of Eq. (6) becomes negative. The consequence would be a blue-shift that results from the surface modification. From Eq. (7) the requirements for a blue-shift translate into the condition that some surfaces show $\genfrac{}{}{0.1ex}{}{\partial \beta}{\partial {\lambda}_{0}}=\genfrac{}{}{0.1ex}{}{2\pi}{{\lambda}_{0}}\left(\genfrac{}{}{0.1ex}{}{\partial N}{\partial {\lambda}_{0}}-\genfrac{}{}{0.1ex}{}{N}{{\lambda}_{0}}\right)>0$, that is, anomalous dispersion of at least *N*/*λ*
_{0} and a sufficient accumulation of phase. It is important to note that the cumulative nature of SP dispersion is intrinsic to the distributed resonant cavity structure studied here, and it enables one to observe dispersive behaviors even in the case of reasonably weak dispersive media.

The dispersion characteristics of SPs on a resonant structure like that defined in Fig. 1 were further examined by the use of Eq. (7) for the peak shift. The real and imaginary parts of the SP propagation constant and the relevant first-derivatives are plotted in Fig. 4
for some different metal/dielectric interfaces: Ag or Au films in contact with air, SiO_{2} or Si. Here the dielectric constant versus frequency data were taken from Ref [24]. The SP resonance of the Ag/air interface occurs in the UV range, whereas the Au/SiO_{2} interface and the Au/air slit show a resonance in the middle of the visible range (~510 nm) [Fig. 4(a)]. Compared to the Ag case, the Au/air and Au/SiO_{2} interfaces show a much reduced resonance. When juxtaposed with a high-dielectric-constant material (Si), however, the Au shows a dramatically enhanced resonance occurring at a significantly red-shifted location (~730 nm). This major change in dispersion characteristic is ascribed to the fact that the Au dielectric function has a relatively large imaginary part compared to its real part at around 500 nm, and this fact significantly changes in the longer wavelength region (*ε _{Au}*: −4.1 +

*i*2.6 at 510 nm and −18.9 +

*i*1.4 at 730 nm).

^{22}In a narrow band around the SP resonance, the derivative of the propagation constant with respect to the free-space wavelength ($\partial \beta /\partial {\lambda}_{0}$) becomes positive and shows peak values of 1.8x10

^{−3}nm

^{−2}for Ag/SiO

_{2}, 1x10

^{−4}nm

^{−2}for Au/SiO

_{2}, and 1.5x10

^{−3}nm

^{−2}for the Au/Si interface [Fig. 4(c)].

The derivative displays a much smaller negative value on the longer wavelength side of the band. The derivative of the propagation constant with respect to the ambient dielectric constant ($\partial \beta /\partial {\epsilon}_{d}$) is positive for both the Au and Ag cases [Fig. 4(d)].

Overall this analysis shows that the metal nanoslit array on a high-index substrate is a promising structure for observing a blue-shift of optical transmission in the visible/near-infrared spectral range, because the strong negative dispersion on the high-index metal/dielectric interface dominates over the positive dispersion on the metal/air interface. Here it should be noted that the above discussion assumes a lossless system, *i.e.,* dielectric functions that are purely real [all *γ*-terms in Eq. (1) are zero]. Under this assumption, the SP resonant peak would be infinitely sharp, and the spectral shift (red or blue) as predicted by Eq. (6) would show a singular behavior as the denominator approaches zero. In a system with loss, the resonance profile becomes less sharp, and the amount of peak shift remains finite.

Figure 4 shows that the Au/Si substrate exhibits a pronounced resonance in the visible wavelength region (500 – 800 nm). While the strong dispersion can easily satisfy the requirement for a blue-shift, it also incurs strong attenuation of the surface plasmon propagation. The imaginary part of the propagation constant at the Au/Si interface shows a peak value of 0.06 nm^{−1}, which corresponds to a propagation depth of ~17 nm [Fig. 4(b)]. Considering the dimension of the metal island (~200 nm), the lossy SPs on the island periphery are not expected to display a clear resonance. To achieve a reasonably-strong negative dispersion yet manage the loss, the Au grating structure was modified by placing a thin layer of amorphous silicon between the Au and silica substrate. Figure 5
shows the wavelength dependence of the propagation constant (both the real and imaginary parts) over a range of Si film thickness (0-40 nm). Consider the case of a Au grating on a 10-nm-thick Si layer that is deposited on a silica substrate. It is apparent from Figs. 4 and 5 that the dispersion associated with the substrate-side of the interface will dominate over that on the air side.

While the Au/SiO_{2} and Au/Si exhibit anomalous dispersion only in a narrow spectral region around 500 nm and 700 nm, respectively, the effect of introducing a “composite” substrate acts to spread the anomalous dispersion over a much broader wavelength range. For example, a 10-nm-thick Si film gives a positive slope of the propagation constant from roughly 520 nm to 680 nm [Fig. 5(a): green curve], thereby enhancing the range of wavelengths over which a blue-shift can occur.

Another important benefit of using this composite substrate is that the imaginary part of the SP propagation constant is now reduced to about 0.01 nm^{−1} [Fig. 5(b): green curve], giving rise to a 100-nm propagation length. The observed dispersion-modification is mainly ascribed to the dielectric nature of the thin amorphous Si layer; its dielectric function does not exhibit any resonance absorption band in this spectral range, and its high-index low-loss nature (e.g., 17.3 + *i*3.0 at 650 nm) is maintained. Rather, the thin layer dielectric shifts the SP resonance point (anomalous dispersion regime) to longer wavelength, according to the SP resonance condition discussed above, that is, at resonance$|{\epsilon}_{m}(\omega )+{\epsilon}_{d}(\omega )|$displays a minimum.

## 4. Blue-shift of optical transmission upon adsorption of a self-assembled monolayer of molecules on a Au nanoslit array

Figure 6
shows the optical transmission spectra measured before and after a SAM layer (1.5-nm-thick alkanethiol film) treatment of the Ag or Au nanoslit array samples that were formed with various different substrate materials and structures: Ag/SiO_{2}, Au/SiO_{2}, Au/Ag(10-nm)/SiO_{2}, and Au/Si(10-nm)/SiO_{2}. For fabrication of large-number-slit arrays an electron beam lithography technique (JEOL 9300) was utilized in defining the one-dimensional grating patterns in an e-beam resist (PMMA) layer that is coated on Cr-deposited (30 nm thickness) fused silica substrates.

A two-step plasma etching process was performed in order to transfer the e-beam-resist grating patterns onto the Cr layer and then onto fused silica using the Cr layer as an etch mask. The typical etch depth onto fused silica was 350 nm. A metal (Ag or Au) layer was angle-deposited on the mesa surface with thermal evaporation. Prior to this metal layer deposition, an amorphous silicon layer that goes in between the metal and substrate was deposited by radio-frequency magnetron sputtering of a silicon target. The Ag sample reveals a strong red-shift (20 - 30 nm) over the entire spectral range tested (550 - 850 nm) [Fig. 6(a)].

This red-shift is expected, because the Ag surfaces (both the air and SiO_{2} sides) show only normal dispersion in this spectral range (Fig. 4). The Au/SiO_{2} sample shows a tendency to blue-shift, but not that strong [Fig. 6(b)]. This slight blue-shift is ascribed to the relatively-weak negative dispersion at the substrate-side interface with Au. The mild, negative dispersion of Au/SiO_{2} is clearly confirmed when a thin (10-nm thick) Ag layer is introduced in between the Au and the SiO_{2} substrate. The SP fields on the metal side are now mostly confined to the Ag layer, and therefore the dispersion on the bottom surface is mainly determined by the Ag/SiO_{2} characteristic. Thus the overall dispersion is governed by contributions from the Au/air and Ag/SiO_{2}, which cancel each other [Fig. 6(c)]. When the Ag is replaced with a thin layer (10-nm thickness) of Si, a clear blue-shift (~15 nm) is observed at around 600 - 700 nm [Fig. 6(d)]. This reversal of spectral shift clearly confirms the negative dispersion of surface plasmons at the Au/Si/SiO_{2} interface and their crucial role in the quadrupolar resonance along the metal stripe periphery.

## 5. Conclusion

In summary, we have investigated the anomalous behavior of surface plasmons that are excited in a resonant cavity structure of a metal nanoslit array. We show that the modification of a metal nanoslit array by a SAM film can give rise to either a red-shift or a blue-shift in the peak transmission wavelength. The sign of the wavelength shift depends on the surface-plasmon dispersion characteristics in the resonant cavity structure that corresponds to the stripe periphery of a nanoslit array, and they can be controlled by the composition of the metal film and the substrate that supports it. A simple model was developed to predict the wavelength shift and its sign. We show that the blue-shift of the transmission peak’s wavelength, observed with adsorption of a SAM film on the metal surface, is caused by the interplay of anomalous dispersion and quadrupolar resonance of surface plasmons in the cavity structure.

## Acknowledgment

This work has been supported by the NSF grants (NIRT-ECS-0403865/ECS-0424210).

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