1. Introduction

The development of new materials with novel physical properties is one of the main drives in nanotechnology research. An exciting example is nanostructured materials which interact with light in a manner greatly different from conventional bulk materials; these structures are the product of collaborative work in optics [1], engineering, chemistry, physics, and materials science. Early experimental studies focused on surface-enhanced Raman scattering (SERS) from such materials, in which the scattering efficiencies can increase by several orders of magnitude with proximity to metallic nanostructures [2, 3]. Recently a good deal of work has focused instead on increasing fluorescence efficiency, motivated by interest in developing highly efficient fluorescence-based sensors for biomolecular detection [4–7]. Increasing the efficiency of fluorescent dyes holds great promise for improving the signal-to-noise ratio for such sensors, simultaneously increasing the stability of the dyes and decreasing the detectable concentrations for many materials, and impacting fields including biology, environmental chemistry, and pathogen detection [8].

Strong interaction of light with noble metal nanostructures occurs at frequencies close to those of particle plasmon resonances [9]. Metallic nanoparticle enhanced fluorescence takes advantage of this effect to produce dramatic increases in the efficiency and thus the intensity of emission from fluorescent molecules positioned in close proximity to such structures. Results using roughened silver surfaces, or silver island films have shown increases in the fluorescence from proximal dyes varying from several-fold up to ~100 times those from the same dyes on a simple glass substrate [4–6, 10–14]. Still greater enhancements can be achieved using more precise, regular arrangements of noble metal structures due to stronger plasmonic response, typically in the visible to IR range [15]. Fabricated structures allow more selective control of the spectral overlap between the absorption of fluorophores and particle plasmon resonances. Fluorescence intensities of up to 350 times the unenhanced values have been observed for materials with judiciously chosen silver particles [16], and further increased enhancements are likely to be possible.

Finding the optimum combination of nanoparticle size, shape, spacing and dielectric environment requires understanding how these affect both the light absorption-induced excitation of the fluorescent molecules and the subsequent radiative decay of the excited states. Simple considerations based upon Fermi’s golden rule predicts the probability should be proportional to the square of the matrix element of the transition, and thus to the square of the local field at the molecules. This near-field intensity includes contributions from the incident light, and the frequency- and polarization-dependent response of the nanoparticles and substrate. In this paper we test the simplest corresponding model for nanoparticle enhanced fluorescence, comparing the measured fluorescent intensity from molecules in proximity to Ag nanostructures whose size, shape and spacing we vary systematically with calculations of the square of the local electric field.

2. Materials and methods

We have discussed details of the sample preparation elsewhere [17]. Briefly, we fabricate arrays of metallic nanostructures of chosen sizes, shapes, patterns, and interparticle distances on a Si (001) substrate. An aluminum oxide adhesion layer, 25 nm thick, is first deposited onto the substrate. We next spin on resist, which we then pattern using e-beam lithography with a modified field emission scanning electron microscope (JEOL JSM6500F). Next a silver film 75 nm in thickness is deposited; finally the resist is removed by a lift off procedure. We characterize the resulting nanostructures using scanning electron microscopy (SEM) for pattern metrology and laser scanning microscopy (LSM) for fluorescence imaging and measurements. All nanostructures in this work are either square columns in a square array, or long nanowires arranged parallel to each other, and all have a center-to-center spacing between structures equal to twice the width of the nanostructure. The column/wire widths vary between 64 and 633 nm.

We coat the nanoparticle-patterned substrates nonspecifically with a sticky, biotin-complexed bovine serum albumin (BSA) spacer layer whose thickness is 3–4 nm. Next we deposit both Cy3 and Cy5 fluorophore-tagged streptavidin, which binds strongly to the biotin, and which increases the total protein layer thickness by another 3–4 nm. Finally we rinse away unbound protein. Fluorescent images of the sample are collected using a confocal laser scanning microscope (Zeiss model LSM 410). The samples are maintained wet, i.e., under a thin layer of dilute buffer consisting of a 5 mM solution of NaH₂PO₄ and Na₂HPO₄ whose pH is adjusted to 7.5. For the Cy3 fluorophore the wavelength of the incident (excitation) light in air is 514 nm, produced by an argon laser; the fluorescence intensity is collected through a filter which passes wavelengths between 535 and 575 nm. In separate measurement we excite the Cy5 fluorophore on the same arrays with incident light of 633 nm wavelength, produced by a He-Ne laser; in this case the fluorescence intensity is collected through a filter which passes wavelengths above 660 nm. Our procedure allows us to measure the period-, wavelength-, and polarization-dependences of the enhancement rapidly, while minimizing the variations in average fluorophore coverage, spacer layer thickness and incident light intensity. In analyzing our images we define fluorescence enhancement ratio as:

where I _e is the fluorescence intensity measured from areas containing fluorophore/spacer coated silver nanostructures. I _f is the fluorescent intensity without silver nanoparticles, i.e. measured from areas where only fluorophore/spacer layer is present. I _B is the “background” intensity measured from an area of the substrate where both fluorophore and silver nanostructures are absent. The normalized intensity ratio N describes the fluorescence enhancement due to the silver nanoparticles, factoring out the effect of variations in fluorophore coverage.

FDTD calculations are performed using the software TEMPEST [18] to map the steady-state electric field strengths within a sample volume during excitation by a plane-wave, monochromatic light source. We vary the polarization, and wavelength of the light source, as well as the organization of layered materials within the calculation volume. We model our arrays by repeating units of the sample volume; the calculations are relatively fast for objects which are functionally two-dimensional, as are the long nanowires. Three dimensional structures could in principle also be modeled, but our experience has been that these calculations are exceedingly slow.

3. Results and discussion

Fluorescence microscopy images of our Ag nanostructure arrays reveal variations with pattern shape, size, and periodicity, and light polarization. Figure 1 shows example results for parallel silver nanowires, in which both the spatial period and orientation relative to the direction of light polarization (the direction of the incident light electric field is horizontal in all images) are varied. We effectively make simultaneous measurements for two different polarizations by fabricating nanowires with two perpendicular orientations on the same sample; an example of our arrays is shown in the SEM image of Fig. 1(a). Fig 1(c) shows a fluorescence image for the same nanowire array-sample, measured using incident light of 514 nm wavelength. One can easily see that the optimum polarization is perpendicular to the long axis of the wires, i.e. for the inner two rows within the image. The blue curves in Figs. 1(d,e) summarize the fluorescence intensity vs. nanowire period: the optimum is at approximately a 0.65 fraction of the wavelength of the incident light in air, or approximately a 0.85 fraction of the wavelength in solution.

Figure 2 shows results for square-cross section silver nanocolumns for which the range of lateral spatial period is similar to that of the nanowire arrays of Fig. 1. For uniformity of conditions these were fabricated on a different region of the same substrate as the nanowire arrays. The overall optimum period for the square Ag nanocolumns is smaller than for the nanowires, i.e. approximately a 0.25 fraction of the incident light wavelength in air or a 0.32 fraction of the wavelength in solution. The maximum fluorescence enhancement ratio is considerably larger for the nanocolumns, approximately 4 times greater than that of the nanowire structures; this is seemingly due to a “lightning-rod” effect, with higher fields associated with the more compact structures.

It is interesting to compare the variation in measured fluorescence and reflectance from these structures. Even in the absence of fluorescent molecules the interaction of light with metallic nanostructures would result in an optical extinction spectrum in which resonances occur at frequencies which depend on the size and period of the particles [19, 20], and indeed it is common to use extinction spectra to quantify particle-light interactions. Since our nanowire/nanocolumn arrays are fabricated on a non-transparent silicon wafer, we instead measure reflectance images; examples are shown in Figs. 1(b) and 2(b). The corresponding summary plots are shown by the red curves in Figs. 1(d,e) and 2.(d), respectively; these are reflectance ratios, normalized to that from the oxide-coated Si(001) substrate without Ag nanostructures. Reflectance values greater than one (bright areas) indicate more reflected intensity from the silver nanostructures than from the substrate; darker areas, with reflectance values less than one, indicate that silver nanostructure arrays reflect less light than does the substrate. The conditions producing minimum reflectance from the nanowire arrays (Fig. 1(b)) match those for maximum fluorescence enhancement: both occur at a lateral spatial period of approximately 0.65 times the incident light wavelength, and for transverse polarization (long wire axes perpendicular to incident light E-field). By contrast, all longitudinal patterns (long wire axes parallel to incident light E-field) produce reflectance greater than one; no significant fluorescence enhancements occur for this polarization. For the square nanocolumn arrays, patterns with periods exhibiting a local minimum in reflectance show local maximum in enhancement, as shown in Fig. 2(b). However, as seen by comparing Figs. 2(b) and 2(c) in this case the optimum in fluorescence enhancement does not coincide with the overall lowest reflectance.

 

Fig. 1. (a) Scanning electron microscope image with enlargements of select areas shown to the left (a1–a4). (b) Reflectance image with incident light of 514 nm. (c) Cy3 fluorescence map. (d–e) Quantitative analysis of fluorescence enhancement (blue) and reflectance intensity (red) along two different orientations of excitation. The period is defined as the line width plus edge-to-edge spacing, and in this case line width equals edge-to-edge spacing. Chosen line widths vary by 1/8 the wavelength of the excitation light, for both wavelengths used (514 nm for the top half, and 633 nm for the bottom half). Line widths in the top two rows are 64 nm, 128 nm, 192 nm, etc. up to 514 nm, and in the bottom rows are 79 nm, 158 nm, 237 nm, etc. up to 633 nm for the largest square. Each half consists of longitudinal and transverse orientations plus a single vertical line. The “LPS” marks consist of arrays of silver nanodots with edge lengths of 120 nm and center-to-center spacings of 220 nm. For transverse excitation polarization, there is an inverse correlation between reflectance measurements and fluorescence enhancement; when reflectance is lowest, fluorescence intensity is highest. Error bars represent the standard deviation for several measurements of different samples.

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Fig. 2. (a) Scanning electron microscope image with enlargements of select areas to the left (a1–a4), highlighting the structure of the smallest square silver nanoparticles arrays. (b) Reflectance image with 514 nm incident light, and (c) the corresponding Cy3 fluorescence map. (d) Quantitative analysis of the fluorescence enhancement (blue) and reflectance intensity (red) for increasing nanoparticle size and spacing. Particle edge lengths and center-to-center distances are the same as the bar widths and spacings in figure 1. The “LPS” mark consists of arrays of 120 nm silver nanodots with a period of 220 nm. Error bars represent the standard deviation for several measurements of different samples.

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In Fig. 3 we compare the variation of the measured fluorescence intensity vs. lateral period and incident light polarization with that of the square of the local field, calculated using the FDTD method. As noted above, our fluorescence tags are located approximately 8 nm above the surface of the nanostructures, the summary plot shows the average intensity 8 nm above the local sample surface (indicated by the green dashed lines in figure 3(a–e)). A comparison of the measured fluorescence and calculated field intensity shows qualitative consistency: both are larger for the polarization perpendicular to the nanowires. The major peak in both plots occurs at a lateral period that is approximately half of the wavelength of the excitation light. However, the relative strength of the secondary peak in the enhancement, at a period of approximately twice the incident light wavelength, is considerably smaller than that for the calculated field-squared. Figure 4 demonstrates a similar analysis for the Cy5 fluorophore. The Cy5 properties are qualitatively consistent with what we observe in Cy3; except the peak is smaller and red-shifted (the optimum enhancement is seen with a larger period between structures). While calculations of the primary peak in the localized electric field strength agree with that of the measured fluorescence enhancement (Fig. 4d), there is again a lack of a simple proportionality: in this case the longer-period secondary peak seen in the calculated field-squared is not evident in the enhancement.

 

Fig. 3. Field intensity calculation by two-dimensional FDTD method and examples are as shown in (a-e). The long axis of the nanobars is normal to the image plane; this is an end-on view of the long structures positioned on a silicon substrate, with a layer of aluminum oxide between the substrate and the silver bars, and water filling the top portion of the frame. Bright areas show the positions of high local electric field. (f, g) Summary plots show the average electric field intensity 8 nm above the surface (at the location of the green dashed lines in (a–e)), compared with fluorescence enhancement along two different polarizations. Excitation polarization compared to bar orientation is indicated by the illustrations within the graphs. Intensity plots (a–e) represent the visualization of calculations for points noted by the labels within graphs (f–g), at periods of 316, 1028, 316, 512, and 1028 nm, respectively. Error bars represent the standard deviation for several measurements of different samples.

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Our finite difference time domain calculations, which are summarized in Fig. 3, show that the electric field intensity consists of a series of fringes with modulations both parallel and perpendicular to the plane of the substrate. The fringe period perpendicular to the substrate agrees with the light wavelength in water while the variations parallel to the substrate plane are clearly correlated with the geometry of the Ag nanowires. The largest calculated field intensity coincides with the largest fluorescence enhancement: this occurs for a spatial period of approximately 0.65 times the free space light wavelength, and for the electric field polarized perpendicular to the long direction of the nanowires, as shown in Fig. 3(g). For these conditions, as seen in Fig. 3(c), the regions of highest calculated field intensity are near the upper corners of the nanowires, with a local minimum at the surface midplane. A second, less intense maximum in the calculated field intensity occurs at a spatial period approximately three times this, i.e. near twice the free space light wavelength; there is also a weak maximum in fluorescence enhancement near this spatial period. As seen in Fig. 3(e) the highest intensity near the nanowires surface is closer to center than at the highest maximum, and a minimum near the surface midplane exists here as well. For spatial periods intermediate between these both the fluorescence enhancement and the field intensity reach a minimum; the calculated field intensities near this minimum shows highest intensity near the midplane of the nanowire.

These observations suggest the excitation of plasmon modes consisting of standing waves at the surface of the nanowires. Such a standing wave consists of two surface plasmons traveling in opposite directions, each of which has a dispersion (k) given by:

where ω is the frequency, c is the speed of light, ε _Ag is the frequency-dependent dielectric function of the Ag nanowire, and ε _w is the dielectric function of the surrounding medium. In our experiments the thickness of the nanowire is 75 nm, which exceeds the skin depth of Ag (δ≈23 nm at optical frequencies) by approximately a factor of 3; thus to a good approximation ε_w is that of the surrounding solution, which is mainly water. Using values of the dielectric functions of Ag and water at a light excitation frequency of 583 THz yields a magnitude of k equal to approximately 1.44 times the value for light propagating in air, or equivalently, a spatial period of 0.69 times the light wavelength in air. This is in very good agreement with the spatial period at which the largest fluorescence enhancement is observed.

The condition for a standing surface plasmon across a nanowire is

where W is width of nanowire and m is an integer. The approximately equal sign in this equation comes from the fact that the edge is not a hard boundary. The actual boundary condition may differ for various reasons: the plasmon might “wrap” around the edge of the wire, in which case W_eff>W. Alternatively the effective width may be smaller because of surface defects near the edges.

 

Fig. 4. Overall summary of Cy5 fluorophore; compare to fig. 1 results for Cy3: (a) reflectance and (b) fluorescence images on nanostructures with the same dimensions as in Figure 1. Graphs show the summary analysis along the transverse mode between fluorescence and (c) reflectance, or (d) calculated average field intensity 8nm above sample surface. Error bars represent the standard deviation for several measurements of different samples. There is good correlation between fluorescence and field intensity, and an inverse correlation between fluorescence and reflectance, for this transverse excitation.

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The lowest order standing wave surface plasmon mode, corresponding to m=1, produces a left-right polarization of charge at the wire edges; this would couple readily to the oscillating E-field of an incident light wave polarized along this direction. In our investigations the center-to-center separation of adjacent nanowires is twice the individual wire width., so that this first mode also satisfies the condition for the Wood’s anomaly, corresponding to diffraction of surface waves along the grating [21, 22], i.e. nλ=a sin(θ), where a is the grating period, and in our case θ=π/2. For sufficiently deep gratings a Wood’s anomaly is also expected for the opposite polarization [21]; this might explain the (considerably weaker) peak seen at this same period for longitudinal polarization (Fig. 3(f)). A peak in the fluorescence enhancement is seen at very nearly this same condition for the square pillar arrays, as see in Fig. 2(d). It appears as a shoulder on the more intense peak centered near 0.25 times the free space light wavelength, which we identify with a Mie-like resonance, i.e. localized particle plasmon [1,17]; this small particle resonance is weaker, and possibly shifted to smaller periods for the nanowire arrays. The second standing wave mode corresponding to m=2 would give a charge distribution which is symmetric about the midplane, and thus would not couple to the incident light wave; this in agreement with the absence of a peak in the fluorescence enhancement at this condition in Fig. 3(g) The third mode, i.e. m=3, also produces a net polarization, but greatly reduced compared to that for m=1; this is also in agreement with the relatively small peak in the fluorescence enhancement seen in Fig. 3(g).

The departure of the observed fluorescence intensity from a simple proportionality can be understood based upon the fact that fluorescence involves absorption of light followed by radiative decay, usually at a lower frequency due to the Franck-Condon effect. The absorption probability is expected to be proportional to the square of the matrix element for the transition, and thus the local field squared at the molecule. However, radiative decay competes with non radiative decay of the excited state, and the competition between these can depend on the environment of the molecule, leading to a departure of the fluorescence intensity from a simple proportionality to the local field squared. This is reminiscent of the simpler situation of Mie scattering from a small spherical metal particle immersed in the field of an incident light wave. In that case, a particle diameter much smaller than the light wavelength gives rise to a simple dipolar particle plasmon, which radiates efficiently, while a larger particle sees a spatial variation in the incident field, and yields a plasmon excitation which includes higher order (quadrupole, octupole, etc.) modes, which do not radiate efficiently. Here, of course, the situation is more complex due to the interaction of the particle plasmon modes with the substrate as well as with the fluorescent molecule itself, making a quantitative model of the dependence of the intensity on the geometry difficult. Geddes et al. [23, 24] and Gerber et al. [25] argued that the interactions between the excited fluorophores and nanoparticles increase the fluorophores’ radiative decay rate (decreasing the lifetime) and this, in turn, enhances fluorescence.

4. Conclusions

We find that the variation of fluorescence enhancement with the lateral period of arrays of Ag nanowires and light polarization is generally well correlated with the calculated square of the local field at the nearby molecules, at least for small period structures. This is in agreement with expectations based upon an absorption probability which is proportional to the square of the matrix element of the transition, and allows inclusion of both geometrical factors and frequency dependent dielectric properties of arrays of metallic nanostructures and their surroundings. A lack of agreement in the relative intensity of peaks in the enhancement for larger period structures indicates that the dependence of both the radiative and nonradiative decay rate on the dielectric environment of the fluorescent molecules, must be included to understand the dependence of fluorescence in these nanostructure arrays. Most significantly, our observations of the variation of the fluorescent intensity and our simulations of the local field intensity provide evidence for the role of surface plasmon standing waves, along with Wood’s anomaly in understanding the enhancement of fluorescence by arrays of metal nanostructures.