1. Introduction

One of the interesting characteristics of metallic nanoparticles is their exhibition of strong absorption peaks in the visible spectral range [1]. The peaks are mainly due to local field enhancement of the surface plasmons which are resonantly excited at the metal nanoparticles. The field enhancement is dominated by two types of plasmon interaction: dipolar far-field coupling and evanescent near-field coupling [2, 3]. The far-field coupling causes conversion of the locally enhanced fields from evanescent to radiative in character via collective dipolar radiation from a particular periodic arrangement of the nanoparticles. Light transport via chains of metal particles [4], transmitting light through a sub-wavelength hole array in a metal film [5], and beaming of light with a single sub-wavelength aperture flanked by a periodic surface corrugation [6] would be described by the far-field interaction of the resonant plasmons excited on every period of the indentations.

On the other hand, the near-field coupling corresponds to multipolar interactions between metallic nanoparticles, and it modifies optical linear/nonlinear permittivity of a composite material embedding the metal particles [3]. An abnormal dependence of optical permittivity on volume fraction of the metal particles dispersed in a metallic thin film [7] can be also understood by this near-field coupling effect. As the volume fraction goes up to one from zero, the amount of the real and imaginary parts of the effective optical permittivity vary more than 19 including zero permittivity. Therefore, use of composite media containing metallic nanoparticles may afford us another degree of freedom to choose dielectric materials for manipulating photonic crystal structures [8, 9] or for realizing plasmonic nonlinear metamaterials [10].

A 2-dimensionally (2-D) periodic distribution of metallic nanoparticles on a dielectric surface has been accomplished by two-photon femtosecond laser-induced photoreduction of metal ions doped into the dielectric [11]. The laser-induced photoreduction can be initialized with a photochemical reaction, leading to particle precipitation and protrusion out of the flat sample surface. Distribution of the nanoparticles on the sample surface basically follows the intensity distribution of the two-photon interference pattern: larger volume fraction appears at the bright interference fringes, while at the dark region both the particle size and the volume fraction are small. If the dielectric medium initially contains metal nanoparticles, instead of the metal ions considered in the photoreduction process, and if the initial volume concentration of the particles inside the dielectric medium is large enough to enhance the near-field interacting, the particle distribution may be determined by a different mechanism. Irradiating this particle-dispersed sample with an intense, linearly polarized continuous-wave laser, the sample may be strongly influenced by the near-field coupling of the localized surface plasmons.

In this paper, we report an influence of the near-field coupling effect on the 3-D periodic arrangement of silver nanoparticles embedded in a glass medium. The periodic silvernanocluster structures are experimentally demonstrated by coherent interference of two continuous-wave laser beams inside the glass medium after embedding the silver nanoparticles with a uniform distribution via Ag ion exchange and a thermal annealing process. We have found that the near-field interaction between the localized surface plasmons excited by intense, linearly polarized, continuous-wave laser beams can activate a photochemical ionization (or, photoionization) of the silver nanoparticles. When the polarization direction of the two beams interfered inside the glass medium is parallel to the planes of the interference fringes, the near-field coupling is enhanced so strongly that the silver particles at the bright interference fringes are ionized, diffused, and aggregated to the existing particles in the dark fringe regions. The dark regions therefore posses a larger volume fraction induced by an increase of both particle size and number density. The larger volume fraction in the dark regions is opposite to the particle distribution generated by the femtosecond laser-induced photoreduction mentioned above. The two beams polarized perpendicular to the fringe planes, on the other hand, induce only a very weak coupling between the surface plasmons which may not be enough to excite the photochemical ionization in the bright regions.

2. Sample preparation

Silver nanoparticles with a diameter of 5 to 30 nm were prepared in the experiment by double ion-exchanging between silver and sodium ions in a glass medium [12] followed by thermal heating at a temperature range of 500 □ ~ 700□. At the first ion-exchange of silver for sodium ions, commercial soda-lime glass substrates with a thickness of 1 mm were immersed for 5 hours in a molten-salt bath with 20 % molar concentration of AgNO₃ in NaNO₃ at 360 □. At the second ion-exchange for 30 min in pure NaNO₃ molten at 360 □, only the silver ions near the glass surface were replaced again by the sodium ions while the rest of them deeply doped inside the glass substrate remain. The silver-ion doped substrate was then annealed for 30 min in an air-conditioned electric furnace at the temperatures of 500, 550, 600, 650, and 700 □, respectively. This annealing caused a precipitation of metallic silver to form silver clusters inside the glass medium with different volume fractions according to the annealing temperatures. There were no silver particles protruding out of the flat sample surface even after a further annealing process.

 

Fig. 1. (a). TEM image of silver nanoclusters, after annealing in air for 30 min at 600 □. (b) XRD spectra and (c) absorption spectra of the silver nanoclusters embedded in a glass medium. The white bars represent 10 µm in length. The inset in (c) shows the comparison between the experimental absorption spectrum annealed at 600 □ and the spectrum estimated by the Mie scattering theory.

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The formation of the silver nanocluster layer inside the glass substrate was evidenced by analyzing a transmission electron microscope (TEM) image in Fig. 1(a), X-ray diffraction (XRD) spectra in Fig. 1(b), and optical absorption spectra in Fig. 1(c). The TEM image shows the silver nanoclusters after annealing in air for 30 min at 600 □. Dark spots represent the silver nanoparticles of about 5 to 30 nm in diameter and 20 to 50 nm in spacing. An increase in the volume fraction of the silver nanoparticles according to the annealing temperature is observed by the XRD and absorption spectra shown in Fig. 1(b) and Fig. 1(c), respectively. For the sample annealed at 500 □, there are no characteristic peaks of silver in either spectra. This means that the annealing temperature is not enough to precipitate and form a measurable metallic silver layer. But, at 600 and 700 □ the XRD peak intensities for |111〉 and |200〉 silver-crystal faces increase with the annealing temperature. This is due to an increase of the volume fraction and the size of the silver particles. The particle size can be numerically estimated from the Scherrer equation [13] by assuming that the clusters, of spheroid-shape, exhibit a uniform size. For example, the particle diameter of the 700 □ annealed sample would be deduced as ~16 nm from the FWHM width of 2 Δθ ~ 0.3° for the |111〉 peak in Fig. 1(b), which is reasonably correlated with the TEM measurement. The absorption spectra normalized to the absorption of the glass substrate in Fig. 1(c) display an optical absorption band peaked at about 410 nm ~ 430 nm, typical of plasmonic absorption of the metallic silver nanoclusters having a diameter of the order of 10 nm. The intensity of the absorption peak increases with the annealing temperature due to the increase of volume fraction of the silver particles. In the inset of Fig. 1(c) the absorption spectrum (dotted curve) calculated by using the Mie scattering estimation [14] is compared with the measured spectrum(solid curve) of the ion-exchanged glass annealed at 600°C. The two curves well agree with each other at the center wavelength of 425 nm when the silver particle size of 18 nm and the refractive index of 1.5 for the surrounding glass medium are assumed in the calculation. The 18 nm particle size estimated by the Mie calculation is therefore in accord with the TEM measurement as well as the XRD result. The difference in band width of the two spectra is mainly due to the particle size distribution which is broader in the fabricated sample.

3. Grating formation

To realize a 3-D Ag nanocluster grating, two linearly polarized beams from a 700 mW, 488 nm continuous-wave Ar-ion laser, are interfered for an exposure time of 4 min on a sample for which the silver nanoparticles had been annealed at 600□ for 30 min. The angle between the two incident beams was about 3 degrees, corresponding to a grating period of 3.5 µm. The beam intensity on the sample was about 10W/mm2 and the exposure time was several minutes, and the polarization direction of the interference beams was parallel (TE-polarized) to the fringe direction of the interference pattern. Formation of the nanocluster gratings was measured by observing the reflection microscope image (1500 times magnification) as shown in Fig. 2(a). The white-bar in the figure represents a scale of 10 µm. The microscope image does not show the particle size and volume fraction clearly, but distinguishable particles can be seen in the bright regions after very careful observation by the microscope. It should be mentioned that we could barely measure such a microscopic image when the two interfering beams have a TM-polarization direction which is perpendicular to the fringe stripes; only the TE-polarized beams allowed a periodic arrangement of nanoparticles.

This strong polarization dependence of the grating formation can be visualized by comparing the fringe contrasts shown in Fig. 2(b), where the solid curve represents the intensity profile of the fringes taken along the dashed line direction in Fig. 2(a) and the dotted curve taken from a microscope image (not shown here because of its very faint fringes) of a sample formed by TM-polarization interference. Note that the dotted curve is ten times magnified in the vertical scale. The fringe spacing well matches the intended grating period of 3.5 µm in both cases, but the fringe contrast is almost 20 times larger in the TE-polarization case. One may claim that this difference in the fringe contrast might originate in a discrepancy in the original visibilities of the interference fringes generated from the TE- and TM-polarization interference, but the difference between the original visibilities is just less than 1% since the interference angle is about 3 degrees in the experimental setup. There was also a distinct difference in diffraction efficiency of these two kinds of the nanocluster gratings measured by a probe beam (633 nm) possessing a negligible absorption at the nanocluster samples as shown in Fig. 1(b).

 

Fig. 2. (a). Optical microscope image of silver nanocluster gratings formed by TE-polarization interference beams, and (b) the fringe intensity profile (solid curve) cut along the dashed line in (a). The dotted curve in (b) is an intensity profile of grating samples (not shown here) formed by TMpolarization interference, where the vertical scale is ten times magnified.

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The nanocluster gratings formed by the TE-polarization interference had an 85 % peak efficiency while the TM-polarization samples had a only 28 % peak efficiency for diffracting light into the first order. These maximum diffraction efficiencies did not depend so much on the polarization direction of the incident probe beam, and only a little degradation within a few percent could be measured. Therefore we finally expect that a mechanism of transferring a uniform Ag nanoparticle distribution into a periodic arrangement should be dominated by the surface plasmons coupling in a direction parallel to the polarization direction of the interference beams. It is well known that coupling of surface-plasmon nearfields excited at adjacent nanoparticles becomes very strong when the excitation light is polarized parallel to the coupling direction [4]. In our experiment a very long chain of coupled surface-plasmon fields may occur along the direction parallel to the fringe stripes when the two interference beams are TE-polarized; but there is not enough space for a strong surface-plasmon coupling when the beams are TM-polarized.

It is worth noting that there were no changes in the grating images after an additional thermal heating of the nanocluster gratings at 700 □ for more than 30 min. This means that the bright spots appearing in the microscope image are not caused by a crystalline dielectric particles since most of the crystalline structures had been disappeared by annealing above 300 □ [15, 16]. In the experiment of the femtosecond photoreduction [11], the silver particles were protruded out of the sample surface and their diameters were measured to be ~100 nm. Thus we believe that the particles appearing in the microscope image are silver nanoparticles with a diameter on the order of 100 nm.

The fringe pattern of the scattered light in the microscope measurement was not observed until we focused the object plane of the microscope at 60 µm under the glass top surface. Only at a depth between 60 µm and 75 µm from the top surface were we able to observe such a grating fringe. A periodic arrangement of these vertical 15-µm-thick nanocluster-slabs embedded in the glass medium was also verified by observing the polished top surface after gradually reducing the glass thickness in about 1 µm steps by mechanical grinding of the glass surface. We found from this sequential observation that the silver particles shown in the bright fringes were continuously distributed along the vertical 15-µm-thick nanocluster-slabs. Therefore, we may regard the silver nanocluster grating as a 3-D periodic structure composed of 1.5-µm-thick, 15-µm-wide silver nanocluster slabs embedded in a dielectric medium.

4. Discussion

Even with the above discussion starting from the experimental results shown in Fig. 2 one may need more physical evidence of the polarization dependent mechanism for forming the 3-D nanocluster gratings. Also, still some points may not be clear for understanding: how the thermally-stable, about 20 nm diameter, uniformly distributed silver nanoparticles in a glass medium can be rearranged periodically with size large enough to be seen by the optical microscope; whether the bright stripes in the grating images are in accord with the constructive interference regions or the destructive.

 

Fig. 3. (a). Optical microscope image and (c) fringe intensity profile along the dashed line of the silver nanocluster gratings after irradiation focused at the central dark area with a TE-polarized (perpendicular to the dashed line) beam. (b) and (d) are those after a TM-polarized beam (parallel to the dashed line) irradiation. The white bars represent 10 µm in length.

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We conducted another experiment to focus a single laser beam (488 nm) onto the Agnanocluster gratings generated by the TE-polarization interference. The exposure energy of the single beam is nearly the same as that used to construct the nanocluster gratings, but the spot size at the focus is about 10 µm in diameter which is much smaller than the grating area of 200 µm. We considered the two cases of polarization direction for the focused exposure beam; TE-polarization parallel to the grating stripes and perpendicular TM-polarization. Figures 3(a) and 3(b) show the microscope images obtained after irradiation with the TEpolarized beam focused on the central area and the TM-polarized one, respectively. At the central areas the bright fringes are obviously diminished in both cases, resulting from a remarkable reduction in particle size and/or particle density after the exposures. For the TEcase in Fig. 3(a), at least one central fringe was almost disconnected through the whole 15-µm-thick vertical grating slab, while there were no complete discontinuities in all the grating slabs for the TM-case. Fringe contrasts shown in Figs. 3(c) and 3(d) which are taken along the dashed lines in Figs. 3(a) and 3(b), respectively, also clearly show these fringe connectivity. The focused irradiation must gradually reduce the particle size and number density via photoionization of the silver metals [15, 17, 18], and this photoionization process strongly depends on the polarization direction relative to the grating fringe direction. The electric-fields around the particle surfaces are enhanced by surface plasmon resonance and they are strongly coupled to each other when the excitation light is polarized parallel to the fringe direction, resulting in acceleration of the photoionization process as shown in Fig. 3(a). The ionized silver metals are then diffused out of the central regions and some of them could stick to the neighboring silver nanoparticles [15, 17]. Thermal heating while irradiating must accelerate the ion diffusion, but it is not essential for the photoionization since the nanocluster gratings were not eliminated by an extra thermal heating above 700 □. If one irradiates the focused beam on the original glass sample with a uniform silver-particle distribution, a bright ring pattern surrounding the dark central part is observed as shown in Fig. 4. This means that the silver nanoparticles in the central region are pushed out to the rim via photoionization, diffusion, and aggregation processes. In consequence, now we can clearly understand the dark and bright stripes in the grating images: the dark-stripe regions possess fewer silver particles and correspond to constructive interference fields; the brightstripe regions where the diffused silver ions are aggregated to a larger particle correspond to destructive interference fields.

 

Fig. 4. Optical microscope image after a single focused beam exposure at the center of a uniformly distributed nanocluster sample. The white ring surrounding the central area reveals a high reflection from silver metals. The white bar represents 10 µm in length.

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A strong polarization dependence of the nanocluster grating formation in Fig. 2 and the elimination in Fig. 3 can be explained by the coupling effect of the neighboring surface plasmons. It is known that, even if the shape of the metal nanoparticles is spherical, the excited plasmon fields are not symmetrically distributed around the metal spheres but elliptically elongated toward the polarization direction of the excitation beam [14]. The elongated plasmon fields are then coupled to each other intensely along the polarization direction [4], and this elongated plasmon coupling induces red-shift for the absorption peak of the metal nanoparticles [19–21]. In the grating formation of our experiment, interference of the two TE-polarized beams leads to line fringes along the direction parallel to the beam polarization. The electric fields of the TE-polarized beams oscillate along the lines of the constructive interference fringes, resulting in strong near-field coupling between the neighboring surface plasmons in the fringe direction. This coupling effect may make a shift of the plasmon resonance peaks in Fig. 1(c) toward a wavelength near the exposure beam wavelength of 488 nm, leading to a further enhancement of plasmon coupling sufficient to ionize most of the silver nanoparticles in the bright fringe regions. Therefore, the TEpolarization interference can produce a nanocluster grating with a clear periodic structure as shown in Figs. 2(a) and 2(b) while the TM-polarization interference hardly produces such a grating structure. This strong plasmon coupling is also exhibited during the single beam erasing of the gratings described in Fig. 3.

4. Conclusion

Metallic nanocluster gratings composed of a 3-dimensionally periodic distribution of silver nanoparticles have been successfully formed in a glass medium. We have found that nearfield coupling of surface plasmons excited at the metallic nanoparticles can be strong enough to periodically rearrange ~ 10 nm silver nanoparticles embedded in a dielectric, and that the plasmon coupling be greatly enhanced when the excitation polarization is parallel to the grating fringes. The metallic nanocluster gratings deeply embedded in a dielectric are very stable to thermal heating without a change in its high diffraction efficiency of 85 % for a 633 nm probe beam. The holographic interference method to form 3-D metallic nanocluster gratings proposed here can be further applicable for implementing an arbitrary periodic arrangement of metal nanoparticles in design of a novel photonic crystal or metamaterial as well as a plasmonic-enhanced nonlinear periodic structure.