Plasmonic Properties of Two Silver Nanocubes - American Chemical

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Chapter 2

Plasmonic Properties of Two Silver Nanocubes: Dependence on Separation Distance, Relative Orientation, Refractive Index of the Substrate, and Exciting Light Propagation Direction Nasrin Hooshmand* Laser Dynamics Laboratory, School of Chemistry and Biochemistry, Georgia Institute of Technology, Atlanta, Georgia 30332-0400, United States *E-mail: [email protected]. Phone: 404-894-4009.

When two Ag or Au nanoparticles are in close proximity to each other and exposed to resonant exciting light, strong electromagnetic fields (hot spots) are formed between the monomers when the exciting light is polarized parallel to the dimer axis. The hot spots are generated due to the strong coupling of the excited oscillating dipoles on the facing facets as well as at the corners of the two nanoparticles of the dimer. The relative orientation of the nanoparticles and the size of the gap between them determine the near field coupling behavior of the two monomers in the dimer. The plasmonic band wavelength of the dimer shifts exponentially to the red as the two monomers approach one another according to the universal exponential rule until at a certain distance when the exponential dependence breaks down. This distance is dependt on the size of the nanoparticle as well as the relative orientation of the two nanoparticles. The contribution from the coupling with the higher order multipoles (e.g. quadrupole) is responsible for the breakdown of the universal exponential rule. In order to examine the sensitivity factor of the face to face (FF) oriented Ag NCs dimer, the localized surface plasmon resonance (LSPR) maximum is determined as a function of the refractive index of the surrounding medium for the two prominent plasmonic bands in the extinction spectrum. It was found that the LSPR bands that have higher sensitivity factors correspond to © 2016 American Chemical Society Ozaki et al.; Frontiers of Plasmon Enhanced Spectroscopy Volume 2 ACS Symposium Series; American Chemical Society: Washington, DC, 2016.


those having large electromagnetic field distribution and not necessary the ones with the highest extinction. We have also carried out a detailed theoretical investigation on the effect of increasing the refractive index of the substrate supporting the two nanocubes and the propagation direction of the exciting light. A substrate of high refractive index showed significant change in the extinction spectra and the field enhancement due to the multipole modes of the Ag NC dimer. It is found that the LSPR spectrum and field distribution around the FF oriented Ag NC dimer are sensitive to the excitation order of the incident light. If it passes through the strong absorbing substrate first, then the plasmonic light produced will be much weaker as the intensity of exciting radiation will be greatly reduced compared with that when the exciting light passes through the FF oriented Ag NC dimer faces first. We demonstrated that the refractive index of the substrate can also have significant influence on the intensity ratio of the multipole to the dipole modes, which can relax the selection rules of the light interacting with the different plasmonic multipolar modes.

Introduction Recently, plasmonic nanoparticles made of Ag or Au received significant attention from researchers in this field as it showed unique physiochemical properties when they interact with the electromagnetic radiation, primarily in the visible region. The localized surface plasmon resonance (LSPR) is an example for one such property. The LSPR originates from the resonant excitations of the collective oscillations of their conduction band electrons (1–5). This can enhance the scattering and localized electromagnetic field intensities around the nanoparticles (5, 6). These properties led to their utilization in versatile chemical and biological applications including bio-imaging, labeling, optical energy transport, and chemical and biological sensing (1, 7–19). The LSPR of plasmonic nanoparticles can be fine-tuned and is strongly dependent on their size, shape, composition and interparticle separation (6, 9, 20–28). It also exhibits remarkable sensitivity to the metal composition as well as the dielectric function of their surrounding medium and the supporting material (solid substrate) (5, 9, 20, 21, 26, 29, 30). Not only the LSPR properties of plasmonic nanoparticles were investigated very well, but also the study of the basic physics of the LSPR in very close proximity of assembled plasmonic nanoparticles were examined (31–33). One of the very important properties to understand the LSPR is the effect of the electromagnetic field distribution on the sensing performance of the aggregated plasmonic metal nanoparticles. Ag is the best candidate to study among most of the metal nanoparticles due to its high plasmon response in the visible region (34). When two or more plasmonic nanostructures get in close proximity and exposed to the resonant radiation, a new set of hybridized collective plasmonic modes and enhanced (35–44) optical fields (hot spots) are generated due to the 22 Ozaki et al.; Frontiers of Plasmon Enhanced Spectroscopy Volume 2 ACS Symposium Series; American Chemical Society: Washington, DC, 2016.


strong coupling of the individual plasmonic modes. However, at very short separation, the hot spots produced in these nanostructures exhibit significant enhancements of their many optical properties such as Raman scattering (45–50), fluorescence (51, 52), infrared absorption (53, 54), etc. This has been very useful in a variety of applications in different fields (17, 30, 55–61). In the past few years, my research is mainly focused on studying the plasmonic coupling phenomena of plasmonic nanoparticles, separated by different distances. The plasmonic coupling of nanoparticle dimer results in red shift of the plasmonic wavelength of the monomer. This plasmonic optical behavior shows an exponential decay depending on the separation distance between the nanoparticles (normalized to the size of the individual particle) (40). This separation distance dependence on plasmonic coupling behavior can be explained if the coupling between the two nanoparticles is considered as purely dipolar in nature (37). This implies that the vectorial combination of the many oscillating dipoles on each nanoparticle will result in a single dipole moment, which interacts with the corresponding single dipole moment of the other nanocube. Studies on plasmonic coupling in Au or Ag nanocube dimers (62, 63) using the discrete dipole approximation (DDA) (20, 23, 64) showed that the LSPR coupling becomes important at short separation distance. In addition, their sensitivity factor is largely dependent on the interparticle gap, cube edge rounding effects, as well as on the refractive index of the embedded medium (28, 29, 63, 65). As the refractive index of the medium as well as the substrate increases, the LSPR band maximum red shifts to a great extent (28, 29, 65–68). Upon plasmonic excitation, Ag or Au nanocubes (NCs) show strong substrate effect on the LSPR coupling properties compared to the spherical nanoparticles as the flat surface and the sharp corners of the NCs make them interact strongly with the external electromagnetic field and nearby dielectric substrate over a large area as well (26, 62, 69, 70). Recent studies showed that the interaction geometry can also result in unique hybridization interactions in the nanoparticle dimers (40, 71, 72). It is found that the interaction of a nancube with a supporting material (substrate) strongly affect the shift of the LSPR band of the nanocube optical properties due to their sharp corner (24). However, placing nanoparticles on a solid support reduces their refractive index sensitivity. The amount of reduction is proportional to the fraction of the nanoparticle surface in contact with the substrate (73, 74). In this chapter, we mainly focus on the interaction between the two Ag nanocubes, the effect of their separation, the substrate, the surrounding medium, as well as the relative orientation of the Ag NC dimer on the plasmonic coupling behavior.

Numerical Method Discrete dipole approximation (DDA) is one of the most powerful methods to model the optical properties of plasmonic nanoparticles that have sizes smaller than the wavelength of exciting incident light (64). The DDA can be extended to particles that have various sizes and shapes by periodic structures. The key advantage of this method is that it includes multipolar effects and finite size effects. Details on the DDA method have been described elsewhere (64, 75, 76). 23 Ozaki et al.; Frontiers of Plasmon Enhanced Spectroscopy Volume 2 ACS Symposium Series; American Chemical Society: Washington, DC, 2016.


The Ag nanocube dimers investigated in this chapter are represented by a cubic array of point dipoles (with volume d3), which are excited by a polarized external field. The corresponding response of each dipole to both the external field and neighboring dipoles to the polarized field is solved self consistently using Maxwell’s equations and the resulting optical spectra are produced (77). The advantage of using the DDA method for this study is two-fold. It is particularly well suited for modeling the nanocube shape due to the cubic lattice of point dipoles used to describe the system. Also, when using DDA, both multipolar and finite size effects are considered. This is particularly important due to the size and separation distances of the nanoparticle dimers that were investigated. In this chapter, we aim to model the optical properties and plasmonic coupling behavior between the Ag NCs (edge length=42 nm) dimer under various conditions. In DDA, the size of the slab (substrate) being used for the calculation is limited by the method of calculation source. It was found that the change in the length, width or the thickness of the slab do not affects the results (24). The Ag NC dimers system is represented by point dipoles (1 dipole/2 nm), which are excited by an incident photon (external field). The size of the cube is defined by an equal volume of a sphere with an effective radius reff = (3v/4π)1/3. Here the reff for that of the pair of the cube by itself is 32.82 nm and that of the dimer and substrate have different volumes.The incident external field was propagated perpendicular to the inter-particle axis and polarized along the inter-particle axis. The refractive index of Ag NCs is assumed to be the same as that of the bulk metal (78). For this calculation, we used the DDSCAT 6.1 code developed by Draine and Flatau (64). The field distribution around the surface of the Ag NCs dimer in both orientations face to face (FF) and edge to edge (EE) was calculated. The plasmonic field enhancement (in log scale of |E|2/|E0|2) was calculated on the surface of a pair of cubes with the DDA technique at different excitation wavelengths.

Plasmonic Coupling Mechanism between a Pair of Ag Nanocubes The near field coupling between the two plasmonic nanoparticles in a dimer occurs at their close proximity (79, 80). Su et al. (81) verified that the plasmonic coupling can be approximated by an exponential function of the interparticle separation distance of Au elliptical particles . This near-exponential behavior was further supported by experimental (82) and theoretical (37, 71) studies of various plasmonic nanoparticle dimers of different shapes. The near-field coupling between the two particles was reported as a universal scaling behavior when the LSPR peak position of dimeric nanoparticles is plotted against the interparticle gap scaled to the size of the particle. This exponential trend fits very well to the near exponential decay, which is well known as the “plasmon ruler equation” (37, 39, 81, 82). In this equation, the coupling between dimeric nanoparticles with gap size of ‘s’, results in red shift of their plasmonic wavelength. The equation shows the exponential decay dependence on the gap size between the two nanoparticles normalized to the size of the individual particle (s/D) (40) is: 24 Ozaki et al.; Frontiers of Plasmon Enhanced Spectroscopy Volume 2 ACS Symposium Series; American Chemical Society: Washington, DC, 2016.


where, Δλ is the shift in the maximum LSPR of the dimeric nanoparticles with respect to the LSPR of the monomer (λ0) and D is the nanoparticle diameter. ‘A’ and ‘τ’ are constants. Studies show that this separation dependence can be simplified if the coupling between the two nanoparticles is considered to be purely dipolar in nature (37). It was found that this equation depends only on nanoparticle shape and independent of the plasmonic metal type. It has been shown that the strength of the plasmonic coupling is associated with the expected electromagnetic field strength generated by the corresponding metal nanoparticle (37). Thus, the plasmonic coupling between the dimeric nanoparticles can be influenced by the shape of the nanoparticle. However, it has been shown that this equation becomes invalid once the FF oriented Ag NC dimer brought in close proximity to each other at short distance (83). In addition, it has been found that the distance at which the dipolar equation fails depends on the shape of the nanoparticle as well as the relative orientations of the nanoparticles. Further investigation of the orientation dependence of the 42 nm Ag NC dimers in FF and EE manners on the near-field coupling (84) showed that the relative orientation of nanoparticles dimer strongly affects the near field coupling behavior. This effect will be drastic when the gap size between the dimer becomes very small. It was found that the contribution from the coupling of the higher order multipoles (e.g. quadrupole-dipole) influences the near field coupling between the cubes. The contribution of multipolar modes in EE Ag NC dimer is much higher than in FF oriented Ag NC dimer due to the higher density of the oscillating dipoles in the EE Ag NC dimer. This will result in the failure of the near field coupling in EE Ag NC dimer at a larger separation distances (Figure 1B). The normalized spectral data of each dimer to the length of the particle along the polarization direction of incident electromagnetic field is shown in Figure 1A and B. These results suggest that the near field coupling behavior between the oscillating electrons on the surfaces of the two nanocubes fails at a gap size of 6 nm (s/L~0.14) for the FF dimer but 14 nm (s/D~0.24) for the EE dimer. This suggests that, the deviation from the expected dipolar coupling behavior for the EE oriented NC dimer happens at a distance that is twice greater than the distance observed for the FF oriented NC dimer. The failure in the dipolar coupling was found to coincide with the overlap of both the electromagnetic field and polarization vector distribution in the gap region between the Ag NCs dimer. There is a clear difference in the maximum value of the electromagnetic field intensity for each orientation (Figure 1C and D). The EE oriented Ag NC dimer exhibits a maximum electromagnetic field intensity of ~7040, which is roughly 40% greater than the maximum electromagnetic field generated by the FF Ag NC dimer (~5000). Overall, these results validate the effect of the relative orientation of the plasmonic faces with the maximum density of the oscillating dipoles of cubic plasmonic nanoparticles on the plasmonic coupling behavior. This suggests that one should not expect to have a single universal plasmonic ruler equation. In 25 Ozaki et al.; Frontiers of Plasmon Enhanced Spectroscopy Volume 2 ACS Symposium Series; American Chemical Society: Washington, DC, 2016.


view of applications of plasmonic nanoparticles, one should focus on utilizing the relative orientation and the number of the coupled plasmonic nanoparticles in order to further enhance the optical properties of the devices for the different applications.

26 Ozaki et al.; Frontiers of Plasmon Enhanced Spectroscopy Volume 2 ACS Symposium Series; American Chemical Society: Washington, DC, 2016.


Figure 1. The plots showing fractional shift in the peak position (Δλ/λ0) of the extinction spectra of a 42 nm Ag NCs dimer oriented in FF (A) and EE (B) against the separation distance between the two nanocubes scaled to either the length of the diagonal of the individual nanocube (s/D) in EE or the edge length of the individual nanocube (s/L) in FF. The calculated electromagnetic field distribution and polarization vector plots for the top surface of FF (C) and EE (D) Ag NC (42 nm) dimers. Adapted with permission from ref. (84). Copyright 2016 American Chemical Society.

Formation of Hot Spots in Dimeric Nanoparticles When two or more Ag or Au nanostructures get in close proximity to each other, a new set of hybridized plasmonic modes and enhanced optical fields (hot spots) are generated between the nanoparticles as a result of their coupling (35–44). This is due to the spatial overlap of the individual plasmonic fields, which induces the formation of hybridized collective plasmonic modes. The hot spots formed at the interparticle gap between the nanoparticles can be modulated and the resulting optical phenomena can be used for varietis of applications (17, 30, 55–61).



Figure 2. (A-C) The effect of increasing the interparticle gap from 2 nm to 4 nm on the distribution of plasmonic fields at the hot spots formed in FF Ag NCs dimer. At a gap size of 3 nm, the hot spot appears to be formed at both the center and the corners of the FF Ag NC dimer. (D and E): The electromagnetic field distribution (A-D) and corresponding polarization vector distribution showing the dependence of hot spot formation on the polarization direction of the incident exciting light for the FF oriented Ag NCs at 2 nm separation distance when the exciting light is polarized parallel to the dimer axis (D) or perpendicular to the dimer axis (E). Adapted with permission from ref. (83). Copyright 2014 American Chemical Society. There are some factors that affect hotspots formation, such as the direction of the light polarization, the relative orientation of the nanoparticles and the separation distance between the nanocubes. Figure 2A and D show the dependence of the hot spots on the polarization direction of the incident light. The light polarized in two directions either along the dimer axis (Figure 2D) or 28 Ozaki et al.; Frontiers of Plasmon Enhanced Spectroscopy Volume 2 ACS Symposium Series; American Chemical Society: Washington, DC, 2016.


perpendicular to it (Figure 2E). As shown in Figure 1A, both hot spot formation and the polarization vector distribution occur between adjacent facets of FF Ag NC dimer with an interparticle separation of 2 nm. Figure 1D shows only the use of incident excitation polarized light along the dimer axis giving rise to the strong overlap of the oscillating dipoles, which would result in the hot spot formation between adjacent dimer facets. Light polarized perpendicular to the dimer axis produces parallel oscillating dipoles on the facing facets that repel one another and does not produce high density of inter-oscillating dipoles which attract one another (i.e. no hot spot formation) (Figure 2E). The hot spots generated between the two Ag NCs in the dimer displays competitive contributions of the oscillating dipoles on the facing facets and dipoles at the corners of the two nanoparticles in the dimer (Figure 2B). At very small separation distance (2 nm) the hot spot formation takes place at the center of the facing facets. However, at larger interparticle gap (4 nm), it forms around the corners of the facing facets of the dimer. Ag NCs dimer clearly exhibits two superior plasmonic modes. This suggests a competitive dipolar coupling between the dipoles at the center of the adjacent facets and those at the corners of adjacent facets of the Ag NCs dimer when the dimer separation is 3 nm. As the separation distance increases to 4 nm, the hot spots are formed only from the dipolar coupling between the oscillating dipoles present at the facing corners. The strength of the hot spots decreases with increasing dimer gap to 6 nm (62). The effect of increasing the interparticle gap from 2 nm to 4 nm on the shape and mechanism of hot spot formation shown in Figure 2A-C. The formation of hot spots and the polarization vector distribution depend on the interparticle gap separation between the two Ag NCs facing facets. It is obvious that the hot spot formation between two nanocubes occur between the facing facets and not between the adjucent corners, which is dependent on the concentration of the oscillating dipole moments on the surface of two particles.

Plasmonic Spectroscopy and Sensitivity Factor of the Ag Nanocube Dimers The sensitivity of the LSPR to either the surrounding medium or the interparticle gap is used in molecular detection in many sensing applications. For plasmonic nanoparticles, one of the important figure of merit is the sensitivity factor, which is used to predict the efficacy of a specific plasmonic nanoparticle system for sensing applications (85, 86). The repulsion between the in-phase oscillating dipoles of a given plasmonic band decreases as the refractive index of the surrounding medium increases. This results in a red shift of the plasmonic band due to the decrease of the energy of the oscillator. The sensitivity of a plasmonic band, thus the sensitivity factor of the nanoparticle, is related to the magnitude of the observed shift of the LSPR maximum per unit change of the refractive index of the surrounding medium (9). This sensitivity factor is strongly dependent on the shape and separation of plasmonic nanoparticles. Nanoparticles having sharp corners have been shown to be most promising for sensing applications (71, 74, 87, 88). 29 Ozaki et al.; Frontiers of Plasmon Enhanced Spectroscopy Volume 2 ACS Symposium Series; American Chemical Society: Washington, DC, 2016.


Since plasmonic spectroscopy is well related to both the electromagnetic field intensity and the extinction spectrum, our group has studied the relationship between the strength of the electromagnetic field and the extinction intensity of the different plasmonic bands. The extinction spectrum and the field distribution of a 42 nm Ag NCs dimer oriented in FF configuration were calculated for a separation distance of 2 nm (Figure 3). In the extinction spectrum of the Ag NCs dimer, a low energy (608 nm) and high energy (585 nm) bands are dominant. In plasmonic spectroscopy, we assume the same description of one electron spectroscopy that the intensity of the extinction of a spectral band depends on the square of the oscillating transition dipole moment. This suggests that the higher energy band is more intense than the lower energy band. At higher energy LSPR band, we observe that the transition dipole moment, which is generated and couples to the exciting light is larger than the transition dipole moment of the lower resonant wavelength. The electromagnetic field generated around the surface of the Ag NCs dimer was calculated at each resonant band at 2 nm separation distance (Figure 3A and C). As shown in Figure 3B, there are two prominent plasmonic bands in the extinction spectrum that have different extinction intensities. The band having the smaller extinction intensity shows the highest electromagnetic field enhancement. It is concluded that, the maximum value of the electromagnetic field intensity distribution seems to be dependent on the degree of localization of the oscillating electronic dipoles. The total number of oscillating dipoles that correspond to the resonant excitation band determines the intensity of the LSPR band. The electromagnetic field distribution corresponds to each plasmonic band in FF oriented Ag NCs dimer are shown in Figure 3A and 3C. This reveals that the maximum field enhancement of the weaker plasmonic band (608 nm) is almost ~4 times greater than the strong plasmonic band at 584 nm. This suggests the lower energy band displays a higher degree of localization of electronic dipole density and results in a higher maximum value of the electromagnetic field distribution. Figure 3D shows the calculated extinction spectra for the Ag NCs dimer in different media such as water, ethanol, carbon tetrachloride, and toluene. It shows that as the refractive index of the medium increases, the plasmonic bands within the spectrum shifts to the lower energy (longer wavelength) due to the reduction in repulsion between the oscillating dipoles. Thus, it appears that the plasmonic band with the highest degree of localization of its oscillating electronic dipole density is significantly stabilized in a medium with a high refractive index. Therefore, the wavelength within this plasmonic band will be the most sensitive to the dielectric function of its environment. In order to calculate the sensitivity factor (SF), the LSPR maximum was determined as a function of the refractive index of the surrounding medium for both prominent plasmonic bands (Figure 3E). It was found that the higher SF (395.5) corresponds to the band with the weaker extinction intensity. Whereas, the stronger band has the lower SF (362.54). Accordingly, the best sensor should be made from nanoparticles that have the largest enhanced plasmonic field rather than the ones with the largest extinction intensity.



Figure 3. (A-C) DDA calculated of the field distribution associated with the extinction spectra (absorption and scattering) of two prominent plasmonic bands for a 42 nm Ag NCs dimer at gap size of 2 nm in a surrounding medium of water. (D)Extinction spectrum for a 42 nm Ag NCs dimer at gap size of 2 nm in a surrounding medium of water, ethanol, carbon tetrachloride, and toluene. (E) The LSPR maxima plotted as a function of the refractive index of the surrounding medium for both prominent plasmonic bands. The slope presents the sensitivity factors using for each plasmonic bands. Adapted with permission from ref. (90). Copyright 2015 American Chemical Society.

Substrate Effect on the Plasmonic Coupling in Ag Nanocube Dimer Studies show that nanocubes with sharp corners can strongly interact with a substrate which can cause the LSPR band to shift (24). In addition, nanocubes show strong induced LSPR coupling when present in close proximity of solid substrate than the equivalent spherical nanoparticles, due to their flat surfaces (26, 62, 69, 70). When the nanoparticles are placed on a solid substrate, it was found that the extent of refractive index sensitivity is reduced and this reduction is directly proportional to the fraction of the nanoparticle surface in contact with 31 Ozaki et al.; Frontiers of Plasmon Enhanced Spectroscopy Volume 2 ACS Symposium Series; American Chemical Society: Washington, DC, 2016.


the substrate (73, 74). Previous studies suggest that the interaction geometries can have significant influence on the exclusive hybridization interactions in nanoparticle dimers than the interparticle gap (40, 71, 72, 89).

Figure 4. The effect of the refractive index of the substrate on the extinction spectra and the field intensity distribution of FF oriented Ag NC dimer (A-C) on a glass substrate (n=1.5) and(D-F) on a high refractive index (AlGaSb, n=4.6). The nanocubes have a separation distance of 2 nm in both cases. The field is distributed around the cubes more on a high refractive index substrate, where the substrate stabilizes the individual oscillating dipoles. Adapted with permission from ref. (90). Copyright 2015 American Chemical Society. Figure 4 shows the schematic illustration, extinction spectra and the field distribution of the FF Ag NCs on a glass substrate (n=1.5) and on a substrate with much higher refractive index value like AlGaSb (n=4.6) at a separation distance of 2 nm. As shown in Figure 4A and D, the exciting light propagates from the top of Ag nanocubes and the electromagnetic field is polarized parallel to the dimer axis. Our study shows that, since the refractive index of glass (n=1.5) and that of the medium used (water, n=1.33) are comparable, the Ag NCs dimer on glass substrate 32 Ozaki et al.; Frontiers of Plasmon Enhanced Spectroscopy Volume 2 ACS Symposium Series; American Chemical Society: Washington, DC, 2016.


shows similar field distribution and extinction spectra to the Ag NCs dimer with no substrate (84, 90). However, on the high refractive index (n=4.6) substrate, there is a significant change in the extinction spectrum and field enhancement (Figure 4E and F) due to the multipole modes of the Ag NC dimer, which is broadened and shifted to lower energy (longer wavelength). This is probably due to the reduction of the electron-electron dipolar repulsion in the configuration with high refractive index substrate. As seen in Figure 4F, the field distributed over a larger area around the cubes and thus the oscillating dipoles have reduced inter dipolar repulsion. Subsequently, the band is shifted to lower energy (Figure 4E). It suggests that, for making good plasmonic sensors it is better to select a composite with lower refaractive index.

The Effect of the Substrate Refractive Index on the Intercube Plasmonic Coupling Recent studies showed that the plasmonic coupling between the Ag NC becomes significant as the separation distance between the nanocubes falls below 10 nm. Subsequently, it becomes very strong as the particles are brought into close proximities at very short distance (e.g. 2 nm) (90, 91). Figure 5 shows the substrate effect on the LSPR bands for the FF oriented Ag NC dimer at variable separation distances and the field distribution around the nanocubes at separation distance of 100 nm. When the separation distance between the two nanocubes on a substrate of high refractive index (n=4.6) increases to 40 nm, both the dipolar and multipolar modes show a constant blue-shift regardless of the separation distances (Figure 5B). On the other hand, on a low refractive index substrate (n=1.5), even though the dipolar mode exhibits continued blue shift under similar conditions as the high refractive index substrate, the LSPR band corresponding to the multipole mode became nearly unchanged when the separation distance is greater than 40 nm (Figure 5A). In this case, as the gap size is gradually reduced to below 100 nm, the dipolar modes exhibited relatively larger blue shift (~600 to 490 nm) than that on the high refractive index substrate (~675 to 625 nm) (Figure 5A and B). This can be attributed to the dipole-dipole interaction between adjacent nanocubes, which is much stronger than the multipole type interaction at very short distance. We further observed that the high refractive index of the substrate remarkably affect the contribution of the multipolar interactions. Interestingly, we notice that the separation distance between the λmax of the dipolar and multipolar modes becomes longer as the distance between the Ag NCs decreases. When the nanocubes on the substrate become very close, the shift in the dipolar modes of the Ag NCs significantly shifts to longer wavelengths. This suggests that the substrate refractive index is not high enough to reduce the interactions between the cubes and therefore, the dipole-dipole coupling between them becomes strong. As shown in Figure 5A and B, the dipolar modes shift more than that observed for the multipolar modes. Compared to the dipolar modes, the multipolar bands lose their intensity at very short distances and becomes significantly weaker due to the lack of the overlap between the dipolar and multipolar modes. This could result in the observed shift in the dipolar modes away from the multipolar modes. 33 Ozaki et al.; Frontiers of Plasmon Enhanced Spectroscopy Volume 2 ACS Symposium Series; American Chemical Society: Washington, DC, 2016.


However, with the increasing the interparticle gap, the multipolar band gains intensity and become stronger due to the stronger interaction between dipole and multipole modes as they become energetically closer to one another. A significant broadening of the dipolar bands was observed (Figure 5B) in the extinction spectra for the FF oriented Ag NC dimer on the AlGaSb substrate (n= 4.6) at longer separations (from 40 nm to 100 nm. It is likely that the strong influence of the substrate and strong coupling of the multipolar modes with the dipolar modes of the Ag NCs occurs at large separations. Compared to the AlGaSb substrate, glass substrate (n=1.5) exhibited smaller effect on the plasmonic coupling between multipolar and dipolar modes. In this case, the coupling between multipolar and dipolar modes is much more continuous and at 2 nm separation, the intense broad band corresponding to the dipole mode splits into two bands (Figure 5A). For separation distances greater than 4 nm, only one broad dipolar band appeared (and was always coupled to one another). However, on the high refractive index substrate, when the gap size becomes less than 40 nm, the multipolar bands are significantly mixed with the dipolar components. At the same time, in the multipolar regions, the bands blue shift to a larger extent (Figure 5B). Nevertheless, as the gap size increased above 40 nm, the wavelength of both the dipolar and multipolar modes became constant. Under the same condition, in the case of Ag NCs on glass substrate, the dipolar region consistently changed by varying the intercube gap separation (Figure 5A). Our previous studies on the low refractive substrate showed that, except at 2 nm separation, the maximum field enhancement occurred around the sharp corners (where the electron density is highest) at the interface between the two cubes in the FF oriented Ag NC dimer on the glass substrate (84, 90). However, on the high refractive index substrate (n=4.6) even at a separation distance of 100 nm, the electromagnetic field was distributed asymmetrically both around the corners and facets and enhanced at the interface between the nanocubes (Figure 5D). Similar to the single Ag NC on AlGaSb substrate (84), the FF oriented Ag NC dimer on AlGaSb substrate showed a significant enhancement in the characteristic electromagnetic field corresponds to the multipolar region at the interface between the two nanocubes. Whereas, the field corresponding to the dipolar mode is largely located at the corners. The enhanced field at the interface can be attributed to the strong influence of the high refractive index substrate on the coupling between the dipolar and multipolar modes of the nanocubes. However, on the glass substrate, the Ag NC dimer at a gap size of 100 nm did not show any noticeable coupling and the field was distributed largely around the corners as in the case of individual nanocube (Figure 5C). The difference in the field distributions on the two substrates clearly shows that the attractive interaction between the oscillating electron dipoles stabilizes the system when weak substrate is used (Figure 5C). However, using substrate with high refractive index, the oscillating dipoles are stabilized and minimized their energy by the high dielectric constant of the substrate thus they are distributed over the overall surface of the nanocube. It results the coupling between the two nanocubes and thus their plasmonic spectra almost independent to the separation distance beyond 8 nm (Figure 5D). On the other hand, on low refractive index substrate, the oscillating dipoles are concentrated at the corners that makes their coupling stronger and 34 Ozaki et al.; Frontiers of Plasmon Enhanced Spectroscopy Volume 2 ACS Symposium Series; American Chemical Society: Washington, DC, 2016.


sensitive to the nanocube separation. This implies that their spectra sensitive to the intercube separation distance (Figure 5A and C).

Figure 5. The effect of the substrate refractive index on the extinction spectra (at different separation distances) of FF oriented Ag NC dimer on the glass (A) and on the AlGaSb (B) substrates. The calculated electromagnetic plasmonic fields at a separation distance of 100 nm for FF oriented Ag NC dimer on the glass (C) and on the AlGaSb (D) substrates are also given. Adapted with permission from ref. (91). Copyright 2016 American Chemical Society.

The Influence of Exciting Light Propagation Direction on the Plamonic Coupling and Electromagnetic Field Generation Plasmonic nanoparticles, with its strong electromagnetic fields, have many applications in the fields of sensors, medical diagnostics and therapeutics, nano-electronics, and many other nano device applications. Its application depends on the wavelength and its plasmonic field intensity (1, 7–17). The LSPR wavelength associated with the electromagnetic field distribution of FF oriented Ag NC on a substrate can be tuned by changing the direction of the incident light. We have performed a comprehensive theoretical study of the effect of the incident light excitation direction with respect to the position of the high refractive index substrate. We found that high refractive index substrate (n=4.6) significantly influences the excitation order of the incident light and subsequent LSPR spectrum and field distribution around the nanoparticles (Figure 6). This can be attributed to the following reasons. In Figure 6D the excitation light first passes through the absorbing substrate that greatly reduces its intensity before it excites the plasmonic oscillation, giving rise to much reduces plasmonic excitation intensity. Accordingly, the palsmonic field enhancement will be greatly diminished by using the high refractive index substrate, which strongly absorbs 35 Ozaki et al.; Frontiers of Plasmon Enhanced Spectroscopy Volume 2 ACS Symposium Series; American Chemical Society: Washington, DC, 2016.


the incident light. Therefore, the broad band observed between 500 and 600 nm (spectrum in Figure 6B) could be due to the absorption of the substrate (AlGaSb) itself. It is clear from Figure 6A-C that the full intensity of the exciting light is used in exciting the plasmon oscillation. This has much stronger dipolar band at ~700 nm (spectrum in Figure 6B) than the spectrum in Figure 6E. On high refractive index substrate, the exciting light propagation direction has to be as in Figure 6A-C to obtain large electromagnetic plasmonic fields (and thus to make sensitive sensors). This suggest that the location of the high refractive index substrate, which can change the intensity of the exciting incident light and can greatly tune the extinction spectra and electromagnetic field distribution around the nanoparticles.

Figure 6. The DDA calculated extinction (B, E) spectra and electromagnetic field distributions (C, F)of FF oriented Ag NC dimer (at a separation distance of 2 nm) on a strong absorbing substrate (AlGaSb), where the incident exciting light propagates from the top of cubes in (A) and from the bottom of the cubes in D. Adapted with permission from ref. (91). Copyright 2016 American Chemical Society. 36 Ozaki et al.; Frontiers of Plasmon Enhanced Spectroscopy Volume 2 ACS Symposium Series; American Chemical Society: Washington, DC, 2016.


Conclusions This chapter summarizes some of the results that we have calculated using the DDA method on the plasmonic properties of a pair of 42 nm Ag nanocubes at different separations and having different relative orientations, when they are placed on substrates of different refractive indices, exposed to resonant light of different intensity and propagation directions. We were able to determine the location of the hot spots formed between the nanocubes at short separation distances and its dependence on the nanocube relative orientation. We found that the hot spot formation between two nanocubes dependent on the concentration of the oscillating dipole moments on the surface of two particles . In addition, the deviation of the expected dipolar coupling behavior is dependent on the geometry and the contribution from the coupling of the higher order multipoles of the nanoparticles. Further, our studies showed that LSPR bands that have higher sensitivity factors correspond to those having large electromagnetic field distribution and not necessarily the largest extinction coefficient. Finally, we demonstrated that the refractive index of solid substrate and the location of the high refractive index substrate can greatly tune the electromagnetic field distribution produced around the nanoparticles.

Acknowledgments The author would like to acknowledge Prof. Mostafa A. El-Sayed and Dr. Sajanlal R. Panikkanvalappil for reading the manuscript and Marvdasht Islamic Azad University for the time allowance to prepare this chapter. The author thanks B. T. Draine and P. J. Flatau for use of their DDA Cod DDSCAT 6.1. The financial support of NSF-DMR grant (1206637) is greatly appreciated.

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