Tunable Nanoscale Confinement of Energy and Resonant Edge Effect

Article pubs.acs.org/JPCC

Tunable Nanoscale Confinement of Energy and Resonant Edge Effect in Triangular Gold Nanoprisms Xi-bin Xu,†,‡,§ Zao Yi,†,‡ Xi-bo Li,‡ Yu-ying Wang,†,‡,§ Jin-pei Liu,∥ Jiang-shan Luo,‡ Bing-chi Luo,‡ You-gen Yi,*,† and Yong-jian Tang*,‡ †

College of Physics and Electronics, Central South University, Changsha 410083, China Research Center of Laser Fusion, China Academy of Engineering Physics, Mianyang, Sichuan 621900, China § Science and Technology on Plasma Physics Laboratory, Research Center of Laser Fusion, China Academy of Engineering Physics, Mianyang, Sichuan 621900, China ∥ Department of Automation, Xiamen University, Xiamen 363105, China ‡

ABSTRACT: Here we provide a simulation based on discrete dipole approximation method of the properties of surface plasmons on triangular gold nanoprisms and investigate their electric-field distribution to identify different multiple surface plasmon resonances. Near-field maps of triangle gold nanoprisms are established. Symmetric field distribution has been obtained perpendicular to the orientation of direction of incident light. We examine how their propagation can be manipulated and discuss some of the parameters that influence optical response of noble metals. Reduction of prism thickness leads to hybridization/mixing between two horizontal triangular surfaces and possibly overall enhancement of absorption crosssection of nanoparticle and shows excellent ability to adjust the resonance peaks. Field distribution mainly distributes in the triangular surface or along the edges. At platelet corners, electric field is weak, and the trend that plasmons are partially transmitted to neighboring edges is displayed. The calculation of the field enhancement also shows that the location of the field enhancement is specified by the different resonance patterns. A “bridge” zone can be found in triangular surfaces at resonance wavelength, which refers to coupling effect between different poles. This is an essential step toward a thorough understanding of plasmon resonance in nanoprisms.

1. INTRODUCTION Recent progresses that allow metals to be structured and characterized on the nanoscale have attracted much interest in surface plasmons (SPs).1−3 These are essentially light waves that are trapped on the surface because of their interaction with the free electrons of the conductor. When the oscillating electric field of the incident light resonantly couples to the conduction electrons, making them collectively oscillate at the same frequency, an intense band in the extinction spectrum will be shown, which is named the surface plasmon resonance (SPR).1 In this interaction, the free electrons respond collectively by oscillating in resonance with the light wave. Recent investigations in the field of plasmonics have focused on metal nanostructures substantially smaller than the wavelength of light. By altering the structure of a metal’s surface, the properties of SPs can be tailored, which offers the potential for developing new types of photonic device. SPs can help us to concentrate and channel light using subwavelength structures, which could lead to miniaturized photonic circuits with length scales much smaller than those currently achieved.2−5Consequently, the optical response reflects the properties of the local electric field at the particle and has a predominantly dipole character that can be optimized by manipulating the system geometry. Concentrating light in the © 2013 American Chemical Society

interaction between light and metals leads to an electric-field enhancement that can be used to manipulate light−matter interactions and boost nonlinear phenomena.3,4 The SPR spectra of noble metal nanocrystals have been demonstrated to markedly depend on the structural characteristics of the nanocrystals such as their size and shape as well as their external dielectric environment.1−9 Detailed information on how all of these parameters can influence the optical properties of nanocrystals is crucial to use the SPR of these nanocrystals for various applications such as those developed in optics, surface-enhanced Raman spectroscopy (SERS), biosensor, and medical diagnostics.10−15 By increasing the particle size, the optical excitation of higher order harmonics, multipolar plasmon resonances, becomes possible and significantly modifies the optical properties.1,3Multipolar SP modes were demonstrated spectrally in the visible and near-infrared regions; meanwhile, correlated theoretical approaches were developed.1,3−8 In the long-wavelength regime where the surfaceplasmon dispersion is close to the light line, the combined excitation consisting of an SP and an electromagnetic wave is Received: May 26, 2013 Revised: August 2, 2013 Published: August 5, 2013 17748

dx.doi.org/10.1021/jp4051929 | J. Phys. Chem. C 2013, 117, 17748−17756

The Journal of Physical Chemistry C

Article

(ethylene glycol) solution and stirred for 5 min to form a yellowish solution. The solution was subsequently exposed to microwave irradiation in a household microwave oven (Panasonic: G80D23CSL-Q6). The total reaction time was 10 min at an average power of 250 W. After the process, the color of the solution had noticeably changed to reddish-brown. The final product solution was then centrifuged at 13 000 rpm for 10 min before being washed three times in distilled water and ethanol consecutively. Specimens of single-crystalline Au nanoplatelets for TEM (H-700) investigation were dropped onto the copper mesh grid with carbon membrane. Figure 1a

called a surface-plasmon polariton (SPP). SPPs have attracted considerable attention due to their potential applications in optical circuits and optical computers.3,16,17 Triangular nanoparticles, also called nanodisks or nanoprisms, have been synthesized by several groups, with various truncations and aspect ratios. They showed that the SPR spectra of these nanoparticles are highly sensitive to the parameters such as size, shape, and dielectric environment.1,3 Various bands have been observed in the SPR spectrum, as it has been already reported for silver and gold nanoprisms. Most of these experimental data were supported by simulations based on the discrete dipole approximation (DDA) method to assign the various bands observed in the SPR spectrum. Among all of these bands, the most intense corresponds to the in-plane dipole resonance.18 Other bands assigned to higher multipolar resonances exhibit much weaker intensity in spectra and are lacking investigation in either experiment or simulation. From all previously reported experiments, it can be found that proper observation and identification of the multipolar SPRs of triangular nanoprisms often remains difficult because of the low intensity and partial superimposition of the corresponding bands. Nanoprisms with very high aspect ratios have been proved to be a choice to have further study.19,20 Despite the previous studies, it is worth noting the current lack of results dealing with the ultrathin triangular prisms of a few nanometers in thickness and the study of their optical properties to provide a complete description and better knowledge of the multipole plasmon modes. Many optical approaches such as scanning near-field optical microscopy and dark-field spectroscopy can be used to study SPR phenomena.21,22 Also, field simulations of triangular nanoplatelets have been investigated to obtain complete acknowledge. The combination of scanning transmission electron microscopy (STEM) with electron-energy-loss spectroscopy (EELS) allows plasmon mapping at a spatial resolution better than λ/40. With the advent of highperformance electron monochromators and in-column energy filters, energy-filtering transmission electron microscopy (EFTEM) utilizing a broad electron beam and parallel acquisition in the low energy-loss range has emerged as a technique that offers rapid data collection and outstanding spatial sampling.23,24 Here the method DDA is used to simulate SPR property of ultrathin triangular prisms, and we take Au skin depth into account. We combine a very thin thickness (5 nm) with edge lengths ranging from 20 to 45 nm. Finally, multipolar excitation peaks of ultrathin triangular gold nanoprisms with various aspect ratios are assigned via the DDA method. Near-field maps of triangle gold nanoprisms are also established. This makes it possible to correctly distinguish the bands corresponding to the in-plane quadrupolar and higher multipolar modes in addition to the dominant dipole resonance. Also, we report on the dependence of the multipolar excitations on the nanoprism geometry.

Figure 1. TEM image of gold triangular nanocrystals and other wellcrystallized particles with different sizes and shapes.

shows the TEM image of gold triangular nanocrystals and other well-crystallized particles with different sizes and shapes. Side surfaces of gold triangular nanocrystals are displayed in Figure 1b. It can be seen that the edge length of triangular prisms varies from 20 to 100 nm and the thickness is ∼20 nm. As deduced from TEM analysis, both triangular prisms and large faceted particles exhibit quite large size and shape dispersions. Most of the nanoprisms appear with homogeneous contrast and slight darkness, which indicates that they are very flat and thin single-domain crystals. Shapes and sizes in simulations made below are all based on the previously mentioned experiment.

3. COMPUTATIONAL APPROACH 3.1. Computational Method. The DDA method is explored to largely tune the resonance peak of Au triangular prisms by taking both their size and geometrical parameters into account. The DDA method is reviewed in the refs 27−33. The DDA starts by dividing the object of interest into a cubic array of N-point dipoles whose positions are denoted ri with polarizabilities αi where αi =

3d3 εi − 1 4π εi + 1

(1) 33

Purcell and Pennypacker used the Clausius−Mossotti polarizabilities to relate to the dielectric function, where d is the interdipole spacing and εi is the complex dielectric function at location ri The dielectric function of the Au and Ag is taken to be the bulk experimental value in the paper. Analytical modification in eq 1 has been reportedly implemented in DDSCAT, the open source code of the DDA method.27−30 The polarization induced in each dipole as a result of interaction with a local electric field Eloc is

2. EXPERIMENTAL SECTION Triangular prisms have been synthesized by several groups using either solution-phase light-mediated syntheses or thermal growth techniques.25,26 Here we use the fabrication of Au nanoplatelets by a microwave-mediated method mentioned in ref 3. 0.5 mL of 0.1 M HAuCl4 (chloroauric acid) aqueous solution was prepared in a Teflon bottle, followed by addition of 0.144 g of glucose and 0.03 g of polyvinylpyrrolidone (PVP) to the solution. The mixture was dissolved in 15 mL of EG

Pi = αi·E loc(ri)

(2)

Eloc for isolated particles is the sum of an incident field and a contribution from all other dipoles in the same particle 17749



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dielectric constant is ignorable because the geometry of target calculated in this paper is larger than 10 nm. The Au triangular prisms are simulated in vacuum with the refractive index of the surrounding medium fixed at unity. The typical dimensions of edge length range from 20 to 45 nm, and prism thickness varies from 5 to 100 nm, which can be divided into two conditions according to Au typical skin depth. In the calculation below, we define AR to be aspect ratio of edge length of triangular surface and thickness. The polarization of incident light is along the y direction in the following calculations, and the accuracy of all of our simulations is ∼10−5.

E loc(ri) = E loc, i = E inc, i + Eself, i = E0 exp(iK ·ri) −

∑ Aij ·Pj (3)

j≠i

E0 and K are the amplitude and wave vector of the incident wave, respectively, and the interaction matrix A has the following form: Aij ·Pj =

exp(ikrij) ⎧ (1 − ikrij) ⎪ ⎨k 2rij × (rij × Pj) + 3 ⎪ rij rij2 ⎩ ⎫ ⎪ × [rij2Pj − 3rij(rij·Pj)]⎬ ⎪ ⎭

4. RESULTS AND DISCUSSION 4.1. Thickness Dependence of the Extinction Spectrum. In this part, edge length of triangular prisms is fixed at 20 nm and thickness of prisms varies from 5 to 60 nm. Figure 3

(4)

where k = ω/c. Defining Ajj = α−1 reduces the scattering j problem to find the polarizations Pj that satisfy a system of 3N complex linear equations: N

∑ Ajk Pk = Einc,j

(5)

k=1

Once eq 5 has been solved for the unknown polarizations Pj, the extinction and absorption cross sections Cext may be evaluated: Cext =

Cabs =

N

4πk |E0|2

∑ Im(Einc,j*·Pj)

4πk |E0|2

∑

(6)

j=1 N j=1

{Im[P(α j

j

−1

) ∗Pj*] −

2 3 2 k |Pj| 3

}

(7)

The scattering cross section can be obtained using the following relation: Cext = Cabs + Csca

Figure 3. Spectrum calculated for triangular prisms with different thickness and fixed edge length.

(8)

3.2. Target Geometry. Each object is treated with an approximately cubic array of polarizable dipoles in response to both the incident electric field and the fields created by all other dipoles in the target.19 The target built to mimic Au triangular nanocrystal is shown in Figure 2. The triangular cross section

shows the photoabsorption cross section of triangular prisms with different aspect ratio (AR) between edge and thickness. Four resonance peaks can be seen in the spectrum; they are located at about 580, 708, 870, and 983 nm for triangular prism with AR = 4. When AR varies from 4 to 0.33, the four resonance peaks blue shift about 60, 30, 70, and 110 nm to 522, 681, 808, and 870 nm, respectively. Also, the absorption intensity decreases when AR becomes smaller. That is to say, thinner triangular prisms with fixed edge length have bigger absorption cross-section and better response to light. The AR for simulation in this stage can be assigned to two different conditions that include triangular prisms with shorter or longer edge length than thickness. For edge length that is bigger than thickness, resonance peaks located in visible and infrared regions have stronger photoabsorption intensity. If we take conditions where AR is 4 and 0.5 as an example, the ratio of absorption intensity is ∼3. For simulation whose purpose is to investigate higher multipolar interaction, triangular prisms with higher AR have the advantage because of their stronger absorption intensity. The size of all triangular prisms calculated here is much smaller than wavelength; consequently, the optical response has a predominantly dipole character that can be adjusted by manipulating the system geometry. So the resonance peaks located between 522 and 582 nm are attributed to dipole SPR. Multipolar SP modes are demonstrated spectrally in the visible and near-infrared regions;

Figure 2. Schematic representation of a nanoprism with triangular faces oriented perpendicularly to the x-axis direction.

has sides of equal edge length for all triangular prisms simulated here. In the target frame, the prism axis is in the x direction. The wave vector of the incident electromagnetic radiation is considered here to propagate along the x axis direction and to be linearly polarized with its electric field being oriented along the y- or z-axis direction. Taking computing times into account, we keep the same geometric incidence configuration for all of our calculations. The dielectric function of Au is taken to be the bulk experimental value, as published in Palik’s handbook.34 The morphological differences are important only above a certain size threshold of ∼5 nm.35 The size-corrected effect of 17750



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resonance peaks located above 681 nm in the spectra can be attributed to multipolar modes. In the longer wavelength region, several multipolar resonance peaks also can be found, and it will be investigated in the following section. The optical response reflects properties of local electric field at the particle; it is essential to simulate field distribution to analyze extinction spectra and obtain comprehensive understanding of SPs. Figure 4 shows the field distribution of two

Figure 5. Calculated electric field |E2|/|E02| of triangular prisms with AR being 4 and 0.33 at different resonance wavelength. Figure 4. Calculated electric field |E2|/|E02| of triangular prisms with AR (a) 4 and (b) 0.33 at resonance wavelengths.

field-enhancement spot that is attributed to the effect of side edges of triangular prism is also classified in Figure 5b. Polarization of four poles appears to be interacting with each other, and the bridge between four poles results from the interaction. In Figure 5c,d, six poles can be found and the poles display distinct field distribution with different resonance peaks of the same triangular prism. It is the same situation as that previously mentioned in Figure 5a,b: a bridge zone appears between six poles. Through analysis of field distribution of Figures 4 and 5, it can be seen that no matter to what the resonance modes are attributed, a bridge zone can be found in the triangular plane. The overlap of field distribution in this bridge zone indicates interaction between hot spots created by poles. Field distribution mainly distributes in the triangular surface or along the edges. At platelet corners, electric field is weak and the trend that plasmons are partially transmitted to neighboring edges is displayed. In general, the surface resonance peaks will red shift while particle geometry becomes bigger. The results calculated here obviously do not have accordance with the changing trend previously mentioned. The resonance peaks blue shift when the thickness of prisms increases with fixed edge length. Undoubtedly, overall size of triangular prism with the same edge length becomes bigger while increasing thickness. In terms of absorption intensity in Figure 3, photoabsorption crosssection does not increase with thicker prisms. Two triangular planes of thicker prisms are separated far away from each other, so the plasmon interaction intensity of two planes is weaker than that of thinner triangular prisms. It must make a great contribution to the shift of plasmon resonance peaks due to plasmon interaction. In the comparison of thicker triangular prisms, plasmon interaction of two triangular planes in thinner prisms has a stronger intensity and dominates the shift of resonance peaks. To verify this conclusion, the electric-field distribution of triangular planes and side flats of triangular prisms is simulated. The results are displayed in Figure 6.

triangular surfaces. Figure 4a displays field distribution on triangular surface of triangular prism with thickness 5 nm and edge length 20 nm at resonance peak 582 nm. Field distribution on triangular surface of prism with thickness 60 nm and edge length 20 nm are shown in Figure 4b. Overall, the enhancement of the electric field of the thinner prism is stronger than that of the thicker prism. Also, we can see that field distribution in two different situations is along the edges of triangular surfaces. Three points are labeled to help analyze field distribution in Figure 4. First, point a in the two pictures shown in Figure 4 displays different field distributions. In Figure 4b, field intensity of point a is the strongest spot of the triangular surface, while that in Figure 4a is weaker than that of points b and c. Also, field intensity of triangular edges A and B is stronger than that of point a in Figure 4a. Point a is one of the ends of the side edge of the prism; the field intensity refers to the influence of side edges on the SP. It can be logically concluded that side edges of thicker triangular prisms play a more important role in SPR by comparing the field intensity of point a in the two pictures shown in Figure 4. Despite field distribution of the zone next to point a, it can seen that field distribution of triangular surface shows dipole character. Points a and b are the two poles. Dipole SP dominates the field distribution and optical response in shorter wavelength. To identify multipolar SPR in longer wavelength, field distribution at resonance peaks 708, 870, and 983 nm of triangular prism with thickness 5 nm and edge length 20 nm is calculated and shown in Figure 5. As a comparison, field distribution of prism with thickness 60 nm and edge length 20 nm at resonance peak 681 nm is also simulated and displayed in Figure 5b. Field distribution of radiation wavelength in visible, and the near-infrared zone is calculated in this stage. The four resonance peaks are located in this zone, among which characteristic SPR peaks generally appear. It can be seen from Figure 5a,b that four poles distribute on the triangular surface of different prisms. For thicker prism, field distribution expands along the orientation perpendicular to incident polarization. Also, the field distribution shrinks from edges of triangular surface to the zone far away from edges. Points c and d in Figure 5c,d refer to this trend. Field intensity of thinner prism shown in Figure 5a is about 10 times stronger than that of the thicker prism shown in Figure 5b. This indicates that the interaction of the two triangular faces of the thinner prism is very strong, while that of the thicker prism is weak. The strong

Figure 6. Calculated electric field |E2|/|E02| of side planes triangular prisms with AR being 4 and 0.33 at resonance wavelength. 17751



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Figure 7. Spectrum calculated for triangular prisms with different edge length and fixed thickness.

Field distribution of side planes of triangular prisms at resonance wavelength is show in Figure 6. It can be seen that field intensity is very strong for triangular prism with edge length 20 nm and thickness 5 nm compared with prism of thickness of 60 nm. For thicker triangular prism, field distribution in the side plane is along the side boundary, and it does not appear as a strong field distribution in the plane, while for thinner triangular prism, shown in Figure 6a, a strong field distribution can be found both along the side boundary and in the zone next to it. That is to say, strong plasmon interaction between two triangular planes appears in thinner triangular prism, while plasmon propagates alongside the boundary for thicker prism. Plasmon interaction between two triangular planes of the thicker prism is so slight to be neglected compared with that of the thinner prism. So the red shift of resonance peaks for triangular prism with decreasing thickness can be explained by the plasmon interaction between two triangular planes. 4.2. Edge-Length Dependence of the Extinction Spectrum. 4.2.1. Triangular Prism with Small AR. The typical skin depth for Au is about 20−25 nm studied here.36 In this stage, the dependence of plasmon resonance on edge length is simulated under two different conditions. One condition is that the thickness of triangular prism is much bigger than edge length, while another includes bigger edge length. The same situation for the two conditions is that the thickness of triangular prism does not change when edge length varies. The condition with bigger prism thickness is calculated in this part first. Figures 7 and 8 show the extinction spectra. The simulated extinction spectrum from 200 to 1500 nm is displayed in Figure 7. To investigate the extinction property of triangular prisms, lines in the zone between 650 and 900 nm are cut and shown in the top right of Figure 7, while Figure 8 shows the lines among the zone from 1000 to 1500 nm. It can be seen that the intensity of extinction spectra near 1500 nm is very small, so the analysis of extinction spectra in this part is limited below 1500 nm. The extinction spectra of triangular prisms calculated in this part show three resonance peaks. Resonance peaks located at ∼520 nm display a little red shift when the edge length of the triangular surface increases. This can be attributed to the increase in volume induced by changing the edge length of triangular surface. Meanwhile, finite red shift indicates that the

Figure 8. Spectrum calculated for triangular prisms with different edge length and fixed thickness in the regime from 1000 to 1500 nm.

increase in edge length does not play a decisive role. A conclusion can be obtained that thickness of triangular prisms plays a decisive role in SPR for thicker prism calculated in the zone next to 520 nm. According to analysis in Section 4.1, the resonance peaks located at ∼520 nm can be attributed to dipole resonance. Also, another two resonance peaks are displayed in extinction spectra. These two resonance peaks are located in the zone from 680 to 780 nm and between 1000 and 1300 nm. The dashed line in extinction spectra labels out the red shift trend of resonance peaks. It can be seen that resonance peaks in these two zones show a significant red shift with an increase in edge length of triangular surface. In both zones, resonance peaks red shift about 200 nm. This indicates that expansion of triangular surface significantly changes the SP property of triangular prism. In the comparison of extinction spectra simulated in Section 4.1, these resonance peaks shown in the two wavelength zones can be attributed to quadrupole resonance and SPR up to six poles. The simulated electricfield distribution can further verify the analysis above. The electric-field distribution of the triangular surface of prism with thickness 100 nm and edge length 20 nm is calculated and shown in Figure 9. In the simulation, radiation wavelength is chosen to be the wavelength of three resonance 17752



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Figure 9. Calculated electric field |E2|/|E02| of horizontal triangular surface of prism with AR being 0.2 at resonance wavelength.

peaks appearing in the extinction spectra above. The arrows in Figure label the poles in field distribution. In Figure 9a−c, there are two poles, four poles, and six poles, respectively. Also, a hot spot with field intensity stronger than two poles appears at position a in Figure 9a. The same as the analysis in Section 4.1, this hot spot refers to the strong electric-field distribution along the side edge of triangular prism. With the analysis of extinction spectra above, this phenomenon further confirms that strong field distribution along the long side edge plays an important role in SP property of thicker triangular prism with high AR. However, field intensity of point a in Figure 9b,c is weaker than that of several poles. Field distribution of wavelengths 810 and 1180 nm majorly distributes in the triangular surface. From the comparison of field intensity and distribution area, it can be concluded that interaction between several poles plays a decisive role in SP property. The effect of field distribution alongside the edge of the triangular prism can significantly influence the property of dipole resonance for a thicker prism. 4.2.2. Triangular Prism with Big AR and Discussion of Edge Effect. In this part, triangular prisms with high AR will be calculated. The thickness of prisms remains constant at 5 nm, while the edge length of triangular surface varies from 20 to 45 nm at the interval of 5 nm. The AR increases from 4 to 9, and the extinction spectra display different trend compared with triangular prisms simulated in Sections 4.1 and 4.2.1. Triangular prisms simulated in this part have wider triangular surface and thinner thickness, which will induce strong interaction between two triangular surfaces at the ends of prisms. Also, triangular surface with big edge length makes the extinction cross section big enough to investigate SP property in the far-infrared zone. Figures 10−12 show the extinction spectra. It can be seen for prisms with AR between 4 and 9 that six resonance peaks appear in the extinction spectra. Taking triangular prism with

Figure 11. Spectrum calculated in the regime from 800 to 1600 nm for triangular prisms with different edge length and fixed thickness. Figure in the top right shows proportional spectrum in the regime from 1000 to 1600 nm.

Figure 12. Spectrum calculated in the regime from 1500 to 2500 nm for triangular prisms with different edge length and fixed thickness.

thickness 5 nm and edge length 45 nm as an example, six resonance peaks are located at 687, 1080, 1243, 1653, 1807, and 2284 nm, respectively. For wavelength larger than 2500 nm, it can be seen from spectra calculated that the extinction intensity is next to zero and no other resonance peaks can be found. Resonance peaks appearing here red shift while the AR varies from 4 to 9. All resonance peaks are labeled by arrows, and the red shift trend accords with the dashed line in spectra. Coupling between the two horizontal triangular surfaces through the side surface of triangular prism is strong for thinner bulk studied here. Strong interaction of SP makes more complicated plasmon hybridization possible. This effect results in more complicated extinction spectra with more resonance peaks appearing. Also, the extinction intensity becomes higher in the comparison of thicker prisms with small AR due to strong coupling between two triangular surfaces. The trend can be easily found through comparison of spectra calculated in Sections 4.1 and 4.2.1. Through analysis of the red shift of resonance peaks shown in the previous calculated Figures, shift of one hundred or more nanometers is displayed by dashed lines. The resonance peak located between 700 and 800 nm appears in spectra of prisms with AR below 7, while no peaks

Figure 10. Spectrum calculated for triangular prisms with different edge length and fixed thickness. Figure in the top right shows proportional amplification in the regime from 500 to 800 nm. 17753



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presents interaction between different poles. All field distributions are calculated at the resonance peaks in infrared zone. It can be seen in the long wavelength region that plasmon resonance is multipolar. When the edge length increases, field distribution appears to be expanded along the edges. Also, field at resonance modes majorly distributes in the triangular surface, and a characteristic “bridge” zone can be obtained. In the longwavelength regime where the SP dispersion is close to the light line, the combined excitation consisting of an SP and an electromagnetic wave is called an SPP. In a comparison of field distribution in the short wavelength regime shown in Sections 4.1 and 4.2.1, field in the long wavelength zone displays a complicated distribution. In the far-infrared zone, SPR still exists. Although the intensity in spectra is very small, strong local electric field enhancement has been discovered. For very thin triangular prisms studied in this part the thickness of prisms is smaller than the typical skin depth. This makes SPs of two triangular surfaces interacting with each other possible and the absorption intensity higher. In Section 4.1, we have compared field distribution of side surfaces of two prisms with different thickness. It can be seen for thicker prism that the field distribution is along the side edge, which just represents longitude distribution. For thinner prism, strong field distribution can be found in the side surface, which confirms the existence of interaction between two triangular surfaces. Figure 15 shows field distribution of side surface of triangular

can be found in spectra with AR above 7, which is superseded by a trough located at ∼780 nm according to its transformation trend. For triangular prism with AR equal to 9, the trough reds shift to ∼830 nm. Peaks in extinction spectra stand for resonance modes, and trough here represents a mode that electrons do not collectively resonate with incident light. The optical response reflects properties of local electric field, so analysis of field distribution is given below to obtain comprehensive understanding of spectra transformation. In Figure 13, field distribution of triangular surface of prisms with

Figure 13. Calculated electric field |E2|/|E02| of triangular prisms with AR being (a) 4 and (b) 9 at resonance wavelength.

edge length is 20 and 45 nm is presented. Arrows in Figure 13a label four poles, and the ellipse refers to the “bridge” zone. In Figure 13b, it can seen that distribution of electric field is along the two upper edges, which is similar to the picture shown in Figures 4a and 9a. Field distribution shown in these two Figures stands for dipole Plasmon resonance and represents predominantly dipole character. For resonance modes, field distribution shows a “bridge” zone in the triangular surface that indicates interaction between different poles. For unresonant mode, field distributes along two upper edges of triangular surface shown in Figure 13b, and a predominantly dipole-like character property is obtained. Through analysis of field distribution combined with spectra, SP of thinner prisms transforms to be unresonant when the AR increases. In Sections 4.1 and 4.2.1, field distribution of prism with thickness 5 nm and edge length 20 nm in the region below 1000 nm has been calculated and analyzed. The field displays three characteristic distributions with two, four, and six poles. So we will simulate field distribution in the far-infrared zone above 1000 nm in this part. As for analyzing the transformation of field, distribution of prisms with edge length 20 and 45 nm is calculated. Arrows in Figure 14 label poles, and ellipses in triangular surface represent the so-called “bridge”’ zone that

Figure 15. Calculated electric field |E2|/|E02| of side surfaces of prisms with AR being 4 at different resonance wavelengths.

prisms with thickness 5 nm and edge length 20 nm at different resonance peaks. Different from field distribution shown in Figure 6b, field distribution of thinner prisms calculated in this part can be seen in side surfaces. It indicates that for very thin triangular prisms incident light can excite SP in side surface. Not like the field excited along the edge of side surface of thick prisms with small AR, field distribution does not display just

Figure 14. Calculated electric field |E2|/|E02| of triangular prisms with AR being (a−c) 4 and (b−f) 9 at different resonance wavelengths in farinfrared zone. 17754



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longitude mode for thinner prisms with high AR. Meanwhile, the same as the triangular surfaces, plasmon also is excited in side surfaces of prisms, which serve as media for interaction between two triangular surfaces. As shown in Figure 15, field distribution appears to be different for different SPR wavelengths. That is to say, the region that transmits Plasmon− plasmon interaction changes while the resonance wavelength varies. Ultrathin triangular prism under typical skin depth for Au makes coupling between the two horizontal triangular surfaces possible and provides rich plasmon phenomena that not only amplify electric field but also localize field distribution.

REFERENCES

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5. CONCLUSIONS Indeed, the response of triangular prisms with different AR to the incident wave is investigated, and large mixing coupling effects and field enhancement of ultrathin triangular prisms are obtained. The response of triangular prism can be profoundly changed when the thickness decreases. The spectra of ultrathin triangular prisms reveal different characteristics compared with thick prisms with small AR. The mixing coupling effect between two horizontal triangular surfaces and plasmon excitation of side surfaces change the SPR property greatly for thin triangular prisms with high AR. No matter changing prism thickness and edge length of triangular surfaces, the resonance peaks red shift. Reduction of prism thickness leads to hybridization/mixing between two horizontal triangular surfaces and possibly overall enhancement of absorption cross-section of nanoparticle and shows excellent ability to adjust the resonance peaks. Furthermore, field distribution of side surface can be regulated with different resonance peaks. The field of side surfaces for thick triangular prisms with small AR just distributes along the edge of the side surface, showing longitude field distribution. For thick triangular prisms, field distribution cannot be found in side surfaces, which indicates weaker interaction between two horizontal surfaces. The calculation of the field enhancement also shows that the location of the field enhancement is specified by the resonance pattern. A “bridge” zone can be found in triangular surfaces at resonance wavelength, which refers to coupling effect between different poles. Overall, field distribution mainly distributes in the triangular surface or along the edges. At platelet corners, electric field is weak and the trend that plasmons are partially transmitted to neighboring edges is displayed.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; Tel: +86 0816 2480827; Fax: +86 0816 2480830 (Y.-g.Y.). E-mail: [email protected]; Tel: +86 0816 2480827; Fax: +86 0816 2480830 (Y.-j.T.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Special thanks to Ms. Yang Qiyan for her help in English correction. The work is supported by the National Natural Science Foundation of China (grant no. 11075143), the developing Foundation of China Academy of Engineering Physics (grant no. 2009A0302020), the Fundamental Research Funds for the Central Universities of Central South University (grant no. 2013zzts011), and the Open-End Fund for the Valuable and Precision Instruments of Central South University (CSUZC2013027). 17755



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