Study on surface plasmons of gold and silver with different structures
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https://www.eduzhai.net Nanoscience and Nanotechnology 2015, 5(4): 71-81 DOI: 10.5923/j.nn.20150504.01 Study of Surface Plasmon Excitation on Different Structures of Gold and Silver Anchu Ashok1,*, Arya Arackal1, George Jacob2 1School of Electronics Engineering, VIT University, Vellore, India 2Center of Nanotechnology Research, VIT University, Vellore, India Abstract Surface Plasmon Polaritons (SPPs) are intrinsically two dimensional excitations existing on the metal dielectric interface, which will decay exponentially with distance. In this work we studied the dependence of shape and gap of the structures on its field enhancement. Triangular structure has more electric field enhancement when compared with circle, ellipse and square, because of their sharp corners, which can make better confinement than any other structures. It has been identified the enhancement in single and double structures, in which double structures shows more field localization due to its coupling of the electric field between the structures. When the gap between two structure decreases, the dipole-dipole interaction and field enhancement increases and leads to a red shift in wavelength. In the study of ellipse we identified a double peak of resonance in longer wavelength (longitudinal resonance) and shorter wavelength (transverse resonance) due to the major axis minor axis of ellipse respectively. In triangular patterns, as the gap between the structures is less, then near field coupling is more. So the total effect is a single resonance peak irrespective of the number of resonators present in the pattern. Keywords SPR, Dipole-Dipole interaction, Coupling 1. Introduction The electromagnetic waves that propagateon metal dielectric interface by the interaction of incident electromagnetic wave with metal are called Surface Plasmon Polaritons (SPPs) . The coupling between light radiation and free electron charges within metals results an exponential decay of these collective electron oscillations from the metal surface. These standing oscillations in the metal dielectric interface will cause resonance termed as surface plasmonicresonance (SPR) . The interaction of the electromagnetic wave with metal leads to the oscillation of the electrons in the metal and it leads to the transfer of energy from the electromagnetic wave to the metal by the process of absorption. The electrons in the metal get accelerated and radiated the energy through scattering process. Mie theory describes the dependence of the absorption and scattering process on the size of the particle . It states that the particle size less than 40nm, absorption of energy dominates the radiation process. On other hand, the particle with 100nm or larger size shows more scattering effect. The controllable optical response of the metal with their size, shape and other physical parameters enable us to * Corresponding author: email@example.com (Anchu Ashok) Published online at https://www.eduzhai.net Copyright © 2015 Scientific & Academic Publishing. All Rights Reserved tailor SP properties for the applications in all the fields of science . In last decade, the strong coupling between light and surface plasmons in nanostructures offers a large possibility of applications in the field of nanoantenna  biosensing , lithography and optical data storage . Nanoparticle pairs yield to high field enhancement between their gap used as a substrate in surface enhanced Raman scattering spectroscopy , with single molecule sensitivities. In this work we are discussing about the shape and gap effect of different structures and the effect in the triangular patterns. 2. Simulation Models In this work Finite Element Method (FEM)  is used to analyses the electric field distribution on different structures of gold and silver. We calculated the field enhancement in the wavelength range 300nm-800nm with an incident electric field of 1 V/m. In this paper, the silver and gold permittivity data are obtained from Palik dielectric model . Maxwell's equation in the matter is used to solve the optical response of the metal which is characterized by a dielectric constant. As discussed above, in the whole work particle size of 100nm has been used to get better scattering and for a good study of surface plasmonic resonance. The effect TM polarized light of 1V/m oncircle (diameter 100nm), square (side length 100nm), ellipse (axis length 72 Anchu Ashok et al.: Study of Surface Plasmon Excitation on Different Structures of Gold and Silver 100:40 nm) and triangle (side length 100nm) structures of gold and silver are compared and demonstrated (Figure 1). 3. Results and Discussion Single structures of Gold and Silver Figure 2 shows the interaction of light with different structures of gold. The triangular structure will have maximum electric field enhancement (9.126V/m) at a wavelength of 550nm, because of the sharp edges and corners. Figure 3 shows the interaction of light with different structures of silver. In silver structures also triangle will give the maximum field enhancement with a resonance wavelength in visible range. Propagation lengths in all the cases are calculated for find the better coupling between the structures. Table 1 shows the effect of light excitation on different structures of gold and silver. Figure 1. Different structures of circle, square, ellipse and triangle with the direction of incident plane wave source Figure 2. The electric field intensity in [a] circle (dia:100nm) [b] square (side length:100nm)[c] ellipse (axis 100:40nm) [d] triangle (side length:100nm) of gold Nanoscience and Nanotechnology 2015, 5(4): 71-81 73 Figure 3. The electric field intensity in (a) circle (b) square(c) ellipse (d) triangle of silver Table 1. Excitation parameters in single structure of gold and silver Structure Lambda (nm) EF( ٭V/m) PL(٭nm) Circle 540 1.6 18 GOLD Ellipse Square 500 550 5.25 2.45 3.07 8.1 Triangle 550 8.234 2.1 Circle 354 2.25 11.51 SILVER Ellipse Square 332.6 387.5 3.45 9.126 8.95 5.42 Triangle 427.6 18.3 4.09 ٭EF- Electric Field, ٭PL-Propagation Length The tabulated data shows that silver will give more field enhancement and localization energy in UV ranges when compared with gold in its visible spectrum. . The propagation length will decrease as the electric field enhancement increases. These fields are highly localized and increase the intensity of the hot spot in that region . Since silver shows more field enhancement, so selected silver as material for the further works. Double structures of silver This section is discussing about double structures of circle, square, ellipse and triangle. The distance chosen between the two structures is less than twice the propagation length. 1. Circle The distance between the two circlesis varied depending on the propagation length and varied between 5.5nm to 20.5nm. When the gap is very small the localized electric field is high because of the strong interaction of dipoles in the gap. Figure 4(a) shows the simulation model of strong hot spot between the structures of silver. The strong interactions of dipole between the circle gives the electric filed intensity of 18.5 V/m in 5.5nm gap and a least electric field of 6V/m in 20.5 nm gap. Figure 4(b) shows that the field excitation of surface plasmons indifferent gaps. The resonant wavelength red shifts on gap reduction due to the increase in inter electrode interaction which inturn leads to the highly localized electric field between the gap . 2. Ellipse Double peak of resonance in Figure 5(b) is because of the asymmetric structure of ellipse. The surface plasmonic resonance in ellipse splits into two modes, transverse mode 74 Anchu Ashok et al.: Study of Surface Plasmon Excitation on Different Structures of Gold and Silver and longitudinal mode of resonance. The longer wavelength represents the longitudinal resonance and the shorter wavelength shows transverse resonance. The aspect ratio plays a major role in the shift in wavelength. As the aspect ratio increases there is a clear red shift in the longitudinal mode . When the gap decreases to a few nanometers the double elliptical structure acts as a single ellipse with very high aspect ratio. So at 3nm gap longitudinal mode is having less electric field intensity than transverse mode with a red shift in wavelength. Also when gap increases, the electric field intensity on transverse mode decreases. In ellipse as the gap decreases the two resonators together provide the effect of a single resonator with high intensity. Orientation of electric field relative to the particle determines the resonance wavelength. The surface plasmon resonance frequencies of the ellipse can be tuned systematically by changing the axis length. 3. Square From the Table 1.single structure of silver square shows the propagation length of 5.42 nm. So here consider the gap between these structures from 1.5 nm to 11.5nm, which gives an effective coupling of two structures. ) ) Electric field (V/m) Wavelength (nm) Figure 4. (a) Electric field distribution in double circular structure of silver (b) Electric field intensity spectra of double circular structure of silver for different gaps Figure 5. (a) Electric field intensity between two structure of ellipse (b) Plots of electric field intensity for different gaps Nanoscience and Nanotechnology 2015, 5(4): 71-81 75 Figure 6. (a)Electric field distribution at the resonant wavelength for two silver square structures (b) Electric field intensity plots at different gaps ) ) Electric field (V/m) Wavelength (nm) Figure 7. (a) Electric field distribution at resonant wavelengths for two silver triangular structures (b) Electric field intensity plots at different gaps between the triangles As discussed above, when the gap decreases inter electrode interaction increases and field localization increases, which leads to the increase in the intensity of hotspot between structures. From Figure 6(b) it is clear that when gap is 1.5nm the electric field intensity is 40.39 V/m at a wavelength of 770.9 nm. 4. Triangle Figure 7(b) shows that as gap decreases there is an increase in electric field intensity between the structures, also there is a red shift in resonance wavelength. The table 2 below shows the excitation parameters for double structured silver. Table 2. Excitation parameters for double structures of silver Structure Ef (V/m)* Lambda (nm) Circle 20.1 375.2 Ellipse 36.551 459.2 Square 40.39 774.9 Triangle 318.43 442.8 *Ef -Electric field Table 2 shows triangle double structure electric field 76 Anchu Ashok et al.: Study of Surface Plasmon Excitation on Different Structures of Gold and Silver intensity is 7.89 times better than square, 8.72 times better than ellipse and 15.85 times better than circle. Many applications like biosensors, optical storage device and SERS, the field enhancement is an important parameter. So triangular pattern may be a better option. Pattering of triangular structure The above results show that the triangle structure is giving maximum field enhancement. This section discuss about patterning of triangle structures as in Figure 8. In this pattern two types of resonators are there, one is corner to corner and other is edge to edge triangle resonator. We already discussed the effect of gap variation between the corners. Here discussing more about the edge to edge effects. Depending upon the gap between the two structures there are two resonances one at high wavelength and other at lower wavelength. The resonance at high wavelength is due to the maximum field enhancement between the gap shown in Figure 9(a) and the resonance at lower wavelength is due to the maximum enhanced field at corners shown in Figure 9(b). At smaller gap there exist both resonances; while increase in gap causes the dipole-dipole interaction to get reduced between the gap and only shorter wavelength resonance exist. This effect is shown in the Figure 9(c). When the gap is about 1nm maximum field enhancement (10.274V/m) is at higher wavelength (590nm). As gap decreases to 4nm and 6nm, the interaction of dipoles decreases and there is a blue shift in wavelength. But in the case of lower wavelength resonance the maximum electric field enhancement occur at 400nm and no shift in wavelength with a change in gap because of the absence of inter electrode interaction in the case of shorter wavelength resonance. At large gap, the higher wavelength resonance vanishes. Figure 8. Linear pattern of triangular structure ) ) ) Figure 9. (a) Maximum electric field intensity between the gap (enlarged portion shows the electric field)(b) maximum electric field intensity in the corners (c) Electric field intensity spectra of the edge to edge triangle with different gaps Nanoscience and Nanotechnology 2015, 5(4): 71-81 77 Figure 10. (a) Electric field intensity in the pattered triangular structure (b) electric field intensity spectra of pattered triangular structure with different gaps Plane wave(300nm to 800nm) a) m m m m m m m m m m m a) b) c) Figure 11. (a) Schematic diagram (b) shows the relation of thickness with resonance wavelength (c) plot shows the electric field enhancement in different thickness in 50 nm sidelength of triangle 78 Anchu Ashok et al.: Study of Surface Plasmon Excitation on Different Structures of Gold and Silver a) b) Figure 12. (a) shows the relation of thickness with resonance wavelength (b) plot shows the electric field enhancement in different thickness in 100 nm sidelength of triangle a) b) c) Figure 13. Electric field intensity on (a) double structure (b) linear pattern (c) 2D pattern of Gold and Silver Nanoscience and Nanotechnology 2015, 5(4): 71-81 79 In Figure 10(a) there are two types of resonators as we discussed previously one is corner to corner resonator and another is edge to edge resonators. The resonance of corner to corner resonator will be on visible range as of edge to edge resonance is at near IR range. When the gap between all structures is about 1nm the two resonators will act as a single resonator and give a single peak of resonance at a wavelength of 400nm. When the gap between the structures increases from 2nm to 4nm the field enhancement decreases. The gap of6nm shows the presence two resonators which will act individually and give two peaks of resonance for edge to edge and corner to corner at shorter wavelength and larger wavelength respectively. And there is an effective blue shift for the larger wavelength resonance. As the spacing increases near field coupling diminishes and reaching single particle resonance. 4. Effect of Thickness in Resonance Wavelength This section deals with the effect of resonance wavelength and the electric field in the thickness. Here it demonstrate a 100 nm and 50 nm side triangle with varying the thickness from 3 nm to 100 nm. Triangle with side length 50 nm and thickness of 25 nm gives a good electric field and resonance wavelength as indicated in Figure 11and in 100 nm side triangle 50 nm thickness (Figure 12) gives the same. These studies shown that if the thickness is half of that of sidelength there is a better electric field and resonance wavelength. So for the further work it is preferred to take the triangle of sidelength 100nm and thickness 50 nm. Following section shows the patterns of triangular structures with triangular void, rhombus void and star void between it. a) b) c) d) Figure 14. Electric field plot on (a) double structure (b) four structure (c) two row of linear structure (d) three row of linear structure of Silver and Gold 80 Anchu Ashok et al.: Study of Surface Plasmon Excitation on Different Structures of Gold and Silver a) b) d) c) Figure 15. Electric field intensity spectra of (a) single pattern (b) double pattern (c) linear array (d) three row of linear structures of Gold and Silver Group 1 Patterns First types of pattern is shown below These structures provide a triangular void in between the patterns. In double structure maximum electric field is due to the dipole-dipole interaction between the corners. The first peak is due to the dipole interaction (LSPs) and the second peak is due to the coupling between the electric field (PSPs). In linear pattern electric field increased due to the interaction as well as coupling between the field enhancements from each corner. In this case the coupling between the hot spot is high, because of the 100 nm distance between these enhancements. This effective coupling increases the electric field enhancement from299.61 V/m to 403.81 V/m in case of Silver. When the linear pattern converts into 2D pattern the effective electric field intensity increased because of the same reason mentioned above. Group 2 Patterns Second group of pattern provide a rhombus void between them. This type of patterns gives the clear information about the relation between the coupling and propagation distance. Figure14(a-b) shows that while converting the double structure to linear structure the electric field intensity reduced because of the less coupling of field enhancement from one structure to the another structure. The distance between two field enhancements is 175 nm which is not sufficient to couple the electric field from one structure to another. So when the structure extends from double to linear pattern the electric field intensity reduced. But when these linear array is converted into 2D array with a rhombus void between that the electric field enhancement increased as a result of the coupling between the above and below linear pattern. (Figure 14 c-d). Group 3 Patterns Next type of pattern give a star void in between the arrangement. From Figure 15 (a-d) electric field intensity increases because of the increment in the field confinement from single pattern to the three row linear structure. Even though the coupling distance is less the increase in the electric field is due to the confinement of the electric field between the
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