Abstract

We developed a method of composite domain control (CDC) for plasmon resonance as an application of multilayered domain control (MLDC). A distinctive characteristic of CDC is the utilization of dielectric and metal particles. Its structure is similar to that fabricated by the sol-gel method. It is considerably thinner than that prepared by MLDC. In addition, it is possible to conveniently and exactly adjust the plasmon resonance utilizing CDC because it combines the characteristics of MLDC. Accordingly, CDC is a conventional method that is more effective than MLDC. Moreover, CDC is suitable in manufacturing with regard to stress reduction, miniaturization, and cost of the products.

© 2006 Optical Society of America

1. Introduction

During recent years, nanotechnologies have been seriously considered by high-tech industries. One of these technologies is the study of surface plasmons; surface plasmons have been studied in many institutes for several decades [1–5], and many applications such as sensors [6, 17], near-field scanning optical microscopes [7, 8, 18], and optical memories [9–11] have been devised. Further, in 2005, we proposed multilayered domain control (MLDC) for the application of surface plasmon resonance. One of the characteristics of MLDC is the easy control of plasmon resonance. The structure of MLDC is shown in Fig. 1. MLDC can be used to easily adjust the apparent plasmon resonance to a desired level and wavelength [16]. Although noble metals have been utilized in conventional studies [12–15], MLDC can potentially substitute noble metals with base metals [16].

 

Fig. 1. (a) Design of MLDC. (b) SEM image of Ag particles. They are deposited using DC sputtering and distributed two-dimensionally. (c) TEM image of the cross section (four Ag layers).

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In the MLDC study, we observed a change in absorbance depending on the distance of the particle layers [16]. However, for a distance less than 10 nm, this change is not discernible because of the formation of islands instead of a complete thin film. We then contrived the method of composite domain control (CDC). In this method, dielectric particles are used to separate the metal particles. A structure of CDC is shown in Figs. 2(a)–2(d). Ag particles are indicated by the white spherical particles in Fig. 2(a), and SiO2 particles are densely distributed as shown in Fig. 2(b). Thus, the dielectric that separates the metal particles is composed of particles instead of a thin film.

Therefore, CDC is suitable in applications involving small packages because its structure is considerably thinner than that of MLDC. In addition, this thin structure is advantageous in stress reduction and also helps in reducing the manufacturing cost of the products. Furthermore, MLDC and CDC have possibilities of applying to non-liner optics [19, 20], surface enhanced Raman scattering (SERS) [21], etc.

 

Fig. 2. (a) SEM image of Ag particles. The particles with an average diameter of 8 nm are randomly distributed on the thin SiO2 film. On an average, they are allowed a spacing of 6 nm. (b) SEM image of SiO2 particles. The particles with an average diameter of 8 nm are randomly distributed on the particles shown in Fig. 2(a). On an average, they are allowed a spacing of 2 nm. (c) Design of CDC. (d) TEM image of a CDC cross section (five Ag layers).

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2. Composite domain control

MLDC was contrived in order to independently control the horizontal as well as vertical factors. Accordingly, it assumes the form of a two-dimensionally stacked structure, as shown in Fig. 1(a) [16]. Further, it is possible for CDC to independently control both the factors because it is fabricated using a similar process. The structure of CDC is fabricated as follows. First, a substrate comprising a borosilicate glass is bombarded with Ar (RF power is 150W, and gas flow rate is 28 sccm). Next, a dielectric material is deposited on the cleaned substrate as the lower dielectric layer. Metal and dielectric particles are formed one after the other on the dielectric layer. Metals are deposited by DC sputtering and the dielectric by RF sputtering. Finally, a dielectric material is deposited as the upper dielectric layer. Thus, particles are completely sealed with the dielectric material. However, it is somewhat unstable to fabricate particles on top of particles. In addition, dielectric materials tend to grow cylindrically during RF sputtering. Thus, dielectric particles are formed in a manner different to that of metal particles. Further, in this paper, we describe the sizes of the metal particles with respect to their diameters and that of the dielectric particles with respect to the sputtering time.

3. Experimental results

In fact, we discuss the plasmon resonance in relation to the absorbance measured using a spectrometer (Hitachi U-4000). The wavelength resonance of this measurement is ±0.2 nm. The peak height and peak wavelength exhibit the properties of surface plasmon resonance. In this paper, we elucidate the unique controllability of plasmon resonance as in the case of MLDC.

The structure of CDC is shown in the TEM image of Fig. 2(d). The metal particles are Ag, and the dielectric particles are SiO2. The average diameter of the Ag particles is 15 nm and that of the SiO2 particles is 15 nm (10 s) (the size dispersion of particles are not managed in this experiment). The two-dimensionality of the metal particle layers appears to be deteriorated in the upper layers, as shown in Fig. 2(d). However, the absorbance peak, which implies the resonance peak, constantly increases depending on the number of layers, as shown in Fig. 3(a). The peak of the Ag group shifts from 1.00 (λ = 445 nm) to 1.51 (λ = 437 nm) and to 2.14 (λ = 427 nm). Similarly, the peak of the Au group shifts from 0.30 (λ = 563 nm) to 0.52 (λ = 552 nm) and to 0.69 (λ = 544 nm). Although the deterioration of the two-dimensionality is reflected in the blue shift, it has an insignificant effect on the controllability.

Therefore, stacking of the metal particle layers is also effective in intensification as in the case of MLDC.

Figure 3(b) shows an effect of the metal domain growth that is intensified due to the multilayered effect. In Fig. 3(b), the average diameters of the Ag particles are 8 nm, 15 nm, and 23 nm and those of the Au particles are 5 nm, 10 nm, and 15 nm. The dielectric SiO2 particles and both the groups in Fig. 3(a) are intensified with five layers. The peak of the Ag group shifts from 0.62 (λ = 441 nm) to 0.85 (λ = 457 nm) and to 1.16 (λ = 473 nm). Similarly, the peak of the Au group shifts from 0.22 (λ = 556 nm) to 0.32 (λ = 568 nm) and to 0.47 (λ = 582 nm). Thus, both absorbance and peak wavelength vary depending on the metal domain growth.

Then, the plasmon resonance is controlled as follows. In order to control the wavelength, one method of rough adjustment is the choice of the materials (permittivity of the metal and dielectric) [17] and that of a minor adjustment is the size of the metal particles. In order to adjust the absorbance, a method of rough adjustment is the stacking of the particle layers and that of minor adjustment is the size of the metal particles. Then, the plasmon resonance is conveniently and exactly controlled with these methods. In Figs. 3(a) and 3(b), the distribution of Ag peaks is 430 < λ < 480, and that of Au peaks is 550 < λ < 590. They show the possibility that only two metal materials cover the wide range of wavelength. It is the same as in the case of MLDC. Therefore, CDC combines the merits of MLDC with a potential for manufacturing.

 

Fig. 3. (a) Each pattern exhibits surface plasmon resonance and each peak corresponds to the resonance peak. The number of layers is 6, 8, and 10 in the Ag group and 5, 9, and 12 in the Au group. All other factors are equal in each group. Expressions in the legends such as “6L/15 nm/15 s,” imply the following. “6L” means the number of metal particle layers. “15 nm” means the average diameter of the metal particles. “15 s” means the time of deposition of the dielectric particles. The sizes of the dielectric particles are regulated by time because they depend on the sizes of the metal particles. (b)Each pattern exhibits surface plasmon resonance and each peak corresponds to the resonance peak, similar to Fig. 3(a). The particle diameters are 8, 15, and 23 nm in the Ag group and 5, 10, and 15 nm in the Au group. All of them are intensified with five layers. All other factors are equal in each group. Expressions in the graph have a similar form as in Fig. 3(a).

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4. FDTD simulation

The structure of CDC is similar to that fabricated by the sol-gel method. The nano metal particles appear to be randomly arranged at the cross sections of both the structures, as shown in Fig. 2(d). However, these particles locate regularity along the vertical direction. Accordingly, CDC is characterized by randomness in the horizontal plane and regularity along the vertical direction. Here, it is advantageous to apply plasmon resonance as in the case of MLDC [16]. It is effective use of coupling with fields that are propagated horizontally from adjacent particles because the particles are arranged two-dimensionally in the horizontal plane. Therefore, CDC is able to effectively utilize the plasmon resonance. FDTD simulation is a suitable method for understanding the origin of this characteristic. We have calculated the field intensity distributions for CDC and the random structures by using a commercial 3D FDTD software (Fujitsu Poynting).

Figures 4(a) and 4(b) are the calculated results of the distribution images of the electric field intensity for CDC and a randomly arranged structure, respectively. The particle sizes are arranged heterogeneously in conformity with their physical structures. The contour lines of CDC in Fig. 4(a) are flat when compared with those of the random structure in Fig. 4(b). It is the characteristic of CDC that contour lines align parallel after getting through metal particles.

 

Fig. 4. (a) Electric field of CDC. (b) Electric field of randomly arranged particles.

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5. Conclusions

We have been studying CDC along with MLDC. Both these methods have allowed convenient and exact adjustment of plasmon resonance. The application of surface plasmons that randomly arranges metal particles in the horizontal plane and regularly in the vertical direction is advantageous. In addition, CDC is suitable in manufacturing with regard to stress reduction, miniaturization, and the cost of the products. Therefore, it is believed that CDC is a more effective conventional method than MLDC. It implies that CDC is a unique and productive method with regard to controllability and effectiveness.

References and links

1. R. Fuchs and K. L. Kliewer, “Optical modes of vibration in. an ionic crystal sphere,” J. Opt. Soc. Am. 58, 319–330 (1968). [CrossRef]  

2. B. J. Messinger, K. U. von Raben, R. K. Chang, and P. W. Barber, “Local fields at the surface of noble-metal microspheres,” Phys. Rev. B 24, 649–657 (1981). [CrossRef]  

3. H. Dohi, Y. Kuwamura, M. Fukui, and O. Tada, “Long-range surface plasmon polaritons in metal film bounded by similar-refractive-index materials,” J. Phys. Soc. Jpn. 53, 2828–2832 (1984). [CrossRef]  

4. Y. Kuwamura, M. Fukui, and O. Tada, “Experimental observation of long-range surface plasmon polaritons,” J. Phys. Soc. Jpn. 52, 2350–2355 (1983). [CrossRef]  

5. M. Fukui and K. Oda, “Studies on metal film growth through instantaneously observed attenuated total reflection spectra,” Appl. Surf. Sci. 33–34, 882–889 (1988). [CrossRef]  

6. J. S. Yuk, S. Yi, J. Han, Y. Kim, and K. Ha, “Surface plasmon resonance intensity in ex situ analysis of protein arrays using a wavelength interrogation-based surface plasmon resonance sensor,” Jpn. J. Appl. Phys. 43, 2756–2760 (2004). [CrossRef]  

7. U. C. Fischer and J. Heimel, “Elastic scattering by a metal sphere with adsorbed molecule as a model for the detection of single molecules by scanning probe enhanced elastic resonant scattering (SPEERS),” Jpn. J. Appl. Phys. 40, 4391–4394 (2001). [CrossRef]  

8. M. Futamata and A. Bruckbauer, “Attenuated total reflection-scanning near-field Raman spectroscopy,” Jpn. J. Appl. Phys. 40, 4423–4429 (2001). [CrossRef]  

9. J. Tominaga, J. Kim, H. Fuji, D. Büchel, T. Kikukawa, L. Men, H. Fukuda, A. Sato, T. Nakano, A. Tachibana, Y. Yamakawa, M. Kumagai, T. Fukaya, and N. Atoda, “Super-resolution near-field structure and signal enhancement by surface plasmons,” Jpn. J. Appl. Phys. 40, 1831–1834 (2001). [CrossRef]  

10. J. Kim, K. Song, and K. Park, “Near-field optical readout combined with atomic force probe recording,” Jpn. J. Appl. Phys. 41, 1903–1904 (2002). [CrossRef]  

11. K. P. Chiu, W. C. Lin, Y. H. Fu, and D. P. Tsai, “Calculation of surface plasmon effect on optical discs,” Jpn. J. Appl. Phys. 43, 4730–4735 (2004). [CrossRef]  

12. T. Okamoto, M. Haraguchi, and M. Fukui, “Light intensity enhancement and optical nonlinear response due to localized surface plasmons in nanosize Ag sphere,” Jpn. J. Appl. Phys. 43, 6507–6512 (2004). [CrossRef]  

13. T. Chen, W. Su, and Y. Lin, “A surface plasmon resonance study of Ag nanoparticles in an aqueous solution,” Jpn. J. Appl. Phys. 43, L119–L122 (2004). [CrossRef]  

14. H. Mertens, J. Verhoeven, A. Polman, and F. D. Tichelaar, “Infrared surface plasmons in two-dimensional silver nanoparticle arrays in silicon,” Appl. Phys. Lett. 85, 1317–1319 (2004). [CrossRef]  

15. Y. Hamanaka, K. Fukuta, A. Nakamura, L. M. Liz-Marzán, and P. Mulvaney, “Enhancement of third-order nonlinear optical susceptibilities in silica-capped Au nanoparticle films with very high concentrations,” Appl. Phys. Lett. 84, 4938–4940 (2004). [CrossRef]  

16. T. Saito, M. Haraguchi, and M. Fukui, “Multilayered domain control for plasmon resonance,” Jpn. J. Appl. Phys. 44, L1234–L1236 (2005). [CrossRef]  

17. M. Fukui and M. Ohtsu, Hikari nano technology no kiso (Ohmsha, Tokyo, 2003), Chap. 3.

18. T. Saiki and Y. Toda, Nano scale no hikari bussei (Ohmsha, Tokyo, 2004), Chap. 4.

19. I.V. Kityk, A. Ali Umar, and M. Oyama, “Circularly polarized light-induced electrogyration in the Au nanoparticles on the ITO,” Physica E 27, 420–426 (2005). [CrossRef]  

20. I.V. Kityk, Ebothé, K. Ozga, K.J. Plucinski, G. Chang, Kobayashi, and M. Oyama, “Non-linear optical properties of the Ag nanoparticles on the ITO,” Physica E 31, 38–42 (2006). [CrossRef]  

21. S. Hayashi and T. Konishi, “Scanning Near-Field Optical Microscopic Observation of Surface-Enhanced Raman Scattering Mediated by Metallic Particle-Surface Gap Modes,” Jpn. J. of Appl. Phys. 44, .5313–5318 (2005) [CrossRef]  

References

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  1. R. Fuchs and K. L. Kliewer, "Optical modes of vibration in. an ionic crystal sphere," J. Opt. Soc. Am. 58, 319-330 (1968).
    [CrossRef]
  2. B. J. Messinger, K. U. von Raben, R. K. Chang, and P. W. Barber, "Local fields at the surface of noble-metal microspheres," Phys. Rev. B 24, 649-657 (1981).
    [CrossRef]
  3. H. Dohi, Y. Kuwamura, M. Fukui, and O. Tada, "Long-range surface plasmon polaritons in metal film bounded by similar-refractive-index materials," J. Phys. Soc. Jpn. 53, 2828-2832 (1984).
    [CrossRef]
  4. Y. Kuwamura, M. Fukui, and O. Tada, "Experimental observation of long-range surface plasmon polaritons," J. Phys. Soc. Jpn. 52, 2350-2355 (1983).
    [CrossRef]
  5. M. Fukui and K. Oda, "Studies on metal film growth through instantaneously observed attenuated total reflection spectra," Appl. Surf. Sci. 33-34, 882-889 (1988).
    [CrossRef]
  6. J. S. Yuk, S. Yi, J. Han, Y. Kim, and K. Ha, "Surface plasmon resonance intensity in ex situ analysis of protein arrays using a wavelength interrogation-based surface plasmon resonance sensor," Jpn. J. Appl. Phys. 43, 2756-2760 (2004).
    [CrossRef]
  7. U. C.  Fischer and J.  Heimel, "Elastic scattering by a metal sphere with adsorbed molecule as a model for the detection of single molecules by scanning probe enhanced elastic resonant scattering (SPEERS)," Jpn. J. Appl. Phys. 40, 4391-4394 (2001).
    [CrossRef]
  8. M. Futamata and A. Bruckbauer, "Attenuated total reflection-scanning near-field Raman spectroscopy," Jpn. J. Appl. Phys. 40, 4423-4429 (2001).
    [CrossRef]
  9. J. Tominaga, J. Kim, H. Fuji, D. Büchel, T. Kikukawa, L. Men, H. Fukuda, A. Sato, T. Nakano, A. Tachibana, Y. Yamakawa, M. Kumagai, T. Fukaya, and N. Atoda, "Super-resolution near-field structure and signal enhancement by surface plasmons," Jpn. J. Appl. Phys. 40, 1831-1834 (2001).
    [CrossRef]
  10. J. Kim, K. Song and K. Park, "Near-field optical readout combined with atomic force probe recording," Jpn. J. Appl. Phys. 41, 1903-1904 (2002).
    [CrossRef]
  11. K. P. Chiu, W. C. Lin, Y. H. Fu, and D. P. Tsai, "Calculation of surface plasmon effect on optical discs," Jpn. J. Appl. Phys. 43, 4730-4735 (2004).
    [CrossRef]
  12. T. Okamoto, M. Haraguchi, and M. Fukui, "Light intensity enhancement and optical nonlinear response due to localized surface plasmons in nanosize Ag sphere," Jpn. J. Appl. Phys. 43, 6507-6512 (2004).
    [CrossRef]
  13. T. Chen, W. Su and Y. Lin, "A surface plasmon resonance study of Ag nanoparticles in an aqueous solution," Jpn. J. Appl. Phys. 43, L119-L122 (2004).
    [CrossRef]
  14. H. Mertens, J. Verhoeven, A. Polman, and F. D. Tichelaar, "Infrared surface plasmons in two-dimensional silver nanoparticle arrays in silicon," Appl. Phys. Lett. 85, 1317-1319 (2004).
    [CrossRef]
  15. Y. Hamanaka, K. Fukuta, A. Nakamura, L. M. Liz-Marzán, and P. Mulvaney, "Enhancement of third-order nonlinear optical susceptibilities in silica-capped Au nanoparticle films with very high concentrations," Appl. Phys. Lett. 84, 4938-4940 (2004).
    [CrossRef]
  16. T. Saito, M. Haraguchi, and M. Fukui, "Multilayered domain control for plasmon resonance," Jpn. J. Appl. Phys. 44, L1234-L1236 (2005).
    [CrossRef]
  17. M. Fukui and M. Ohtsu, Hikari nano technology no kiso (Ohmsha, Tokyo, 2003), Chap. 3.
  18. T. Saiki and Y. Toda, Nano scale no hikari bussei (Ohmsha, Tokyo, 2004), Chap. 4.
  19. I. V. Kityk, A. Ali Umar, M. Oyama, "Circularly polarized light-induced electrogyration in the Au nanoparticles on the ITO," Physica E 27, 420-426 (2005).
    [CrossRef]
  20. I.V. Kityk, Ebothe´, K. Ozga, K.J. Plucinski, G. Chang, Kobayashi, M. Oyama, "Non-linear optical properties of the Ag nanoparticles on the ITO," Physica E 31, 38-42 (2006).
    [CrossRef]
  21. S. Hayashi and T. Konishi, "Scanning near-field optical microscopic observation of surface-enhanced raman scattering mediated by metallic particle-surface gap modes," Jpn. J. of Appl. Phys. 44,.5313-5318 (2005)
    [CrossRef]

2006 (1)

I.V. Kityk, Ebothe´, K. Ozga, K.J. Plucinski, G. Chang, Kobayashi, M. Oyama, "Non-linear optical properties of the Ag nanoparticles on the ITO," Physica E 31, 38-42 (2006).
[CrossRef]

I.V. Kityk, Ebothe´, K. Ozga, K.J. Plucinski, G. Chang, Kobayashi, M. Oyama, "Non-linear optical properties of the Ag nanoparticles on the ITO," Physica E 31, 38-42 (2006).
[CrossRef]

2005 (2)

T. Saito, M. Haraguchi, and M. Fukui, "Multilayered domain control for plasmon resonance," Jpn. J. Appl. Phys. 44, L1234-L1236 (2005).
[CrossRef]

I. V. Kityk, A. Ali Umar, M. Oyama, "Circularly polarized light-induced electrogyration in the Au nanoparticles on the ITO," Physica E 27, 420-426 (2005).
[CrossRef]

2004 (6)

K. P. Chiu, W. C. Lin, Y. H. Fu, and D. P. Tsai, "Calculation of surface plasmon effect on optical discs," Jpn. J. Appl. Phys. 43, 4730-4735 (2004).
[CrossRef]

T. Okamoto, M. Haraguchi, and M. Fukui, "Light intensity enhancement and optical nonlinear response due to localized surface plasmons in nanosize Ag sphere," Jpn. J. Appl. Phys. 43, 6507-6512 (2004).
[CrossRef]

T. Chen, W. Su and Y. Lin, "A surface plasmon resonance study of Ag nanoparticles in an aqueous solution," Jpn. J. Appl. Phys. 43, L119-L122 (2004).
[CrossRef]

H. Mertens, J. Verhoeven, A. Polman, and F. D. Tichelaar, "Infrared surface plasmons in two-dimensional silver nanoparticle arrays in silicon," Appl. Phys. Lett. 85, 1317-1319 (2004).
[CrossRef]

Y. Hamanaka, K. Fukuta, A. Nakamura, L. M. Liz-Marzán, and P. Mulvaney, "Enhancement of third-order nonlinear optical susceptibilities in silica-capped Au nanoparticle films with very high concentrations," Appl. Phys. Lett. 84, 4938-4940 (2004).
[CrossRef]

J. S. Yuk, S. Yi, J. Han, Y. Kim, and K. Ha, "Surface plasmon resonance intensity in ex situ analysis of protein arrays using a wavelength interrogation-based surface plasmon resonance sensor," Jpn. J. Appl. Phys. 43, 2756-2760 (2004).
[CrossRef]

2002 (1)

J. Kim, K. Song and K. Park, "Near-field optical readout combined with atomic force probe recording," Jpn. J. Appl. Phys. 41, 1903-1904 (2002).
[CrossRef]

2001 (3)

U. C.  Fischer and J.  Heimel, "Elastic scattering by a metal sphere with adsorbed molecule as a model for the detection of single molecules by scanning probe enhanced elastic resonant scattering (SPEERS)," Jpn. J. Appl. Phys. 40, 4391-4394 (2001).
[CrossRef]

M. Futamata and A. Bruckbauer, "Attenuated total reflection-scanning near-field Raman spectroscopy," Jpn. J. Appl. Phys. 40, 4423-4429 (2001).
[CrossRef]

J. Tominaga, J. Kim, H. Fuji, D. Büchel, T. Kikukawa, L. Men, H. Fukuda, A. Sato, T. Nakano, A. Tachibana, Y. Yamakawa, M. Kumagai, T. Fukaya, and N. Atoda, "Super-resolution near-field structure and signal enhancement by surface plasmons," Jpn. J. Appl. Phys. 40, 1831-1834 (2001).
[CrossRef]

1988 (1)

M. Fukui and K. Oda, "Studies on metal film growth through instantaneously observed attenuated total reflection spectra," Appl. Surf. Sci. 33-34, 882-889 (1988).
[CrossRef]

1984 (1)

H. Dohi, Y. Kuwamura, M. Fukui, and O. Tada, "Long-range surface plasmon polaritons in metal film bounded by similar-refractive-index materials," J. Phys. Soc. Jpn. 53, 2828-2832 (1984).
[CrossRef]

1983 (1)

Y. Kuwamura, M. Fukui, and O. Tada, "Experimental observation of long-range surface plasmon polaritons," J. Phys. Soc. Jpn. 52, 2350-2355 (1983).
[CrossRef]

1981 (1)

B. J. Messinger, K. U. von Raben, R. K. Chang, and P. W. Barber, "Local fields at the surface of noble-metal microspheres," Phys. Rev. B 24, 649-657 (1981).
[CrossRef]

1968 (1)

Ali Umar, A.

I. V. Kityk, A. Ali Umar, M. Oyama, "Circularly polarized light-induced electrogyration in the Au nanoparticles on the ITO," Physica E 27, 420-426 (2005).
[CrossRef]

Atoda, N.

J. Tominaga, J. Kim, H. Fuji, D. Büchel, T. Kikukawa, L. Men, H. Fukuda, A. Sato, T. Nakano, A. Tachibana, Y. Yamakawa, M. Kumagai, T. Fukaya, and N. Atoda, "Super-resolution near-field structure and signal enhancement by surface plasmons," Jpn. J. Appl. Phys. 40, 1831-1834 (2001).
[CrossRef]

Barber, P. W.

B. J. Messinger, K. U. von Raben, R. K. Chang, and P. W. Barber, "Local fields at the surface of noble-metal microspheres," Phys. Rev. B 24, 649-657 (1981).
[CrossRef]

Bruckbauer, A.

M. Futamata and A. Bruckbauer, "Attenuated total reflection-scanning near-field Raman spectroscopy," Jpn. J. Appl. Phys. 40, 4423-4429 (2001).
[CrossRef]

Büchel, D.

J. Tominaga, J. Kim, H. Fuji, D. Büchel, T. Kikukawa, L. Men, H. Fukuda, A. Sato, T. Nakano, A. Tachibana, Y. Yamakawa, M. Kumagai, T. Fukaya, and N. Atoda, "Super-resolution near-field structure and signal enhancement by surface plasmons," Jpn. J. Appl. Phys. 40, 1831-1834 (2001).
[CrossRef]

Chang, R. K.

B. J. Messinger, K. U. von Raben, R. K. Chang, and P. W. Barber, "Local fields at the surface of noble-metal microspheres," Phys. Rev. B 24, 649-657 (1981).
[CrossRef]

Chen, T.

T. Chen, W. Su and Y. Lin, "A surface plasmon resonance study of Ag nanoparticles in an aqueous solution," Jpn. J. Appl. Phys. 43, L119-L122 (2004).
[CrossRef]

Chiu, K. P.

K. P. Chiu, W. C. Lin, Y. H. Fu, and D. P. Tsai, "Calculation of surface plasmon effect on optical discs," Jpn. J. Appl. Phys. 43, 4730-4735 (2004).
[CrossRef]

Dohi, H.

H. Dohi, Y. Kuwamura, M. Fukui, and O. Tada, "Long-range surface plasmon polaritons in metal film bounded by similar-refractive-index materials," J. Phys. Soc. Jpn. 53, 2828-2832 (1984).
[CrossRef]

Ebothe´, I.V.

I.V. Kityk, Ebothe´, K. Ozga, K.J. Plucinski, G. Chang, Kobayashi, M. Oyama, "Non-linear optical properties of the Ag nanoparticles on the ITO," Physica E 31, 38-42 (2006).
[CrossRef]

Fischer, U. C.

U. C.  Fischer and J.  Heimel, "Elastic scattering by a metal sphere with adsorbed molecule as a model for the detection of single molecules by scanning probe enhanced elastic resonant scattering (SPEERS)," Jpn. J. Appl. Phys. 40, 4391-4394 (2001).
[CrossRef]

Fu, Y. H.

K. P. Chiu, W. C. Lin, Y. H. Fu, and D. P. Tsai, "Calculation of surface plasmon effect on optical discs," Jpn. J. Appl. Phys. 43, 4730-4735 (2004).
[CrossRef]

Fuchs, R.

Fuji, H.

J. Tominaga, J. Kim, H. Fuji, D. Büchel, T. Kikukawa, L. Men, H. Fukuda, A. Sato, T. Nakano, A. Tachibana, Y. Yamakawa, M. Kumagai, T. Fukaya, and N. Atoda, "Super-resolution near-field structure and signal enhancement by surface plasmons," Jpn. J. Appl. Phys. 40, 1831-1834 (2001).
[CrossRef]

Fukaya, T.

J. Tominaga, J. Kim, H. Fuji, D. Büchel, T. Kikukawa, L. Men, H. Fukuda, A. Sato, T. Nakano, A. Tachibana, Y. Yamakawa, M. Kumagai, T. Fukaya, and N. Atoda, "Super-resolution near-field structure and signal enhancement by surface plasmons," Jpn. J. Appl. Phys. 40, 1831-1834 (2001).
[CrossRef]

Fukuda, H.

J. Tominaga, J. Kim, H. Fuji, D. Büchel, T. Kikukawa, L. Men, H. Fukuda, A. Sato, T. Nakano, A. Tachibana, Y. Yamakawa, M. Kumagai, T. Fukaya, and N. Atoda, "Super-resolution near-field structure and signal enhancement by surface plasmons," Jpn. J. Appl. Phys. 40, 1831-1834 (2001).
[CrossRef]

Fukui, M.

T. Saito, M. Haraguchi, and M. Fukui, "Multilayered domain control for plasmon resonance," Jpn. J. Appl. Phys. 44, L1234-L1236 (2005).
[CrossRef]

T. Okamoto, M. Haraguchi, and M. Fukui, "Light intensity enhancement and optical nonlinear response due to localized surface plasmons in nanosize Ag sphere," Jpn. J. Appl. Phys. 43, 6507-6512 (2004).
[CrossRef]

M. Fukui and K. Oda, "Studies on metal film growth through instantaneously observed attenuated total reflection spectra," Appl. Surf. Sci. 33-34, 882-889 (1988).
[CrossRef]

H. Dohi, Y. Kuwamura, M. Fukui, and O. Tada, "Long-range surface plasmon polaritons in metal film bounded by similar-refractive-index materials," J. Phys. Soc. Jpn. 53, 2828-2832 (1984).
[CrossRef]

Y. Kuwamura, M. Fukui, and O. Tada, "Experimental observation of long-range surface plasmon polaritons," J. Phys. Soc. Jpn. 52, 2350-2355 (1983).
[CrossRef]

Fukuta, K.

Y. Hamanaka, K. Fukuta, A. Nakamura, L. M. Liz-Marzán, and P. Mulvaney, "Enhancement of third-order nonlinear optical susceptibilities in silica-capped Au nanoparticle films with very high concentrations," Appl. Phys. Lett. 84, 4938-4940 (2004).
[CrossRef]

Futamata, M.

M. Futamata and A. Bruckbauer, "Attenuated total reflection-scanning near-field Raman spectroscopy," Jpn. J. Appl. Phys. 40, 4423-4429 (2001).
[CrossRef]

Ha, K.

J. S. Yuk, S. Yi, J. Han, Y. Kim, and K. Ha, "Surface plasmon resonance intensity in ex situ analysis of protein arrays using a wavelength interrogation-based surface plasmon resonance sensor," Jpn. J. Appl. Phys. 43, 2756-2760 (2004).
[CrossRef]

Hamanaka, Y.

Y. Hamanaka, K. Fukuta, A. Nakamura, L. M. Liz-Marzán, and P. Mulvaney, "Enhancement of third-order nonlinear optical susceptibilities in silica-capped Au nanoparticle films with very high concentrations," Appl. Phys. Lett. 84, 4938-4940 (2004).
[CrossRef]

Han, J.

J. S. Yuk, S. Yi, J. Han, Y. Kim, and K. Ha, "Surface plasmon resonance intensity in ex situ analysis of protein arrays using a wavelength interrogation-based surface plasmon resonance sensor," Jpn. J. Appl. Phys. 43, 2756-2760 (2004).
[CrossRef]

Haraguchi, M.

T. Saito, M. Haraguchi, and M. Fukui, "Multilayered domain control for plasmon resonance," Jpn. J. Appl. Phys. 44, L1234-L1236 (2005).
[CrossRef]

T. Okamoto, M. Haraguchi, and M. Fukui, "Light intensity enhancement and optical nonlinear response due to localized surface plasmons in nanosize Ag sphere," Jpn. J. Appl. Phys. 43, 6507-6512 (2004).
[CrossRef]

Heimel, J.

U. C.  Fischer and J.  Heimel, "Elastic scattering by a metal sphere with adsorbed molecule as a model for the detection of single molecules by scanning probe enhanced elastic resonant scattering (SPEERS)," Jpn. J. Appl. Phys. 40, 4391-4394 (2001).
[CrossRef]

Kikukawa, T.

J. Tominaga, J. Kim, H. Fuji, D. Büchel, T. Kikukawa, L. Men, H. Fukuda, A. Sato, T. Nakano, A. Tachibana, Y. Yamakawa, M. Kumagai, T. Fukaya, and N. Atoda, "Super-resolution near-field structure and signal enhancement by surface plasmons," Jpn. J. Appl. Phys. 40, 1831-1834 (2001).
[CrossRef]

Kim, J.

J. Kim, K. Song and K. Park, "Near-field optical readout combined with atomic force probe recording," Jpn. J. Appl. Phys. 41, 1903-1904 (2002).
[CrossRef]

J. Tominaga, J. Kim, H. Fuji, D. Büchel, T. Kikukawa, L. Men, H. Fukuda, A. Sato, T. Nakano, A. Tachibana, Y. Yamakawa, M. Kumagai, T. Fukaya, and N. Atoda, "Super-resolution near-field structure and signal enhancement by surface plasmons," Jpn. J. Appl. Phys. 40, 1831-1834 (2001).
[CrossRef]

Kim, Y.

J. S. Yuk, S. Yi, J. Han, Y. Kim, and K. Ha, "Surface plasmon resonance intensity in ex situ analysis of protein arrays using a wavelength interrogation-based surface plasmon resonance sensor," Jpn. J. Appl. Phys. 43, 2756-2760 (2004).
[CrossRef]

Kityk, I. V.

I. V. Kityk, A. Ali Umar, M. Oyama, "Circularly polarized light-induced electrogyration in the Au nanoparticles on the ITO," Physica E 27, 420-426 (2005).
[CrossRef]

Kityk, I.V.

I.V. Kityk, Ebothe´, K. Ozga, K.J. Plucinski, G. Chang, Kobayashi, M. Oyama, "Non-linear optical properties of the Ag nanoparticles on the ITO," Physica E 31, 38-42 (2006).
[CrossRef]

Kliewer, K. L.

Kumagai, M.

J. Tominaga, J. Kim, H. Fuji, D. Büchel, T. Kikukawa, L. Men, H. Fukuda, A. Sato, T. Nakano, A. Tachibana, Y. Yamakawa, M. Kumagai, T. Fukaya, and N. Atoda, "Super-resolution near-field structure and signal enhancement by surface plasmons," Jpn. J. Appl. Phys. 40, 1831-1834 (2001).
[CrossRef]

Kuwamura, Y.

H. Dohi, Y. Kuwamura, M. Fukui, and O. Tada, "Long-range surface plasmon polaritons in metal film bounded by similar-refractive-index materials," J. Phys. Soc. Jpn. 53, 2828-2832 (1984).
[CrossRef]

Y. Kuwamura, M. Fukui, and O. Tada, "Experimental observation of long-range surface plasmon polaritons," J. Phys. Soc. Jpn. 52, 2350-2355 (1983).
[CrossRef]

Lin, W. C.

K. P. Chiu, W. C. Lin, Y. H. Fu, and D. P. Tsai, "Calculation of surface plasmon effect on optical discs," Jpn. J. Appl. Phys. 43, 4730-4735 (2004).
[CrossRef]

Lin, Y.

T. Chen, W. Su and Y. Lin, "A surface plasmon resonance study of Ag nanoparticles in an aqueous solution," Jpn. J. Appl. Phys. 43, L119-L122 (2004).
[CrossRef]

Liz-Marzán, L. M.

Y. Hamanaka, K. Fukuta, A. Nakamura, L. M. Liz-Marzán, and P. Mulvaney, "Enhancement of third-order nonlinear optical susceptibilities in silica-capped Au nanoparticle films with very high concentrations," Appl. Phys. Lett. 84, 4938-4940 (2004).
[CrossRef]

Men, L.

J. Tominaga, J. Kim, H. Fuji, D. Büchel, T. Kikukawa, L. Men, H. Fukuda, A. Sato, T. Nakano, A. Tachibana, Y. Yamakawa, M. Kumagai, T. Fukaya, and N. Atoda, "Super-resolution near-field structure and signal enhancement by surface plasmons," Jpn. J. Appl. Phys. 40, 1831-1834 (2001).
[CrossRef]

Mertens, H.

H. Mertens, J. Verhoeven, A. Polman, and F. D. Tichelaar, "Infrared surface plasmons in two-dimensional silver nanoparticle arrays in silicon," Appl. Phys. Lett. 85, 1317-1319 (2004).
[CrossRef]

Messinger, B. J.

B. J. Messinger, K. U. von Raben, R. K. Chang, and P. W. Barber, "Local fields at the surface of noble-metal microspheres," Phys. Rev. B 24, 649-657 (1981).
[CrossRef]

Mulvaney, P.

Y. Hamanaka, K. Fukuta, A. Nakamura, L. M. Liz-Marzán, and P. Mulvaney, "Enhancement of third-order nonlinear optical susceptibilities in silica-capped Au nanoparticle films with very high concentrations," Appl. Phys. Lett. 84, 4938-4940 (2004).
[CrossRef]

Nakamura, A.

Y. Hamanaka, K. Fukuta, A. Nakamura, L. M. Liz-Marzán, and P. Mulvaney, "Enhancement of third-order nonlinear optical susceptibilities in silica-capped Au nanoparticle films with very high concentrations," Appl. Phys. Lett. 84, 4938-4940 (2004).
[CrossRef]

Nakano, T.

J. Tominaga, J. Kim, H. Fuji, D. Büchel, T. Kikukawa, L. Men, H. Fukuda, A. Sato, T. Nakano, A. Tachibana, Y. Yamakawa, M. Kumagai, T. Fukaya, and N. Atoda, "Super-resolution near-field structure and signal enhancement by surface plasmons," Jpn. J. Appl. Phys. 40, 1831-1834 (2001).
[CrossRef]

Oda, K.

M. Fukui and K. Oda, "Studies on metal film growth through instantaneously observed attenuated total reflection spectra," Appl. Surf. Sci. 33-34, 882-889 (1988).
[CrossRef]

Okamoto, T.

T. Okamoto, M. Haraguchi, and M. Fukui, "Light intensity enhancement and optical nonlinear response due to localized surface plasmons in nanosize Ag sphere," Jpn. J. Appl. Phys. 43, 6507-6512 (2004).
[CrossRef]

Oyama, M.

I. V. Kityk, A. Ali Umar, M. Oyama, "Circularly polarized light-induced electrogyration in the Au nanoparticles on the ITO," Physica E 27, 420-426 (2005).
[CrossRef]

Park, K.

J. Kim, K. Song and K. Park, "Near-field optical readout combined with atomic force probe recording," Jpn. J. Appl. Phys. 41, 1903-1904 (2002).
[CrossRef]

Polman, A.

H. Mertens, J. Verhoeven, A. Polman, and F. D. Tichelaar, "Infrared surface plasmons in two-dimensional silver nanoparticle arrays in silicon," Appl. Phys. Lett. 85, 1317-1319 (2004).
[CrossRef]

Saito, T.

T. Saito, M. Haraguchi, and M. Fukui, "Multilayered domain control for plasmon resonance," Jpn. J. Appl. Phys. 44, L1234-L1236 (2005).
[CrossRef]

Sato, A.

J. Tominaga, J. Kim, H. Fuji, D. Büchel, T. Kikukawa, L. Men, H. Fukuda, A. Sato, T. Nakano, A. Tachibana, Y. Yamakawa, M. Kumagai, T. Fukaya, and N. Atoda, "Super-resolution near-field structure and signal enhancement by surface plasmons," Jpn. J. Appl. Phys. 40, 1831-1834 (2001).
[CrossRef]

Song, K.

J. Kim, K. Song and K. Park, "Near-field optical readout combined with atomic force probe recording," Jpn. J. Appl. Phys. 41, 1903-1904 (2002).
[CrossRef]

Su, W.

T. Chen, W. Su and Y. Lin, "A surface plasmon resonance study of Ag nanoparticles in an aqueous solution," Jpn. J. Appl. Phys. 43, L119-L122 (2004).
[CrossRef]

Tachibana, A.

J. Tominaga, J. Kim, H. Fuji, D. Büchel, T. Kikukawa, L. Men, H. Fukuda, A. Sato, T. Nakano, A. Tachibana, Y. Yamakawa, M. Kumagai, T. Fukaya, and N. Atoda, "Super-resolution near-field structure and signal enhancement by surface plasmons," Jpn. J. Appl. Phys. 40, 1831-1834 (2001).
[CrossRef]

Tada, O.

H. Dohi, Y. Kuwamura, M. Fukui, and O. Tada, "Long-range surface plasmon polaritons in metal film bounded by similar-refractive-index materials," J. Phys. Soc. Jpn. 53, 2828-2832 (1984).
[CrossRef]

Y. Kuwamura, M. Fukui, and O. Tada, "Experimental observation of long-range surface plasmon polaritons," J. Phys. Soc. Jpn. 52, 2350-2355 (1983).
[CrossRef]

Tichelaar, F. D.

H. Mertens, J. Verhoeven, A. Polman, and F. D. Tichelaar, "Infrared surface plasmons in two-dimensional silver nanoparticle arrays in silicon," Appl. Phys. Lett. 85, 1317-1319 (2004).
[CrossRef]

Tominaga, J.

J. Tominaga, J. Kim, H. Fuji, D. Büchel, T. Kikukawa, L. Men, H. Fukuda, A. Sato, T. Nakano, A. Tachibana, Y. Yamakawa, M. Kumagai, T. Fukaya, and N. Atoda, "Super-resolution near-field structure and signal enhancement by surface plasmons," Jpn. J. Appl. Phys. 40, 1831-1834 (2001).
[CrossRef]

Tsai, D. P.

K. P. Chiu, W. C. Lin, Y. H. Fu, and D. P. Tsai, "Calculation of surface plasmon effect on optical discs," Jpn. J. Appl. Phys. 43, 4730-4735 (2004).
[CrossRef]

Verhoeven, J.

H. Mertens, J. Verhoeven, A. Polman, and F. D. Tichelaar, "Infrared surface plasmons in two-dimensional silver nanoparticle arrays in silicon," Appl. Phys. Lett. 85, 1317-1319 (2004).
[CrossRef]

von Raben, K. U.

B. J. Messinger, K. U. von Raben, R. K. Chang, and P. W. Barber, "Local fields at the surface of noble-metal microspheres," Phys. Rev. B 24, 649-657 (1981).
[CrossRef]

Yamakawa, Y.

J. Tominaga, J. Kim, H. Fuji, D. Büchel, T. Kikukawa, L. Men, H. Fukuda, A. Sato, T. Nakano, A. Tachibana, Y. Yamakawa, M. Kumagai, T. Fukaya, and N. Atoda, "Super-resolution near-field structure and signal enhancement by surface plasmons," Jpn. J. Appl. Phys. 40, 1831-1834 (2001).
[CrossRef]

Yi, S.

J. S. Yuk, S. Yi, J. Han, Y. Kim, and K. Ha, "Surface plasmon resonance intensity in ex situ analysis of protein arrays using a wavelength interrogation-based surface plasmon resonance sensor," Jpn. J. Appl. Phys. 43, 2756-2760 (2004).
[CrossRef]

Yuk, J. S.

J. S. Yuk, S. Yi, J. Han, Y. Kim, and K. Ha, "Surface plasmon resonance intensity in ex situ analysis of protein arrays using a wavelength interrogation-based surface plasmon resonance sensor," Jpn. J. Appl. Phys. 43, 2756-2760 (2004).
[CrossRef]

Appl. Phys. Lett. (2)

H. Mertens, J. Verhoeven, A. Polman, and F. D. Tichelaar, "Infrared surface plasmons in two-dimensional silver nanoparticle arrays in silicon," Appl. Phys. Lett. 85, 1317-1319 (2004).
[CrossRef]

Y. Hamanaka, K. Fukuta, A. Nakamura, L. M. Liz-Marzán, and P. Mulvaney, "Enhancement of third-order nonlinear optical susceptibilities in silica-capped Au nanoparticle films with very high concentrations," Appl. Phys. Lett. 84, 4938-4940 (2004).
[CrossRef]

Appl. Surf. Sci. (1)

M. Fukui and K. Oda, "Studies on metal film growth through instantaneously observed attenuated total reflection spectra," Appl. Surf. Sci. 33-34, 882-889 (1988).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Phys. Soc. Jpn. (2)

H. Dohi, Y. Kuwamura, M. Fukui, and O. Tada, "Long-range surface plasmon polaritons in metal film bounded by similar-refractive-index materials," J. Phys. Soc. Jpn. 53, 2828-2832 (1984).
[CrossRef]

Y. Kuwamura, M. Fukui, and O. Tada, "Experimental observation of long-range surface plasmon polaritons," J. Phys. Soc. Jpn. 52, 2350-2355 (1983).
[CrossRef]

Jpn. J. Appl. Phys. (9)

T. Saito, M. Haraguchi, and M. Fukui, "Multilayered domain control for plasmon resonance," Jpn. J. Appl. Phys. 44, L1234-L1236 (2005).
[CrossRef]

J. S. Yuk, S. Yi, J. Han, Y. Kim, and K. Ha, "Surface plasmon resonance intensity in ex situ analysis of protein arrays using a wavelength interrogation-based surface plasmon resonance sensor," Jpn. J. Appl. Phys. 43, 2756-2760 (2004).
[CrossRef]

U. C.  Fischer and J.  Heimel, "Elastic scattering by a metal sphere with adsorbed molecule as a model for the detection of single molecules by scanning probe enhanced elastic resonant scattering (SPEERS)," Jpn. J. Appl. Phys. 40, 4391-4394 (2001).
[CrossRef]

M. Futamata and A. Bruckbauer, "Attenuated total reflection-scanning near-field Raman spectroscopy," Jpn. J. Appl. Phys. 40, 4423-4429 (2001).
[CrossRef]

J. Tominaga, J. Kim, H. Fuji, D. Büchel, T. Kikukawa, L. Men, H. Fukuda, A. Sato, T. Nakano, A. Tachibana, Y. Yamakawa, M. Kumagai, T. Fukaya, and N. Atoda, "Super-resolution near-field structure and signal enhancement by surface plasmons," Jpn. J. Appl. Phys. 40, 1831-1834 (2001).
[CrossRef]

J. Kim, K. Song and K. Park, "Near-field optical readout combined with atomic force probe recording," Jpn. J. Appl. Phys. 41, 1903-1904 (2002).
[CrossRef]

K. P. Chiu, W. C. Lin, Y. H. Fu, and D. P. Tsai, "Calculation of surface plasmon effect on optical discs," Jpn. J. Appl. Phys. 43, 4730-4735 (2004).
[CrossRef]

T. Okamoto, M. Haraguchi, and M. Fukui, "Light intensity enhancement and optical nonlinear response due to localized surface plasmons in nanosize Ag sphere," Jpn. J. Appl. Phys. 43, 6507-6512 (2004).
[CrossRef]

T. Chen, W. Su and Y. Lin, "A surface plasmon resonance study of Ag nanoparticles in an aqueous solution," Jpn. J. Appl. Phys. 43, L119-L122 (2004).
[CrossRef]

Phys. Rev. B (1)

B. J. Messinger, K. U. von Raben, R. K. Chang, and P. W. Barber, "Local fields at the surface of noble-metal microspheres," Phys. Rev. B 24, 649-657 (1981).
[CrossRef]

Physica E (2)

I. V. Kityk, A. Ali Umar, M. Oyama, "Circularly polarized light-induced electrogyration in the Au nanoparticles on the ITO," Physica E 27, 420-426 (2005).
[CrossRef]

I.V. Kityk, Ebothe´, K. Ozga, K.J. Plucinski, G. Chang, Kobayashi, M. Oyama, "Non-linear optical properties of the Ag nanoparticles on the ITO," Physica E 31, 38-42 (2006).
[CrossRef]

Other (3)

S. Hayashi and T. Konishi, "Scanning near-field optical microscopic observation of surface-enhanced raman scattering mediated by metallic particle-surface gap modes," Jpn. J. of Appl. Phys. 44,.5313-5318 (2005)
[CrossRef]

M. Fukui and M. Ohtsu, Hikari nano technology no kiso (Ohmsha, Tokyo, 2003), Chap. 3.

T. Saiki and Y. Toda, Nano scale no hikari bussei (Ohmsha, Tokyo, 2004), Chap. 4.

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Figures (4)

Fig. 1.
Fig. 1.

(a) Design of MLDC. (b) SEM image of Ag particles. They are deposited using DC sputtering and distributed two-dimensionally. (c) TEM image of the cross section (four Ag layers).

Fig. 2.
Fig. 2.

(a) SEM image of Ag particles. The particles with an average diameter of 8 nm are randomly distributed on the thin SiO2 film. On an average, they are allowed a spacing of 6 nm. (b) SEM image of SiO2 particles. The particles with an average diameter of 8 nm are randomly distributed on the particles shown in Fig. 2(a). On an average, they are allowed a spacing of 2 nm. (c) Design of CDC. (d) TEM image of a CDC cross section (five Ag layers).

Fig. 3.
Fig. 3.

(a) Each pattern exhibits surface plasmon resonance and each peak corresponds to the resonance peak. The number of layers is 6, 8, and 10 in the Ag group and 5, 9, and 12 in the Au group. All other factors are equal in each group. Expressions in the legends such as “6L/15 nm/15 s,” imply the following. “6L” means the number of metal particle layers. “15 nm” means the average diameter of the metal particles. “15 s” means the time of deposition of the dielectric particles. The sizes of the dielectric particles are regulated by time because they depend on the sizes of the metal particles. (b)Each pattern exhibits surface plasmon resonance and each peak corresponds to the resonance peak, similar to Fig. 3(a). The particle diameters are 8, 15, and 23 nm in the Ag group and 5, 10, and 15 nm in the Au group. All of them are intensified with five layers. All other factors are equal in each group. Expressions in the graph have a similar form as in Fig. 3(a).

Fig. 4.
Fig. 4.

(a) Electric field of CDC. (b) Electric field of randomly arranged particles.

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