## Characterization of large array of plasmonic nanoparticles on layered substrate: dipole mode analysis integrated with complex image method |

Optics Express, Vol. 19, Issue S2, pp. A173-A193 (2011)

http://dx.doi.org/10.1364/OE.19.00A173

Acrobat PDF (2083 KB)

### Abstract

In this paper, an efficient analytical method for characterizing large array of plasmonic nanoparticles located over planarly layered substrate is introduced. The model is called dipole mode complex image (DMCI) method since the main idea lies in modeling a subwavelength spherical nanoparticle at its electric scattering resonance with an induced electric dipole and representing the electromagnetic (EM) fields of this electric dipole over the layered substrate in terms of finite complex images. The major advantages of the proposed method are its accuracy and rapid calculation in characterizing various kinds of large periodic and aperiodic arrays of nanoparticles on layered substrates. The computational time can be reduced significantly in compared to the traditional methods. The accuracy of the theoretical model is validated through comparison with numerical integration of Sommerfeld integrals. Moreover, the analytical results are compared well with those determined by full-wave finite difference time domain (FDTD) method. To demonstrate the capability of our technique, the performances of large arrays of nanoparticles on layered silicon substrates for efficient sunlight energy incoupling are studied.

© 2011 OSA

## 1. Introduction

1. S. A. Maier and H. A. Atwater, “Plasmonics: Localization and guiding of electromagnetic energy in metallic/dielectric structures,” J. Appl. Phys. **98**(1), 011101 (2005). [CrossRef]

6. Y. C. Jun, R. D. Kekatpure, J. S. White, and M. L. Brongersma, “Nonresonant enhancement of spontaneous emission in metal-dielectric-metal plasmon waveguide structures,” Phys. Rev. B **78**(15), 153111 (2008). [CrossRef]

7. A. Alù and N. Engheta, “Polarizabilities and effective parameters for collections of spherical nanoparticles formed by pairs of concentric double-negative, single-negative, and/or double-positive metamaterial layers,” J. Appl. Phys. **97**(9), 094310 (2005). [CrossRef]

8. S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. **97**(1), 017402 (2006). [CrossRef] [PubMed]

13. A. Rashidi and H. Mosallaei, “Array of plasmonic particles enabling optical near-field concentration: A nonlinear inverse scattering design approach,” Phys. Rev. B **82**(3), 035117 (2010). [CrossRef]

14. V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, “Plasmonic nanostructure design for efficient light coupling into solar cells,” Nano Lett. **8**(12), 4391–4397 (2008). [CrossRef]

18. S. M. Sadeghi, “Plasmonic metaresonances: Molecular resonances in quantum dot–metallic nanoparticle conjugates,” Phys. Rev. B **79**(23), 233309 (2009). [CrossRef]

20. J. S. Biteen, N. S. Lewis, H. A. Atwater, H. Mertens, and A. Polman, “Spectral tuning of plasmon-enhanced silicon quantum dot luminescence,” Appl. Phys. Lett. **88**(13), 131109 (2006). [CrossRef]

21. Y. Lia, H. J. Schluesenerb, and S. Xua, “Gold nanoparticle-based biosensors,” Gold Bull. **43**(1), 29–41 (2010). [CrossRef]

23. J. Liu and Y. Lu, “A colorimetric lead biosensor using DNAzyme-directed assembly of gold nanoparticles,” J. Am. Chem. Soc. **125**(22), 6642–6643 (2003). [CrossRef] [PubMed]

24. D. Pacifici, H. J. Lezec, L. A. Sweatlock, R. J. Walters, and H. A. Atwater, “Universal optical transmission features in periodic and quasiperiodic hole arrays,” Opt. Express **16**(12), 9222–9238 (2008). [CrossRef] [PubMed]

27. M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: Quasiperiodic media,” Phys. Rev. Lett. **58**(23), 2436–2438 (1987). [CrossRef] [PubMed]

11. J. Li, A. Salandrino, and N. Engheta, “Shaping light beams in the nanometer scale: A Yagi-Uda nanoantenna in the optical domain,” Phys. Rev. B **76**(24), 245403 (2007). [CrossRef]

13. A. Rashidi and H. Mosallaei, “Array of plasmonic particles enabling optical near-field concentration: A nonlinear inverse scattering design approach,” Phys. Rev. B **82**(3), 035117 (2010). [CrossRef]

28. A. Ahmadi, S. Ghadarghadr, and H. Mosallaei, “An optical reflectarray nanoantenna: the concept and design,” Opt. Express **18**(1), 123–133 (2010). [CrossRef] [PubMed]

31. M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of the Green’s tensor for stratified media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics **62**(44 Pt B), 5797–5807 (2000). [CrossRef] [PubMed]

32. B. Hu and W. C. Chew, “Fast inhomogeneous plane wave algorithm for scattering from objects above the multilayered medium,” IEEE Trans. Geosci. Rem. Sens. **39**(5), 1028–1038 (2001). [CrossRef]

34. M. M. Tajdini and A. A. Shishegar, “A novel analysis of microstrip structures using the Gaussian Green’s function method,” IEEE Trans. Antenn. Propag. **58**(1), 88–94 (2010). [CrossRef]

35. Y. L. Chow, J. J. Yang, D. G. Fang, and G. E. Howard, “A closed form spatial Green’s function for the thick microstrip substrate,” IEEE Trans. Microw. Theory Tech. **39**(3), 588–592 (1991). [CrossRef]

## 2. Performance of a core-shell dielectric-plasmonic nanoparticle: A review

7. A. Alù and N. Engheta, “Polarizabilities and effective parameters for collections of spherical nanoparticles formed by pairs of concentric double-negative, single-negative, and/or double-positive metamaterial layers,” J. Appl. Phys. **97**(9), 094310 (2005). [CrossRef]

11. J. Li, A. Salandrino, and N. Engheta, “Shaping light beams in the nanometer scale: A Yagi-Uda nanoantenna in the optical domain,” Phys. Rev. B **76**(24), 245403 (2007). [CrossRef]

41. A. F. Koenderink and A. Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B **74**(3), 033402 (2006). [CrossRef]

## 3. Array of nanoparticles on layered substrate

*N*plasmonic nanoparticles over a planarly layered medium (as shown in Fig. 2 ), the induced dipole moment for each nanoparticle is derived analogous to Eq. (3) by solving the following linear system of equations for

*N*plasmonic nanoparticles. As illustrated in Eq. (4), the EM fields of a plasmonic nanoparticle can be attained by applying specific vector operators to a spherical wave. The spherical wave can be expressed as an integral summation of plane waves in the

*z*direction multiplied by conical waves in the

*ρ*direction over all wave numbers

*q*th plasmonic nanoparticle (

*i*th layer to the amplitude of the incident

*i*th layer.

*i*th layer and

*i*th layer into account. The total transmission and reflection coefficients

*z*component of the EM fields and the boundary conditions are given. Here, we achieve all the EM field components directly from Eq. (4) because it allows applying the CI method elegantly on the problem.

*q*th plasmonic nanoparticle above the substrate when in Eq. (9) all the reflection coefficients equal to zero.

*q*th plasmonic nanoparticle is accomplished as

35. Y. L. Chow, J. J. Yang, D. G. Fang, and G. E. Howard, “A closed form spatial Green’s function for the thick microstrip substrate,” IEEE Trans. Microw. Theory Tech. **39**(3), 588–592 (1991). [CrossRef]

*i*th layer of a planarly

*N*-layered medium for either

*i*th layer can be designated as

*t*as it has been done in [35

35. Y. L. Chow, J. J. Yang, D. G. Fang, and G. E. Howard, “A closed form spatial Green’s function for the thick microstrip substrate,” IEEE Trans. Microw. Theory Tech. **39**(3), 588–592 (1991). [CrossRef]

46. A. Alparslan, M. I. Aksun, and K. A. Michalski, “Closed-form Green’s functions in planar layered media for all ranges and materials,” IEEE Trans. Microw. Theory Tech. **58**(3), 602–613 (2010). [CrossRef]

*N*and the truncation point

*T*[36

36. J. J. Yang, Y. L. Chow, G. E. Howard, and D. G. Fang, “Complex images of an electric dipole in homogenous and layered dielectrics between two ground planes,” IEEE Trans. Microw. Theory Tech. **40**(3), 595–598 (1992). [CrossRef]

34. M. M. Tajdini and A. A. Shishegar, “A novel analysis of microstrip structures using the Gaussian Green’s function method,” IEEE Trans. Antenn. Propag. **58**(1), 88–94 (2010). [CrossRef]

*T*is taken usually around 18. The coefficients can then be modified to obtain the best results.

## 4. Numerical results

14. V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, “Plasmonic nanostructure design for efficient light coupling into solar cells,” Nano Lett. **8**(12), 4391–4397 (2008). [CrossRef]

_{2}material (

*j*0.01) and radius

*a*with silver coating of plasmonic material with Drude parameter

47. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B **6**(12), 4370–4379 (1972). [CrossRef]

*b*= 30 nm is reviewed. Figure 4 demonstrates the magnitude and phase of the polarizability factor

*ξ*. It is noted that by tuning the radii ratio

*a/b*the plasmonic resonance of the nanoparticle can be controlled. For instance, the polarizability factor of the concentric nanoparticle reaches its maximum at

*a*= 0.785

*b*. Another interesting feature is that at the resonance the phase of the polarizability factor is close to zero, which means at the resonance the induced dipole is nearly in phase with the incident field. For the sake of comparison, the magnitudes of the electric dipole moment

_{2}(

*j*0.01) with thickness of 0.16

*j*0.1) with thickness of 0.3

*j*3.81) with thickness of 0.4

47. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B **6**(12), 4370–4379 (1972). [CrossRef]

16. K. Nakayama, K. Tanabe, and H. A. Atwater, “Plasmonic nanoparticle enhanced light absorption in GaAs solar cells,” Appl. Phys. Lett. **93**(12), 121904 (2008). [CrossRef]

*T*is opted 18. The reflection coefficients from the entire substrate are expanded into 10 term series when

*T*is taken 20 for the

*t*. Excellent agreement can be observed between the exact calculation and CI method. Tables 1–3 list the complex terms for the six spectral coefficients to show the typical values in the complex image series. It is valuable to compare the numerical results obtained via the complete integration of the spectral coefficients with the expressions accomplished by the CI method. Figures 10 –12 demonstrate the magnitude of the total transmission and reflection coefficients of the structure of Fig. 6 for both

*x*-component of the electric field via the array when

*y*= 40 nm and

*z*= 70 nm is obtained by means of the exact formulation and CI method as illustrated in Fig. 13(b). The results are in good agreement.

*z*-directed and one

*y*-directed unit electric dipoles, nine

*z*-directed unit electric dipoles and 8 core-shell nanoparticles with one

*z*-directed unit electric dipole at the center, respectively. The wavelength is 500 nm and all the plasmonic nanoparticles are same as in Fig. 13 and in their resonance frequency. Figures 14(b)–16(b) demonstrate the analytical results for these structures and Figs. 14(c)–16(c) illustrate the FDTD results. All the electric field distributions are normalized to their maximum values in the observation plane. The results are in good agreement. If the spectral coefficients of the layer are expanded into exponential terms accurately, the calculation of the EM fields is extremely fast and takes only few minutes in compared to hours for FDTD method. It is noticed that owing to the small size and spherical complexity of the nanoparticles and the cubical meshing of our FDTD method, a fine discretization with stair-casing around the boundaries is required for FDTD modeling (making FDTD computation very complex). The resonant frequency achieved by the FDTD technique for the core-shell plasmonic nanoparticles in Fig. 16 has almost 2.8% error compared to the theoretical prediction. Utilizing smaller cell-size may reduce the error.

_{2}cores and silver coatings. The external electric field is a plane wave as in Fig. 13. The diameter of all particles is 60 nm. All plasmonic nanoparticles are at their maximum scattering and therefore, the diameter of the cores for all particles is 47 nm. The

*z*-component of the electric field intensity is calculated analytically inside the GaAs-AlGaAs medium. The result is demonstrated in Fig. 17(b). All results are normalized to the maximum of the

*z*-component of the electric field intensity in case of no nanoparticle to show the effect of the plasmonic nanoparticles.

## 5. Conclusions

_{2}layer on the top and a gold substrate in the back) are demonstrated. The DMCI technique is a very capable and powerful method that can be used for characterizing various plasmonic applications involving large arrays of nanoparticles on layered substrates, leading to energy-efficient photovoltaic applications.

## Appendix A: The Prony method

*F(t)*in terms of

*N*exponential terms as

*t*belongs to the interval

*N*samples of data are required. If the 2

*N*equally spaced data are sampled from the function, i.e.,

*N*th order polynomial equation of

*t*. Two-level CI approximation is exploited in this paper for the exponential expansion of the spectral coefficients through transformation relation of Eq. (23). By changing the variable of the total transmission and reflection coefficients from

*t*to

## Acknowledgments

## References and links

1. | S. A. Maier and H. A. Atwater, “Plasmonics: Localization and guiding of electromagnetic energy in metallic/dielectric structures,” J. Appl. Phys. |

2. | S. I. Bozhevolnyi and V. M. Shalaev, “Nanophotonics with surface plasmons Part I,” Photon. Spectra |

3. | S. I. Bozhevolnyi and V. M. Shalaev, “Nanophotonics with surface plasmons Part II,” Photon. Spectra |

4. | J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. |

5. | A. Hryciw, Y. C. Jun, and M. L. Brongersma, “Plasmonics: Electrifying plasmonics on silicon,” Nat. Mater. |

6. | Y. C. Jun, R. D. Kekatpure, J. S. White, and M. L. Brongersma, “Nonresonant enhancement of spontaneous emission in metal-dielectric-metal plasmon waveguide structures,” Phys. Rev. B |

7. | A. Alù and N. Engheta, “Polarizabilities and effective parameters for collections of spherical nanoparticles formed by pairs of concentric double-negative, single-negative, and/or double-positive metamaterial layers,” J. Appl. Phys. |

8. | S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. |

9. | L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, “Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles,” Phys. Rev. B |

10. | D. R. Matthews, H. D. Summers, K. Njoh, S. Chappell, R. Errington, and P. Smith, “Optical antenna arrays in the visible range,” Opt. Express |

11. | J. Li, A. Salandrino, and N. Engheta, “Shaping light beams in the nanometer scale: A Yagi-Uda nanoantenna in the optical domain,” Phys. Rev. B |

12. | S. Ghadarghadr, Z. Hao, and H. Mosallaei, “Plasmonic array nanoantennas on layered substrates: modeling and radiation characteristics,” Opt. Express |

13. | A. Rashidi and H. Mosallaei, “Array of plasmonic particles enabling optical near-field concentration: A nonlinear inverse scattering design approach,” Phys. Rev. B |

14. | V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, “Plasmonic nanostructure design for efficient light coupling into solar cells,” Nano Lett. |

15. | S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. |

16. | K. Nakayama, K. Tanabe, and H. A. Atwater, “Plasmonic nanoparticle enhanced light absorption in GaAs solar cells,” Appl. Phys. Lett. |

17. | M. M. Tajdini, S. Ghadarghadr, and H. Mosallaei, “Plasmonic nanoparticles manipulating solar systems: a dipole mode-complex image analysis,” presented at 2010 Photonic Metamaterials Plasmonics Conf., 7–9 Jun. 2010. |

18. | S. M. Sadeghi, “Plasmonic metaresonances: Molecular resonances in quantum dot–metallic nanoparticle conjugates,” Phys. Rev. B |

19. | Y. Jin and X. Gao, “Plasmonic fluorescent quantum dots,” Nat. Nanotechnol. |

20. | J. S. Biteen, N. S. Lewis, H. A. Atwater, H. Mertens, and A. Polman, “Spectral tuning of plasmon-enhanced silicon quantum dot luminescence,” Appl. Phys. Lett. |

21. | Y. Lia, H. J. Schluesenerb, and S. Xua, “Gold nanoparticle-based biosensors,” Gold Bull. |

22. | Y. Xiao, F. Patolsky, E. Katz, J. F. Hainfeld, and I. Willner, ““Plugging into Enzymes”: nanowiring of redox enzymes by a gold nanoparticle,” Science |

23. | J. Liu and Y. Lu, “A colorimetric lead biosensor using DNAzyme-directed assembly of gold nanoparticles,” J. Am. Chem. Soc. |

24. | D. Pacifici, H. J. Lezec, L. A. Sweatlock, R. J. Walters, and H. A. Atwater, “Universal optical transmission features in periodic and quasiperiodic hole arrays,” Opt. Express |

25. | L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. |

26. | R. Dallapiccola, A. Gopinath, F. Stellacci, and L. Dal Negro, “Quasi-periodic distribution of plasmon modes in two-dimensional Fibonacci arrays of metal nanoparticles,” Opt. Express |

27. | M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: Quasiperiodic media,” Phys. Rev. Lett. |

28. | A. Ahmadi, S. Ghadarghadr, and H. Mosallaei, “An optical reflectarray nanoantenna: the concept and design,” Opt. Express |

29. | W. C. Chew, |

30. | K. A. Michalski and J. R. Mosig, “Multilayered media Green’s function in integral equation formulations,” IEEE Trans. Antenn. Propag. |

31. | M. Paulus, P. Gay-Balmaz, and O. J. F. Martin, “Accurate and efficient computation of the Green’s tensor for stratified media,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics |

32. | B. Hu and W. C. Chew, “Fast inhomogeneous plane wave algorithm for scattering from objects above the multilayered medium,” IEEE Trans. Geosci. Rem. Sens. |

33. | M. M. Tajdini, and A. A. Shishegar, “The Gaussian expansion of the Green’s function of an electric current in a parallel-plate waveguide,” |

34. | M. M. Tajdini and A. A. Shishegar, “A novel analysis of microstrip structures using the Gaussian Green’s function method,” IEEE Trans. Antenn. Propag. |

35. | Y. L. Chow, J. J. Yang, D. G. Fang, and G. E. Howard, “A closed form spatial Green’s function for the thick microstrip substrate,” IEEE Trans. Microw. Theory Tech. |

36. | J. J. Yang, Y. L. Chow, G. E. Howard, and D. G. Fang, “Complex images of an electric dipole in homogenous and layered dielectrics between two ground planes,” IEEE Trans. Microw. Theory Tech. |

37. | M. E. Yavuz, M. I. Aksun, and G. Dural, “Critical study of the problems in discrete complex image method,” |

38. | H. Alaeian and R. Faraji-Dana, “A fast and accurate analysis of 2-D periodic devices using complex images Green’s functions,” J. Lightwave Technol. |

39. | M. I. Aksun and G. Dural, “Clarification of issues on the closed-form Green’s functions in stratified media,” IEEE Trans. Antenn. Propag. |

40. | M. I. Aksun, M. E. Yavuz, and G. Dural, “Comments on the problems in DCIM,” in Proc. 2003 IEEE APS Int. Symp. USNC/CNC/URSI North Am. Radio Sci. Meeting Conf., Jun. 22–27, 2003, 673–676. |

41. | A. F. Koenderink and A. Polman, “Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains,” Phys. Rev. B |

42. | S. Ghadarghadr and H. Mosallaei, “Coupled dielectric nanoparticles manipulating metamaterials optical characteristics,” IEEE Trans. NanoTechnol. |

43. | P. C. Waterman and N. E. Pedersen, “Electromagnetic scattering by periodic arrays of particles,” J. Appl. Phys. |

44. | P. C. Waterman, “Symmetry, unitarity, and geometry in electromagnetic scattering,” Phys. Rev. D Part. Fields |

45. | R. W. Hamming, |

46. | A. Alparslan, M. I. Aksun, and K. A. Michalski, “Closed-form Green’s functions in planar layered media for all ranges and materials,” IEEE Trans. Microw. Theory Tech. |

47. | P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B |

**OCIS Codes**

(040.5350) Detectors : Photovoltaic

(230.4170) Optical devices : Multilayers

(260.2110) Physical optics : Electromagnetic optics

(350.6050) Other areas of optics : Solar energy

(250.5403) Optoelectronics : Plasmonics

**ToC Category:**

Plasmonics

**History**

Original Manuscript: December 21, 2010

Revised Manuscript: January 14, 2011

Manuscript Accepted: January 17, 2011

Published: February 17, 2011

**Citation**

Mohammad Mahdi Tajdini and Hossein Mosallaei, "Characterization of large array of plasmonic nanoparticles on layered substrate: dipole mode analysis integrated with complex image method," Opt. Express **19**, A173-A193 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-S2-A173

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### References

- S. A. Maier and H. A. Atwater, “Plasmonics: Localization and guiding of electromagnetic energy in metallic/dielectric structures,” J. Appl. Phys. 98(1), 011101 (2005). [CrossRef]
- S. I. Bozhevolnyi and V. M. Shalaev, “Nanophotonics with surface plasmons Part I,” Photon. Spectra 40, 58–66 (2006).
- S. I. Bozhevolnyi and V. M. Shalaev, “Nanophotonics with surface plasmons Part II,” Photon. Spectra 40, 66–72 (2006).
- J. A. Schuller, E. S. Barnard, W. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9(3), 193–204 (2010). [CrossRef] [PubMed]
- A. Hryciw, Y. C. Jun, and M. L. Brongersma, “Plasmonics: Electrifying plasmonics on silicon,” Nat. Mater. 9(1), 3–4 (2010). [CrossRef]
- Y. C. Jun, R. D. Kekatpure, J. S. White, and M. L. Brongersma, “Nonresonant enhancement of spontaneous emission in metal-dielectric-metal plasmon waveguide structures,” Phys. Rev. B 78(15), 153111 (2008). [CrossRef]
- A. Alù and N. Engheta, “Polarizabilities and effective parameters for collections of spherical nanoparticles formed by pairs of concentric double-negative, single-negative, and/or double-positive metamaterial layers,” J. Appl. Phys. 97(9), 094310 (2005). [CrossRef]
- S. Kühn, U. Håkanson, L. Rogobete, and V. Sandoghdar, “Enhancement of single-molecule fluorescence using a gold nanoparticle as an optical nanoantenna,” Phys. Rev. Lett. 97(1), 017402 (2006). [CrossRef] [PubMed]
- L. A. Sweatlock, S. A. Maier, H. A. Atwater, J. J. Penninkhof, and A. Polman, “Highly confined electromagnetic fields in arrays of strongly coupled Ag nanoparticles,” Phys. Rev. B 71(23), 235408 (2005). [CrossRef]
- D. R. Matthews, H. D. Summers, K. Njoh, S. Chappell, R. Errington, and P. Smith, “Optical antenna arrays in the visible range,” Opt. Express 15(6), 3478–3487 (2007). [CrossRef] [PubMed]
- J. Li, A. Salandrino, and N. Engheta, “Shaping light beams in the nanometer scale: A Yagi-Uda nanoantenna in the optical domain,” Phys. Rev. B 76(24), 245403 (2007). [CrossRef]
- S. Ghadarghadr, Z. Hao, and H. Mosallaei, “Plasmonic array nanoantennas on layered substrates: modeling and radiation characteristics,” Opt. Express 17(21), 18556–18570 (2009). [CrossRef]
- A. Rashidi and H. Mosallaei, “Array of plasmonic particles enabling optical near-field concentration: A nonlinear inverse scattering design approach,” Phys. Rev. B 82(3), 035117 (2010). [CrossRef]
- V. E. Ferry, L. A. Sweatlock, D. Pacifici, and H. A. Atwater, “Plasmonic nanostructure design for efficient light coupling into solar cells,” Nano Lett. 8(12), 4391–4397 (2008). [CrossRef]
- S. Pillai, K. R. Catchpole, T. Trupke, and M. A. Green, “Surface plasmon enhanced silicon solar cells,” J. Appl. Phys. 101(9), 093105 (2007). [CrossRef]
- K. Nakayama, K. Tanabe, and H. A. Atwater, “Plasmonic nanoparticle enhanced light absorption in GaAs solar cells,” Appl. Phys. Lett. 93(12), 121904 (2008). [CrossRef]
- M. M. Tajdini, S. Ghadarghadr, and H. Mosallaei, “Plasmonic nanoparticles manipulating solar systems: a dipole mode-complex image analysis,” presented at 2010 Photonic Metamaterials Plasmonics Conf., 7–9 Jun. 2010.
- S. M. Sadeghi, “Plasmonic metaresonances: Molecular resonances in quantum dot–metallic nanoparticle conjugates,” Phys. Rev. B 79(23), 233309 (2009). [CrossRef]
- Y. Jin and X. Gao, “Plasmonic fluorescent quantum dots,” Nat. Nanotechnol. 4(9), 571–576 (2009). [CrossRef] [PubMed]
- J. S. Biteen, N. S. Lewis, H. A. Atwater, H. Mertens, and A. Polman, “Spectral tuning of plasmon-enhanced silicon quantum dot luminescence,” Appl. Phys. Lett. 88(13), 131109 (2006). [CrossRef]
- Y. Lia, H. J. Schluesenerb, and S. Xua, “Gold nanoparticle-based biosensors,” Gold Bull. 43(1), 29–41 (2010). [CrossRef]
- Y. Xiao, F. Patolsky, E. Katz, J. F. Hainfeld, and I. Willner, ““Plugging into Enzymes”: nanowiring of redox enzymes by a gold nanoparticle,” Science 299(5614), 1877–1881 (2003). [CrossRef] [PubMed]
- J. Liu and Y. Lu, “A colorimetric lead biosensor using DNAzyme-directed assembly of gold nanoparticles,” J. Am. Chem. Soc. 125(22), 6642–6643 (2003). [CrossRef] [PubMed]
- D. Pacifici, H. J. Lezec, L. A. Sweatlock, R. J. Walters, and H. A. Atwater, “Universal optical transmission features in periodic and quasiperiodic hole arrays,” Opt. Express 16(12), 9222–9238 (2008). [CrossRef] [PubMed]
- L. Dal Negro, C. J. Oton, Z. Gaburro, L. Pavesi, P. Johnson, A. Lagendijk, R. Righini, M. Colocci, and D. S. Wiersma, “Light transport through the band-edge states of Fibonacci quasicrystals,” Phys. Rev. Lett. 90(5), 055501 (2003). [CrossRef] [PubMed]
- R. Dallapiccola, A. Gopinath, F. Stellacci, and L. Dal Negro, “Quasi-periodic distribution of plasmon modes in two-dimensional Fibonacci arrays of metal nanoparticles,” Opt. Express 16(8), 5544–5555 (2008). [CrossRef] [PubMed]
- M. Kohmoto, B. Sutherland, and K. Iguchi, “Localization of optics: Quasiperiodic media,” Phys. Rev. Lett. 58(23), 2436–2438 (1987). [CrossRef] [PubMed]
- A. Ahmadi, S. Ghadarghadr, and H. Mosallaei, “An optical reflectarray nanoantenna: the concept and design,” Opt. Express 18(1), 123–133 (2010). [CrossRef] [PubMed]
- W. C. Chew, Waves and Fields in Inhomogeneous Media, (IEEE Press, 1995).
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