## Optical design of organic solar cell with hybrid plasmonic system |

Optics Express, Vol. 19, Issue 17, pp. 15908-15918 (2011)

http://dx.doi.org/10.1364/OE.19.015908

Acrobat PDF (1762 KB)

### Abstract

We propose a novel optical design of organic solar cell with a hybrid plasmonic system, which comprises a plasmonic cavity coupled with a dielectric core-metal shell nanosphere. From a rigorous solution of Maxwell’s equations, called volume integral equation method, optical absorption of the active polymer material has a four-fold increase. The significant enhancement mainly attributes to the coupling of symmetric surface wave modes supported by the cavity resonator. The dispersion relation of the plasmonic cavity is characterized by solving an 1D eigenvalue problem of the air/metal/polymer/metal/air structure with finite thicknesses of metal layers. We demonstrate that the optical enhancement strongly depends on the decay length of surface plasmon waves penetrated into the active material. Furthermore, the coherent interplay between the cavity and the dielectric core-metal shell nanosphere is undoubtedly confirmed by our theoretical model. The work offers detailed physical explanations to the hybrid plasmonic cavity device structure for enhancing the optical absorption of organic photovoltaics.

© 2011 OSA

## 1. Introduction

1. K. L. Chopra, P. D. Paulson, and V. Dutta, “Thin-film solar cells: an overview,” Prog. Photovoltaics **12**, 69–92 (2004). [CrossRef]

2. H. Hoppe and N. S. Sariciftci, “Organic solar cells: an overview,” J. Mater. Res. **19**, 1924–1945 (2004). [CrossRef]

*n*≈ 1.8) induces not only the weak optical absorption of OSCs but also fundamental (half-wavelength) limits of the optical design. On one hand, the strong Fabry-Pérot photonic mode or waveguide mode [3

3. R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater. **21**, 3504–3509 (2009). [CrossRef]

4. W. E. I. Sha, W. C. H. Choy, and W. C. Chew, “A comprehensive study for the plasmonic thin-film solar cell with periodic structure,” Opt. Express **18**, 5993–6007 (2010). [CrossRef] [PubMed]

5. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature **424**, 824–830 (2003). [CrossRef] [PubMed]

8. H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. **9**, 205–213 (2010). [CrossRef] [PubMed]

9. A. J. Morfa, K. L. Rowlen, T. H. Reilly, M. J. Romero, and J. van de Lagemaat, “Plasmon-enhanced solar energy conversion in organic bulk heterojunction photovoltaics,” Appl. Phys. Lett. **92**, 013504 (2008). [CrossRef]

13. W. E. I. Sha, W. C. H. Choy, and W. C. Chew, “Angular response of thin-film organic solar cells with periodic metal back nanostrips,” Opt. Lett. **36**, 478–480 (2011). [CrossRef] [PubMed]

14. D. Duche, P. Torchio, L. Escoubas, F. Monestier, J. J. Simon, F. Flory, and G. Mathian, “Improving light absorption in organic solar cells by plasmonic contribution,” Sol. Energy Mater. Sol. Cells **93**, 1377–1382 (2009). [CrossRef]

18. J. Jung, T. Sondergaard, T. G. Pedersen, K. Pedersen, A. N. Larsen, and B. B. Nielsen, “Dyadic Green’s functions of thin films: Applications within plasmonic solar cells,” Phys. Rev. B **83**, 085419 (2011). [CrossRef]

19. 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**, 4391–4397 (2008). [CrossRef]

## 2. Theoretical Model

*i*

_{0}is the imaginary unit,

*ɛ*

_{0}(

*μ*

_{0}) is the permittivity (permeability) of free space,

**E**

*(*

^{i}**r**) is the incident electric field of the light,

*ɛ*(

**r**) is the position-dependent permittivity of the inhomogeneous materials,

**J**is the volumetric polarization current to be solved, and

**Ḡ**(

**r**,

**r**′) is the dyadic Green’s tensor in free space. The widely adopted approach for solving the VIE is the discrete dipole approximation (DDA) method [20

20. B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A **11**, 1491–1499 (1994). [CrossRef]

*E*-field induced by the scalar (piecewise constant) basis functions, the DDA method cannot accurately characterize the subwavelength plasmonic physics [21

21. A. M. Kern and O. J. F. Martin, “Surface integral formulation for 3D simulations of plasmonic and high permittivity nanostructures,” J. Opt. Soc. Am. A **26**, 732–740 (2009). [CrossRef]

22. A. W. Glisson and D. R. Wilton, “Simple and efficient numerical methods for problems of electromagnetic radiation and scattering from surfaces,” IEEE Trans. Antennas Propag. **28**, 593–603 (1980). [CrossRef]

**J**can be written as Considering the Cartesian coordinate system, we use the short notation (

*u*

_{1},

*u*

_{2},

*u*

_{3}) substituting for (

*x,y,z*), then we have where where

*K*

_{0}is the wave number of free space.

*(*

_{k}*u*

_{1}) and Π

*(*

_{m}*u*

_{2}) are defined by

*u*

_{1}and Δ

*u*

_{2}are the grid sizes of each small cuboid along x and y directions, respectively. Other functions in Eq. (8) can be defined in the same way.

23. M. F. Catedra, E. Gago, and L. Nuno, “A numerical scheme to obtain the RCS of three-dimensional bodies of resonant size using the conjugate gradient method and the fast Fourier transform,” IEEE Trans. Antennas Propag. **37**, 528–537 (1989). [CrossRef]

24. H. A. Vandervorst, “Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems,” SIAM J. Sci. Stat. Comput. **13**, 631–644 (1992). [CrossRef]

*O*(

*N*log

*N*) and memory of

*O*(

*N*).

*n*=

_{c}*n*+

_{r}*i*

_{0}

*k*is the complex refractive index of the active material,

_{i}*λ*is the incident wavelength, and

*c*

_{0}is the speed of light in free space. It is worth mentioning that the absorption of various concentrators (involving single metallic cavity, single nanosphere, or plasmonic hybrid system) should be precluded in the volume integral above. A spectral enhancement factor (SEF) is the absorption spectrum of the OSC incorporating concentrators over that excluding concentrators. Integrating with a standard solar irradiance spectrum (air mass 1.5 global), one can get the total absorption of OSCs where Γ is the solar irradiance spectrum. Likewise, a total enhancement factor (TEF) is the total absorption of the OSC incorporating concentrators over that excluding concentrators. To understand the mode hybridization for plasmon coupling, the polarization charge distribution on the surface of metallic nanostructure is given as follows where

**P**= (

*ɛ*–

*ɛ*

_{0})

**E**is the polarization density. Based on the divergence-free condition, the polarization charge is definitely zero except on the heterogeneous boundaries. From the VIE solution, one can obtain the polarization current

**J**and the total electric field

**E**. After a postprocessing procedure with Eqs. (14) and (15), the SEF and TEF can be easily accessible. In addition, both the two layered OSC structure and embedded concentrators are meshed by the volumetric cuboid cells with a uniform grid size of 1 nm.

## 3. Results and Discussions

*E*-field polarized along the

*x*direction. Figure 2(a) shows the real and imaginary parts of the refractive index of the active material measured from ellipsometry [25

25. W. C. H. Choy and H. H. Fong, “Comprehensive investigation of absolute optical properties of organic materials,” J. Phys. D: Appl. Phys. **41**, 155109 (2008). [CrossRef]

26. A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. **37**, 5271–5283 (1998). [CrossRef]

_{2}as a dielectric layer is adopted for the core-shell sphere and its refractive index can be found in the literature [27].

28. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science **302**, 419–422 (2003). [CrossRef] [PubMed]

29. W. C. Chew, *Waves and Fields in Inhomogenous Media* (Wiley-IEEE Press, 1999). [CrossRef]

30. L. Tsang, J. A. Kong, and K. H. Ding, *Scattering of Electromagnetic Waves: Theories and Applications* (Wiley, 2000). [CrossRef]

*m*is the order of the modified spherical Bessel (Hankel) functions, and

*m*= 1) of

*r*,

_{i}*ɛ*,

_{i}*μ*, and

_{i}*K*are the radius, permittivity, permeability, and wave number of the

_{i}*i*th spherical layer, respectively. Figure 2(b) and 2(c) show the SEFs and the SCS of the nanospheres, respectively. As seen in Figs. 2(b) and 2(c), the peaks of the SEFs agree with those of the SCS well. The small dielectric nanosphere, although has no loss and large refractive index (n=4), is not a good concentrator for OSCs. The dielectric nanosphere with positive refractive index cannot produce a strong dipole resonance compared to the metal nanosphere. Moreover, in contrast to the DC-MS sphere that has a metal layer adjacent to different materials (SiO

_{2}and polymer), the resonance of the MC-DS sphere is blue-shifted because only one material SiO

_{2}with lower refractive index is adjacent to the metal layer. The near field of the MC-DS sphere confines to the shell layer and cannot sufficiently scatter to the active layer. As a result, the optical enhancement by the MC-DS sphere is very weak. Figure 2(d) shows a tunable plasmon resonance by engineering the geometry of the DC-MS sphere. The resonance is red-shifted and becomes damped as the core radius increases.

31. B. Prade, J. Y. Vinet, and A. Mysyrowicz, “Guided optical waves in planar heterostructures with negative dielectric-constant,” Phys. Rev. B **44**, 13556–13572 (1991). [CrossRef]

29. W. C. Chew, *Waves and Fields in Inhomogenous Media* (Wiley-IEEE Press, 1999). [CrossRef]

*p*=

*ɛ*and

*ϕ*=

*H*for TM wave, and

_{y}*p*=

*μ*and

*ϕ*=

*E*for TE wave. The eigenvalue equation [Eq. (23)] can be easily solved by the finite-difference method [4

_{y}4. W. E. I. Sha, W. C. H. Choy, and W. C. Chew, “A comprehensive study for the plasmonic thin-film solar cell with periodic structure,” Opt. Express **18**, 5993–6007 (2010). [CrossRef] [PubMed]

32. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic-waves,” J. Comput. Phys. **114**, 185–200 (1994). [CrossRef]

33. W. C. Chew and W. H. Weedon, “A 3-D perfectly matched medium from modified Maxwell’s equations with stretched coordinates,” Microw. Opt. Technol. Lett. **7**, 599–604 (1994). [CrossRef]

31. B. Prade, J. Y. Vinet, and A. Mysyrowicz, “Guided optical waves in planar heterostructures with negative dielectric-constant,” Phys. Rev. B **44**, 13556–13572 (1991). [CrossRef]

29. W. C. Chew, *Waves and Fields in Inhomogenous Media* (Wiley-IEEE Press, 1999). [CrossRef]

*E*-fields concentrate at the surfaces of the metals. Contrarily, a long decay length induces a concentrated

*E*-field in the center of the active material. Figure 4 demonstrates the near-field distributions in the active layer at the wavelengths denoted with the arrows of Fig. 3(a). At 800 nm, the slowly decaying near field away from the metal claddings leads to the most significant enhancement.

## 4. Conclusion

## Acknowledgments

## References and links

1. | K. L. Chopra, P. D. Paulson, and V. Dutta, “Thin-film solar cells: an overview,” Prog. Photovoltaics |

2. | H. Hoppe and N. S. Sariciftci, “Organic solar cells: an overview,” J. Mater. Res. |

3. | R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater. |

4. | W. E. I. Sha, W. C. H. Choy, and W. C. Chew, “A comprehensive study for the plasmonic thin-film solar cell with periodic structure,” Opt. Express |

5. | W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature |

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

7. | S. A. Maier, |

8. | H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. |

9. | A. J. Morfa, K. L. Rowlen, T. H. Reilly, M. J. Romero, and J. van de Lagemaat, “Plasmon-enhanced solar energy conversion in organic bulk heterojunction photovoltaics,” Appl. Phys. Lett. |

10. | W. L. Bai, Q. Q. Gan, G. F. Song, L. H. Chen, Z. Kafafi, and F. Bartoli, “Broadband short-range surface plasmon structures for absorption enhancement in organic photovoltaics,” Opt. Express |

11. | M. G. Kang, T. Xu, H. J. Park, X. G. Luo, and L. J. Guo, “Efficiency enhancement of organic solar cells using transparent plasmonic Ag nanowire electrodes,” Adv. Mater. |

12. | C. J. Min, J. Li, G. Veronis, J. Y. Lee, S. H. Fan, and P. Peumans, “Enhancement of optical absorption in thin-film organic solar cells through the excitation of plasmonic modes in metallic gratings,” Appl. Phys. Lett. |

13. | W. E. I. Sha, W. C. H. Choy, and W. C. Chew, “Angular response of thin-film organic solar cells with periodic metal back nanostrips,” Opt. Lett. |

14. | D. Duche, P. Torchio, L. Escoubas, F. Monestier, J. J. Simon, F. Flory, and G. Mathian, “Improving light absorption in organic solar cells by plasmonic contribution,” Sol. Energy Mater. Sol. Cells |

15. | J. Jung, T. G. Pedersen, T. Sondergaard, K. Pedersen, A. N. Larsen, and B. B. Nielsen, “Electrostatic plasmon resonances of metal nanospheres in layered geometries,” Phys. Rev. B |

16. | S. J. Tsai, M. Ballarotto, D. B. Romero, W. N. Herman, H. C. Kan, and R. J. Phaneuf, “Effect of gold nanopillar arrays on the absorption spectrum of a bulk heterojunction organic solar cell,” Opt. Express |

17. | I. Diukman, L. Tzabari, N. Berkovitch, N. Tessler, and M. Orenstein, “Controlling absorption enhancement in organic photovoltaic cells by patterning Au nano disks within the active layer,” Opt. Express |

18. | J. Jung, T. Sondergaard, T. G. Pedersen, K. Pedersen, A. N. Larsen, and B. B. Nielsen, “Dyadic Green’s functions of thin films: Applications within plasmonic solar cells,” Phys. Rev. B |

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

20. | B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A |

21. | A. M. Kern and O. J. F. Martin, “Surface integral formulation for 3D simulations of plasmonic and high permittivity nanostructures,” J. Opt. Soc. Am. A |

22. | A. W. Glisson and D. R. Wilton, “Simple and efficient numerical methods for problems of electromagnetic radiation and scattering from surfaces,” IEEE Trans. Antennas Propag. |

23. | M. F. Catedra, E. Gago, and L. Nuno, “A numerical scheme to obtain the RCS of three-dimensional bodies of resonant size using the conjugate gradient method and the fast Fourier transform,” IEEE Trans. Antennas Propag. |

24. | H. A. Vandervorst, “Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems,” SIAM J. Sci. Stat. Comput. |

25. | W. C. H. Choy and H. H. Fong, “Comprehensive investigation of absolute optical properties of organic materials,” J. Phys. D: Appl. Phys. |

26. | A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. |

27. | E. D. Palik, |

28. | E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science |

29. | W. C. Chew, |

30. | L. Tsang, J. A. Kong, and K. H. Ding, |

31. | B. Prade, J. Y. Vinet, and A. Mysyrowicz, “Guided optical waves in planar heterostructures with negative dielectric-constant,” Phys. Rev. B |

32. | J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic-waves,” J. Comput. Phys. |

33. | W. C. Chew and W. H. Weedon, “A 3-D perfectly matched medium from modified Maxwell’s equations with stretched coordinates,” Microw. Opt. Technol. Lett. |

**OCIS Codes**

(040.5350) Detectors : Photovoltaic

(050.1755) Diffraction and gratings : Computational electromagnetic methods

(250.5403) Optoelectronics : Plasmonics

(310.6628) Thin films : Subwavelength structures, nanostructures

**ToC Category:**

Solar Energy

**History**

Original Manuscript: June 7, 2011

Revised Manuscript: July 14, 2011

Manuscript Accepted: July 15, 2011

Published: August 4, 2011

**Citation**

Wei E. I. Sha, Wallace C. H. Choy, Yongpin P. Chen, and Weng Cho Chew, "Optical design of organic solar cell with hybrid plasmonic system," Opt. Express **19**, 15908-15918 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-17-15908

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### References

- K. L. Chopra, P. D. Paulson, and V. Dutta, “Thin-film solar cells: an overview,” Prog. Photovoltaics 12, 69–92 (2004). [CrossRef]
- H. Hoppe and N. S. Sariciftci, “Organic solar cells: an overview,” J. Mater. Res. 19, 1924–1945 (2004). [CrossRef]
- R. A. Pala, J. White, E. Barnard, J. Liu, and M. L. Brongersma, “Design of plasmonic thin-film solar cells with broadband absorption enhancements,” Adv. Mater. 21, 3504–3509 (2009). [CrossRef]
- W. E. I. Sha, W. C. H. Choy, and W. C. Chew, “A comprehensive study for the plasmonic thin-film solar cell with periodic structure,” Opt. Express 18, 5993–6007 (2010). [CrossRef] [PubMed]
- W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003). [CrossRef] [PubMed]
- J. A. Schuller, E. S. Barnard, W. S. Cai, Y. C. Jun, J. S. White, and M. L. Brongersma, “Plasmonics for extreme light concentration and manipulation,” Nat. Mater. 9, 193–204 (2010). [CrossRef] [PubMed]
- S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
- H. A. Atwater and A. Polman, “Plasmonics for improved photovoltaic devices,” Nat. Mater. 9, 205–213 (2010). [CrossRef] [PubMed]
- A. J. Morfa, K. L. Rowlen, T. H. Reilly, M. J. Romero, and J. van de Lagemaat, “Plasmon-enhanced solar energy conversion in organic bulk heterojunction photovoltaics,” Appl. Phys. Lett. 92, 013504 (2008). [CrossRef]
- W. L. Bai, Q. Q. Gan, G. F. Song, L. H. Chen, Z. Kafafi, and F. Bartoli, “Broadband short-range surface plasmon structures for absorption enhancement in organic photovoltaics,” Opt. Express 18, A620–A630 (2010). [CrossRef] [PubMed]
- M. G. Kang, T. Xu, H. J. Park, X. G. Luo, and L. J. Guo, “Efficiency enhancement of organic solar cells using transparent plasmonic Ag nanowire electrodes,” Adv. Mater. 22, 4378–4383 (2010). [CrossRef] [PubMed]
- C. J. Min, J. Li, G. Veronis, J. Y. Lee, S. H. Fan, and P. Peumans, “Enhancement of optical absorption in thin-film organic solar cells through the excitation of plasmonic modes in metallic gratings,” Appl. Phys. Lett. 96, 133302 (2010). [CrossRef]
- W. E. I. Sha, W. C. H. Choy, and W. C. Chew, “Angular response of thin-film organic solar cells with periodic metal back nanostrips,” Opt. Lett. 36, 478–480 (2011). [CrossRef] [PubMed]
- D. Duche, P. Torchio, L. Escoubas, F. Monestier, J. J. Simon, F. Flory, and G. Mathian, “Improving light absorption in organic solar cells by plasmonic contribution,” Sol. Energy Mater. Sol. Cells 93, 1377–1382 (2009). [CrossRef]
- J. Jung, T. G. Pedersen, T. Sondergaard, K. Pedersen, A. N. Larsen, and B. B. Nielsen, “Electrostatic plasmon resonances of metal nanospheres in layered geometries,” Phys. Rev. B 81, 125413 (2010). [CrossRef]
- S. J. Tsai, M. Ballarotto, D. B. Romero, W. N. Herman, H. C. Kan, and R. J. Phaneuf, “Effect of gold nanopillar arrays on the absorption spectrum of a bulk heterojunction organic solar cell,” Opt. Express 18, A528–A535 (2010). [CrossRef] [PubMed]
- I. Diukman, L. Tzabari, N. Berkovitch, N. Tessler, and M. Orenstein, “Controlling absorption enhancement in organic photovoltaic cells by patterning Au nano disks within the active layer,” Opt. Express 19, A64–A71 (2011). [CrossRef] [PubMed]
- J. Jung, T. Sondergaard, T. G. Pedersen, K. Pedersen, A. N. Larsen, and B. B. Nielsen, “Dyadic Green’s functions of thin films: Applications within plasmonic solar cells,” Phys. Rev. B 83, 085419 (2011). [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, 4391–4397 (2008). [CrossRef]
- B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994). [CrossRef]
- A. M. Kern and O. J. F. Martin, “Surface integral formulation for 3D simulations of plasmonic and high permittivity nanostructures,” J. Opt. Soc. Am. A 26, 732–740 (2009). [CrossRef]
- A. W. Glisson and D. R. Wilton, “Simple and efficient numerical methods for problems of electromagnetic radiation and scattering from surfaces,” IEEE Trans. Antennas Propag. 28, 593–603 (1980). [CrossRef]
- M. F. Catedra, E. Gago, and L. Nuno, “A numerical scheme to obtain the RCS of three-dimensional bodies of resonant size using the conjugate gradient method and the fast Fourier transform,” IEEE Trans. Antennas Propag. 37, 528–537 (1989). [CrossRef]
- H. A. Vandervorst, “Bi-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems,” SIAM J. Sci. Stat. Comput. 13, 631–644 (1992). [CrossRef]
- W. C. H. Choy and H. H. Fong, “Comprehensive investigation of absolute optical properties of organic materials,” J. Phys. D: Appl. Phys. 41, 155109 (2008). [CrossRef]
- A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical properties of metallic films for vertical-cavity optoelectronic devices,” Appl. Opt. 37, 5271–5283 (1998). [CrossRef]
- E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1998).
- E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003). [CrossRef] [PubMed]
- W. C. Chew, Waves and Fields in Inhomogenous Media (Wiley-IEEE Press, 1999). [CrossRef]
- L. Tsang, J. A. Kong, and K. H. Ding, Scattering of Electromagnetic Waves: Theories and Applications (Wiley, 2000). [CrossRef]
- B. Prade, J. Y. Vinet, and A. Mysyrowicz, “Guided optical waves in planar heterostructures with negative dielectric-constant,” Phys. Rev. B 44, 13556–13572 (1991). [CrossRef]
- J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic-waves,” J. Comput. Phys. 114, 185–200 (1994). [CrossRef]
- W. C. Chew and W. H. Weedon, “A 3-D perfectly matched medium from modified Maxwell’s equations with stretched coordinates,” Microw. Opt. Technol. Lett. 7, 599–604 (1994). [CrossRef]

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