Numerical study on surface plasmon polariton behaviors in periodic metal-dielectric structures using a plane-wave-assisted boundary integral-equation method
Optics Express, Vol. 15, Issue 14, pp. 9048-9062 (2007)
http://dx.doi.org/10.1364/OE.15.009048
Acrobat PDF (449 KB)
Abstract
A novel hybrid technique based on the boundary integral-equation method is proposed for studying the surface plasmon polariton behaviors in two-dimensional periodic structures. Considering the periodicity property of the problem, we use the plane-wave expansion concept and the periodic boundary condition instead of using the periodic Green’s function. The diffraction efficiency can then be readily calculated once the equivalent electric and magnetic currents are solved that avoids invoking the numerical calculation of the radiation integral. The numerical validity is verified with the cases of highly conducting materials and practical metals. Numerical convergence can be easily achieved even in the case of a large incident angle as 80°. Based on the numerical scheme, a metal-dielectric wavy structure is designed for enhancing the transmittance of optical signal through the structure. The excitation of the coupled surface plasmon polaritons for the high transmission is demonstrated.
© 2007 Optical Society of America
1. Introduction
5. K. Yashiro and S. Ohkawa, “Boundary element method for electromagnetic scattering from cylinders,” IEEE Trans. Antennas Propagat. 33, 383–389 (1985). [CrossRef]
12. K. Yasumoto and K. Yoshitomi, “Efficient calculation of lattice sums for free-space periodic Green’s function,” IEEE Trans. Antennas Propagat. 47, 1050–1055 (1999). [CrossRef]
13. H. Rogier and D. De Zutter, “A fast converging series expansion for the 2-d periodic Green’s function based on perfectly matched layers,” IEEE Trans. Microwave Theory Tech. 52, 1199–1206 (2004). [CrossRef]
6. L. C. Trintinalia and H. Ling, “Integral equation modeling of multilayered doubly-periodic lossy structures using periodic boundary condition and a connection scheme,” IEEE Trans. Antennas Propagat. 52, 2253–2261 (2004). [CrossRef]
2. Plane-wave-assisted boundary integral-equation method
15. K.-M. Chen, “A mathematical formulation of the equivalence principle,” IEEE Trans. Microwave Theory Tech. 37, 1576–1581 (1989). [CrossRef]
3. Simulation results
3. A. Numerical verifications
9. E. Popov, B. Chernov, M. Nevière, and N. Bonod, “Differential theory: Application to highly conducting gratings,” J. Opt. Soc. Am. A 21, 199–206 (2004). [CrossRef]
17. L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870–1876 (1996). [CrossRef]
9. E. Popov, B. Chernov, M. Nevière, and N. Bonod, “Differential theory: Application to highly conducting gratings,” J. Opt. Soc. Am. A 21, 199–206 (2004). [CrossRef]
3. B. Simulation results of a wavy structure
18. D. K. Gifford and D. G. Hall, “Extraordinary transmission of organic photoluminescence through an otherwise opaque metal layer via surface plasmon cross coupling,” Appl. Phys. Lett. 80, 3679–3681 (2002). [CrossRef]
21. U. Schroter and D. Heitmann, “Grating couplers for surface plasmons excited on thin metal films in the Kretschmann-Raether configuration,” Phys. Rev. B 60, 4992–4999 (1999). [CrossRef]
22. I. R. Hooper and J. R. Sambles, “Coupled surface plasmon polaritons on thin metal slabs corrugated on both surfaces,” Phys. Rev. B 70, 045421 (2004). [CrossRef]
19. S. Wedge and W. L. Barnes, “Surface plasmon-polariton mediated light emission through thin metal films,” Opt. Express 12, 3673–3685 (2004). [CrossRef] [PubMed]
19. S. Wedge and W. L. Barnes, “Surface plasmon-polariton mediated light emission through thin metal films,” Opt. Express 12, 3673–3685 (2004). [CrossRef] [PubMed]
23. D. Crouse and P. Keshavareddy, “Role of optical and surface plasmon modes in enhanced transmission and applications,” Opt. Express 13, 7760–7771 (2005). [CrossRef] [PubMed]
4. Conclusions
Acknowledgments
References and links
1. | H. Raether, Surface Plasmons (Springer-Verlag, Berlin, 1988). |
2. | T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998). [CrossRef] |
3. | K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propagat. 14, 302–307 (1966). [CrossRef] |
4. | S. D. Gedney and R. Mittra, “Analysis of the electromagnetic scattering by thick gratings using a combined FEM/MM solution,” IEEE Trans. Antennas Propagat. 39, 1605–1614 (1991). [CrossRef] |
5. | K. Yashiro and S. Ohkawa, “Boundary element method for electromagnetic scattering from cylinders,” IEEE Trans. Antennas Propagat. 33, 383–389 (1985). [CrossRef] |
6. | L. C. Trintinalia and H. Ling, “Integral equation modeling of multilayered doubly-periodic lossy structures using periodic boundary condition and a connection scheme,” IEEE Trans. Antennas Propagat. 52, 2253–2261 (2004). [CrossRef] |
7. | T. Sondergaard, S. I. Bozhevolnyi, and A. Boltasseva, “Theoretical analysis of ridge grating for long-range surface plasmon polaritons,” Phys. Rev. B 73, 045320 (2006). [CrossRef] |
8. | M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of metallic surface-relief gratings,” J. Opt. Soc. Am. A 3, 1780–1796 (1986). [CrossRef] |
9. | E. Popov, B. Chernov, M. Nevière, and N. Bonod, “Differential theory: Application to highly conducting gratings,” J. Opt. Soc. Am. A 21, 199–206 (2004). [CrossRef] |
10. | K. Watanabe, “Study of the differential theory of lamellar gratings made of highly conducting materials,” J. Opt. Soc. Am. A 23, 69–72 (2006). [CrossRef] |
11. | E. Popov, M. Nevieˋre, B. Gralak, and G. Tayeb, “Staircase approximation validity for arbitrary-shaped gratings,” J. Opt. Soc. Am. A 19, 33–42 (2002). [CrossRef] |
12. | K. Yasumoto and K. Yoshitomi, “Efficient calculation of lattice sums for free-space periodic Green’s function,” IEEE Trans. Antennas Propagat. 47, 1050–1055 (1999). [CrossRef] |
13. | H. Rogier and D. De Zutter, “A fast converging series expansion for the 2-d periodic Green’s function based on perfectly matched layers,” IEEE Trans. Microwave Theory Tech. 52, 1199–1206 (2004). [CrossRef] |
14. | J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941). |
15. | K.-M. Chen, “A mathematical formulation of the equivalence principle,” IEEE Trans. Microwave Theory Tech. 37, 1576–1581 (1989). [CrossRef] |
16. | C. A. Balanis, Advanced Engineering Electromagnetics (John Wiley & Sons, New York, 1989). |
17. | L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870–1876 (1996). [CrossRef] |
18. | D. K. Gifford and D. G. Hall, “Extraordinary transmission of organic photoluminescence through an otherwise opaque metal layer via surface plasmon cross coupling,” Appl. Phys. Lett. 80, 3679–3681 (2002). [CrossRef] |
19. | S. Wedge and W. L. Barnes, “Surface plasmon-polariton mediated light emission through thin metal films,” Opt. Express 12, 3673–3685 (2004). [CrossRef] [PubMed] |
20. | C. Bonnand, J. Bellessa, C. Symonds, and J. C. Plenet, “Polaritonic emission via surface plasmon cross coupling,” Appl. Phys. Lett. 89, 231119 (2006). [CrossRef] |
21. | U. Schroter and D. Heitmann, “Grating couplers for surface plasmons excited on thin metal films in the Kretschmann-Raether configuration,” Phys. Rev. B 60, 4992–4999 (1999). [CrossRef] |
22. | I. R. Hooper and J. R. Sambles, “Coupled surface plasmon polaritons on thin metal slabs corrugated on both surfaces,” Phys. Rev. B 70, 045421 (2004). [CrossRef] |
23. | D. Crouse and P. Keshavareddy, “Role of optical and surface plasmon modes in enhanced transmission and applications,” Opt. Express 13, 7760–7771 (2005). [CrossRef] [PubMed] |
OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(050.2770) Diffraction and gratings : Gratings
(240.6680) Optics at surfaces : Surface plasmons
ToC Category:
Optics at Surfaces
History
Original Manuscript: May 24, 2007
Revised Manuscript: June 28, 2007
Manuscript Accepted: June 29, 2007
Published: July 9, 2007
Citation
Yean-woei Kiang, Jyh-Yang Wang, and C. C. Yang, "Numerical study on surface plasmon polariton
behaviors in periodic metal-dielectric structures
using a plane-wave-assisted boundary integral-equation method," Opt. Express 15, 9048-9062 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-14-9048
Sort: Year | Journal | Reset
References
- H. Raether, Surface Plasmons (Springer-Verlag, Berlin, 1988).
- T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998). [CrossRef]
- K. S. Yee, "Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media," IEEE Trans. Antennas Propagat. 14, 302-307 (1966). [CrossRef]
- S. D. Gedney and R. Mittra, "Analysis of the electromagnetic scattering by thick gratings using a combined FEM/MM solution," IEEE Trans. Antennas Propagat. 39, 1605-1614 (1991). [CrossRef]
- K. Yashiro and S. Ohkawa, "Boundary element method for electromagnetic scattering from cylinders," IEEE Trans. Antennas Propagat. 33, 383-389 (1985). [CrossRef]
- L. C. Trintinalia and H. Ling, "Integral equation modeling of multilayered doubly-periodic lossy structures using periodic boundary condition and a connection scheme," IEEE Trans. Antennas Propagat. 52, 2253-2261 (2004). [CrossRef]
- T. Sondergaard, S. I. Bozhevolnyi, and A. Boltasseva, "Theoretical analysis of ridge grating for long-range surface plasmon polaritons," Phys. Rev. B 73, 045320 (2006). [CrossRef]
- M. G. Moharam and T. K. Gaylord, "Rigorous coupled-wave analysis of metallic surface-relief gratings," J. Opt. Soc. Am. A 3, 1780-1796 (1986). [CrossRef]
- E. Popov, B. Chernov, M. Nevière, and N. Bonod, "Differential theory: Application to highly conducting gratings," J. Opt. Soc. Am. A 21, 199-206 (2004). [CrossRef]
- K. Watanabe, "Study of the differential theory of lamellar gratings made of highly conducting materials," J. Opt. Soc. Am. A 23, 69-72 (2006). [CrossRef]
- E. Popov, M. Nevie`re, B. Gralak, and G. Tayeb, "Staircase approximation validity for arbitrary-shaped gratings," J. Opt. Soc. Am. A 19, 33-42 (2002). [CrossRef]
- K. Yasumoto and K. Yoshitomi, "Efficient calculation of lattice sums for free-space periodic Green’s function," IEEE Trans. Antennas Propagat. 47, 1050-1055 (1999). [CrossRef]
- H. Rogier and D. De Zutter, "A fast converging series expansion for the 2-d periodic Green’s function based on perfectly matched layers," IEEE Trans. Microwave Theory Tech. 52, 1199-1206 (2004). [CrossRef]
- J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
- K.-M. Chen, "A mathematical formulation of the equivalence principle," IEEE Trans. Microwave Theory Tech. 37, 1576-1581 (1989). [CrossRef]
- C. A. Balanis, Advanced Engineering Electromagnetics (John Wiley & Sons, New York, 1989).
- L. Li, "Use of Fourier series in the analysis of discontinuous periodic structures," J. Opt. Soc. Am. A 13, 1870-1876 (1996). [CrossRef]
- D. K. Gifford and D. G. Hall, "Extraordinary transmission of organic photoluminescence through an otherwise opaque metal layer via surface plasmon cross coupling," Appl. Phys. Lett. 80, 3679-3681 (2002). [CrossRef]
- S. Wedge and W. L. Barnes, "Surface plasmon-polariton mediated light emission through thin metal films," Opt. Express 12, 3673-3685 (2004). [CrossRef] [PubMed]
- C. Bonnand, J. Bellessa, C. Symonds, and J. C. Plenet, "Polaritonic emission via surface plasmon cross coupling," Appl. Phys. Lett. 89, 231119 (2006). [CrossRef]
- U. Schroter and D. Heitmann, "Grating couplers for surface plasmons excited on thin metal films in the Kretschmann-Raether configuration," Phys. Rev. B 60, 4992-4999 (1999). [CrossRef]
- I. R. Hooper and J. R. Sambles, "Coupled surface plasmon polaritons on thin metal slabs corrugated on both surfaces," Phys. Rev. B 70, 045421 (2004). [CrossRef]
- D. Crouse and P. Keshavareddy, "Role of optical and surface plasmon modes in enhanced transmission and applications," Opt. Express 13, 7760-7771 (2005). [CrossRef] [PubMed]
Cited By |
Alert me when this paper is cited |
OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.
« Previous Article | Next Article »
OSA is a member of CrossRef.