Resonant mode coupling of optical resonances in stacked nanostructures

doi:10.1364/OE.18.007569

Resonant mode coupling of optical resonances in stacked nanostructures

Nikolay A. Gippius, Thomas Weiss, Sergei G. Tikhodeev, and Harald Giessen »View Author Affiliations

Optics Express, Vol. 18, Issue 7, pp. 7569-7574 (2010)
http://dx.doi.org/10.1364/OE.18.007569

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Abstract

We propose a method to obtain the resonance frequencies of coupled optical modes for a stack of two periodically corrugated slabs. The method is based on the modes in each slab, which are derived by the Fourier modal method in combination with the optical scattering matrix theory. We then use the resonant mode approximation of the scattering matrices to develop a linear eigenvalue problem with dimensions equal to the number of resonant modes. Its solutions are the resonance frequencies of the coupled system and exhibit a good agreement with exact solutions. We demonstrate the capabilities of this method for pairs of planar waveguides and gratings of one-dimensional wires.

OCIS Codes
(090.1970) Holography : Diffractive optics
(160.3918) Materials : Metamaterials

ToC Category:
Metamaterials

History
Original Manuscript: February 4, 2010
Revised Manuscript: March 24, 2010
Manuscript Accepted: March 24, 2010
Published: March 26, 2010

Citation
Nikolay A. Gippius, Thomas Weiss, Sergei G. Tikhodeev, and Harald Giessen, "Resonant mode coupling of optical resonances in stacked nanostructures," Opt. Express 18, 7569-7574 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-7-7569

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References

J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tunnermann, F. Lederer, and T. Pertsch, "Multipole approach to metamaterials," Phys. Rev. A 78, 438111 (2008). [CrossRef]
N. Liu, H. Liu, S. Zhu, and H. Giessen, "Stereometamaterials," Nat. Photonics 3, 157-162 (2009). [CrossRef]
N. Liu, L. Langguth, T. Weiss, J. Kastel, M. Fleischhauer, T. Pfau, and H. Giessen, "Plasmonic electromagnetically induced transparency at the Drude damping limit," Nat. Mater. 8, 758-762 (2009). [CrossRef] [PubMed]
D. M. Whittaker and I. S. Culshaw, "Scattering matrix treatment of patterned multilayer photonic structures," Phys. Rev. B 60, 2610-2618 (1999). [CrossRef]
S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, "Quasiguided modes and optical properties of photonic crystal slabs," Phys. Rev. B 66, 451021 (2002). [CrossRef]
N. A. Gippius, S. G. Tikhodeev, and T. Ishihara, "Optical properties of photonic crystal slabs with an asymmetrical unit cell," Phys. Rev. B 72, 451381 (2005). [CrossRef]
N. A. Gippius and S. G. Tikhodeev, "Application of the scattering matrix method for calculating the optical properties of metamaterials," Phys.-Usp. 52, 967-971 (2009). [CrossRef]
L. Li, "New formulation of the Fourier modal method for crossed surface-relief gratings," J. Opt. Soc. Am. A 14, 2758-2767 (1997). [CrossRef]
G. Granet and J. P. Plumey, "Parametric formulation of the Fourier modal method for crossed surface-relief gratings," J. Opt. A, Pure Appl. Opt. 4, 145-149 (2002). [CrossRef]
G. Gantzounis and N. Stefanou, "Layer-multiple-scattering method for photonic crystals of nonspherical particles," Phys. Rev. B 73, 035115 (2006). [CrossRef]
L. Landau and E. M. Lifshitz, Quantum Mechanics. Non-Relativistic Theory (Pergamon, 1966).
V. Podolskiy, A. Sarychev, and V. Shalaev, "Plasmon modes and negative refraction in metal nanowire composites," Opt. Express 11, 735-745 (2003). [CrossRef] [PubMed]
P. G. Etchegoin, E. C. Le Ru, and M. Meyer, "An analytic model for the optical properties of gold," J. Chem. Phys. 125, 164705-1-3 (2006). [CrossRef] [PubMed]

Chipouline, A.
Culshaw, I. S.
Etchegoin, P. G.
Fleischhauer, M.
Gantzounis, G.
Giessen, H.
Gippius, N. A.
Granet, G.
Ishihara, T.
Kastel, J.
Langguth, L.
Le Ru, E. C.
Lederer, F.
Li, L.
Liu, H.
Liu, N.
Menzel, C.
Meyer, M.
Muljarov, E. A.
Pertsch, T.
Petschulat, J.
Pfau, T.
Plumey, J. P.
Podolskiy, V.
Rockstuhl, C.
Sarychev, A.
Shalaev, V.
Stefanou, N.
Tikhodeev, S. G.
Tunnermann, A.
Weiss, T.
Whittaker, D. M.
Yablonskii, A. L.
Zhu, S.

J. Chem. Phys

P. G. Etchegoin, E. C. Le Ru, and M. Meyer, "An analytic model for the optical properties of gold," J. Chem. Phys. 125, 164705-1-3 (2006). [CrossRef] [PubMed]

J. Opt. A, Pure Appl. Opt.

G. Granet and J. P. Plumey, "Parametric formulation of the Fourier modal method for crossed surface-relief gratings," J. Opt. A, Pure Appl. Opt. 4, 145-149 (2002). [CrossRef]

J. Opt. Soc. Am. A

L. Li, "New formulation of the Fourier modal method for crossed surface-relief gratings," J. Opt. Soc. Am. A 14, 2758-2767 (1997). [CrossRef]

Nat. Mater.

N. Liu, L. Langguth, T. Weiss, J. Kastel, M. Fleischhauer, T. Pfau, and H. Giessen, "Plasmonic electromagnetically induced transparency at the Drude damping limit," Nat. Mater. 8, 758-762 (2009). [CrossRef] [PubMed]

Nat. Photonics

N. Liu, H. Liu, S. Zhu, and H. Giessen, "Stereometamaterials," Nat. Photonics 3, 157-162 (2009). [CrossRef]

Opt. Express

V. Podolskiy, A. Sarychev, and V. Shalaev, "Plasmon modes and negative refraction in metal nanowire composites," Opt. Express 11, 735-745 (2003). [CrossRef] [PubMed]

Phys. Rev. A

J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tunnermann, F. Lederer, and T. Pertsch, "Multipole approach to metamaterials," Phys. Rev. A 78, 438111 (2008). [CrossRef]

Phys. Rev. B

G. Gantzounis and N. Stefanou, "Layer-multiple-scattering method for photonic crystals of nonspherical particles," Phys. Rev. B 73, 035115 (2006). [CrossRef]
D. M. Whittaker and I. S. Culshaw, "Scattering matrix treatment of patterned multilayer photonic structures," Phys. Rev. B 60, 2610-2618 (1999). [CrossRef]
S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, "Quasiguided modes and optical properties of photonic crystal slabs," Phys. Rev. B 66, 451021 (2002). [CrossRef]
N. A. Gippius, S. G. Tikhodeev, and T. Ishihara, "Optical properties of photonic crystal slabs with an asymmetrical unit cell," Phys. Rev. B 72, 451381 (2005). [CrossRef]

Usp.

N. A. Gippius and S. G. Tikhodeev, "Application of the scattering matrix method for calculating the optical properties of metamaterials," Phys.-Usp. 52, 967-971 (2009). [CrossRef]

Other

L. Landau and E. M. Lifshitz, Quantum Mechanics. Non-Relativistic Theory (Pergamon, 1966).

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[1] J. Petschulat, C. Menzel, A. Chipouline, C. Rockstuhl, A. Tunnermann, F. Lederer, and T. Pertsch, "Multipole approach to metamaterials," Phys. Rev. A 78, 438111 (2008). [CrossRef]

[2] N. Liu, H. Liu, S. Zhu, and H. Giessen, "Stereometamaterials," Nat. Photonics 3, 157-162 (2009). [CrossRef]

[3] N. Liu, L. Langguth, T. Weiss, J. Kastel, M. Fleischhauer, T. Pfau, and H. Giessen, "Plasmonic electromagnetically induced transparency at the Drude damping limit," Nat. Mater. 8, 758-762 (2009). [CrossRef] [PubMed]

[4] D. M. Whittaker and I. S. Culshaw, "Scattering matrix treatment of patterned multilayer photonic structures," Phys. Rev. B 60, 2610-2618 (1999). [CrossRef]

[5] S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, "Quasiguided modes and optical properties of photonic crystal slabs," Phys. Rev. B 66, 451021 (2002). [CrossRef]

[6] N. A. Gippius, S. G. Tikhodeev, and T. Ishihara, "Optical properties of photonic crystal slabs with an asymmetrical unit cell," Phys. Rev. B 72, 451381 (2005). [CrossRef]

[7] N. A. Gippius and S. G. Tikhodeev, "Application of the scattering matrix method for calculating the optical properties of metamaterials," Phys.-Usp. 52, 967-971 (2009). [CrossRef]

[8] L. Li, "New formulation of the Fourier modal method for crossed surface-relief gratings," J. Opt. Soc. Am. A 14, 2758-2767 (1997). [CrossRef]

[9] G. Granet and J. P. Plumey, "Parametric formulation of the Fourier modal method for crossed surface-relief gratings," J. Opt. A, Pure Appl. Opt. 4, 145-149 (2002). [CrossRef]

[10] G. Gantzounis and N. Stefanou, "Layer-multiple-scattering method for photonic crystals of nonspherical particles," Phys. Rev. B 73, 035115 (2006). [CrossRef]

[11] L. Landau and E. M. Lifshitz, Quantum Mechanics. Non-Relativistic Theory (Pergamon, 1966).

[12] V. Podolskiy, A. Sarychev, and V. Shalaev, "Plasmon modes and negative refraction in metal nanowire composites," Opt. Express 11, 735-745 (2003). [CrossRef] [PubMed]

[13] P. G. Etchegoin, E. C. Le Ru, and M. Meyer, "An analytic model for the optical properties of gold," J. Chem. Phys. 125, 164705-1-3 (2006). [CrossRef] [PubMed]

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Resonant mode coupling of optical resonances in stacked nanostructures

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Abstract

References

J. Chem. Phys

J. Opt. A, Pure Appl. Opt.

J. Opt. Soc. Am. A

Nat. Mater.

Nat. Photonics

Opt. Express

Phys. Rev. A

Phys. Rev. B

Usp.

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