Collective behavior of impedance matched plasmonic nanocavities

A. Polyakov; M. Zolotorev; P. J. Schuck; H. A. Padmore

doi:10.1364/OE.20.007685

Collective behavior of impedance matched plasmonic nanocavities

A. Polyakov, M. Zolotorev, P. J. Schuck, and H. A. Padmore

Optics Express
Vol. 20,
Issue 7,
pp. 7685-7693
(2012)
•https://doi.org/10.1364/OE.20.007685

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A. Polyakov, M. Zolotorev, P. J. Schuck, and H. A. Padmore, "Collective behavior of impedance matched plasmonic nanocavities," Opt. Express 20, 7685-7693 (2012)

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Related Topics
Table of Contents Category
- Optics at Surfaces
Optics & Photonics Topics
?

The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Polarization-selective devices (240.5440)
- Plasmonics (250.5403)
- Metal optics (260.3910)

About this Article
History
- Original Manuscript: November 14, 2011
- Revised Manuscript: January 20, 2012
- Manuscript Accepted: January 22, 2012
- Published: March 20, 2012
Virtual Issues
Virtual Journal for Biomedical Optics Vol. 7, Iss. 5

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Open Access

Abstract

Nanometer sized cavities arranged as a subwavelength metallic grating can provide omni-directional and complete absorption of light. We present an explanation of this extraordinary phenomenon as a collective resonant response of a system based on a surface impedance model. This model gives a straightforward way to design systems for optimum light trapping performance and as well gives fundamental insights into the interaction of light with metals at the nanoscale.

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References

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|
Year
|
Author
|
Publication

V. E. Ferry, J. N. Munday, and H. A. Atwater, “Design considerations for plasmonic photovoltaics,” Adv. Mater. 22(43), 4794 (2010).
[Crossref] [PubMed]
I. Thomann, B. A. Pinaud, Z. Chen, B. M. Clemens, T. F. Jaramillo, and M. L. Brongersma, “Plasmon enhanced solar-to-fuel energy conversion,” Nano Lett. 11, 3440–3446 (2011).
[Crossref] [PubMed]
J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Ríos, “Why metallic surfaces with grooves a few nanometers deep and wide may strongly absorb visible light,” Phys. Rev. Lett. 100(6), 066408 (2008).
[Crossref] [PubMed]
A. Polyakov, S. Cabrini, S. Dhuey, B. Harteneck, P. J. Schuck, and H. A. Padmore, “Plasmonic light trapping in nanostructured metal surfaces,” App. Phys. Lett. 98(20), 203104 (2011).
[Crossref]
R. Gordon, “Light in a subwavelength slit in a metal: Propagation and reflection,” Phys. Rev. B 73(15), 153405 (2006).
[Crossref]
S. Zhang, H. Liu, and G. Mu, “Electromagnetic enhancement by a single nano-groove in metallic substrate,” J. Opt. Soc. Am. A 27(7), 1555–1560 (2010).
[Crossref]
P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. B 95(26), 263902 (2005).
[Crossref]
J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73, 035407 (2006).
[Crossref]
V. V. Temnov and U. Woggon, “Surface plasmon interferometry: measuring group velocity of surface plasmons,” Opt. Lett. 32, 1235–1237 (2007).
[Crossref] [PubMed]
P. Lalanne and J. P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nat. Phys. 2, 551–556 (2006).
[Crossref]
H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ’t Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94, 053901 (2005).
[Crossref] [PubMed]
T. V. Teperik, V. V. Popov, and F. J. G. de Abajo, “Void plasmons and total absorption of light in nanoporous metallic films,” Phys. Rev. B 71, 085408 (2005).
[Crossref]
J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847–848 (2004).
[Crossref] [PubMed]
T. Lopez-Rios, D. Mendoza, F. J. Sanchez-Dehesa, and B. Pannetier, “Surface shape resonances in lamellar metallic grating,” Phys. Rev. Lett. 81(3), 665–668 (1998).
[Crossref]
A. Kubo, N. Pontius, and H. Petek, “Femtosecond microscopy of surface plasmon polariton wave packet evolution at the silver/vacuum interface,” Nano Lett. 7, 470–475 (2007).
[Crossref] [PubMed]
E. Laux, C. Genet, T. Skauli, and T. W. Ebbesen, “Plasmonic photon sorters for spectral and polarimetric imaging,” Nat. Photonics 2(3), 161–164 (2008).
[Crossref]
E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969).
[Crossref]
H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).

2011 (2)

I. Thomann, B. A. Pinaud, Z. Chen, B. M. Clemens, T. F. Jaramillo, and M. L. Brongersma, “Plasmon enhanced solar-to-fuel energy conversion,” Nano Lett. 11, 3440–3446 (2011).
[Crossref] [PubMed]

A. Polyakov, S. Cabrini, S. Dhuey, B. Harteneck, P. J. Schuck, and H. A. Padmore, “Plasmonic light trapping in nanostructured metal surfaces,” App. Phys. Lett. 98(20), 203104 (2011).
[Crossref]

2010 (2)

S. Zhang, H. Liu, and G. Mu, “Electromagnetic enhancement by a single nano-groove in metallic substrate,” J. Opt. Soc. Am. A 27(7), 1555–1560 (2010).
[Crossref]

V. E. Ferry, J. N. Munday, and H. A. Atwater, “Design considerations for plasmonic photovoltaics,” Adv. Mater. 22(43), 4794 (2010).
[Crossref] [PubMed]

2008 (2)

J. Le Perchec, P. Quémerais, A. Barbara, and T. López-Ríos, “Why metallic surfaces with grooves a few nanometers deep and wide may strongly absorb visible light,” Phys. Rev. Lett. 100(6), 066408 (2008).
[Crossref] [PubMed]

E. Laux, C. Genet, T. Skauli, and T. W. Ebbesen, “Plasmonic photon sorters for spectral and polarimetric imaging,” Nat. Photonics 2(3), 161–164 (2008).
[Crossref]

2007 (2)

A. Kubo, N. Pontius, and H. Petek, “Femtosecond microscopy of surface plasmon polariton wave packet evolution at the silver/vacuum interface,” Nano Lett. 7, 470–475 (2007).
[Crossref] [PubMed]

V. V. Temnov and U. Woggon, “Surface plasmon interferometry: measuring group velocity of surface plasmons,” Opt. Lett. 32, 1235–1237 (2007).
[Crossref] [PubMed]

2006 (3)

P. Lalanne and J. P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nat. Phys. 2, 551–556 (2006).
[Crossref]

R. Gordon, “Light in a subwavelength slit in a metal: Propagation and reflection,” Phys. Rev. B 73(15), 153405 (2006).
[Crossref]

J. A. Dionne, L. A. Sweatlock, H. A. Atwater, and A. Polman, “Plasmon slot waveguides: Towards chip-scale propagation with subwavelength-scale localization,” Phys. Rev. B 73, 035407 (2006).
[Crossref]

2005 (3)

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. B 95(26), 263902 (2005).
[Crossref]

H. F. Schouten, N. Kuzmin, G. Dubois, T. D. Visser, G. Gbur, P. F. A. Alkemade, H. Blok, G. W. ’t Hooft, D. Lenstra, and E. R. Eliel, “Plasmon-assisted two-slit transmission: Young’s experiment revisited,” Phys. Rev. Lett. 94, 053901 (2005).
[Crossref] [PubMed]

T. V. Teperik, V. V. Popov, and F. J. G. de Abajo, “Void plasmons and total absorption of light in nanoporous metallic films,” Phys. Rev. B 71, 085408 (2005).
[Crossref]

2004 (1)

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847–848 (2004).
[Crossref] [PubMed]

1998 (1)

T. Lopez-Rios, D. Mendoza, F. J. Sanchez-Dehesa, and B. Pannetier, “Surface shape resonances in lamellar metallic grating,” Phys. Rev. Lett. 81(3), 665–668 (1998).
[Crossref]

1969 (1)

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969).
[Crossref]

’t Hooft, G. W.

Alkemade, P. F. A.

Atwater, H. A.

V. E. Ferry, J. N. Munday, and H. A. Atwater, “Design considerations for plasmonic photovoltaics,” Adv. Mater. 22(43), 4794 (2010).
[Crossref] [PubMed]

Barbara, A.

Blok, H.

Brongersma, M. L.

I. Thomann, B. A. Pinaud, Z. Chen, B. M. Clemens, T. F. Jaramillo, and M. L. Brongersma, “Plasmon enhanced solar-to-fuel energy conversion,” Nano Lett. 11, 3440–3446 (2011).
[Crossref] [PubMed]

Cabrini, S.

A. Polyakov, S. Cabrini, S. Dhuey, B. Harteneck, P. J. Schuck, and H. A. Padmore, “Plasmonic light trapping in nanostructured metal surfaces,” App. Phys. Lett. 98(20), 203104 (2011).
[Crossref]

Chen, Z.

I. Thomann, B. A. Pinaud, Z. Chen, B. M. Clemens, T. F. Jaramillo, and M. L. Brongersma, “Plasmon enhanced solar-to-fuel energy conversion,” Nano Lett. 11, 3440–3446 (2011).
[Crossref] [PubMed]

Clemens, B. M.

I. Thomann, B. A. Pinaud, Z. Chen, B. M. Clemens, T. F. Jaramillo, and M. L. Brongersma, “Plasmon enhanced solar-to-fuel energy conversion,” Nano Lett. 11, 3440–3446 (2011).
[Crossref] [PubMed]

de Abajo, F. J. G.

T. V. Teperik, V. V. Popov, and F. J. G. de Abajo, “Void plasmons and total absorption of light in nanoporous metallic films,” Phys. Rev. B 71, 085408 (2005).
[Crossref]

Dhuey, S.

A. Polyakov, S. Cabrini, S. Dhuey, B. Harteneck, P. J. Schuck, and H. A. Padmore, “Plasmonic light trapping in nanostructured metal surfaces,” App. Phys. Lett. 98(20), 203104 (2011).
[Crossref]

Dionne, J. A.

Dubois, G.

Ebbesen, T. W.

E. Laux, C. Genet, T. Skauli, and T. W. Ebbesen, “Plasmonic photon sorters for spectral and polarimetric imaging,” Nat. Photonics 2(3), 161–164 (2008).
[Crossref]

Economou, E. N.

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969).
[Crossref]

Eliel, E. R.

Ferry, V. E.

V. E. Ferry, J. N. Munday, and H. A. Atwater, “Design considerations for plasmonic photovoltaics,” Adv. Mater. 22(43), 4794 (2010).
[Crossref] [PubMed]

Garcia-Vidal, F. J.

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847–848 (2004).
[Crossref] [PubMed]

Gbur, G.

Genet, C.

E. Laux, C. Genet, T. Skauli, and T. W. Ebbesen, “Plasmonic photon sorters for spectral and polarimetric imaging,” Nat. Photonics 2(3), 161–164 (2008).
[Crossref]

Gordon, R.

R. Gordon, “Light in a subwavelength slit in a metal: Propagation and reflection,” Phys. Rev. B 73(15), 153405 (2006).
[Crossref]

Harteneck, B.

A. Polyakov, S. Cabrini, S. Dhuey, B. Harteneck, P. J. Schuck, and H. A. Padmore, “Plasmonic light trapping in nanostructured metal surfaces,” App. Phys. Lett. 98(20), 203104 (2011).
[Crossref]

Hugonin, J. P.

P. Lalanne and J. P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nat. Phys. 2, 551–556 (2006).
[Crossref]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. B 95(26), 263902 (2005).
[Crossref]

Jaramillo, T. F.

I. Thomann, B. A. Pinaud, Z. Chen, B. M. Clemens, T. F. Jaramillo, and M. L. Brongersma, “Plasmon enhanced solar-to-fuel energy conversion,” Nano Lett. 11, 3440–3446 (2011).
[Crossref] [PubMed]

Kubo, A.

A. Kubo, N. Pontius, and H. Petek, “Femtosecond microscopy of surface plasmon polariton wave packet evolution at the silver/vacuum interface,” Nano Lett. 7, 470–475 (2007).
[Crossref] [PubMed]

Kuzmin, N.

Lalanne, P.

P. Lalanne and J. P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nat. Phys. 2, 551–556 (2006).
[Crossref]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. B 95(26), 263902 (2005).
[Crossref]

Laux, E.

E. Laux, C. Genet, T. Skauli, and T. W. Ebbesen, “Plasmonic photon sorters for spectral and polarimetric imaging,” Nat. Photonics 2(3), 161–164 (2008).
[Crossref]

Le Perchec, J.

Lenstra, D.

Liu, H.

S. Zhang, H. Liu, and G. Mu, “Electromagnetic enhancement by a single nano-groove in metallic substrate,” J. Opt. Soc. Am. A 27(7), 1555–1560 (2010).
[Crossref]

Lopez-Rios, T.

T. Lopez-Rios, D. Mendoza, F. J. Sanchez-Dehesa, and B. Pannetier, “Surface shape resonances in lamellar metallic grating,” Phys. Rev. Lett. 81(3), 665–668 (1998).
[Crossref]

López-Ríos, T.

Martin-Moreno, L.

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847–848 (2004).
[Crossref] [PubMed]

Mendoza, D.

T. Lopez-Rios, D. Mendoza, F. J. Sanchez-Dehesa, and B. Pannetier, “Surface shape resonances in lamellar metallic grating,” Phys. Rev. Lett. 81(3), 665–668 (1998).
[Crossref]

Mu, G.

S. Zhang, H. Liu, and G. Mu, “Electromagnetic enhancement by a single nano-groove in metallic substrate,” J. Opt. Soc. Am. A 27(7), 1555–1560 (2010).
[Crossref]

Munday, J. N.

V. E. Ferry, J. N. Munday, and H. A. Atwater, “Design considerations for plasmonic photovoltaics,” Adv. Mater. 22(43), 4794 (2010).
[Crossref] [PubMed]

Padmore, H. A.

A. Polyakov, S. Cabrini, S. Dhuey, B. Harteneck, P. J. Schuck, and H. A. Padmore, “Plasmonic light trapping in nanostructured metal surfaces,” App. Phys. Lett. 98(20), 203104 (2011).
[Crossref]

Pannetier, B.

T. Lopez-Rios, D. Mendoza, F. J. Sanchez-Dehesa, and B. Pannetier, “Surface shape resonances in lamellar metallic grating,” Phys. Rev. Lett. 81(3), 665–668 (1998).
[Crossref]

Pendry, J. B.

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847–848 (2004).
[Crossref] [PubMed]

Petek, H.

A. Kubo, N. Pontius, and H. Petek, “Femtosecond microscopy of surface plasmon polariton wave packet evolution at the silver/vacuum interface,” Nano Lett. 7, 470–475 (2007).
[Crossref] [PubMed]

Pinaud, B. A.

I. Thomann, B. A. Pinaud, Z. Chen, B. M. Clemens, T. F. Jaramillo, and M. L. Brongersma, “Plasmon enhanced solar-to-fuel energy conversion,” Nano Lett. 11, 3440–3446 (2011).
[Crossref] [PubMed]

Polman, A.

Polyakov, A.

A. Polyakov, S. Cabrini, S. Dhuey, B. Harteneck, P. J. Schuck, and H. A. Padmore, “Plasmonic light trapping in nanostructured metal surfaces,” App. Phys. Lett. 98(20), 203104 (2011).
[Crossref]

Pontius, N.

A. Kubo, N. Pontius, and H. Petek, “Femtosecond microscopy of surface plasmon polariton wave packet evolution at the silver/vacuum interface,” Nano Lett. 7, 470–475 (2007).
[Crossref] [PubMed]

Popov, V. V.

T. V. Teperik, V. V. Popov, and F. J. G. de Abajo, “Void plasmons and total absorption of light in nanoporous metallic films,” Phys. Rev. B 71, 085408 (2005).
[Crossref]

Quémerais, P.

Raether, H.

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).

Rodier, J. C.

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. B 95(26), 263902 (2005).
[Crossref]

Sanchez-Dehesa, F. J.

T. Lopez-Rios, D. Mendoza, F. J. Sanchez-Dehesa, and B. Pannetier, “Surface shape resonances in lamellar metallic grating,” Phys. Rev. Lett. 81(3), 665–668 (1998).
[Crossref]

Schouten, H. F.

Schuck, P. J.

A. Polyakov, S. Cabrini, S. Dhuey, B. Harteneck, P. J. Schuck, and H. A. Padmore, “Plasmonic light trapping in nanostructured metal surfaces,” App. Phys. Lett. 98(20), 203104 (2011).
[Crossref]

Skauli, T.

E. Laux, C. Genet, T. Skauli, and T. W. Ebbesen, “Plasmonic photon sorters for spectral and polarimetric imaging,” Nat. Photonics 2(3), 161–164 (2008).
[Crossref]

Sweatlock, L. A.

Temnov, V. V.

V. V. Temnov and U. Woggon, “Surface plasmon interferometry: measuring group velocity of surface plasmons,” Opt. Lett. 32, 1235–1237 (2007).
[Crossref] [PubMed]

Teperik, T. V.

T. V. Teperik, V. V. Popov, and F. J. G. de Abajo, “Void plasmons and total absorption of light in nanoporous metallic films,” Phys. Rev. B 71, 085408 (2005).
[Crossref]

Thomann, I.

I. Thomann, B. A. Pinaud, Z. Chen, B. M. Clemens, T. F. Jaramillo, and M. L. Brongersma, “Plasmon enhanced solar-to-fuel energy conversion,” Nano Lett. 11, 3440–3446 (2011).
[Crossref] [PubMed]

Visser, T. D.

Woggon, U.

V. V. Temnov and U. Woggon, “Surface plasmon interferometry: measuring group velocity of surface plasmons,” Opt. Lett. 32, 1235–1237 (2007).
[Crossref] [PubMed]

Zhang, S.

S. Zhang, H. Liu, and G. Mu, “Electromagnetic enhancement by a single nano-groove in metallic substrate,” J. Opt. Soc. Am. A 27(7), 1555–1560 (2010).
[Crossref]

Adv. Mater. (1)

V. E. Ferry, J. N. Munday, and H. A. Atwater, “Design considerations for plasmonic photovoltaics,” Adv. Mater. 22(43), 4794 (2010).
[Crossref] [PubMed]

App. Phys. Lett. (1)

A. Polyakov, S. Cabrini, S. Dhuey, B. Harteneck, P. J. Schuck, and H. A. Padmore, “Plasmonic light trapping in nanostructured metal surfaces,” App. Phys. Lett. 98(20), 203104 (2011).
[Crossref]

J. Opt. Soc. Am. A (1)

S. Zhang, H. Liu, and G. Mu, “Electromagnetic enhancement by a single nano-groove in metallic substrate,” J. Opt. Soc. Am. A 27(7), 1555–1560 (2010).
[Crossref]

Nano Lett. (2)

I. Thomann, B. A. Pinaud, Z. Chen, B. M. Clemens, T. F. Jaramillo, and M. L. Brongersma, “Plasmon enhanced solar-to-fuel energy conversion,” Nano Lett. 11, 3440–3446 (2011).
[Crossref] [PubMed]

A. Kubo, N. Pontius, and H. Petek, “Femtosecond microscopy of surface plasmon polariton wave packet evolution at the silver/vacuum interface,” Nano Lett. 7, 470–475 (2007).
[Crossref] [PubMed]

Nat. Photonics (1)

E. Laux, C. Genet, T. Skauli, and T. W. Ebbesen, “Plasmonic photon sorters for spectral and polarimetric imaging,” Nat. Photonics 2(3), 161–164 (2008).
[Crossref]

Nat. Phys. (1)

P. Lalanne and J. P. Hugonin, “Interaction between optical nano-objects at metallo-dielectric interfaces,” Nat. Phys. 2, 551–556 (2006).
[Crossref]

Opt. Lett. (1)

V. V. Temnov and U. Woggon, “Surface plasmon interferometry: measuring group velocity of surface plasmons,” Opt. Lett. 32, 1235–1237 (2007).
[Crossref] [PubMed]

Phys. Rev. (1)

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969).
[Crossref]

Phys. Rev. B (4)

T. V. Teperik, V. V. Popov, and F. J. G. de Abajo, “Void plasmons and total absorption of light in nanoporous metallic films,” Phys. Rev. B 71, 085408 (2005).
[Crossref]

R. Gordon, “Light in a subwavelength slit in a metal: Propagation and reflection,” Phys. Rev. B 73(15), 153405 (2006).
[Crossref]

P. Lalanne, J. P. Hugonin, and J. C. Rodier, “Theory of surface plasmon generation at nanoslit apertures,” Phys. Rev. B 95(26), 263902 (2005).
[Crossref]

Phys. Rev. Lett. (3)

T. Lopez-Rios, D. Mendoza, F. J. Sanchez-Dehesa, and B. Pannetier, “Surface shape resonances in lamellar metallic grating,” Phys. Rev. Lett. 81(3), 665–668 (1998).
[Crossref]

Science (1)

J. B. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, “Mimicking surface plasmons with structured surfaces,” Science 305, 847–848 (2004).
[Crossref] [PubMed]

Other (1)

H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings (Springer-Verlag, 1988).

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Fig. 1 Schematic of the plasmonic nano-grooves on a metal surface. The SPPs propagate down the NG along the z-axis, then reflect off the bottom and travel back to the mouth. On resonance, all incident energy is trapped within the grooves.

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Fig. 2 Reflectivity response for a combined double grating where one NG set is inserted in between another one. The dimensions for the sets NG1 and NG2 are w₁ = 19 nm, h₁ = 45 nm, w₂ = 10.8 nm, and h₂ = 56.1 nm. Period for both gratings is p = 300 nm. The independent behavior of the two gratings when combined shows that, on resonance, the SPPs traveling on the flat surface do not contribute to the reflectivity response of the NG grating.

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Fig. 3 Effect of the NG period on the reflectivity response in gold. The NGs constitute a set of resonant cavities: (a) SPP field penetration into the metal is the dominant factor for a dense grating, where complete absorption is achieved only for extreme h; (b) in a sparse grating NGs act as resonant cavities useful for field enhancement and field localization close to the metal surface. The inset shows the change in the real part of the plasmon wavelength due to the change in the NG period.

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Fig. 4 Angular bandwidth is affected by the NG period. As the period is increased approaching the wavelength of incident light the angular bandwidth sharply drops and the reflectivity response acquires more of a grating-like character: a sharp resonance that is highly sensitive to the angle of incidence and wavelength.

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Fig. 5 Resonant behavior of the nano-groove. Producing a minimum reflectivity on-resonance at constant incident wavelength for a range of NG periods requires adjusting the NG dimensions. In the region of validity (shown in gray background), the analytic model presented here agrees well with the numerical FDTD calculations on the absolute scale as shown in (a). On the relative scale, the NG period-to-width ratio–shown in (b)–is flat in the validity region, which is closely approximated by our model: the NG width increases linearly with the period accompanied by bandwidth (FWHM) narrowing as shown for Au (black) and Cu (blue).

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Equations (8)

Equations on this page are rendered with MathJax. Learn more.

Z_{surf} = \frac{E_{0}}{H_{0}} \times \frac{w}{p} \frac{Q}{2}

R = r r *, r = \frac{Z_{surf} - Z_{0}}{Z_{surf} + Z_{0}}

Z_{surf} = i \times \frac{k_{p l}}{k_{0}^{R}} \cdot \frac{w}{2 p} \cdot Q

Q = \frac{2}{π} \times \frac{1}{\frac{Δ k_{p l}}{k_{p l}^{R}} + i \frac{k_{p l}^{″}}{k_{p l}^{R}}}

\frac{Δ k_{p l}}{k_{p l}^{R}} = \frac{d k_{p l}}{k_{p l}^{R}} \frac{Δ ω}{d ω} \frac{ω_{R}}{ω_{R}} = \frac{Δ ω}{ω_{R}} \frac{ω_{R}}{k_{p l}^{R}} \cdot \frac{d k_{p l}}{d ω}

Z_{surf} = i \times \frac{α / ω}{Δ ω / ω + i \cdot β / ω}, {\begin{array}{l} α / ω = \frac{1}{Z_{0}} \frac{ω c}{π p} {\frac{k_{p l}}{ω}}^{2} \frac{d ω}{d k_{p l}} \\ β / ω = \frac{k_{p l}^{″}}{ω} \frac{d ω}{d k_{p l}} \end{array}

R = \frac{Δ ω^{2} + {(α - β)}^{2}}{Δ ω^{2} + {(α + β)}^{2}}

\frac{p}{w} = \frac{1}{π} \frac{{[k_{p l}^{'}]}^{2}}{k_{0}^{R} k_{p l}^{″}}