Abstract

We theoretically examine thermal emission from metallic films with surfaces that are patterned with a series of circular concentric grooves (a bull’s eye pattern). Due to thermal excitation of surface plasmons, theory predicts that a single beam of light can be emitted from these films in the normal direction that is narrow, both in terms of its spectrum and its angular divergence. Thus, we show that metallic films can generate monochromatic directional beams of light by a simple thermal process.

© 2010 Optical Society of America

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  1. H. Raether, Surface Plasmons (Springer-Verlag, Berlin, 1988).
  2. A. Polman, "Plasmonics applied," Science 322, 868-869 (2008).
    [CrossRef] [PubMed]
  3. W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
    [CrossRef] [PubMed]
  4. E. Ozbay, "Plasmonics: merging photonics and electronics at nanoscale dimensions," Science 311, 189-193 (2006).
    [CrossRef] [PubMed]
  5. 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]
  6. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcıa-Vidal, and T. W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 820-822 (2002).
    [CrossRef] [PubMed]
  7. L. Martın-Moreno, F. J. Garcıa-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, "Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations," Phys. Rev. Lett. 90, 167401 (2003).
    [CrossRef] [PubMed]
  8. Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P. A. Lemoine, K. Joulain, J. P. Mulet, Y. Chen, and J. J. Greffet, "Thermal radiation scanning tunnelling microscopy," Nature 444, 740-743 (2006).
    [CrossRef] [PubMed]
  9. P. J. Hesketh, J. N. Zemel, and B. Gebhart, "Organ pipe radiant modes of periodic micromachined silicon surfaces," Nature (London) 324, 549-551 (1986).
    [CrossRef]
  10. A. Heinzel, V. Boerner, A. Gombert, B. Blasi, V. Wittwer, and J. Luther, "Radiation filters and emitters for the NIR based on periodically structured metal surfaces," J. Mod. Opt. 47, 2399-2419 (2000).
  11. J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, and Y. Chen, "Coherent emission of light by thermal sources," Nature (London) 416, 61-64 (2002).
    [CrossRef] [PubMed]
  12. M. Laroche, C. Arnold, F. Marquier, R. Carminati, J. J. Greffet, S. Collin, N. Bardou, and J. L. Pelouard, "Highly directional radiation generated by a tungsten thermal source," Opt. Lett. 30, 2623-2625 (2005).
    [CrossRef] [PubMed]
  13. Y. T. Chang, Y. H. Ye, D. C. Tzuang, Y. T. Wu, C. H. Yang, C. F. Chan, Y. W. Jiang, and S. C. Lee, "Localized surface plasmons in Al/Si structure and Ag/SiO2/Ag emitter with different concentric metal rings," Appl. Phys. Lett. 92, 233109 (2008).
    [CrossRef]
  14. C. M. Cornelius and J. P. Dowling, "Modification of Planck blackbody radiation by photonic band-gap structures," Phys. Rev. A 59, 4736-4746 (1999).
    [CrossRef]
  15. J. G. Fleming, S.-Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, "All-metallic three-dimensional photonic crystals with a large infrared bandgap," Nature (London) 417, 52-55 (2002).
    [CrossRef] [PubMed]
  16. M. U. Pralle, N. Moelders, M. P. McNeal, I. Puscasu, A. C. Greenwald, J. T. Daly, E. A. Johnson, T. George, D. S. Choi, I. El-Kady, and R. Biswas, "Photonic crystal enhanced narrow-band infrared emitters," Appl. Phys. Lett. 81, 4685-4687 (2002).
    [CrossRef]
  17. I. Celanovic, D. Perreault, and J. Kassakian, "Resonant-cavity enhanced thermal emission," Phys. Rev. B 72075127 (2005).
    [CrossRef]
  18. S. E. Han, A. Stein, and D. J. Norris, "Tailoring self-assembled metallic photonic crystals for modified thermal emission," Phys. Rev. Lett. 99, 053906 (2007).
    [CrossRef] [PubMed]
  19. X. D. Yu, Y. J. Lee, R. Furstenberg, J. O. White, and P. V. Braun, "Filling fraction dependent properties of inverse opal metallic photonic crystals," Adv. Mater. 19, 1689-1692 (2007).
    [CrossRef]
  20. H. Caglayan, I. Bulu, and E. Ozbay, "Extraordinary grating-coupled microwave transmission through a subwavelength annular aperture," Opt. Express 13, 1666-1671 (2005).
    [CrossRef] [PubMed]
  21. E. Popov, M. Neviere, A.-L. Fehrembach, and N. Bonod, "Optimization of plasmon excitation at structured apertures," Appl. Opt. 44, 6141-6154 (2005).
    [CrossRef] [PubMed]
  22. S. E. Han, "Theory of thermal emission from periodic structures," Phys. Rev. B 80, 155108 (2009).
    [CrossRef]
  23. We used the transfer matrix formalism introduced in J. B. Pendry and A. MacKinnon, "Calculation of photon dispersion relations," Phys. Rev. Lett. 69, 2772-2775 (1992). A unit cell is discretized by a 80×80 mesh. For◦C, we used the dielectric function for tungsten from D. W. Lynch and W. R. Hunter, in Handbook of Optical Constants of Solids, edited by E. D. Palik (Academic Press, Orlando, 1985).
    [CrossRef] [PubMed]
  24. <jrn>24. F. Marquier, C. Arnold, M. Laroche, J. J. Greffet, and Y. Chen, "Degree of polarization of thermal light emitted by gratings supporting surface waves," Opt. Express 16, 5305-5313 (2008).Q1</jrn>
    [CrossRef] [PubMed]
  25. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).Q2
  26. N. Dahan, A. Niv, G. Biener, Y. Gorodetski, V. Kleiner, and E. Hasman, "Enhanced coherency of thermal emission: Beyond the limitation imposed by delocalized surface waves," Phys. Rev. B 76, 045427 (2007).
    [CrossRef]
  27. G. Biener, N. Dahan, A. Niv, V. Kleiner, and E. Hasman, "Highly coherent thermal emission obtained by plasmonic bandgap structures," Appl. Phys. Lett. 92, 081913 (2008).
    [CrossRef]
  28. T. Erdogan and D. G. Hall, "Circularly symmetric distributed feedback semiconductor laser: an analysis," J. Appl. Phys. 68, 1435-1444 (1990).
    [CrossRef]
  29. R. H. Jordan and D. G. Hall, "Free-space azimuthal paraxial wave equation: the azimuthal Bessel-Gauss beam solution," Opt. Lett. 19, 427-429 (1994).
    [CrossRef] [PubMed]
  30. J. Durnin, J. J. Miceli, Jr, and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
    [CrossRef] [PubMed]

2009

S. E. Han, "Theory of thermal emission from periodic structures," Phys. Rev. B 80, 155108 (2009).
[CrossRef]

2008

G. Biener, N. Dahan, A. Niv, V. Kleiner, and E. Hasman, "Highly coherent thermal emission obtained by plasmonic bandgap structures," Appl. Phys. Lett. 92, 081913 (2008).
[CrossRef]

A. Polman, "Plasmonics applied," Science 322, 868-869 (2008).
[CrossRef] [PubMed]

Y. T. Chang, Y. H. Ye, D. C. Tzuang, Y. T. Wu, C. H. Yang, C. F. Chan, Y. W. Jiang, and S. C. Lee, "Localized surface plasmons in Al/Si structure and Ag/SiO2/Ag emitter with different concentric metal rings," Appl. Phys. Lett. 92, 233109 (2008).
[CrossRef]

2007

N. Dahan, A. Niv, G. Biener, Y. Gorodetski, V. Kleiner, and E. Hasman, "Enhanced coherency of thermal emission: Beyond the limitation imposed by delocalized surface waves," Phys. Rev. B 76, 045427 (2007).
[CrossRef]

S. E. Han, A. Stein, and D. J. Norris, "Tailoring self-assembled metallic photonic crystals for modified thermal emission," Phys. Rev. Lett. 99, 053906 (2007).
[CrossRef] [PubMed]

X. D. Yu, Y. J. Lee, R. Furstenberg, J. O. White, and P. V. Braun, "Filling fraction dependent properties of inverse opal metallic photonic crystals," Adv. Mater. 19, 1689-1692 (2007).
[CrossRef]

2006

E. Ozbay, "Plasmonics: merging photonics and electronics at nanoscale dimensions," Science 311, 189-193 (2006).
[CrossRef] [PubMed]

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P. A. Lemoine, K. Joulain, J. P. Mulet, Y. Chen, and J. J. Greffet, "Thermal radiation scanning tunnelling microscopy," Nature 444, 740-743 (2006).
[CrossRef] [PubMed]

2005

2003

L. Martın-Moreno, F. J. Garcıa-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, "Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations," Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef] [PubMed]

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

2002

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcıa-Vidal, and T. W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 820-822 (2002).
[CrossRef] [PubMed]

J. G. Fleming, S.-Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, "All-metallic three-dimensional photonic crystals with a large infrared bandgap," Nature (London) 417, 52-55 (2002).
[CrossRef] [PubMed]

M. U. Pralle, N. Moelders, M. P. McNeal, I. Puscasu, A. C. Greenwald, J. T. Daly, E. A. Johnson, T. George, D. S. Choi, I. El-Kady, and R. Biswas, "Photonic crystal enhanced narrow-band infrared emitters," Appl. Phys. Lett. 81, 4685-4687 (2002).
[CrossRef]

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, and Y. Chen, "Coherent emission of light by thermal sources," Nature (London) 416, 61-64 (2002).
[CrossRef] [PubMed]

2000

A. Heinzel, V. Boerner, A. Gombert, B. Blasi, V. Wittwer, and J. Luther, "Radiation filters and emitters for the NIR based on periodically structured metal surfaces," J. Mod. Opt. 47, 2399-2419 (2000).

1999

C. M. Cornelius and J. P. Dowling, "Modification of Planck blackbody radiation by photonic band-gap structures," Phys. Rev. A 59, 4736-4746 (1999).
[CrossRef]

1998

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]

1994

1990

T. Erdogan and D. G. Hall, "Circularly symmetric distributed feedback semiconductor laser: an analysis," J. Appl. Phys. 68, 1435-1444 (1990).
[CrossRef]

1987

J. Durnin, J. J. Miceli, Jr, and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef] [PubMed]

1986

P. J. Hesketh, J. N. Zemel, and B. Gebhart, "Organ pipe radiant modes of periodic micromachined silicon surfaces," Nature (London) 324, 549-551 (1986).
[CrossRef]

Arnold, C.

Bardou, N.

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Biener, G.

G. Biener, N. Dahan, A. Niv, V. Kleiner, and E. Hasman, "Highly coherent thermal emission obtained by plasmonic bandgap structures," Appl. Phys. Lett. 92, 081913 (2008).
[CrossRef]

N. Dahan, A. Niv, G. Biener, Y. Gorodetski, V. Kleiner, and E. Hasman, "Enhanced coherency of thermal emission: Beyond the limitation imposed by delocalized surface waves," Phys. Rev. B 76, 045427 (2007).
[CrossRef]

Biswas, R.

M. U. Pralle, N. Moelders, M. P. McNeal, I. Puscasu, A. C. Greenwald, J. T. Daly, E. A. Johnson, T. George, D. S. Choi, I. El-Kady, and R. Biswas, "Photonic crystal enhanced narrow-band infrared emitters," Appl. Phys. Lett. 81, 4685-4687 (2002).
[CrossRef]

J. G. Fleming, S.-Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, "All-metallic three-dimensional photonic crystals with a large infrared bandgap," Nature (London) 417, 52-55 (2002).
[CrossRef] [PubMed]

Blasi, B.

A. Heinzel, V. Boerner, A. Gombert, B. Blasi, V. Wittwer, and J. Luther, "Radiation filters and emitters for the NIR based on periodically structured metal surfaces," J. Mod. Opt. 47, 2399-2419 (2000).

Boerner, V.

A. Heinzel, V. Boerner, A. Gombert, B. Blasi, V. Wittwer, and J. Luther, "Radiation filters and emitters for the NIR based on periodically structured metal surfaces," J. Mod. Opt. 47, 2399-2419 (2000).

Bonod, N.

Braun, P. V.

X. D. Yu, Y. J. Lee, R. Furstenberg, J. O. White, and P. V. Braun, "Filling fraction dependent properties of inverse opal metallic photonic crystals," Adv. Mater. 19, 1689-1692 (2007).
[CrossRef]

Bulu, I.

Caglayan, H.

Carminati, R.

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P. A. Lemoine, K. Joulain, J. P. Mulet, Y. Chen, and J. J. Greffet, "Thermal radiation scanning tunnelling microscopy," Nature 444, 740-743 (2006).
[CrossRef] [PubMed]

M. Laroche, C. Arnold, F. Marquier, R. Carminati, J. J. Greffet, S. Collin, N. Bardou, and J. L. Pelouard, "Highly directional radiation generated by a tungsten thermal source," Opt. Lett. 30, 2623-2625 (2005).
[CrossRef] [PubMed]

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, and Y. Chen, "Coherent emission of light by thermal sources," Nature (London) 416, 61-64 (2002).
[CrossRef] [PubMed]

Celanovic, I.

I. Celanovic, D. Perreault, and J. Kassakian, "Resonant-cavity enhanced thermal emission," Phys. Rev. B 72075127 (2005).
[CrossRef]

Chan, C. F.

Y. T. Chang, Y. H. Ye, D. C. Tzuang, Y. T. Wu, C. H. Yang, C. F. Chan, Y. W. Jiang, and S. C. Lee, "Localized surface plasmons in Al/Si structure and Ag/SiO2/Ag emitter with different concentric metal rings," Appl. Phys. Lett. 92, 233109 (2008).
[CrossRef]

Chang, Y. T.

Y. T. Chang, Y. H. Ye, D. C. Tzuang, Y. T. Wu, C. H. Yang, C. F. Chan, Y. W. Jiang, and S. C. Lee, "Localized surface plasmons in Al/Si structure and Ag/SiO2/Ag emitter with different concentric metal rings," Appl. Phys. Lett. 92, 233109 (2008).
[CrossRef]

Chen, Y.

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P. A. Lemoine, K. Joulain, J. P. Mulet, Y. Chen, and J. J. Greffet, "Thermal radiation scanning tunnelling microscopy," Nature 444, 740-743 (2006).
[CrossRef] [PubMed]

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, and Y. Chen, "Coherent emission of light by thermal sources," Nature (London) 416, 61-64 (2002).
[CrossRef] [PubMed]

Choi, D. S.

M. U. Pralle, N. Moelders, M. P. McNeal, I. Puscasu, A. C. Greenwald, J. T. Daly, E. A. Johnson, T. George, D. S. Choi, I. El-Kady, and R. Biswas, "Photonic crystal enhanced narrow-band infrared emitters," Appl. Phys. Lett. 81, 4685-4687 (2002).
[CrossRef]

Collin, S.

Cornelius, C. M.

C. M. Cornelius and J. P. Dowling, "Modification of Planck blackbody radiation by photonic band-gap structures," Phys. Rev. A 59, 4736-4746 (1999).
[CrossRef]

Dahan, N.

G. Biener, N. Dahan, A. Niv, V. Kleiner, and E. Hasman, "Highly coherent thermal emission obtained by plasmonic bandgap structures," Appl. Phys. Lett. 92, 081913 (2008).
[CrossRef]

N. Dahan, A. Niv, G. Biener, Y. Gorodetski, V. Kleiner, and E. Hasman, "Enhanced coherency of thermal emission: Beyond the limitation imposed by delocalized surface waves," Phys. Rev. B 76, 045427 (2007).
[CrossRef]

Daly, J. T.

M. U. Pralle, N. Moelders, M. P. McNeal, I. Puscasu, A. C. Greenwald, J. T. Daly, E. A. Johnson, T. George, D. S. Choi, I. El-Kady, and R. Biswas, "Photonic crystal enhanced narrow-band infrared emitters," Appl. Phys. Lett. 81, 4685-4687 (2002).
[CrossRef]

De Wilde, Y.

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P. A. Lemoine, K. Joulain, J. P. Mulet, Y. Chen, and J. J. Greffet, "Thermal radiation scanning tunnelling microscopy," Nature 444, 740-743 (2006).
[CrossRef] [PubMed]

Degiron, A.

L. Martın-Moreno, F. J. Garcıa-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, "Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations," Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef] [PubMed]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcıa-Vidal, and T. W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 820-822 (2002).
[CrossRef] [PubMed]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

Devaux, E.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcıa-Vidal, and T. W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 820-822 (2002).
[CrossRef] [PubMed]

Dowling, J. P.

C. M. Cornelius and J. P. Dowling, "Modification of Planck blackbody radiation by photonic band-gap structures," Phys. Rev. A 59, 4736-4746 (1999).
[CrossRef]

Durnin, J.

J. Durnin, J. J. Miceli, Jr, and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef] [PubMed]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

L. Martın-Moreno, F. J. Garcıa-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, "Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations," Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef] [PubMed]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcıa-Vidal, and T. W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 820-822 (2002).
[CrossRef] [PubMed]

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]

Eberly, J. H.

J. Durnin, J. J. Miceli, Jr, and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef] [PubMed]

El-Kady, I.

M. U. Pralle, N. Moelders, M. P. McNeal, I. Puscasu, A. C. Greenwald, J. T. Daly, E. A. Johnson, T. George, D. S. Choi, I. El-Kady, and R. Biswas, "Photonic crystal enhanced narrow-band infrared emitters," Appl. Phys. Lett. 81, 4685-4687 (2002).
[CrossRef]

J. G. Fleming, S.-Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, "All-metallic three-dimensional photonic crystals with a large infrared bandgap," Nature (London) 417, 52-55 (2002).
[CrossRef] [PubMed]

Erdogan, T.

T. Erdogan and D. G. Hall, "Circularly symmetric distributed feedback semiconductor laser: an analysis," J. Appl. Phys. 68, 1435-1444 (1990).
[CrossRef]

Fehrembach, A.-L.

Fleming, J. G.

J. G. Fleming, S.-Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, "All-metallic three-dimensional photonic crystals with a large infrared bandgap," Nature (London) 417, 52-55 (2002).
[CrossRef] [PubMed]

Formanek, F.

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P. A. Lemoine, K. Joulain, J. P. Mulet, Y. Chen, and J. J. Greffet, "Thermal radiation scanning tunnelling microscopy," Nature 444, 740-743 (2006).
[CrossRef] [PubMed]

Furstenberg, R.

X. D. Yu, Y. J. Lee, R. Furstenberg, J. O. White, and P. V. Braun, "Filling fraction dependent properties of inverse opal metallic photonic crystals," Adv. Mater. 19, 1689-1692 (2007).
[CrossRef]

Garcia-Vidal, F. J.

L. Martın-Moreno, F. J. Garcıa-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, "Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations," Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef] [PubMed]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcıa-Vidal, and T. W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 820-822 (2002).
[CrossRef] [PubMed]

Gebhart, B.

P. J. Hesketh, J. N. Zemel, and B. Gebhart, "Organ pipe radiant modes of periodic micromachined silicon surfaces," Nature (London) 324, 549-551 (1986).
[CrossRef]

George, T.

M. U. Pralle, N. Moelders, M. P. McNeal, I. Puscasu, A. C. Greenwald, J. T. Daly, E. A. Johnson, T. George, D. S. Choi, I. El-Kady, and R. Biswas, "Photonic crystal enhanced narrow-band infrared emitters," Appl. Phys. Lett. 81, 4685-4687 (2002).
[CrossRef]

Ghaemi, H. F.

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]

Gombert, A.

A. Heinzel, V. Boerner, A. Gombert, B. Blasi, V. Wittwer, and J. Luther, "Radiation filters and emitters for the NIR based on periodically structured metal surfaces," J. Mod. Opt. 47, 2399-2419 (2000).

Gorodetski, Y.

N. Dahan, A. Niv, G. Biener, Y. Gorodetski, V. Kleiner, and E. Hasman, "Enhanced coherency of thermal emission: Beyond the limitation imposed by delocalized surface waves," Phys. Rev. B 76, 045427 (2007).
[CrossRef]

Gralak, B.

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P. A. Lemoine, K. Joulain, J. P. Mulet, Y. Chen, and J. J. Greffet, "Thermal radiation scanning tunnelling microscopy," Nature 444, 740-743 (2006).
[CrossRef] [PubMed]

Greenwald, A. C.

M. U. Pralle, N. Moelders, M. P. McNeal, I. Puscasu, A. C. Greenwald, J. T. Daly, E. A. Johnson, T. George, D. S. Choi, I. El-Kady, and R. Biswas, "Photonic crystal enhanced narrow-band infrared emitters," Appl. Phys. Lett. 81, 4685-4687 (2002).
[CrossRef]

Greffet, J. J.

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P. A. Lemoine, K. Joulain, J. P. Mulet, Y. Chen, and J. J. Greffet, "Thermal radiation scanning tunnelling microscopy," Nature 444, 740-743 (2006).
[CrossRef] [PubMed]

M. Laroche, C. Arnold, F. Marquier, R. Carminati, J. J. Greffet, S. Collin, N. Bardou, and J. L. Pelouard, "Highly directional radiation generated by a tungsten thermal source," Opt. Lett. 30, 2623-2625 (2005).
[CrossRef] [PubMed]

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, and Y. Chen, "Coherent emission of light by thermal sources," Nature (London) 416, 61-64 (2002).
[CrossRef] [PubMed]

Hall, D. G.

R. H. Jordan and D. G. Hall, "Free-space azimuthal paraxial wave equation: the azimuthal Bessel-Gauss beam solution," Opt. Lett. 19, 427-429 (1994).
[CrossRef] [PubMed]

T. Erdogan and D. G. Hall, "Circularly symmetric distributed feedback semiconductor laser: an analysis," J. Appl. Phys. 68, 1435-1444 (1990).
[CrossRef]

Han, S. E.

S. E. Han, "Theory of thermal emission from periodic structures," Phys. Rev. B 80, 155108 (2009).
[CrossRef]

S. E. Han, A. Stein, and D. J. Norris, "Tailoring self-assembled metallic photonic crystals for modified thermal emission," Phys. Rev. Lett. 99, 053906 (2007).
[CrossRef] [PubMed]

Hasman, E.

G. Biener, N. Dahan, A. Niv, V. Kleiner, and E. Hasman, "Highly coherent thermal emission obtained by plasmonic bandgap structures," Appl. Phys. Lett. 92, 081913 (2008).
[CrossRef]

N. Dahan, A. Niv, G. Biener, Y. Gorodetski, V. Kleiner, and E. Hasman, "Enhanced coherency of thermal emission: Beyond the limitation imposed by delocalized surface waves," Phys. Rev. B 76, 045427 (2007).
[CrossRef]

Heinzel, A.

A. Heinzel, V. Boerner, A. Gombert, B. Blasi, V. Wittwer, and J. Luther, "Radiation filters and emitters for the NIR based on periodically structured metal surfaces," J. Mod. Opt. 47, 2399-2419 (2000).

Hesketh, P. J.

P. J. Hesketh, J. N. Zemel, and B. Gebhart, "Organ pipe radiant modes of periodic micromachined silicon surfaces," Nature (London) 324, 549-551 (1986).
[CrossRef]

Ho, K. M.

J. G. Fleming, S.-Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, "All-metallic three-dimensional photonic crystals with a large infrared bandgap," Nature (London) 417, 52-55 (2002).
[CrossRef] [PubMed]

Jiang, Y. W.

Y. T. Chang, Y. H. Ye, D. C. Tzuang, Y. T. Wu, C. H. Yang, C. F. Chan, Y. W. Jiang, and S. C. Lee, "Localized surface plasmons in Al/Si structure and Ag/SiO2/Ag emitter with different concentric metal rings," Appl. Phys. Lett. 92, 233109 (2008).
[CrossRef]

Johnson, E. A.

M. U. Pralle, N. Moelders, M. P. McNeal, I. Puscasu, A. C. Greenwald, J. T. Daly, E. A. Johnson, T. George, D. S. Choi, I. El-Kady, and R. Biswas, "Photonic crystal enhanced narrow-band infrared emitters," Appl. Phys. Lett. 81, 4685-4687 (2002).
[CrossRef]

Jordan, R. H.

Joulain, K.

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P. A. Lemoine, K. Joulain, J. P. Mulet, Y. Chen, and J. J. Greffet, "Thermal radiation scanning tunnelling microscopy," Nature 444, 740-743 (2006).
[CrossRef] [PubMed]

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, and Y. Chen, "Coherent emission of light by thermal sources," Nature (London) 416, 61-64 (2002).
[CrossRef] [PubMed]

Kassakian, J.

I. Celanovic, D. Perreault, and J. Kassakian, "Resonant-cavity enhanced thermal emission," Phys. Rev. B 72075127 (2005).
[CrossRef]

Kleiner, V.

G. Biener, N. Dahan, A. Niv, V. Kleiner, and E. Hasman, "Highly coherent thermal emission obtained by plasmonic bandgap structures," Appl. Phys. Lett. 92, 081913 (2008).
[CrossRef]

N. Dahan, A. Niv, G. Biener, Y. Gorodetski, V. Kleiner, and E. Hasman, "Enhanced coherency of thermal emission: Beyond the limitation imposed by delocalized surface waves," Phys. Rev. B 76, 045427 (2007).
[CrossRef]

Laroche, M.

Lee, S. C.

Y. T. Chang, Y. H. Ye, D. C. Tzuang, Y. T. Wu, C. H. Yang, C. F. Chan, Y. W. Jiang, and S. C. Lee, "Localized surface plasmons in Al/Si structure and Ag/SiO2/Ag emitter with different concentric metal rings," Appl. Phys. Lett. 92, 233109 (2008).
[CrossRef]

Lee, Y. J.

X. D. Yu, Y. J. Lee, R. Furstenberg, J. O. White, and P. V. Braun, "Filling fraction dependent properties of inverse opal metallic photonic crystals," Adv. Mater. 19, 1689-1692 (2007).
[CrossRef]

Lemoine, P. A.

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P. A. Lemoine, K. Joulain, J. P. Mulet, Y. Chen, and J. J. Greffet, "Thermal radiation scanning tunnelling microscopy," Nature 444, 740-743 (2006).
[CrossRef] [PubMed]

Lezec, H. J.

L. Martın-Moreno, F. J. Garcıa-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, "Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations," Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef] [PubMed]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcıa-Vidal, and T. W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 820-822 (2002).
[CrossRef] [PubMed]

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]

Lin, S.-Y.

J. G. Fleming, S.-Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, "All-metallic three-dimensional photonic crystals with a large infrared bandgap," Nature (London) 417, 52-55 (2002).
[CrossRef] [PubMed]

Linke, R. A.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcıa-Vidal, and T. W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 820-822 (2002).
[CrossRef] [PubMed]

Luther, J.

A. Heinzel, V. Boerner, A. Gombert, B. Blasi, V. Wittwer, and J. Luther, "Radiation filters and emitters for the NIR based on periodically structured metal surfaces," J. Mod. Opt. 47, 2399-2419 (2000).

Mainguy, S.

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, and Y. Chen, "Coherent emission of light by thermal sources," Nature (London) 416, 61-64 (2002).
[CrossRef] [PubMed]

Marquier, F.

Martin-Moreno, L.

L. Martın-Moreno, F. J. Garcıa-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, "Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations," Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef] [PubMed]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcıa-Vidal, and T. W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 820-822 (2002).
[CrossRef] [PubMed]

McNeal, M. P.

M. U. Pralle, N. Moelders, M. P. McNeal, I. Puscasu, A. C. Greenwald, J. T. Daly, E. A. Johnson, T. George, D. S. Choi, I. El-Kady, and R. Biswas, "Photonic crystal enhanced narrow-band infrared emitters," Appl. Phys. Lett. 81, 4685-4687 (2002).
[CrossRef]

Miceli, J. J.

J. Durnin, J. J. Miceli, Jr, and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef] [PubMed]

Moelders, N.

M. U. Pralle, N. Moelders, M. P. McNeal, I. Puscasu, A. C. Greenwald, J. T. Daly, E. A. Johnson, T. George, D. S. Choi, I. El-Kady, and R. Biswas, "Photonic crystal enhanced narrow-band infrared emitters," Appl. Phys. Lett. 81, 4685-4687 (2002).
[CrossRef]

Mulet, J. P.

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P. A. Lemoine, K. Joulain, J. P. Mulet, Y. Chen, and J. J. Greffet, "Thermal radiation scanning tunnelling microscopy," Nature 444, 740-743 (2006).
[CrossRef] [PubMed]

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, and Y. Chen, "Coherent emission of light by thermal sources," Nature (London) 416, 61-64 (2002).
[CrossRef] [PubMed]

Neviere, M.

Niv, A.

G. Biener, N. Dahan, A. Niv, V. Kleiner, and E. Hasman, "Highly coherent thermal emission obtained by plasmonic bandgap structures," Appl. Phys. Lett. 92, 081913 (2008).
[CrossRef]

N. Dahan, A. Niv, G. Biener, Y. Gorodetski, V. Kleiner, and E. Hasman, "Enhanced coherency of thermal emission: Beyond the limitation imposed by delocalized surface waves," Phys. Rev. B 76, 045427 (2007).
[CrossRef]

Norris, D. J.

S. E. Han, A. Stein, and D. J. Norris, "Tailoring self-assembled metallic photonic crystals for modified thermal emission," Phys. Rev. Lett. 99, 053906 (2007).
[CrossRef] [PubMed]

Ozbay, E.

Pelouard, J. L.

Perreault, D.

I. Celanovic, D. Perreault, and J. Kassakian, "Resonant-cavity enhanced thermal emission," Phys. Rev. B 72075127 (2005).
[CrossRef]

Polman, A.

A. Polman, "Plasmonics applied," Science 322, 868-869 (2008).
[CrossRef] [PubMed]

Popov, E.

Pralle, M. U.

M. U. Pralle, N. Moelders, M. P. McNeal, I. Puscasu, A. C. Greenwald, J. T. Daly, E. A. Johnson, T. George, D. S. Choi, I. El-Kady, and R. Biswas, "Photonic crystal enhanced narrow-band infrared emitters," Appl. Phys. Lett. 81, 4685-4687 (2002).
[CrossRef]

Puscasu, I.

M. U. Pralle, N. Moelders, M. P. McNeal, I. Puscasu, A. C. Greenwald, J. T. Daly, E. A. Johnson, T. George, D. S. Choi, I. El-Kady, and R. Biswas, "Photonic crystal enhanced narrow-band infrared emitters," Appl. Phys. Lett. 81, 4685-4687 (2002).
[CrossRef]

Stein, A.

S. E. Han, A. Stein, and D. J. Norris, "Tailoring self-assembled metallic photonic crystals for modified thermal emission," Phys. Rev. Lett. 99, 053906 (2007).
[CrossRef] [PubMed]

Thio, T.

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]

Tzuang, D. C.

Y. T. Chang, Y. H. Ye, D. C. Tzuang, Y. T. Wu, C. H. Yang, C. F. Chan, Y. W. Jiang, and S. C. Lee, "Localized surface plasmons in Al/Si structure and Ag/SiO2/Ag emitter with different concentric metal rings," Appl. Phys. Lett. 92, 233109 (2008).
[CrossRef]

White, J. O.

X. D. Yu, Y. J. Lee, R. Furstenberg, J. O. White, and P. V. Braun, "Filling fraction dependent properties of inverse opal metallic photonic crystals," Adv. Mater. 19, 1689-1692 (2007).
[CrossRef]

Wittwer, V.

A. Heinzel, V. Boerner, A. Gombert, B. Blasi, V. Wittwer, and J. Luther, "Radiation filters and emitters for the NIR based on periodically structured metal surfaces," J. Mod. Opt. 47, 2399-2419 (2000).

Wolff, P. A.

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]

Wu, Y. T.

Y. T. Chang, Y. H. Ye, D. C. Tzuang, Y. T. Wu, C. H. Yang, C. F. Chan, Y. W. Jiang, and S. C. Lee, "Localized surface plasmons in Al/Si structure and Ag/SiO2/Ag emitter with different concentric metal rings," Appl. Phys. Lett. 92, 233109 (2008).
[CrossRef]

Yang, C. H.

Y. T. Chang, Y. H. Ye, D. C. Tzuang, Y. T. Wu, C. H. Yang, C. F. Chan, Y. W. Jiang, and S. C. Lee, "Localized surface plasmons in Al/Si structure and Ag/SiO2/Ag emitter with different concentric metal rings," Appl. Phys. Lett. 92, 233109 (2008).
[CrossRef]

Ye, Y. H.

Y. T. Chang, Y. H. Ye, D. C. Tzuang, Y. T. Wu, C. H. Yang, C. F. Chan, Y. W. Jiang, and S. C. Lee, "Localized surface plasmons in Al/Si structure and Ag/SiO2/Ag emitter with different concentric metal rings," Appl. Phys. Lett. 92, 233109 (2008).
[CrossRef]

Yu, X. D.

X. D. Yu, Y. J. Lee, R. Furstenberg, J. O. White, and P. V. Braun, "Filling fraction dependent properties of inverse opal metallic photonic crystals," Adv. Mater. 19, 1689-1692 (2007).
[CrossRef]

Zemel, J. N.

P. J. Hesketh, J. N. Zemel, and B. Gebhart, "Organ pipe radiant modes of periodic micromachined silicon surfaces," Nature (London) 324, 549-551 (1986).
[CrossRef]

Adv. Mater.

X. D. Yu, Y. J. Lee, R. Furstenberg, J. O. White, and P. V. Braun, "Filling fraction dependent properties of inverse opal metallic photonic crystals," Adv. Mater. 19, 1689-1692 (2007).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

G. Biener, N. Dahan, A. Niv, V. Kleiner, and E. Hasman, "Highly coherent thermal emission obtained by plasmonic bandgap structures," Appl. Phys. Lett. 92, 081913 (2008).
[CrossRef]

Y. T. Chang, Y. H. Ye, D. C. Tzuang, Y. T. Wu, C. H. Yang, C. F. Chan, Y. W. Jiang, and S. C. Lee, "Localized surface plasmons in Al/Si structure and Ag/SiO2/Ag emitter with different concentric metal rings," Appl. Phys. Lett. 92, 233109 (2008).
[CrossRef]

M. U. Pralle, N. Moelders, M. P. McNeal, I. Puscasu, A. C. Greenwald, J. T. Daly, E. A. Johnson, T. George, D. S. Choi, I. El-Kady, and R. Biswas, "Photonic crystal enhanced narrow-band infrared emitters," Appl. Phys. Lett. 81, 4685-4687 (2002).
[CrossRef]

J. Appl. Phys.

T. Erdogan and D. G. Hall, "Circularly symmetric distributed feedback semiconductor laser: an analysis," J. Appl. Phys. 68, 1435-1444 (1990).
[CrossRef]

J. Mod. Opt.

A. Heinzel, V. Boerner, A. Gombert, B. Blasi, V. Wittwer, and J. Luther, "Radiation filters and emitters for the NIR based on periodically structured metal surfaces," J. Mod. Opt. 47, 2399-2419 (2000).

Nature

W. L. Barnes, A. Dereux, and T. W. Ebbesen, "Surface plasmon subwavelength optics," Nature 424, 824-830 (2003).
[CrossRef] [PubMed]

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]

Y. De Wilde, F. Formanek, R. Carminati, B. Gralak, P. A. Lemoine, K. Joulain, J. P. Mulet, Y. Chen, and J. J. Greffet, "Thermal radiation scanning tunnelling microscopy," Nature 444, 740-743 (2006).
[CrossRef] [PubMed]

Nature (London)

P. J. Hesketh, J. N. Zemel, and B. Gebhart, "Organ pipe radiant modes of periodic micromachined silicon surfaces," Nature (London) 324, 549-551 (1986).
[CrossRef]

J. J. Greffet, R. Carminati, K. Joulain, J. P. Mulet, S. Mainguy, and Y. Chen, "Coherent emission of light by thermal sources," Nature (London) 416, 61-64 (2002).
[CrossRef] [PubMed]

J. G. Fleming, S.-Y. Lin, I. El-Kady, R. Biswas, and K. M. Ho, "All-metallic three-dimensional photonic crystals with a large infrared bandgap," Nature (London) 417, 52-55 (2002).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Rev. A

C. M. Cornelius and J. P. Dowling, "Modification of Planck blackbody radiation by photonic band-gap structures," Phys. Rev. A 59, 4736-4746 (1999).
[CrossRef]

Phys. Rev. B

I. Celanovic, D. Perreault, and J. Kassakian, "Resonant-cavity enhanced thermal emission," Phys. Rev. B 72075127 (2005).
[CrossRef]

S. E. Han, "Theory of thermal emission from periodic structures," Phys. Rev. B 80, 155108 (2009).
[CrossRef]

N. Dahan, A. Niv, G. Biener, Y. Gorodetski, V. Kleiner, and E. Hasman, "Enhanced coherency of thermal emission: Beyond the limitation imposed by delocalized surface waves," Phys. Rev. B 76, 045427 (2007).
[CrossRef]

Phys. Rev. Lett.

J. Durnin, J. J. Miceli, Jr, and J. H. Eberly, "Diffraction-free beams," Phys. Rev. Lett. 58, 1499-1501 (1987).
[CrossRef] [PubMed]

S. E. Han, A. Stein, and D. J. Norris, "Tailoring self-assembled metallic photonic crystals for modified thermal emission," Phys. Rev. Lett. 99, 053906 (2007).
[CrossRef] [PubMed]

L. Martın-Moreno, F. J. Garcıa-Vidal, H. J. Lezec, A. Degiron, and T. W. Ebbesen, "Theory of highly directional emission from a single subwavelength aperture surrounded by surface corrugations," Phys. Rev. Lett. 90, 167401 (2003).
[CrossRef] [PubMed]

Science

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcıa-Vidal, and T. W. Ebbesen, "Beaming light from a subwavelength aperture," Science 297, 820-822 (2002).
[CrossRef] [PubMed]

E. Ozbay, "Plasmonics: merging photonics and electronics at nanoscale dimensions," Science 311, 189-193 (2006).
[CrossRef] [PubMed]

A. Polman, "Plasmonics applied," Science 322, 868-869 (2008).
[CrossRef] [PubMed]

Other

H. Raether, Surface Plasmons (Springer-Verlag, Berlin, 1988).

We used the transfer matrix formalism introduced in J. B. Pendry and A. MacKinnon, "Calculation of photon dispersion relations," Phys. Rev. Lett. 69, 2772-2775 (1992). A unit cell is discretized by a 80×80 mesh. For◦C, we used the dielectric function for tungsten from D. W. Lynch and W. R. Hunter, in Handbook of Optical Constants of Solids, edited by E. D. Palik (Academic Press, Orlando, 1985).
[CrossRef] [PubMed]

<jrn>24. F. Marquier, C. Arnold, M. Laroche, J. J. Greffet, and Y. Chen, "Degree of polarization of thermal light emitted by gratings supporting surface waves," Opt. Express 16, 5305-5313 (2008).Q1</jrn>
[CrossRef] [PubMed]

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, 1995).Q2

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Figures (5)

Fig. 1.
Fig. 1.

Calculated absorptivity versus in-plane wavevector for unpolarized light at λ of (a) 4.078, (b) 3.502, and (c) 3.069μm for a tungsten 1D grating ruled along y and periodic in x with period a = 3.5μm. The circular plot boundary is k = 2π/λ. The cross-section of the grooves is rectangular with a depth of 165 nm and a width of 2.625 μm.

Fig. 2.
Fig. 2.

Calculated (a) emissivity spectra at various angles θ from the surface normal and (b) angular dependence of emissivity at the peak maximum λ = 3.502 μm for a tungsten bull’s eye structure with groove parameters as in Fig. 1. The dielectric function for 25 °C was used. The spectrum at θ = 0 is enlarged in the inset of (a).

Fig. 3.
Fig. 3.

Calculated temperature dependence of (a) the peak wavelength λmax, (b) the quality factor Q, and (c) the angular width Δθ for the tungsten bull’s eye structure with groove parameters as in Fig. 1. (a) and (b) are for the surface normal direction and (c) is at λmax.

Fig. 4.
Fig. 4.

Calculated (a) emissivity spectra at various angles θ from the surface normal and (b) angular dependence of emissivity at the peak maximum λ = 3.502 μm for a tungsten bull’s eye structure supporting a coupled cavity resonance. The cross-section of the groove is rectangular and the period, depth, and width of the groove are 3.5, 1.825, and 1.925 μm, respectively.

Fig. 5.
Fig. 5.

Calculated (a) emissivity spectra at various angles θ from the surface normal and (b) angular dependence of the emissivity at the peak maximum (λ = 557 nm) for a silver bull’s eye structure supporting a coupled cavity resonance. The cross-section of the groove is rectangular and the period, depth, and width of the groove are 550, 280, and 358 nm, respectively.

Equations (4)

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

E j r ϕ z = n E j , n r z e inϕ ,
E ± , n = E ϕ , n ± i E r , n ,
[ 2 r 2 + 1 r r ( n ± 1 ) 2 r 2 + k 2 + 2 z 2 ] E ± , n r z = 0 ,
[ 2 r 2 + 2 z 2 + k 2 ] E ± , n r z 0 .

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