Abstract

The similarities and differences between two types of surface waves that can exist on a plane metal–lossless dielectric interface, on the one hand, and on a plane lossy–lossless dielectric interface, on the other hand, are analyzed numerically. They both can lead to total absorption of light by surface relief gratings and show different behavior in transmission by lamellar gratings.

© 2007 Optical Society of America

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References

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  1. R. W. Wood, "On a remarkable case of uneven distribution of light in a diffraction grating spectrum," Philos. Mag. 4, 396-402 (1902).
  2. T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through subwavelength hole arrays," Nature 391, 667-669 (1998).
    [CrossRef]
  3. M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, "Zero-mode waveguides for single-molecule analysis at high concentrations," Science 299, 682-686 (2003).
    [CrossRef] [PubMed]
  4. E. Popov, S. Enoch, G. Tayeb, M. Nevière, B. Gralak, and N. Bonod, "Enhanced transmission due to non-plasmon resonances in one and two dimensional gratings," Appl. Opt. 43, 999-1008 (2004).
    [CrossRef] [PubMed]
  5. E. Popov, L. Mashev, and D. Maystre, "Theoretical study of the anomalies of coated dielectric gratings," Opt. Acta 33, 607 (1986).
    [CrossRef]
  6. F. Marquier, K. Joulain, and J.-J. Greffet, "Resonant infrared transmission through SiC films," Opt. Lett. 29, 2178-2180 (2004).
    [CrossRef] [PubMed]
  7. F. Miyamaru, M. Tanaka, and M. Hangyo, "Resonant electromagnetic wave transmission through strontium titanate hole arrays without surface plasmon polaritons," Phys. Rev. B 74, 115-117 (2006).
    [CrossRef]
  8. M. Nevière and E. Popov, Light Propagation in Periodic Media: Diffraction Theory and Design (Marcel Dekker, 2003).
  9. M. C. Hutley and D. Maystre, "The total absorption of light by a diffraction grating," Opt. Commun. 19, 431-436 (1976).
    [CrossRef]
  10. R. Petit, ed., Electromagnetic Theory of Gratings (Springer, 1980), Chap. 5.
  11. A. Snyder and J. Love, ed., Optical Waveguide Theory (Chapman & Hall, 1983).
  12. E. Popov, M. Nevière, S. Enoch, and R. Reinisch, "Theory of light transmission through subwavelength periodic hole arrays," Phys. Rev. B 62, 16100-16108 (2000).
    [CrossRef]

2006 (1)

F. Miyamaru, M. Tanaka, and M. Hangyo, "Resonant electromagnetic wave transmission through strontium titanate hole arrays without surface plasmon polaritons," Phys. Rev. B 74, 115-117 (2006).
[CrossRef]

2004 (2)

2003 (1)

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, "Zero-mode waveguides for single-molecule analysis at high concentrations," Science 299, 682-686 (2003).
[CrossRef] [PubMed]

2000 (1)

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, "Theory of light transmission through subwavelength periodic hole arrays," Phys. Rev. B 62, 16100-16108 (2000).
[CrossRef]

1998 (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through subwavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

1986 (1)

E. Popov, L. Mashev, and D. Maystre, "Theoretical study of the anomalies of coated dielectric gratings," Opt. Acta 33, 607 (1986).
[CrossRef]

1976 (1)

M. C. Hutley and D. Maystre, "The total absorption of light by a diffraction grating," Opt. Commun. 19, 431-436 (1976).
[CrossRef]

1902 (1)

R. W. Wood, "On a remarkable case of uneven distribution of light in a diffraction grating spectrum," Philos. Mag. 4, 396-402 (1902).

Bonod, N.

Craighead, H. G.

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, "Zero-mode waveguides for single-molecule analysis at high concentrations," Science 299, 682-686 (2003).
[CrossRef] [PubMed]

Ebbesen, T. W.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through subwavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Enoch, S.

E. Popov, S. Enoch, G. Tayeb, M. Nevière, B. Gralak, and N. Bonod, "Enhanced transmission due to non-plasmon resonances in one and two dimensional gratings," Appl. Opt. 43, 999-1008 (2004).
[CrossRef] [PubMed]

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, "Theory of light transmission through subwavelength periodic hole arrays," Phys. Rev. B 62, 16100-16108 (2000).
[CrossRef]

Foquet, M.

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, "Zero-mode waveguides for single-molecule analysis at high concentrations," Science 299, 682-686 (2003).
[CrossRef] [PubMed]

Ghaemi, H. F.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through subwavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Gralak, B.

Greffet, J.-J.

Hangyo, M.

F. Miyamaru, M. Tanaka, and M. Hangyo, "Resonant electromagnetic wave transmission through strontium titanate hole arrays without surface plasmon polaritons," Phys. Rev. B 74, 115-117 (2006).
[CrossRef]

Hutley, M. C.

M. C. Hutley and D. Maystre, "The total absorption of light by a diffraction grating," Opt. Commun. 19, 431-436 (1976).
[CrossRef]

Joulain, K.

Korlach, J.

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, "Zero-mode waveguides for single-molecule analysis at high concentrations," Science 299, 682-686 (2003).
[CrossRef] [PubMed]

Levene, M. J.

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, "Zero-mode waveguides for single-molecule analysis at high concentrations," Science 299, 682-686 (2003).
[CrossRef] [PubMed]

Lezec, H. J.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through subwavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Love, J.

A. Snyder and J. Love, ed., Optical Waveguide Theory (Chapman & Hall, 1983).

Marquier, F.

Mashev, L.

E. Popov, L. Mashev, and D. Maystre, "Theoretical study of the anomalies of coated dielectric gratings," Opt. Acta 33, 607 (1986).
[CrossRef]

Maystre, D.

E. Popov, L. Mashev, and D. Maystre, "Theoretical study of the anomalies of coated dielectric gratings," Opt. Acta 33, 607 (1986).
[CrossRef]

M. C. Hutley and D. Maystre, "The total absorption of light by a diffraction grating," Opt. Commun. 19, 431-436 (1976).
[CrossRef]

Miyamaru, F.

F. Miyamaru, M. Tanaka, and M. Hangyo, "Resonant electromagnetic wave transmission through strontium titanate hole arrays without surface plasmon polaritons," Phys. Rev. B 74, 115-117 (2006).
[CrossRef]

Nevière, M.

E. Popov, S. Enoch, G. Tayeb, M. Nevière, B. Gralak, and N. Bonod, "Enhanced transmission due to non-plasmon resonances in one and two dimensional gratings," Appl. Opt. 43, 999-1008 (2004).
[CrossRef] [PubMed]

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, "Theory of light transmission through subwavelength periodic hole arrays," Phys. Rev. B 62, 16100-16108 (2000).
[CrossRef]

M. Nevière and E. Popov, Light Propagation in Periodic Media: Diffraction Theory and Design (Marcel Dekker, 2003).

Petit, R.

R. Petit, ed., Electromagnetic Theory of Gratings (Springer, 1980), Chap. 5.

Popov, E.

E. Popov, S. Enoch, G. Tayeb, M. Nevière, B. Gralak, and N. Bonod, "Enhanced transmission due to non-plasmon resonances in one and two dimensional gratings," Appl. Opt. 43, 999-1008 (2004).
[CrossRef] [PubMed]

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, "Theory of light transmission through subwavelength periodic hole arrays," Phys. Rev. B 62, 16100-16108 (2000).
[CrossRef]

E. Popov, L. Mashev, and D. Maystre, "Theoretical study of the anomalies of coated dielectric gratings," Opt. Acta 33, 607 (1986).
[CrossRef]

M. Nevière and E. Popov, Light Propagation in Periodic Media: Diffraction Theory and Design (Marcel Dekker, 2003).

Reinisch, R.

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, "Theory of light transmission through subwavelength periodic hole arrays," Phys. Rev. B 62, 16100-16108 (2000).
[CrossRef]

Snyder, A.

A. Snyder and J. Love, ed., Optical Waveguide Theory (Chapman & Hall, 1983).

Tanaka, M.

F. Miyamaru, M. Tanaka, and M. Hangyo, "Resonant electromagnetic wave transmission through strontium titanate hole arrays without surface plasmon polaritons," Phys. Rev. B 74, 115-117 (2006).
[CrossRef]

Tayeb, G.

Thio, T.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through subwavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Turner, S. W.

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, "Zero-mode waveguides for single-molecule analysis at high concentrations," Science 299, 682-686 (2003).
[CrossRef] [PubMed]

Webb, W. W.

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, "Zero-mode waveguides for single-molecule analysis at high concentrations," Science 299, 682-686 (2003).
[CrossRef] [PubMed]

Wolff, P. A.

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through subwavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Wood, R. W.

R. W. Wood, "On a remarkable case of uneven distribution of light in a diffraction grating spectrum," Philos. Mag. 4, 396-402 (1902).

Appl. Opt. (1)

Nature (1)

T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, T. Thio, and P. A. Wolff, "Extraordinary optical transmission through subwavelength hole arrays," Nature 391, 667-669 (1998).
[CrossRef]

Opt. Acta (1)

E. Popov, L. Mashev, and D. Maystre, "Theoretical study of the anomalies of coated dielectric gratings," Opt. Acta 33, 607 (1986).
[CrossRef]

Opt. Commun. (1)

M. C. Hutley and D. Maystre, "The total absorption of light by a diffraction grating," Opt. Commun. 19, 431-436 (1976).
[CrossRef]

Opt. Lett. (1)

Philos. Mag. (1)

R. W. Wood, "On a remarkable case of uneven distribution of light in a diffraction grating spectrum," Philos. Mag. 4, 396-402 (1902).

Phys. Rev. B (2)

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, "Theory of light transmission through subwavelength periodic hole arrays," Phys. Rev. B 62, 16100-16108 (2000).
[CrossRef]

F. Miyamaru, M. Tanaka, and M. Hangyo, "Resonant electromagnetic wave transmission through strontium titanate hole arrays without surface plasmon polaritons," Phys. Rev. B 74, 115-117 (2006).
[CrossRef]

Science (1)

M. J. Levene, J. Korlach, S. W. Turner, M. Foquet, H. G. Craighead, and W. W. Webb, "Zero-mode waveguides for single-molecule analysis at high concentrations," Science 299, 682-686 (2003).
[CrossRef] [PubMed]

Other (3)

R. Petit, ed., Electromagnetic Theory of Gratings (Springer, 1980), Chap. 5.

A. Snyder and J. Love, ed., Optical Waveguide Theory (Chapman & Hall, 1983).

M. Nevière and E. Popov, Light Propagation in Periodic Media: Diffraction Theory and Design (Marcel Dekker, 2003).

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Figures (8)

Fig. 1
Fig. 1

Trajectory of the normalized propagation constant (i.e., effective index) of the surface wave, obtained as the root of Eq. (1), in the complex k plane when the dielectric permittivity of the substrate varies from highly conducting metal to (a) lossy dielectric case and to (b) lossless dielectric. Plane interface and vacuum as cladding.

Fig. 2
Fig. 2

In-depth decay constants inside the substrate and the cladding for the plasmon surface wave (solid lines) and complex-type surface wave (dashed lines).

Fig. 3
Fig. 3

(a), (c) Map of the zeroth-order efficiency and (b), (d) the total reflectivity in normal incidence (TM polarization) as a function of wavelength and groove depth for a lamellar grating having a period of d = 1 and made of metal with (a), (b) ε 2 = 300 + i 50 and (c), (d) lossy dielectric with ε 2 = 300 + i 50 . The substrate is filled with the same material as the lamellae and the groove width is equal to the lamella width. Inset of (a) represents the grating geometry.

Fig. 4
Fig. 4

Spectral dependence of reflectivity in normal incidence in the vicinity of the absorption dips of Fig. 3, metallic grating on the left and dielectric on the right. Groove depth: (a) h = 0.524 d , (b) h = 0.57 d .

Fig. 5
Fig. 5

Transmission through a (a) rectangular-rod metallic and (b) dielectric grating having a period of d = 1 , groove width equal to 0.0285 d in normally incident TM polarized light as a function of the wavelength and groove depth (grating thickness). Vacuum in the cladding, the substrate, and the grooves.

Fig. 6
Fig. 6

Dependence of the zeroth transmitted order on the grating thickness for several wavelength values for a metallic and a lossy dielectric grating in the vicinity of the resonance anomaly in Fig. 5.

Fig. 7
Fig. 7

Transmission for a biperiodic array of square holes in a metallic layer with ε = 300 + i 50 and a period d equal to 1 (arbitrary unit); the edge of the square holes is w = 0.3 d , the thickness of the layer e varies, and the array is lying in vacuum.

Fig. 8
Fig. 8

Transmission for a biperiodic array of square holes in a lossy dielectric layer with ε = 300 + i 50 and a period d equal to 1 (arbitrary unit), the edge of the square holes is w = 0.3 d , the thickness of the layer e varies, and the array is lying in vacuum.

Tables (1)

Tables Icon

Table 1 Normalized Propagation Constants of the TEM Modes a

Equations (5)

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k 1 , y / ε 1 + k 2 , y / ε 2 = 0 ,
k j , y = ε 0 ε j k x 2 ,   j = 1 , 2 ,
k x = k 0 ε 1 ε 2 ε 1 + ε 2 ,
k 0 / k x = ε 2 1 + ε 2 .
ε 1 / k 1 , y + ε 2 / k 2 , y ε 1 / k 1 , y + ε 2 / k 2 , y ;

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