Abstract

A transmission-type surface plasmon resonance configuration with dielectric gratings regularly patterned on a silver film was investigated with the aim of enhancing the diffraction efficiency of radiative surface plasmons. The theoretical work was conducted using rigorous coupled-wave analysis in terms of first order diffraction efficiency and conversion efficiency (CE). The results show that pyramid gratings can produce a higher transmittance compared with other grating profiles. Design optimization of the pyramid grating at a wide range of grating thicknesses and periods resulted in a maximum transmittance that was larger than 77% and a peak CE of about 85%. This study demonstrates the potential of using transmitted surface plasmon waves in various optical devices, such as optical biosensors, optical imaging systems, and polarization filters.

© 2009 Optical Society of America

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References

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    [CrossRef] [PubMed]
  2. S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005).
    [CrossRef]
  3. J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B 54, 3-15 (1999).
    [CrossRef]
  4. H. Raether, Surface Plasmons on Smooth and Rough Surfaces and on Gratings, Springer Tracts in Modern Physics (Springer-Verlag, 1988).
  5. E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimensions,” Science 311, 189-193 (2006).
    [CrossRef] [PubMed]
  6. B. Huang, F. Yu, and R. N. Zare, “Surface plasmon resonance imaging using a high numerical aperture microscope objective,” Anal. Chem. 79, 2979-2983 (2007).
    [CrossRef] [PubMed]
  7. J. M. Montgomery and S. K. Gray, “Enhancing surface plasmon polariton propagation lengths via coupling to asymmetric waveguide structures,” Phys. Rev. B 77, 125407 (2008).
    [CrossRef]
  8. W. Rothballer, “The influence of surface plasma oscillations on the diffraction orders of sinusoidal surface gratings,” Opt. Commun. 20, 429-433 (1977).
    [CrossRef]
  9. M. J. Jory, P. S. Vukusic, and J. R. Sambles, “Development of a prototype gas sensor using surface plasmon resonance on gratings,” Sens. Actuators B 17, 203-209 (1994).
    [CrossRef]
  10. S. Park, G. Lee, S. H. Song, C. H. Oh, and P. S. Kim, “Resonant coupling of surface plasmons to radiation modes by use of dielectric gratings,” Opt. Lett. 28, 1870-1872 (2003).
    [CrossRef] [PubMed]
  11. C. Lenaerts, F. Michel, B. Tilkens, Y. Lion, and Y. Renotte, “High transmission efficiency for surface plasmon resonance by use of a dielectric grating,” Appl. Opt. 44, 6017-6022(2005).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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  17. K. M. Byun, S. J. Kim, and D. Kim, “Design study of highly sensitive nanowire-enhanced surface plasmon resonance biosensors using rigorous coupled wave analysis,” Opt. Express 13, 3737-3742 (2005).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  20. K. M. Byun, D. Kim, and S. J. Kim, “Investigation of the profile effect on the sensitivity enhancement of nanowire-mediated localized surface plasmon resonance biosensors,” Sens. Actuators B 117, 401-407 (2006).
    [CrossRef]
  21. J. A. Rogers and R. G. Nuzzo, “Recent progresses in soft lithography,” Mater. Today 8, 50-56 (2005).
    [CrossRef]
  22. Z. Yu and S. Y. Chou, “Triangular profile imprint molds in nanograting fabrication,” Nano Lett. 4, 341-344 (2004).
    [CrossRef]
  23. C.-H. Chang, R. K. Heilmann, R. C. Fleming, J. Carter, E. Murphy, M. L. Schattenburg, T. C. Bailey, J. G. Ekerdt, R. D. Frankel, and R. Voisin, “Fabrication of sawtooth diffraction gratings using nanoimprint lithography,” J. Vac. Sci. Technol. B 21, 2755-2759 (2003).
    [CrossRef]

2008 (1)

J. M. Montgomery and S. K. Gray, “Enhancing surface plasmon polariton propagation lengths via coupling to asymmetric waveguide structures,” Phys. Rev. B 77, 125407 (2008).
[CrossRef]

2007 (3)

2006 (2)

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

K. M. Byun, D. Kim, and S. J. Kim, “Investigation of the profile effect on the sensitivity enhancement of nanowire-mediated localized surface plasmon resonance biosensors,” Sens. Actuators B 117, 401-407 (2006).
[CrossRef]

2005 (6)

J. A. Rogers and R. G. Nuzzo, “Recent progresses in soft lithography,” Mater. Today 8, 50-56 (2005).
[CrossRef]

K. M. Byun, S. J. Kim, and D. Kim, “Design study of highly sensitive nanowire-enhanced surface plasmon resonance biosensors using rigorous coupled wave analysis,” Opt. Express 13, 3737-3742 (2005).
[CrossRef] [PubMed]

C. Lenaerts, F. Michel, B. Tilkens, Y. Lion, and Y. Renotte, “High transmission efficiency for surface plasmon resonance by use of a dielectric grating,” Appl. Opt. 44, 6017-6022(2005).
[CrossRef] [PubMed]

S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

Y.-J. Hung, I. I. Smolyaninov, Q. Balzano, and C. C. Davis, “Strong optical coupling effects through a continuous metal film with a surface dielectric grating,” Proc. SPIE 5927, 386-394 (2005).

S. Park, H. S. Won, G. Lee, S. H. Song, C. H. Oh, and P. S. Kim, “Grating-assisted emission of surface plasmons,” J. Korean Phys. Soc. 46, 492-497 (2005).

2004 (1)

Z. Yu and S. Y. Chou, “Triangular profile imprint molds in nanograting fabrication,” Nano Lett. 4, 341-344 (2004).
[CrossRef]

2003 (2)

C.-H. Chang, R. K. Heilmann, R. C. Fleming, J. Carter, E. Murphy, M. L. Schattenburg, T. C. Bailey, J. G. Ekerdt, R. D. Frankel, and R. Voisin, “Fabrication of sawtooth diffraction gratings using nanoimprint lithography,” J. Vac. Sci. Technol. B 21, 2755-2759 (2003).
[CrossRef]

S. Park, G. Lee, S. H. Song, C. H. Oh, and P. S. Kim, “Resonant coupling of surface plasmons to radiation modes by use of dielectric gratings,” Opt. Lett. 28, 1870-1872 (2003).
[CrossRef] [PubMed]

1999 (1)

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B 54, 3-15 (1999).
[CrossRef]

1994 (1)

M. J. Jory, P. S. Vukusic, and J. R. Sambles, “Development of a prototype gas sensor using surface plasmon resonance on gratings,” Sens. Actuators B 17, 203-209 (1994).
[CrossRef]

1993 (2)

1982 (1)

1977 (1)

W. Rothballer, “The influence of surface plasma oscillations on the diffraction orders of sinusoidal surface gratings,” Opt. Commun. 20, 429-433 (1977).
[CrossRef]

Atwater, H. A.

S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

Bailey, T. C.

C.-H. Chang, R. K. Heilmann, R. C. Fleming, J. Carter, E. Murphy, M. L. Schattenburg, T. C. Bailey, J. G. Ekerdt, R. D. Frankel, and R. Voisin, “Fabrication of sawtooth diffraction gratings using nanoimprint lithography,” J. Vac. Sci. Technol. B 21, 2755-2759 (2003).
[CrossRef]

Balzano, Q.

Y.-J. Hung, I. I. Smolyaninov, Q. Balzano, and C. C. Davis, “Strong optical coupling effects through a continuous metal film with a surface dielectric grating,” Proc. SPIE 5927, 386-394 (2005).

Byun, K. M.

Carter, J.

C.-H. Chang, R. K. Heilmann, R. C. Fleming, J. Carter, E. Murphy, M. L. Schattenburg, T. C. Bailey, J. G. Ekerdt, R. D. Frankel, and R. Voisin, “Fabrication of sawtooth diffraction gratings using nanoimprint lithography,” J. Vac. Sci. Technol. B 21, 2755-2759 (2003).
[CrossRef]

Chang, C.-H.

C.-H. Chang, R. K. Heilmann, R. C. Fleming, J. Carter, E. Murphy, M. L. Schattenburg, T. C. Bailey, J. G. Ekerdt, R. D. Frankel, and R. Voisin, “Fabrication of sawtooth diffraction gratings using nanoimprint lithography,” J. Vac. Sci. Technol. B 21, 2755-2759 (2003).
[CrossRef]

Chou, S. Y.

Z. Yu and S. Y. Chou, “Triangular profile imprint molds in nanograting fabrication,” Nano Lett. 4, 341-344 (2004).
[CrossRef]

Davis, C. C.

Y.-J. Hung, I. I. Smolyaninov, Q. Balzano, and C. C. Davis, “Strong optical coupling effects through a continuous metal film with a surface dielectric grating,” Proc. SPIE 5927, 386-394 (2005).

Ekerdt, J. G.

C.-H. Chang, R. K. Heilmann, R. C. Fleming, J. Carter, E. Murphy, M. L. Schattenburg, T. C. Bailey, J. G. Ekerdt, R. D. Frankel, and R. Voisin, “Fabrication of sawtooth diffraction gratings using nanoimprint lithography,” J. Vac. Sci. Technol. B 21, 2755-2759 (2003).
[CrossRef]

Fleming, R. C.

C.-H. Chang, R. K. Heilmann, R. C. Fleming, J. Carter, E. Murphy, M. L. Schattenburg, T. C. Bailey, J. G. Ekerdt, R. D. Frankel, and R. Voisin, “Fabrication of sawtooth diffraction gratings using nanoimprint lithography,” J. Vac. Sci. Technol. B 21, 2755-2759 (2003).
[CrossRef]

Frankel, R. D.

C.-H. Chang, R. K. Heilmann, R. C. Fleming, J. Carter, E. Murphy, M. L. Schattenburg, T. C. Bailey, J. G. Ekerdt, R. D. Frankel, and R. Voisin, “Fabrication of sawtooth diffraction gratings using nanoimprint lithography,” J. Vac. Sci. Technol. B 21, 2755-2759 (2003).
[CrossRef]

Gauglitz, G.

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B 54, 3-15 (1999).
[CrossRef]

Gaylord, T. K.

Gray, S. K.

J. M. Montgomery and S. K. Gray, “Enhancing surface plasmon polariton propagation lengths via coupling to asymmetric waveguide structures,” Phys. Rev. B 77, 125407 (2008).
[CrossRef]

Haggans, C. W.

Heilmann, R. K.

C.-H. Chang, R. K. Heilmann, R. C. Fleming, J. Carter, E. Murphy, M. L. Schattenburg, T. C. Bailey, J. G. Ekerdt, R. D. Frankel, and R. Voisin, “Fabrication of sawtooth diffraction gratings using nanoimprint lithography,” J. Vac. Sci. Technol. B 21, 2755-2759 (2003).
[CrossRef]

Homola, J.

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B 54, 3-15 (1999).
[CrossRef]

Huang, B.

B. Huang, F. Yu, and R. N. Zare, “Surface plasmon resonance imaging using a high numerical aperture microscope objective,” Anal. Chem. 79, 2979-2983 (2007).
[CrossRef] [PubMed]

Hung, Y.-J.

Y.-J. Hung, I. I. Smolyaninov, Q. Balzano, and C. C. Davis, “Strong optical coupling effects through a continuous metal film with a surface dielectric grating,” Proc. SPIE 5927, 386-394 (2005).

Hutley, M. C.

M. C. Hutley, Diffraction Gratings (Academic, 1982).

Jory, M. J.

M. J. Jory, P. S. Vukusic, and J. R. Sambles, “Development of a prototype gas sensor using surface plasmon resonance on gratings,” Sens. Actuators B 17, 203-209 (1994).
[CrossRef]

Kamiyama, T.

Kim, D.

Kim, P. S.

S. Park, H. S. Won, G. Lee, S. H. Song, C. H. Oh, and P. S. Kim, “Grating-assisted emission of surface plasmons,” J. Korean Phys. Soc. 46, 492-497 (2005).

S. Park, G. Lee, S. H. Song, C. H. Oh, and P. S. Kim, “Resonant coupling of surface plasmons to radiation modes by use of dielectric gratings,” Opt. Lett. 28, 1870-1872 (2003).
[CrossRef] [PubMed]

Kim, S. J.

Lee, G.

S. Park, H. S. Won, G. Lee, S. H. Song, C. H. Oh, and P. S. Kim, “Grating-assisted emission of surface plasmons,” J. Korean Phys. Soc. 46, 492-497 (2005).

S. Park, G. Lee, S. H. Song, C. H. Oh, and P. S. Kim, “Resonant coupling of surface plasmons to radiation modes by use of dielectric gratings,” Opt. Lett. 28, 1870-1872 (2003).
[CrossRef] [PubMed]

Lenaerts, C.

Li, L.

Lion, Y.

Maier, S. A.

S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

Michel, F.

Moharam, M. G.

Montgomery, J. M.

J. M. Montgomery and S. K. Gray, “Enhancing surface plasmon polariton propagation lengths via coupling to asymmetric waveguide structures,” Phys. Rev. B 77, 125407 (2008).
[CrossRef]

Murphy, E.

C.-H. Chang, R. K. Heilmann, R. C. Fleming, J. Carter, E. Murphy, M. L. Schattenburg, T. C. Bailey, J. G. Ekerdt, R. D. Frankel, and R. Voisin, “Fabrication of sawtooth diffraction gratings using nanoimprint lithography,” J. Vac. Sci. Technol. B 21, 2755-2759 (2003).
[CrossRef]

Nuzzo, R. G.

J. A. Rogers and R. G. Nuzzo, “Recent progresses in soft lithography,” Mater. Today 8, 50-56 (2005).
[CrossRef]

Oh, C. H.

S. Park, H. S. Won, G. Lee, S. H. Song, C. H. Oh, and P. S. Kim, “Grating-assisted emission of surface plasmons,” J. Korean Phys. Soc. 46, 492-497 (2005).

S. Park, G. Lee, S. H. Song, C. H. Oh, and P. S. Kim, “Resonant coupling of surface plasmons to radiation modes by use of dielectric gratings,” Opt. Lett. 28, 1870-1872 (2003).
[CrossRef] [PubMed]

Okamoto, T.

Ozbay, E.

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

Park, S.

S. Park, H. S. Won, G. Lee, S. H. Song, C. H. Oh, and P. S. Kim, “Grating-assisted emission of surface plasmons,” J. Korean Phys. Soc. 46, 492-497 (2005).

S. Park, G. Lee, S. H. Song, C. H. Oh, and P. S. Kim, “Resonant coupling of surface plasmons to radiation modes by use of dielectric gratings,” Opt. Lett. 28, 1870-1872 (2003).
[CrossRef] [PubMed]

Raether, H.

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

Renotte, Y.

Rogers, J. A.

J. A. Rogers and R. G. Nuzzo, “Recent progresses in soft lithography,” Mater. Today 8, 50-56 (2005).
[CrossRef]

Rothballer, W.

W. Rothballer, “The influence of surface plasma oscillations on the diffraction orders of sinusoidal surface gratings,” Opt. Commun. 20, 429-433 (1977).
[CrossRef]

Sambles, J. R.

M. J. Jory, P. S. Vukusic, and J. R. Sambles, “Development of a prototype gas sensor using surface plasmon resonance on gratings,” Sens. Actuators B 17, 203-209 (1994).
[CrossRef]

Schattenburg, M. L.

C.-H. Chang, R. K. Heilmann, R. C. Fleming, J. Carter, E. Murphy, M. L. Schattenburg, T. C. Bailey, J. G. Ekerdt, R. D. Frankel, and R. Voisin, “Fabrication of sawtooth diffraction gratings using nanoimprint lithography,” J. Vac. Sci. Technol. B 21, 2755-2759 (2003).
[CrossRef]

Smolyaninov, I. I.

Y.-J. Hung, I. I. Smolyaninov, Q. Balzano, and C. C. Davis, “Strong optical coupling effects through a continuous metal film with a surface dielectric grating,” Proc. SPIE 5927, 386-394 (2005).

Song, S. H.

S. Park, H. S. Won, G. Lee, S. H. Song, C. H. Oh, and P. S. Kim, “Grating-assisted emission of surface plasmons,” J. Korean Phys. Soc. 46, 492-497 (2005).

S. Park, G. Lee, S. H. Song, C. H. Oh, and P. S. Kim, “Resonant coupling of surface plasmons to radiation modes by use of dielectric gratings,” Opt. Lett. 28, 1870-1872 (2003).
[CrossRef] [PubMed]

Tilkens, B.

Voisin, R.

C.-H. Chang, R. K. Heilmann, R. C. Fleming, J. Carter, E. Murphy, M. L. Schattenburg, T. C. Bailey, J. G. Ekerdt, R. D. Frankel, and R. Voisin, “Fabrication of sawtooth diffraction gratings using nanoimprint lithography,” J. Vac. Sci. Technol. B 21, 2755-2759 (2003).
[CrossRef]

Vukusic, P. S.

M. J. Jory, P. S. Vukusic, and J. R. Sambles, “Development of a prototype gas sensor using surface plasmon resonance on gratings,” Sens. Actuators B 17, 203-209 (1994).
[CrossRef]

Won, H. S.

S. Park, H. S. Won, G. Lee, S. H. Song, C. H. Oh, and P. S. Kim, “Grating-assisted emission of surface plasmons,” J. Korean Phys. Soc. 46, 492-497 (2005).

Yamaguchi, I.

Yee, S. S.

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B 54, 3-15 (1999).
[CrossRef]

Yoon, S. J.

Yu, F.

B. Huang, F. Yu, and R. N. Zare, “Surface plasmon resonance imaging using a high numerical aperture microscope objective,” Anal. Chem. 79, 2979-2983 (2007).
[CrossRef] [PubMed]

Yu, Z.

Z. Yu and S. Y. Chou, “Triangular profile imprint molds in nanograting fabrication,” Nano Lett. 4, 341-344 (2004).
[CrossRef]

Zare, R. N.

B. Huang, F. Yu, and R. N. Zare, “Surface plasmon resonance imaging using a high numerical aperture microscope objective,” Anal. Chem. 79, 2979-2983 (2007).
[CrossRef] [PubMed]

Anal. Chem. (1)

B. Huang, F. Yu, and R. N. Zare, “Surface plasmon resonance imaging using a high numerical aperture microscope objective,” Anal. Chem. 79, 2979-2983 (2007).
[CrossRef] [PubMed]

Appl. Opt. (2)

J. Appl. Phys. (1)

S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

J. Korean Phys. Soc. (1)

S. Park, H. S. Won, G. Lee, S. H. Song, C. H. Oh, and P. S. Kim, “Grating-assisted emission of surface plasmons,” J. Korean Phys. Soc. 46, 492-497 (2005).

J. Opt. Soc. Am. (1)

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

J. Vac. Sci. Technol. B (1)

C.-H. Chang, R. K. Heilmann, R. C. Fleming, J. Carter, E. Murphy, M. L. Schattenburg, T. C. Bailey, J. G. Ekerdt, R. D. Frankel, and R. Voisin, “Fabrication of sawtooth diffraction gratings using nanoimprint lithography,” J. Vac. Sci. Technol. B 21, 2755-2759 (2003).
[CrossRef]

Mater. Today (1)

J. A. Rogers and R. G. Nuzzo, “Recent progresses in soft lithography,” Mater. Today 8, 50-56 (2005).
[CrossRef]

Nano Lett. (1)

Z. Yu and S. Y. Chou, “Triangular profile imprint molds in nanograting fabrication,” Nano Lett. 4, 341-344 (2004).
[CrossRef]

Opt. Commun. (1)

W. Rothballer, “The influence of surface plasma oscillations on the diffraction orders of sinusoidal surface gratings,” Opt. Commun. 20, 429-433 (1977).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. B (1)

J. M. Montgomery and S. K. Gray, “Enhancing surface plasmon polariton propagation lengths via coupling to asymmetric waveguide structures,” Phys. Rev. B 77, 125407 (2008).
[CrossRef]

Proc. SPIE (1)

Y.-J. Hung, I. I. Smolyaninov, Q. Balzano, and C. C. Davis, “Strong optical coupling effects through a continuous metal film with a surface dielectric grating,” Proc. SPIE 5927, 386-394 (2005).

Science (1)

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

Sens. Actuators B (3)

J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors: review,” Sens. Actuators B 54, 3-15 (1999).
[CrossRef]

M. J. Jory, P. S. Vukusic, and J. R. Sambles, “Development of a prototype gas sensor using surface plasmon resonance on gratings,” Sens. Actuators B 17, 203-209 (1994).
[CrossRef]

K. M. Byun, D. Kim, and S. J. Kim, “Investigation of the profile effect on the sensitivity enhancement of nanowire-mediated localized surface plasmon resonance biosensors,” Sens. Actuators B 117, 401-407 (2006).
[CrossRef]

Other (2)

M. C. Hutley, Diffraction Gratings (Academic, 1982).

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

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Figures (10)

Fig. 1
Fig. 1

Transmittance curves of the first-order beams diffracted by dielectric gratings deposited on an attenuated total reflection configuration with and without a metal film. A 40 nm thick silver film with a dielectric function of 18 + 0.5 i at λ = 633 nm was used as the metal layer [10].

Fig. 2
Fig. 2

(a) Schematic diagram of a transmission-type SPR configuration with dielectric gratings. A thin silver film with a thickness of 40 nm is deposited on a prism substrate. PMMA dielectric gratings with a period Λ and a thickness d g are regularly patterned on the metal layer. TM-polarized light is incident through the prism substrate at a fixed wavelength of λ = 633 nm . The transmitted light radiates into the air environment. (b) Rectangle, pyramid, left-biased sawtooth, and right-biased sawtooth dielectric grating profiles. The fill factor is fixed at f = 0.5 .

Fig. 3
Fig. 3

Calculated reflectance (0R, the solid line) and transmittance curves (1T, the dotted line) for a rectangular grating as a function of incidence angle when d g varies from 30 nm to 300 nm .

Fig. 4
Fig. 4

(a) Resonance and (b) transmittance characteristics of a SPR structure with the rectangular grating. The effects of grating thickness on the resonance angles and transmittance (1T) are shown when grating thickness is increased from 30 to 300 nm in steps of 10 nm . The dielectric grating has a period of Λ = 600 nm .

Fig. 5
Fig. 5

(a) Minimum reflectance at resonance and (b) conversion efficiency of a SPR structure with rectangular gratings when the grating thickness varies from 30 to 300 nm . The dielectric grating has a period of Λ = 600 nm .

Fig. 6
Fig. 6

Transmittance characteristics of four different grating profiles as a function of the grating thickness.

Fig. 7
Fig. 7

Conversion efficiencies of four different grating profiles as a function of the grating thickness.

Fig. 8
Fig. 8

(a) Transmittance and (b) conversion efficiency of the first-order diffraction beam for the pyramid grating when the grating thickness varies from 150 nm to 400 nm and the period from 200 nm to 600 nm . The black and white lines indicate the resonance conditions of K = k SPR and K = 2 k SPR , respectively.

Fig. 9
Fig. 9

Phase diagrams of momentum matching between the SP and photon when (a)  K = k SPR and (b)  K = 2 k SPR .

Fig. 10
Fig. 10

Linear regression analyses between incidence angle and refractive index of a dielectric binding layer for an SPR biosensor with and without a dielectric pyramid grating of d g = 310 nm and Λ = 330 nm in an air environment. θ in ( 0 R MIN ) and θ in ( 1 T MAX ) denote the incidence angle at minimum reflectance and maximum transmittance, respectively.

Equations (6)

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

k SPR = k 0 ε p sin θ SPR ,
k i = k SPR - i K = k 0 ε p sin θ SPR i 2 π Λ , i = 0 , ± 1 , ± 2 , ,
θ i T = sin 1 ( k i k 0 ) ,
θ i R = sin 1 ( k i ε p k 0 ) .
K = k SPR = k 0 ε p sin θ SPR = 2 π Λ .
K = 2 k SPR = 2 k 0 ε p sin θ SPR = 2 π Λ .

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