Abstract

The conical rigorous coupled-wave analysis (RCWA) is employed to calculate the polarization conversion through the excitation of surface plasmons on metallic gratings. Various examples are examined with this numerical scheme. Our calculated results are consistent with those obtained from experiment and from other numerical methods. Three types of subwavelength surface-relief gratings are studied for the capability of broadband polarization conversion in the visible region. For wide-angle applications, various incident angles are studied and high polarization conversion efficiency is achieved.

© 2008 Optical Society of America

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  1. G. P. Bryan-Brown and J. R. Sambles, “Polarization conversion through the excitation of surface plasmons on a metallic grating,” J. Mol. Spectrosc. 37, 1227-1232 (1990).
  2. S. J. Elston, G. P. Bryan-Brown, T. W. Preist, and J. R. Sambles, “Surface-resonance polarization conversion mediated by broken surface symmetry,” Phys. Rev. B 44, 3483-3485 (1991).
    [CrossRef]
  3. Y.-L. Kok and N. C. Gallagher, “Relative phases of electromagnetic waves diffracted by a perfectly conducting rectangular-grooved grating,” J. Opt. Soc. Am. A 5, 65-73 (1988).
    [CrossRef] [PubMed]
  4. C. W. Haggans, L. Li, T. Fujita, and R. K. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Mol. Spectrosc. 40, 675-686 (1993).
  5. S. R. Seshadri, “Polarization conversion by reflection in a thin-film grating,” J. Opt. Soc. Am. A 18, 1765-1776 (2001).
    [CrossRef]
  6. I. R. Hooper and J. R. Sambles, “Surface plasmon polaritons on narrow-ridged short-pitch metal gratings in the conical mount,” J. Opt. Soc. Am. A 20, 836-843 (2003).
    [CrossRef]
  7. A. V. Kats, M. L. Nesterov, and A. Yu. Nikitin, “Polarization properties of a periodically-modulated metal film in regions of anomalous optical transparency,” Phys. Rev. B 72, 193405 (2005).
    [CrossRef]
  8. I. R. Hooper and J. R. Sambles, “Broadband polarization-converting mirror for the visible region of the spectrum,” Opt. Lett. 27, 2152-2154 (2002).
    [CrossRef]
  9. B. T. Hallam, C. R. Lawrence, I. R. Hooper, and J. R. Sambles, “Broad-band polarization conversion from a finite periodic structure in the microwave regime,” Appl. Phys. Lett. 84, 849-851 (2004).
    [CrossRef]
  10. N. Passilly, K. Ventola, P. Karvinen, P. Laakkonen, J. Turunen, and J. Tervo, “Polarization conversion in conical diffraction by metallic and dielectric subwavelength gratings,” Appl. Opt. 46, 4258-4265 (2007).
    [CrossRef] [PubMed]
  11. J. Chandezon, M. T. Dupuis, G. Cornet, and D. Maystre, “Multicoated gratings - a differential formalism applicable in the entire optical region,” J. Opt. Soc. Am. 72, 839-846 (1982).
    [CrossRef]
  12. Y. Okuno, “The mode-matching method,” in Analysis Methods for Electromagnetic Wave Problems, E.Yamashita, ed. (Artech House, 1990), pp. 107-138.
  13. Y. Okuno and T. Suyama, “Numerical analysis of surface plasmons excited on a thin metal grating,” J. Zhejiang Univ., Sci. 7, 55-70 (2006).
    [CrossRef]
  14. T. Suyama, Y. Okuno, and T. Matsuda, “Enhancement of TM-TE mode conversion caused by excitation of surface plasmons on a metal grating and its application for refractive index measurement,” Electromagn. Waves 72, 91-103 (2007).
    [CrossRef]
  15. M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068-1076 (1995).
    [CrossRef]
  16. M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12, 1077-1086 (1995).
    [CrossRef]
  17. L. Li, “A modal analysis of lamellar diffraction gratings in conical mountings,” J. Mol. Spectrosc. 40, 553-573 (1993).
  18. P. C. Logofatu, S. A. Coulombe, B. K. Minhas, and J. R. McNeil, “Identity of the cross-reflection coefficients for symmetric surface-relief gratings,” J. Opt. Soc. Am. A 16, 1108-1114 (1999).
    [CrossRef]
  19. D.-E. Yi, Y.-B. Yan, H.-T. Liu, S. Lu, and G.-F. Jin, “Broadband achromatic phase retarder by subwavelength grating,” Opt. Commun. 227, 49-55 (2003).
    [CrossRef]
  20. R. A. Depine and M. Lester, “Internal symmetries gratings in conical diffraction from metallic gratings,” J. Mol. Spectrosc. 48, 1405-1411 (2001).
  21. A. V. Kats and I. S. Spevak, “Analytical theory of resonance diffraction and transformation of light polarization,” Phys. Rev. B 65, 195406 (2002).
    [CrossRef]
  22. R. Petit, Electromagnetic Theory of Gratings (Springer-Verlag, 1980).
    [CrossRef]
  23. L. Li and C. W. Haggans, “Convergence of the coupled-wave method for metallic lamellar diffraction gratings,” J. Opt. Soc. Am. A 10, 1184-1189 (1993).
    [CrossRef]
  24. P. Lalanne and G. M. Morris, “Highly improved convergence of the coupled-wave method for TM polarization,” J. Opt. Soc. Am. A 13, 779-784 (1996).
    [CrossRef]
  25. G. Granet and B. Guizal, “Efficient implementation of the coupled-wave method for metallic lamellar gratings in TM polarization,” J. Opt. Soc. Am. A 13, 1019-1023 (1996).
    [CrossRef]
  26. P. Lalanne, “Convergence performance of the coupled-wave and the differential methods for thin gratings,” J. Opt. Soc. Am. A 14, 1583-1591 (1997).
    [CrossRef]
  27. E. Popov and M. Nevière, “Maxwell equations in Fourier space: fast-converging formulation for diffraction by arbitrary shaped, periodic, anisotropic media,” J. Opt. Soc. Am. A 18, 2886-2895 (2001).
    [CrossRef]
  28. L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870-1876 (1996).
    [CrossRef]
  29. C. C. Tsai and S. T. Wu, are preparing a manuscript to be called “Fast convergence formulation of rigorous coupled-wave analysis for surface relief gratings”.
  30. R. A. Depine and C. I. Valencia, “Reciprocity relations for s-p polarization conversion,” Opt. Commun. 117, 223-227 (1995).
    [CrossRef]
  31. E. D. Palik, Handbook of Optical Constants (Academic, 1997).
  32. D. K. Yang and S. T. Wu, Fundamentals of Liquid Crystal Devices (Wiley, 2006).
    [CrossRef]
  33. R. A. Depine and M. E. Inchaussandague, “Polarization conversion from highly conducting, asymmetric trapezoidal gratings,” Appl. Opt. 42, 3742-3744 (2003).
    [CrossRef] [PubMed]
  34. T. Inagaki, M. Motosuga, K. Yamamori, and E. T. Arakawa, “Photoacoustic study of plasmon resonance absorption in a diffraction grating,” Phys. Rev. B 28, 1740-1744 (1983).
    [CrossRef]
  35. M. B. Sobnack, W. C. Tan, N. P. Wanstall, T. W. Preist, and J. R. Sambles, “Stationary surface plasmons on a zero-order metal grating,” Phys. Rev. Lett. 80, 5667-5670 (1998).
    [CrossRef]
  36. W. C. Tan, T. W. Preist, J. R. Sambles, and N. P. Wanstall, “Flat surface-plasmon-polariton bands and resonant optical absorption on short-pitch metal gratings,” Phys. Rev. B 59, 12661-12666 (1999).
    [CrossRef]
  37. H. Raether, Surface Plasmons (Springer-Verlag, 1988).

2007 (2)

T. Suyama, Y. Okuno, and T. Matsuda, “Enhancement of TM-TE mode conversion caused by excitation of surface plasmons on a metal grating and its application for refractive index measurement,” Electromagn. Waves 72, 91-103 (2007).
[CrossRef]

N. Passilly, K. Ventola, P. Karvinen, P. Laakkonen, J. Turunen, and J. Tervo, “Polarization conversion in conical diffraction by metallic and dielectric subwavelength gratings,” Appl. Opt. 46, 4258-4265 (2007).
[CrossRef] [PubMed]

2006 (1)

Y. Okuno and T. Suyama, “Numerical analysis of surface plasmons excited on a thin metal grating,” J. Zhejiang Univ., Sci. 7, 55-70 (2006).
[CrossRef]

2005 (1)

A. V. Kats, M. L. Nesterov, and A. Yu. Nikitin, “Polarization properties of a periodically-modulated metal film in regions of anomalous optical transparency,” Phys. Rev. B 72, 193405 (2005).
[CrossRef]

2004 (1)

B. T. Hallam, C. R. Lawrence, I. R. Hooper, and J. R. Sambles, “Broad-band polarization conversion from a finite periodic structure in the microwave regime,” Appl. Phys. Lett. 84, 849-851 (2004).
[CrossRef]

2003 (3)

2002 (2)

I. R. Hooper and J. R. Sambles, “Broadband polarization-converting mirror for the visible region of the spectrum,” Opt. Lett. 27, 2152-2154 (2002).
[CrossRef]

A. V. Kats and I. S. Spevak, “Analytical theory of resonance diffraction and transformation of light polarization,” Phys. Rev. B 65, 195406 (2002).
[CrossRef]

2001 (3)

1999 (2)

W. C. Tan, T. W. Preist, J. R. Sambles, and N. P. Wanstall, “Flat surface-plasmon-polariton bands and resonant optical absorption on short-pitch metal gratings,” Phys. Rev. B 59, 12661-12666 (1999).
[CrossRef]

P. C. Logofatu, S. A. Coulombe, B. K. Minhas, and J. R. McNeil, “Identity of the cross-reflection coefficients for symmetric surface-relief gratings,” J. Opt. Soc. Am. A 16, 1108-1114 (1999).
[CrossRef]

1998 (1)

M. B. Sobnack, W. C. Tan, N. P. Wanstall, T. W. Preist, and J. R. Sambles, “Stationary surface plasmons on a zero-order metal grating,” Phys. Rev. Lett. 80, 5667-5670 (1998).
[CrossRef]

1997 (1)

1996 (3)

1995 (3)

1993 (3)

L. Li, “A modal analysis of lamellar diffraction gratings in conical mountings,” J. Mol. Spectrosc. 40, 553-573 (1993).

C. W. Haggans, L. Li, T. Fujita, and R. K. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Mol. Spectrosc. 40, 675-686 (1993).

L. Li and C. W. Haggans, “Convergence of the coupled-wave method for metallic lamellar diffraction gratings,” J. Opt. Soc. Am. A 10, 1184-1189 (1993).
[CrossRef]

1991 (1)

S. J. Elston, G. P. Bryan-Brown, T. W. Preist, and J. R. Sambles, “Surface-resonance polarization conversion mediated by broken surface symmetry,” Phys. Rev. B 44, 3483-3485 (1991).
[CrossRef]

1990 (1)

G. P. Bryan-Brown and J. R. Sambles, “Polarization conversion through the excitation of surface plasmons on a metallic grating,” J. Mol. Spectrosc. 37, 1227-1232 (1990).

1988 (1)

1983 (1)

T. Inagaki, M. Motosuga, K. Yamamori, and E. T. Arakawa, “Photoacoustic study of plasmon resonance absorption in a diffraction grating,” Phys. Rev. B 28, 1740-1744 (1983).
[CrossRef]

1982 (1)

Arakawa, E. T.

T. Inagaki, M. Motosuga, K. Yamamori, and E. T. Arakawa, “Photoacoustic study of plasmon resonance absorption in a diffraction grating,” Phys. Rev. B 28, 1740-1744 (1983).
[CrossRef]

Bryan-Brown, G. P.

S. J. Elston, G. P. Bryan-Brown, T. W. Preist, and J. R. Sambles, “Surface-resonance polarization conversion mediated by broken surface symmetry,” Phys. Rev. B 44, 3483-3485 (1991).
[CrossRef]

G. P. Bryan-Brown and J. R. Sambles, “Polarization conversion through the excitation of surface plasmons on a metallic grating,” J. Mol. Spectrosc. 37, 1227-1232 (1990).

Chandezon, J.

Cornet, G.

Coulombe, S. A.

Depine, R. A.

R. A. Depine and M. E. Inchaussandague, “Polarization conversion from highly conducting, asymmetric trapezoidal gratings,” Appl. Opt. 42, 3742-3744 (2003).
[CrossRef] [PubMed]

R. A. Depine and M. Lester, “Internal symmetries gratings in conical diffraction from metallic gratings,” J. Mol. Spectrosc. 48, 1405-1411 (2001).

R. A. Depine and C. I. Valencia, “Reciprocity relations for s-p polarization conversion,” Opt. Commun. 117, 223-227 (1995).
[CrossRef]

Dupuis, M. T.

Elston, S. J.

S. J. Elston, G. P. Bryan-Brown, T. W. Preist, and J. R. Sambles, “Surface-resonance polarization conversion mediated by broken surface symmetry,” Phys. Rev. B 44, 3483-3485 (1991).
[CrossRef]

Fujita, T.

C. W. Haggans, L. Li, T. Fujita, and R. K. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Mol. Spectrosc. 40, 675-686 (1993).

Gallagher, N. C.

Gaylord, T. K.

Granet, G.

Grann, E. B.

Guizal, B.

Haggans, C. W.

L. Li and C. W. Haggans, “Convergence of the coupled-wave method for metallic lamellar diffraction gratings,” J. Opt. Soc. Am. A 10, 1184-1189 (1993).
[CrossRef]

C. W. Haggans, L. Li, T. Fujita, and R. K. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Mol. Spectrosc. 40, 675-686 (1993).

Hallam, B. T.

B. T. Hallam, C. R. Lawrence, I. R. Hooper, and J. R. Sambles, “Broad-band polarization conversion from a finite periodic structure in the microwave regime,” Appl. Phys. Lett. 84, 849-851 (2004).
[CrossRef]

Hooper, I. R.

Inagaki, T.

T. Inagaki, M. Motosuga, K. Yamamori, and E. T. Arakawa, “Photoacoustic study of plasmon resonance absorption in a diffraction grating,” Phys. Rev. B 28, 1740-1744 (1983).
[CrossRef]

Inchaussandague, M. E.

Jin, G.-F.

D.-E. Yi, Y.-B. Yan, H.-T. Liu, S. Lu, and G.-F. Jin, “Broadband achromatic phase retarder by subwavelength grating,” Opt. Commun. 227, 49-55 (2003).
[CrossRef]

Karvinen, P.

Kats, A. V.

A. V. Kats, M. L. Nesterov, and A. Yu. Nikitin, “Polarization properties of a periodically-modulated metal film in regions of anomalous optical transparency,” Phys. Rev. B 72, 193405 (2005).
[CrossRef]

A. V. Kats and I. S. Spevak, “Analytical theory of resonance diffraction and transformation of light polarization,” Phys. Rev. B 65, 195406 (2002).
[CrossRef]

Kok, Y.-L.

Kostuk, R. K.

C. W. Haggans, L. Li, T. Fujita, and R. K. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Mol. Spectrosc. 40, 675-686 (1993).

Laakkonen, P.

Lalanne, P.

Lawrence, C. R.

B. T. Hallam, C. R. Lawrence, I. R. Hooper, and J. R. Sambles, “Broad-band polarization conversion from a finite periodic structure in the microwave regime,” Appl. Phys. Lett. 84, 849-851 (2004).
[CrossRef]

Lester, M.

R. A. Depine and M. Lester, “Internal symmetries gratings in conical diffraction from metallic gratings,” J. Mol. Spectrosc. 48, 1405-1411 (2001).

Li, L.

L. Li, “Use of Fourier series in the analysis of discontinuous periodic structures,” J. Opt. Soc. Am. A 13, 1870-1876 (1996).
[CrossRef]

L. Li, “A modal analysis of lamellar diffraction gratings in conical mountings,” J. Mol. Spectrosc. 40, 553-573 (1993).

C. W. Haggans, L. Li, T. Fujita, and R. K. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Mol. Spectrosc. 40, 675-686 (1993).

L. Li and C. W. Haggans, “Convergence of the coupled-wave method for metallic lamellar diffraction gratings,” J. Opt. Soc. Am. A 10, 1184-1189 (1993).
[CrossRef]

Liu, H.-T.

D.-E. Yi, Y.-B. Yan, H.-T. Liu, S. Lu, and G.-F. Jin, “Broadband achromatic phase retarder by subwavelength grating,” Opt. Commun. 227, 49-55 (2003).
[CrossRef]

Logofatu, P. C.

Lu, S.

D.-E. Yi, Y.-B. Yan, H.-T. Liu, S. Lu, and G.-F. Jin, “Broadband achromatic phase retarder by subwavelength grating,” Opt. Commun. 227, 49-55 (2003).
[CrossRef]

Matsuda, T.

T. Suyama, Y. Okuno, and T. Matsuda, “Enhancement of TM-TE mode conversion caused by excitation of surface plasmons on a metal grating and its application for refractive index measurement,” Electromagn. Waves 72, 91-103 (2007).
[CrossRef]

Maystre, D.

McNeil, J. R.

Minhas, B. K.

Moharam, M. G.

Morris, G. M.

Motosuga, M.

T. Inagaki, M. Motosuga, K. Yamamori, and E. T. Arakawa, “Photoacoustic study of plasmon resonance absorption in a diffraction grating,” Phys. Rev. B 28, 1740-1744 (1983).
[CrossRef]

Nesterov, M. L.

A. V. Kats, M. L. Nesterov, and A. Yu. Nikitin, “Polarization properties of a periodically-modulated metal film in regions of anomalous optical transparency,” Phys. Rev. B 72, 193405 (2005).
[CrossRef]

Nevière, M.

Nikitin, A. Yu.

A. V. Kats, M. L. Nesterov, and A. Yu. Nikitin, “Polarization properties of a periodically-modulated metal film in regions of anomalous optical transparency,” Phys. Rev. B 72, 193405 (2005).
[CrossRef]

Okuno, Y.

T. Suyama, Y. Okuno, and T. Matsuda, “Enhancement of TM-TE mode conversion caused by excitation of surface plasmons on a metal grating and its application for refractive index measurement,” Electromagn. Waves 72, 91-103 (2007).
[CrossRef]

Y. Okuno and T. Suyama, “Numerical analysis of surface plasmons excited on a thin metal grating,” J. Zhejiang Univ., Sci. 7, 55-70 (2006).
[CrossRef]

Y. Okuno, “The mode-matching method,” in Analysis Methods for Electromagnetic Wave Problems, E.Yamashita, ed. (Artech House, 1990), pp. 107-138.

Palik, E. D.

E. D. Palik, Handbook of Optical Constants (Academic, 1997).

Passilly, N.

Petit, R.

R. Petit, Electromagnetic Theory of Gratings (Springer-Verlag, 1980).
[CrossRef]

Pommet, D. A.

Popov, E.

Preist, T. W.

W. C. Tan, T. W. Preist, J. R. Sambles, and N. P. Wanstall, “Flat surface-plasmon-polariton bands and resonant optical absorption on short-pitch metal gratings,” Phys. Rev. B 59, 12661-12666 (1999).
[CrossRef]

M. B. Sobnack, W. C. Tan, N. P. Wanstall, T. W. Preist, and J. R. Sambles, “Stationary surface plasmons on a zero-order metal grating,” Phys. Rev. Lett. 80, 5667-5670 (1998).
[CrossRef]

S. J. Elston, G. P. Bryan-Brown, T. W. Preist, and J. R. Sambles, “Surface-resonance polarization conversion mediated by broken surface symmetry,” Phys. Rev. B 44, 3483-3485 (1991).
[CrossRef]

Raether, H.

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

Sambles, J. R.

B. T. Hallam, C. R. Lawrence, I. R. Hooper, and J. R. Sambles, “Broad-band polarization conversion from a finite periodic structure in the microwave regime,” Appl. Phys. Lett. 84, 849-851 (2004).
[CrossRef]

I. R. Hooper and J. R. Sambles, “Surface plasmon polaritons on narrow-ridged short-pitch metal gratings in the conical mount,” J. Opt. Soc. Am. A 20, 836-843 (2003).
[CrossRef]

I. R. Hooper and J. R. Sambles, “Broadband polarization-converting mirror for the visible region of the spectrum,” Opt. Lett. 27, 2152-2154 (2002).
[CrossRef]

W. C. Tan, T. W. Preist, J. R. Sambles, and N. P. Wanstall, “Flat surface-plasmon-polariton bands and resonant optical absorption on short-pitch metal gratings,” Phys. Rev. B 59, 12661-12666 (1999).
[CrossRef]

M. B. Sobnack, W. C. Tan, N. P. Wanstall, T. W. Preist, and J. R. Sambles, “Stationary surface plasmons on a zero-order metal grating,” Phys. Rev. Lett. 80, 5667-5670 (1998).
[CrossRef]

S. J. Elston, G. P. Bryan-Brown, T. W. Preist, and J. R. Sambles, “Surface-resonance polarization conversion mediated by broken surface symmetry,” Phys. Rev. B 44, 3483-3485 (1991).
[CrossRef]

G. P. Bryan-Brown and J. R. Sambles, “Polarization conversion through the excitation of surface plasmons on a metallic grating,” J. Mol. Spectrosc. 37, 1227-1232 (1990).

Seshadri, S. R.

Sobnack, M. B.

M. B. Sobnack, W. C. Tan, N. P. Wanstall, T. W. Preist, and J. R. Sambles, “Stationary surface plasmons on a zero-order metal grating,” Phys. Rev. Lett. 80, 5667-5670 (1998).
[CrossRef]

Spevak, I. S.

A. V. Kats and I. S. Spevak, “Analytical theory of resonance diffraction and transformation of light polarization,” Phys. Rev. B 65, 195406 (2002).
[CrossRef]

Suyama, T.

T. Suyama, Y. Okuno, and T. Matsuda, “Enhancement of TM-TE mode conversion caused by excitation of surface plasmons on a metal grating and its application for refractive index measurement,” Electromagn. Waves 72, 91-103 (2007).
[CrossRef]

Y. Okuno and T. Suyama, “Numerical analysis of surface plasmons excited on a thin metal grating,” J. Zhejiang Univ., Sci. 7, 55-70 (2006).
[CrossRef]

Tan, W. C.

W. C. Tan, T. W. Preist, J. R. Sambles, and N. P. Wanstall, “Flat surface-plasmon-polariton bands and resonant optical absorption on short-pitch metal gratings,” Phys. Rev. B 59, 12661-12666 (1999).
[CrossRef]

M. B. Sobnack, W. C. Tan, N. P. Wanstall, T. W. Preist, and J. R. Sambles, “Stationary surface plasmons on a zero-order metal grating,” Phys. Rev. Lett. 80, 5667-5670 (1998).
[CrossRef]

Tervo, J.

Tsai, C. C.

C. C. Tsai and S. T. Wu, are preparing a manuscript to be called “Fast convergence formulation of rigorous coupled-wave analysis for surface relief gratings”.

Turunen, J.

Valencia, C. I.

R. A. Depine and C. I. Valencia, “Reciprocity relations for s-p polarization conversion,” Opt. Commun. 117, 223-227 (1995).
[CrossRef]

Ventola, K.

Wanstall, N. P.

W. C. Tan, T. W. Preist, J. R. Sambles, and N. P. Wanstall, “Flat surface-plasmon-polariton bands and resonant optical absorption on short-pitch metal gratings,” Phys. Rev. B 59, 12661-12666 (1999).
[CrossRef]

M. B. Sobnack, W. C. Tan, N. P. Wanstall, T. W. Preist, and J. R. Sambles, “Stationary surface plasmons on a zero-order metal grating,” Phys. Rev. Lett. 80, 5667-5670 (1998).
[CrossRef]

Wu, S. T.

D. K. Yang and S. T. Wu, Fundamentals of Liquid Crystal Devices (Wiley, 2006).
[CrossRef]

C. C. Tsai and S. T. Wu, are preparing a manuscript to be called “Fast convergence formulation of rigorous coupled-wave analysis for surface relief gratings”.

Yamamori, K.

T. Inagaki, M. Motosuga, K. Yamamori, and E. T. Arakawa, “Photoacoustic study of plasmon resonance absorption in a diffraction grating,” Phys. Rev. B 28, 1740-1744 (1983).
[CrossRef]

Yan, Y.-B.

D.-E. Yi, Y.-B. Yan, H.-T. Liu, S. Lu, and G.-F. Jin, “Broadband achromatic phase retarder by subwavelength grating,” Opt. Commun. 227, 49-55 (2003).
[CrossRef]

Yang, D. K.

D. K. Yang and S. T. Wu, Fundamentals of Liquid Crystal Devices (Wiley, 2006).
[CrossRef]

Yi, D.-E.

D.-E. Yi, Y.-B. Yan, H.-T. Liu, S. Lu, and G.-F. Jin, “Broadband achromatic phase retarder by subwavelength grating,” Opt. Commun. 227, 49-55 (2003).
[CrossRef]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

B. T. Hallam, C. R. Lawrence, I. R. Hooper, and J. R. Sambles, “Broad-band polarization conversion from a finite periodic structure in the microwave regime,” Appl. Phys. Lett. 84, 849-851 (2004).
[CrossRef]

Electromagn. Waves (1)

T. Suyama, Y. Okuno, and T. Matsuda, “Enhancement of TM-TE mode conversion caused by excitation of surface plasmons on a metal grating and its application for refractive index measurement,” Electromagn. Waves 72, 91-103 (2007).
[CrossRef]

J. Mol. Spectrosc. (4)

G. P. Bryan-Brown and J. R. Sambles, “Polarization conversion through the excitation of surface plasmons on a metallic grating,” J. Mol. Spectrosc. 37, 1227-1232 (1990).

C. W. Haggans, L. Li, T. Fujita, and R. K. Kostuk, “Lamellar gratings as polarization components for specularly reflected beams,” J. Mol. Spectrosc. 40, 675-686 (1993).

R. A. Depine and M. Lester, “Internal symmetries gratings in conical diffraction from metallic gratings,” J. Mol. Spectrosc. 48, 1405-1411 (2001).

L. Li, “A modal analysis of lamellar diffraction gratings in conical mountings,” J. Mol. Spectrosc. 40, 553-573 (1993).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (12)

S. R. Seshadri, “Polarization conversion by reflection in a thin-film grating,” J. Opt. Soc. Am. A 18, 1765-1776 (2001).
[CrossRef]

E. Popov and M. Nevière, “Maxwell equations in Fourier space: fast-converging formulation for diffraction by arbitrary shaped, periodic, anisotropic media,” J. Opt. Soc. Am. A 18, 2886-2895 (2001).
[CrossRef]

I. R. Hooper and J. R. Sambles, “Surface plasmon polaritons on narrow-ridged short-pitch metal gratings in the conical mount,” J. Opt. Soc. Am. A 20, 836-843 (2003).
[CrossRef]

P. C. Logofatu, S. A. Coulombe, B. K. Minhas, and J. R. McNeil, “Identity of the cross-reflection coefficients for symmetric surface-relief gratings,” J. Opt. Soc. Am. A 16, 1108-1114 (1999).
[CrossRef]

P. Lalanne, “Convergence performance of the coupled-wave and the differential methods for thin gratings,” J. Opt. Soc. Am. A 14, 1583-1591 (1997).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

(a) Configuration of conical diffraction by one-dimensional surface-relief grating with incident angle θ, azimuthal angle ϕ, polarization angle ψ, and grating period Λ. (b) (1) Three regions of RCWA for light incident from medium I into medium II with coupled wave in groove region III and the staircase approximation for continuous surface-relief gratings, where Δ l i is the sum of two segments on each side of slice i. (2) Three grating profiles that enable broadband R p s 0 : the Gaussian ridge, the trapezoidal, and the binary grating. Their corresponding R p s 0 ( λ ) are shown in Fig. 6.

Fig. 2
Fig. 2

R p s 0 of incident angle θ at azimuthal angle ϕ = 45 ° for a shallow sinusoidal silver grating of ε = 16 + 0.71 i , Λ = 800.8 nm , d = 25.2 nm , and λ = 632.8 nm , which is consistent with both the experimental and theoretical results given in Fig. 2 of [2]. The maximum R p s 0 = 0.089 occurs at θ = 18.08 ° .

Fig. 3
Fig. 3

(a) Maximum R p s 0 for various ϕ with the same grating profile in of Fig. 2. The peak maximum R p s 0 occurs at ϕ = 45 ° and is zero at ϕ = 0 ° or 90 ° , which coincides with the Fig. 3 in [2]. The conversion efficiency follows the square rule of a sinusoidal function, R p s ( θ , ϕ ) sin 2 ( 2 ϕ ) [1, 21]. The curve of squares for the conversion from p to s and that of crosses for s to p conversion under the same incidence conditions clearly coincide. (b) Corresponding incidence angle θ to ϕ for the maximum R p s 0 ( ϕ , θ ) .

Fig. 4
Fig. 4

Maximum R p s 0 of the groove depth d ranging from 0 to 150 nm with the same grating profile as Fig. 2, but here Λ = 842.5 nm . The portion of d from 0 to 90 nm in this figure is consistent with the experimental result in Fig. 4 of [1]. The peak of R p s 0 ( d ) = 0.65 occurs at d = 95 nm ; R p s 0 then starts to decrease, but it rises again at d = 110 nm .

Fig. 5
Fig. 5

Broadband R p s 0 ( λ ) curves of a silver Gaussian-ridge grating of 50 nm width (FWHM), 240 nm height, and grating pitch Λ varying from 250 nm to 350 nm . The simulation condition is at normal incidence with ϕ = 45 ° and the permittivity dispersion of silver obtained from polynomial fitting to experimental data. The peak of R p s 0 ( λ ) is moving toward the center of visible spectrum as the Λ increases. The curve of solid squares of Λ = 250 nm is consistent with the result in [8].

Fig. 6
Fig. 6

Performance of broadband R p s 0 ( λ ) for the three grating profiles in Fig. 1b with the same simulation conditions as Fig. 5; the pitch of the Gaussian-ridge grating is Λ = 310 nm , chosen to be more centered in the visible spectrum.

Fig. 7
Fig. 7

(a) Two R p s 0 ( θ , ϕ ) branches of resonance curves for a shallow sinusoidal grating of ε = 8.23 + 0.29 i , Λ = 575.27 nm , d = 11.5 nm , and λ = 632.8 nm . The first branch is the dominant set with maximum R p s 0 = 1.74 % at ( θ , ϕ ) = ( 2.75 ° , 45 ° ) , and the second set has its maximum R p s 0 = 0.96 % at ( θ , ϕ ) = ( 53.75 ° , 66 ° ) . (b) The major region of second-branch resonance in (a) within the ϕ range from 60 ° to 80 ° . (c) Two R p s 0 ( θ , ϕ ) branches of resonance curves for the grating profile in Fig. 2. (d) The two R p s 0 curves with increasing depth d in (c). The curve of squares is the first resonance branch with ( θ , ϕ ) = ( 21 ° , 45 ° ) , and that of crosses is the second branch with ( θ , ϕ ) = ( 76.5 ° , 74 ° ) . The R p s 0 of the second branch is larger than that of the first branch when d > 0.27 Λ ( 230 nm ) .

Fig. 8
Fig. 8

(a) Average broadband polarization conversion efficiency R p s 0 ̿ ( ϕ ) over θ and λ of the trapezoidal grating profile in Fig. 1b, with the ϕ ranging from 30 ° to 60 ° . The peak of R p s 0 ̿ ( ϕ ) is 84.5% at ϕ = 48 ° . (b) The R p s ( θ , λ ) diagram of ϕ = 48 ° in (a), which is over 80% in most regions of ( θ , λ ) with the maximum R p s 0 ( 30 ° , 650 ) = 90 % and the minimum R p s 0 ( 60 ° , 450 ) = 38 % . (c) Top view of (b).

Equations (16)

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E i n c = u exp [ j k 0 n I ( x sin θ cos ϕ + y sin θ sin ϕ + z cos θ ) ] .
u = ( sin ψ sin ϕ cos ψ cos θ cos ϕ ) x ( sin ψ cos ϕ + cos ψ cos θ sin ϕ ) y + ( cos ψ sin θ ) z ,
E ( H ) R = i E ( H ) R i exp [ j ( k x i x + k y i y + k I , z i z ) ] ,
E ( H ) T = i E ( H ) T i exp [ j k x i x + k y i y + k II , z i ( z d ) ] ,
E G = i S ( z ) i exp [ j ( k x i x + k y i y ) ] ,
H G = j ( ε 0 μ 0 ) i U ( z ) i exp [ j ( k x i x + k y i y ) ] ,
d d z [ S y S x U y U x ] = [ 0 0 K y Q z z 1 K x K y Q z z 1 K y + I 0 0 K x Q z z 1 K x I K x Q z z 1 K y K y K x K y 2 + Q x x 0 0 K x 2 Q y y K x K y 0 0 ] [ S y S x U y U x ] ,
Q ε = [ Q x x 0 0 0 Q y y 0 0 0 Q z z ] = [ n z 2 E + n x 2 A 1 0 0 0 E 0 0 0 n x 2 E + n z 2 A 1 ] .
n x i 2 = Δ l i n x 2 ( p ) d l i Δ l i ,
n z i 2 = Δ l i n z 2 ( p ) d l i Δ l i ,
d 2 d z 2 [ S y S x ] = [ K y Q z z 1 K y Q y y + K x 2 Q y y K y Q z z 1 K x Q x x K x K y K x Q z z 1 K y Q y y K y K x K x Q z z 1 K x Q x x Q x x ] [ S y S x ] .
[ E R ( T ) i E R ( T ) i ] = [ R ( ϕ i ) ] [ E R ( T ) x i E R ( T ) y i ] .
E R ( T ) i = μ 0 ε 0 ( k I ( II ) , z i k 0 n I ( II ) 2 ) H R ( T ) i ,
H R ( T ) i = ± ε 0 μ 0 ( k I ( II ) , z i k 0 ) E R ( T ) i .
DE R i = E R i 2 Re ( k I , z i k 0 n I cos θ ) + H R i 2 Re ( k I , z i n I 2 k 0 n I cos θ ) ,
R p s 0 ̿ ( ϕ ) = R p s 0 ( θ , λ ) d θ d λ Δ θ Δ λ ,

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