Abstract

A normalized modal analysis of binary gratings under normal TE incidence involving the most condensed set of optogeometrical parameters gives a complete solution to the problem of canceling the 0th transmitted order in phase masks of a low-to-high refractive index ratio down to 0.5 with a large tolerance on the corrugation duty cycle or a large spectral bandwidth. The solution is presented in the form of single normalized 3D charts which shed light on the fulfillment of the 0th-order cancellation condition: balanced excitation and π-phase difference between two grating modes. Examples of tolerant gratings are given.

© 2010 Optical Society of America

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  1. K. Hill, B. Malo, F. Bilodeau, D. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett. 62, 1035–1037 (1993).
    [CrossRef]
  2. E. Gamet, A. V. Tishchenko, and O. Parriaux, “Cancellation of the zeroth order in a phase mask by mode interplay in a high index contrast binary grating,” Appl. Opt. 46, 6719–6726 (2007).
    [CrossRef]
  3. MC-Grating, MC Grating Software Development Company (www.mcgrating.com).
  4. J. Zheng, C. ZhouB. Wang, and J. Feng, “Beam splitting of low-contrast binary gratings under second Bragg angle incidence,” J. Opt. Soc. Am. A 25, 1075–1083 (2008).
    [CrossRef]
  5. J. Feng, C. Zhou, J. Zheng, and B. Wang, “Modal analysis of deep-etched low-contrast two-port beam splitter grating,” Opt. Commun. 281, 5298–5301 (2008).
    [CrossRef]
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    [CrossRef]
  7. J. Feng, C. Zhou, J. Zheng, H. Cao, and P. Lv, “Design and fabrication of a polarization-independent two-port beam splitter,” Appl. Opt. 48, 5636–5641 (2009).
    [CrossRef]
  8. E. Gamet, F. Pigeon, and O. Parriaux, “Duty cycle tolerant binary gratings for fabricable short period phase masks,” J. Eur. Opt. Soc. Rapid Publ. 4, 09047 (2009).
  9. S. Jeon, V. Malyarchuk, J. A. Rogers, and G. P. Wiederrecht, “Fabricating three-dimensional nanostructures using two photon lithography in a single exposure step,” Opt. Express 14, 2300–2308 (2006).
    [CrossRef]
  10. L. Botten, M. Craig, R. McPhedran, J. Adams, and J. Andrewartha, “The dielectric lamellar diffraction grating,” J. Mod. Opt. 28, 413–428 (1981).
    [CrossRef]
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    [CrossRef]
  12. P. Sheng, R. Stepleman, and P. Sanda, “Exact eigenfunctions for square-wave gratings: application to diffraction and surface-plasmon calculations,” Phys. Rev. B 26, 2907–2916 (1982).
    [CrossRef]
  13. M. Foresti, L. Menez, and A. Tishchenko, “Modal method in deep metal-dielectric gratings: the decisive role of hidden modes,” J. Opt. Soc. Am. A 23, 2501–2509 (2006).
    [CrossRef]
  14. M. Moharam and T. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981).
    [CrossRef]
  15. T. Clausnitzer, T. Kämpfe, E. B. Kley, A. Tünnermann, U. Peschel, A. Tishchenko, and O. Parriaux, “An intelligible explanation of highly-efficient diffraction in deep dielectric rectangular transmission gratings,” Opt. Express 13, 10448–10456 (2005).
    [CrossRef]

2009 (2)

E. Gamet, F. Pigeon, and O. Parriaux, “Duty cycle tolerant binary gratings for fabricable short period phase masks,” J. Eur. Opt. Soc. Rapid Publ. 4, 09047 (2009).

J. Feng, C. Zhou, J. Zheng, H. Cao, and P. Lv, “Design and fabrication of a polarization-independent two-port beam splitter,” Appl. Opt. 48, 5636–5641 (2009).
[CrossRef]

2008 (3)

2007 (1)

2006 (2)

2005 (2)

1993 (1)

K. Hill, B. Malo, F. Bilodeau, D. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett. 62, 1035–1037 (1993).
[CrossRef]

1982 (1)

P. Sheng, R. Stepleman, and P. Sanda, “Exact eigenfunctions for square-wave gratings: application to diffraction and surface-plasmon calculations,” Phys. Rev. B 26, 2907–2916 (1982).
[CrossRef]

1981 (2)

L. Botten, M. Craig, R. McPhedran, J. Adams, and J. Andrewartha, “The dielectric lamellar diffraction grating,” J. Mod. Opt. 28, 413–428 (1981).
[CrossRef]

M. Moharam and T. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981).
[CrossRef]

Adams, J.

L. Botten, M. Craig, R. McPhedran, J. Adams, and J. Andrewartha, “The dielectric lamellar diffraction grating,” J. Mod. Opt. 28, 413–428 (1981).
[CrossRef]

Albert, J.

K. Hill, B. Malo, F. Bilodeau, D. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett. 62, 1035–1037 (1993).
[CrossRef]

Andrewartha, J.

L. Botten, M. Craig, R. McPhedran, J. Adams, and J. Andrewartha, “The dielectric lamellar diffraction grating,” J. Mod. Opt. 28, 413–428 (1981).
[CrossRef]

Bilodeau, F.

K. Hill, B. Malo, F. Bilodeau, D. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett. 62, 1035–1037 (1993).
[CrossRef]

Botten, L.

L. Botten, M. Craig, R. McPhedran, J. Adams, and J. Andrewartha, “The dielectric lamellar diffraction grating,” J. Mod. Opt. 28, 413–428 (1981).
[CrossRef]

Cao, H.

Clausnitzer, T.

Craig, M.

L. Botten, M. Craig, R. McPhedran, J. Adams, and J. Andrewartha, “The dielectric lamellar diffraction grating,” J. Mod. Opt. 28, 413–428 (1981).
[CrossRef]

Feng, J.

Foresti, M.

Gamet, E.

E. Gamet, F. Pigeon, and O. Parriaux, “Duty cycle tolerant binary gratings for fabricable short period phase masks,” J. Eur. Opt. Soc. Rapid Publ. 4, 09047 (2009).

E. Gamet, A. V. Tishchenko, and O. Parriaux, “Cancellation of the zeroth order in a phase mask by mode interplay in a high index contrast binary grating,” Appl. Opt. 46, 6719–6726 (2007).
[CrossRef]

Gaylord, T.

Hill, K.

K. Hill, B. Malo, F. Bilodeau, D. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett. 62, 1035–1037 (1993).
[CrossRef]

Jeon, S.

Jia, W.

Johnson, D.

K. Hill, B. Malo, F. Bilodeau, D. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett. 62, 1035–1037 (1993).
[CrossRef]

Kämpfe, T.

Kley, E. B.

Lv, P.

Malo, B.

K. Hill, B. Malo, F. Bilodeau, D. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett. 62, 1035–1037 (1993).
[CrossRef]

Malyarchuk, V.

McPhedran, R.

L. Botten, M. Craig, R. McPhedran, J. Adams, and J. Andrewartha, “The dielectric lamellar diffraction grating,” J. Mod. Opt. 28, 413–428 (1981).
[CrossRef]

Menez, L.

Moharam, M.

Parriaux, O.

Peschel, U.

Pigeon, F.

E. Gamet, F. Pigeon, and O. Parriaux, “Duty cycle tolerant binary gratings for fabricable short period phase masks,” J. Eur. Opt. Soc. Rapid Publ. 4, 09047 (2009).

Rogers, J. A.

Sanda, P.

P. Sheng, R. Stepleman, and P. Sanda, “Exact eigenfunctions for square-wave gratings: application to diffraction and surface-plasmon calculations,” Phys. Rev. B 26, 2907–2916 (1982).
[CrossRef]

Sheng, P.

P. Sheng, R. Stepleman, and P. Sanda, “Exact eigenfunctions for square-wave gratings: application to diffraction and surface-plasmon calculations,” Phys. Rev. B 26, 2907–2916 (1982).
[CrossRef]

Stepleman, R.

P. Sheng, R. Stepleman, and P. Sanda, “Exact eigenfunctions for square-wave gratings: application to diffraction and surface-plasmon calculations,” Phys. Rev. B 26, 2907–2916 (1982).
[CrossRef]

Tishchenko, A.

Tishchenko, A. V.

Tünnermann, A.

Wang, B.

J. Zheng, C. ZhouB. Wang, and J. Feng, “Beam splitting of low-contrast binary gratings under second Bragg angle incidence,” J. Opt. Soc. Am. A 25, 1075–1083 (2008).
[CrossRef]

J. Feng, C. Zhou, J. Zheng, and B. Wang, “Modal analysis of deep-etched low-contrast two-port beam splitter grating,” Opt. Commun. 281, 5298–5301 (2008).
[CrossRef]

Wiederrecht, G. P.

Zheng, J.

Zhou, C.

Appl. Opt. (3)

Appl. Phys. Lett. (1)

K. Hill, B. Malo, F. Bilodeau, D. Johnson, and J. Albert, “Bragg gratings fabricated in monomode photosensitive optical fiber by UV exposure through a phase mask,” Appl. Phys. Lett. 62, 1035–1037 (1993).
[CrossRef]

J. Eur. Opt. Soc. Rapid Publ. (1)

E. Gamet, F. Pigeon, and O. Parriaux, “Duty cycle tolerant binary gratings for fabricable short period phase masks,” J. Eur. Opt. Soc. Rapid Publ. 4, 09047 (2009).

J. Mod. Opt. (1)

L. Botten, M. Craig, R. McPhedran, J. Adams, and J. Andrewartha, “The dielectric lamellar diffraction grating,” J. Mod. Opt. 28, 413–428 (1981).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Opt. Commun. (1)

J. Feng, C. Zhou, J. Zheng, and B. Wang, “Modal analysis of deep-etched low-contrast two-port beam splitter grating,” Opt. Commun. 281, 5298–5301 (2008).
[CrossRef]

Opt. Express (2)

Opt. Quantum Electron. (1)

A. Tishchenko, “A phenomenological representation of deep and high contrast lamellar gratings by means of the modal method,” Opt. Quantum Electron. 37, 309–330 (2005).
[CrossRef]

Phys. Rev. B (1)

P. Sheng, R. Stepleman, and P. Sanda, “Exact eigenfunctions for square-wave gratings: application to diffraction and surface-plasmon calculations,” Phys. Rev. B 26, 2907–2916 (1982).
[CrossRef]

Other (1)

MC-Grating, MC Grating Software Development Company (www.mcgrating.com).

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