Abstract

A phase-step in a phase mask is not copied into the substrate but is split into two half-amplitude phase-shifts in the near-field because of the presence of an additional interference fringe system of the two beams diffracted from the two grating sections separated by the phase-step. In the case of multiple phase-shifts, the split phase-shifts from two adjacent phase-steps can crossover in the propagation without interfere. This paper contributes to understanding the near-field diffraction of irregular phase gratings with multiple phase-shifts, and provides a theoretical base for designing multiple phase-shifted phase masks for high channel-count phase-only sampled fiber Bragg gratings [1,2].

© 2005 Optical Society of America

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References

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  1. Y. Sheng, J. E Rothenberg, H. Li, Y. Wang and J. Zweiback, �??Split of phase-shift in a phase mask for fiber Bragg gratings,�?? IEEE Photonics Technol. Lett. 16, 1316-1318 (2004)
    [CrossRef]
  2. E. Rothenberg, Y. Sheng , H. Li, W. Ying and J. Zweiback, �??Diffraction compensation of masks for high channel-count phase-only sampled fiber Bragg gratings,�?? OSA Topical meeting on Bragg gratings, Photosensitivity and Poling in Glass Waveguides, Post deadline paper, PDP-2, September (2003).
  3. P. E. Dyer, R. J. Farley, and R. Giedl, �??Analysis of grating formation with excimer laser irradiated phase mask,�?? Opt. Commun. 115, 327-334 (1995)
    [CrossRef] [PubMed]
  4. J. A. R. Williams et al. "The effects of phase steps in e-beam written phase masks used for fiber grating fabrication by near-field holography,�?? ECOC 97, 187-190 (1997)
  5. Y. Qiu, Y. Sheng, and C. Beaulieu, "Optimal phase masks for fiber Bragg grating fabrication,�?? J. Lightwave Technol. 17, 2366-2370 (1999).
    [CrossRef]
  6. J. D. Mills, C. W. J. Hillman, B. H. Blott and W. S. Brocklesby, "Imaging of free-space interference patterns used to manufacture fiber Bragg gratings,�?? Appl. Opt. 39, 6129-6135 (2000)
    [CrossRef]
  7. N. M. Dragomir, C. Rollinson, S. Wade, A. J. Stevenson, S. F. Collins and G. W. Baxter, "Nondestructive imaging of a type I optical fiber Bragg grating,�?? Opt. Lett. 28, 789-791 (2003)
    [CrossRef] [PubMed]
  8. Y. Sheng, Y. Qiu and J. Wang , �??Diffraction of phase mask with stitching errors in fabrication of fiber Bragg gratings�??, Opt. Eng., Special section on Diffractive Optics 43, 2570-2574, (2004)
  9. R. Kashyyap, �??Fiber Bragg gratings�?? Chap. 6.1 (Academic, San Diego, 1999)
  10. V. Jayaraman. Z. Chuang and L. Coldren, �??Theory, Design, and Performance of Extended tuning Range Semiconductor Lasers with Sampled Gratings�?? IEEE J. Quantum Electron. 29, 1824-1834 (1993)
    [CrossRef]
  11. J.E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox and J. Zweiback, �??Dammann fiber Bragg gratings and phase-only sampling for high channel counts,�?? IEEE Photonics Technol. Lett. 14, 1309-1311, (2002).
    [CrossRef]
  12. H. Li, Y. Sheng, Y. Li and J. E. Rothenberg, " Phased-Only Sampled Fiber Bragg Gratings for High Channel Counts Chromatic Dispersion Compensation,�?? J. Lightwave Technol. 21, 2074-2083 (2003).
    [CrossRef]
  13. Y. Sheng, J. E. Rothenberg, H. Li, W. Ying and J. Zweiback, �??Phase mask design and phase mask for writing optical fiber Bragg gratings,�?? International Patent PCT, WO 03/062880 (2003).
  14. L. Poladian, B. Ashton and W. Padden, �??Interactive design and fabrication of complex FBGs,�?? OFC paper WL1, Tech. Digest vol.1, 378-79 (2003)
  15. B. J. Lin, �??Electromagnetic Near-Field Diffraction of a medium Slit,�?? J. Opt. Soc. Am. 62, 976-981 (1972)
    [CrossRef]
  16. Z. S. Hegedus, �??Contact printing of Bragg gratings in optical fibers: rigorous diffraction analysis,�?? Appl. Opt. 36, 247-252 (1997)

Appl. Opt. (2)

J. D. Mills, C. W. J. Hillman, B. H. Blott and W. S. Brocklesby, "Imaging of free-space interference patterns used to manufacture fiber Bragg gratings,�?? Appl. Opt. 39, 6129-6135 (2000)
[CrossRef]

Z. S. Hegedus, �??Contact printing of Bragg gratings in optical fibers: rigorous diffraction analysis,�?? Appl. Opt. 36, 247-252 (1997)

ECOC 1997 (1)

J. A. R. Williams et al. "The effects of phase steps in e-beam written phase masks used for fiber grating fabrication by near-field holography,�?? ECOC 97, 187-190 (1997)

IEEE J. Quantum Electron. (1)

V. Jayaraman. Z. Chuang and L. Coldren, �??Theory, Design, and Performance of Extended tuning Range Semiconductor Lasers with Sampled Gratings�?? IEEE J. Quantum Electron. 29, 1824-1834 (1993)
[CrossRef]

IEEE Photonics Technol. Lett. (2)

J.E. Rothenberg, H. Li, Y. Li, J. Popelek, Y. Sheng, Y. Wang, R. B. Wilcox and J. Zweiback, �??Dammann fiber Bragg gratings and phase-only sampling for high channel counts,�?? IEEE Photonics Technol. Lett. 14, 1309-1311, (2002).
[CrossRef]

Y. Sheng, J. E Rothenberg, H. Li, Y. Wang and J. Zweiback, �??Split of phase-shift in a phase mask for fiber Bragg gratings,�?? IEEE Photonics Technol. Lett. 16, 1316-1318 (2004)
[CrossRef]

J. Lightwave Technol. (2)

H. Li, Y. Sheng, Y. Li and J. E. Rothenberg, " Phased-Only Sampled Fiber Bragg Gratings for High Channel Counts Chromatic Dispersion Compensation,�?? J. Lightwave Technol. 21, 2074-2083 (2003).
[CrossRef]

Y. Qiu, Y. Sheng, and C. Beaulieu, "Optimal phase masks for fiber Bragg grating fabrication,�?? J. Lightwave Technol. 17, 2366-2370 (1999).
[CrossRef]

J. Opt. Soc. Am. (1)

OFC 2003 (1)

L. Poladian, B. Ashton and W. Padden, �??Interactive design and fabrication of complex FBGs,�?? OFC paper WL1, Tech. Digest vol.1, 378-79 (2003)

Opt. Commun. (1)

P. E. Dyer, R. J. Farley, and R. Giedl, �??Analysis of grating formation with excimer laser irradiated phase mask,�?? Opt. Commun. 115, 327-334 (1995)
[CrossRef] [PubMed]

Opt. Eng. Special section on Diff. Optic (1)

Y. Sheng, Y. Qiu and J. Wang , �??Diffraction of phase mask with stitching errors in fabrication of fiber Bragg gratings�??, Opt. Eng., Special section on Diffractive Optics 43, 2570-2574, (2004)

Opt. Lett. (1)

OSA Topical mtg Bragg gratings 2003 (1)

E. Rothenberg, Y. Sheng , H. Li, W. Ying and J. Zweiback, �??Diffraction compensation of masks for high channel-count phase-only sampled fiber Bragg gratings,�?? OSA Topical meeting on Bragg gratings, Photosensitivity and Poling in Glass Waveguides, Post deadline paper, PDP-2, September (2003).

Other (2)

R. Kashyyap, �??Fiber Bragg gratings�?? Chap. 6.1 (Academic, San Diego, 1999)

Y. Sheng, J. E. Rothenberg, H. Li, W. Ying and J. Zweiback, �??Phase mask design and phase mask for writing optical fiber Bragg gratings,�?? International Patent PCT, WO 03/062880 (2003).

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Figures (3)

Fig. 1.
Fig. 1.

Near-field diffraction of a phase mask with one phase step δ ; (a) regions of superposition of the 4 diffracted beams; (b) a small central part of the calculated interference pattern of the 4 beams, illustrating the phase shift split.

Fig. 2.
Fig. 2.

Near-field diffraction of a phase mask with two phase shifts; (a): regions of superposition of the 6 diffracted beams; (b): part of the interference pattern calculated by superposing the beam 1–6, described in the text, in the respective regions.

Fig. 3.
Fig. 3.

Near-field intensity distribution of a phase mask with one phase-shift.; Left-Top: from 0 to 5 μm computed by the FDTD; Left-Bottom from 5 to 15 μm computed by Fourier free space propagation filter; Right-Top: Plot of the amplitude in arbitrary scale of the near field at y=15 μm ; Right-Bottom: Plot of the fringe periods at y=15 μm .

Equations (3)

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e j 2 πy cos θ λ [ e j 2 π ( x x 01 ) Λ + e j 2 π ( x x 02 ) Λ ] =
= 2 e j 2 πy cos θ λ e j 2 π ( x 02 x 01 ) 2 Λ cos ( 2 π Λ ( x x 01 δ 2 ) )
1 + cos ( 2 π ( x x 01 γ + δ 2 ) ( Λ 2 )

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