Abstract

A technologically important use of the free-space interference patterns formed by phase gratings is in the creation of the refractive-index variation along optical fiber Bragg gratings. The patterns can be imaged directly by use of a tapered optical fiber tip, which acts as a local probe of the optical field. We present measurements of these patterns under varying conditions and compare them with theoretical predictions. In discussing the results within the context of fiber grating manufacture, we also demonstrate the effects of incident-beam misalignment and wave-front curvature.

© 2000 Optical Society of America

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  1. K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
    [CrossRef]
  2. P. E. Dyer, R. J. Farley, R. Giedl, K. C. Byron, D. Reid, “High reflectivity fibre gratings produced by incubated damage using a 193 nm ArF laser,” Electron. Lett. 30, 860–862 (1994).
    [CrossRef]
  3. W. H. Loh, R. I. Laming, X. Gu, M. N. Zervas, M. J. Cole, T. Widdowson, A. D. Ellis, “10 cm chirped fibre Bragg gratings for dispersion compensation at 10 Gbit/s over 400 km of non-dispersion shifted fibre,” Electron. Lett. 31, 2203–2204 (1995).
    [CrossRef]
  4. F. Bakhti, P. Sansonetti, C. Sinet, L. Gasca, L. Martineau, S. Lacroix, X. Daxhelet, F. Gonthier, “Optical add/drop multiplexer based on UV-written Bragg grating in a fused 100% coupler,” Electron. Lett. 33, 803–804 (1997).
    [CrossRef]
  5. A. Asseh, H. Storoy, J. T. Kringlebotn, W. Margulis, B. Sahlgren, S. Sandgren, R. Stubbe, G. Edwall, “10 cm YB3+ DFB fiber laser with permanent phase-shifted grating,” Electron. Lett. 31, 969–970 (1995).
    [CrossRef]
  6. G. Meltz, W. W. Morey, W. H. Glenn, “Formation of Bragg gratings in optical fibers by a transverse holographic method,” Opt. Lett. 14, 823–825 (1989).
    [CrossRef] [PubMed]
  7. K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, 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]
  8. H. Talbot, “Facts relating to optical science,” Philos. Mag. 9, 401–407 (1836).
  9. Lord Rayleigh, “On the manufacture and theory of diffraction grating,” Philos. Mag. 11, 196–205 (1881).
  10. G. Wojcik, J. Mould, R. Ferguson, R. Martino, K. K. Low, “Some image modeling issues for I-line, 5× phase shifting masks,” in Optical Laser Microlithography VII, T. A. Brunner, ed., Proc. SPIE2197, 455–465 (1994).
    [CrossRef]
  11. J. D. Prohaska, E. Snitzer, J. Winthrop, “Theoretical description of fiber Bragg reflectors prepared by Fresnel diffraction images,” Appl. Opt. 33, 3896–3900 (1994).
    [CrossRef] [PubMed]
  12. P. E. Dyer, R. J. Farley, R. Giedl, “Analysis of grating formation with excimer-laser irradiated phase masks,” Opt. Commun. 115, 327–334 (1995).
    [CrossRef]
  13. B. Hecht, H. Bielefeldt, Y. Inouye, D. W. Pohl, L. Novotny, “Facts and artifacts in near-field optical microscopy,” J. Appl. Phys. 81, 2492–2498 (1997).
    [CrossRef]
  14. R. Toledo-Crow, J. K. Rogers, F. Seiferth, M. Vaez-Iravani, “Contrast mechanisms and imaging modes in near field optical microscopy,” Ultramicroscopy 57, 293–297 (1995).
    [CrossRef]
  15. C. Kittel, Introduction to Solid State Physics, 6th ed. (Wiley, New York, 1986).
  16. K. Karrai, R. D. Grober, “Piezoelectric tip-sample distance control for near field optical microscopes,” Appl. Phys. Lett. 66, 1842–1844 (1995).
    [CrossRef]
  17. D. Courjon, C. Bainier, “Near field microscopy and near field optics,” Rep. Prog. Phys. 57, 989–1028 (1994).
    [CrossRef]
  18. M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, S. Barcelos, “Compensation of imperfect phase mask with moving fiber-scanning beam technique for production of fiber gratings,” Electron. Lett. 31, 1483–1485 (1995).
    [CrossRef]

1997 (2)

F. Bakhti, P. Sansonetti, C. Sinet, L. Gasca, L. Martineau, S. Lacroix, X. Daxhelet, F. Gonthier, “Optical add/drop multiplexer based on UV-written Bragg grating in a fused 100% coupler,” Electron. Lett. 33, 803–804 (1997).
[CrossRef]

B. Hecht, H. Bielefeldt, Y. Inouye, D. W. Pohl, L. Novotny, “Facts and artifacts in near-field optical microscopy,” J. Appl. Phys. 81, 2492–2498 (1997).
[CrossRef]

1995 (6)

R. Toledo-Crow, J. K. Rogers, F. Seiferth, M. Vaez-Iravani, “Contrast mechanisms and imaging modes in near field optical microscopy,” Ultramicroscopy 57, 293–297 (1995).
[CrossRef]

K. Karrai, R. D. Grober, “Piezoelectric tip-sample distance control for near field optical microscopes,” Appl. Phys. Lett. 66, 1842–1844 (1995).
[CrossRef]

M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, S. Barcelos, “Compensation of imperfect phase mask with moving fiber-scanning beam technique for production of fiber gratings,” Electron. Lett. 31, 1483–1485 (1995).
[CrossRef]

P. E. Dyer, R. J. Farley, R. Giedl, “Analysis of grating formation with excimer-laser irradiated phase masks,” Opt. Commun. 115, 327–334 (1995).
[CrossRef]

A. Asseh, H. Storoy, J. T. Kringlebotn, W. Margulis, B. Sahlgren, S. Sandgren, R. Stubbe, G. Edwall, “10 cm YB3+ DFB fiber laser with permanent phase-shifted grating,” Electron. Lett. 31, 969–970 (1995).
[CrossRef]

W. H. Loh, R. I. Laming, X. Gu, M. N. Zervas, M. J. Cole, T. Widdowson, A. D. Ellis, “10 cm chirped fibre Bragg gratings for dispersion compensation at 10 Gbit/s over 400 km of non-dispersion shifted fibre,” Electron. Lett. 31, 2203–2204 (1995).
[CrossRef]

1994 (3)

P. E. Dyer, R. J. Farley, R. Giedl, K. C. Byron, D. Reid, “High reflectivity fibre gratings produced by incubated damage using a 193 nm ArF laser,” Electron. Lett. 30, 860–862 (1994).
[CrossRef]

J. D. Prohaska, E. Snitzer, J. Winthrop, “Theoretical description of fiber Bragg reflectors prepared by Fresnel diffraction images,” Appl. Opt. 33, 3896–3900 (1994).
[CrossRef] [PubMed]

D. Courjon, C. Bainier, “Near field microscopy and near field optics,” Rep. Prog. Phys. 57, 989–1028 (1994).
[CrossRef]

1993 (1)

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, 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]

1989 (1)

1978 (1)

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

1881 (1)

Lord Rayleigh, “On the manufacture and theory of diffraction grating,” Philos. Mag. 11, 196–205 (1881).

1836 (1)

H. Talbot, “Facts relating to optical science,” Philos. Mag. 9, 401–407 (1836).

Albert, J.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, 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]

Asseh, A.

A. Asseh, H. Storoy, J. T. Kringlebotn, W. Margulis, B. Sahlgren, S. Sandgren, R. Stubbe, G. Edwall, “10 cm YB3+ DFB fiber laser with permanent phase-shifted grating,” Electron. Lett. 31, 969–970 (1995).
[CrossRef]

Bainier, C.

D. Courjon, C. Bainier, “Near field microscopy and near field optics,” Rep. Prog. Phys. 57, 989–1028 (1994).
[CrossRef]

Bakhti, F.

F. Bakhti, P. Sansonetti, C. Sinet, L. Gasca, L. Martineau, S. Lacroix, X. Daxhelet, F. Gonthier, “Optical add/drop multiplexer based on UV-written Bragg grating in a fused 100% coupler,” Electron. Lett. 33, 803–804 (1997).
[CrossRef]

Barcelos, S.

M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, S. Barcelos, “Compensation of imperfect phase mask with moving fiber-scanning beam technique for production of fiber gratings,” Electron. Lett. 31, 1483–1485 (1995).
[CrossRef]

Bielefeldt, H.

B. Hecht, H. Bielefeldt, Y. Inouye, D. W. Pohl, L. Novotny, “Facts and artifacts in near-field optical microscopy,” J. Appl. Phys. 81, 2492–2498 (1997).
[CrossRef]

Bilodeau, F.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, 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]

Byron, K. C.

P. E. Dyer, R. J. Farley, R. Giedl, K. C. Byron, D. Reid, “High reflectivity fibre gratings produced by incubated damage using a 193 nm ArF laser,” Electron. Lett. 30, 860–862 (1994).
[CrossRef]

Cole, M. J.

W. H. Loh, R. I. Laming, X. Gu, M. N. Zervas, M. J. Cole, T. Widdowson, A. D. Ellis, “10 cm chirped fibre Bragg gratings for dispersion compensation at 10 Gbit/s over 400 km of non-dispersion shifted fibre,” Electron. Lett. 31, 2203–2204 (1995).
[CrossRef]

M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, S. Barcelos, “Compensation of imperfect phase mask with moving fiber-scanning beam technique for production of fiber gratings,” Electron. Lett. 31, 1483–1485 (1995).
[CrossRef]

Courjon, D.

D. Courjon, C. Bainier, “Near field microscopy and near field optics,” Rep. Prog. Phys. 57, 989–1028 (1994).
[CrossRef]

Daxhelet, X.

F. Bakhti, P. Sansonetti, C. Sinet, L. Gasca, L. Martineau, S. Lacroix, X. Daxhelet, F. Gonthier, “Optical add/drop multiplexer based on UV-written Bragg grating in a fused 100% coupler,” Electron. Lett. 33, 803–804 (1997).
[CrossRef]

Dyer, P. E.

P. E. Dyer, R. J. Farley, R. Giedl, “Analysis of grating formation with excimer-laser irradiated phase masks,” Opt. Commun. 115, 327–334 (1995).
[CrossRef]

P. E. Dyer, R. J. Farley, R. Giedl, K. C. Byron, D. Reid, “High reflectivity fibre gratings produced by incubated damage using a 193 nm ArF laser,” Electron. Lett. 30, 860–862 (1994).
[CrossRef]

Edwall, G.

A. Asseh, H. Storoy, J. T. Kringlebotn, W. Margulis, B. Sahlgren, S. Sandgren, R. Stubbe, G. Edwall, “10 cm YB3+ DFB fiber laser with permanent phase-shifted grating,” Electron. Lett. 31, 969–970 (1995).
[CrossRef]

Ellis, A. D.

W. H. Loh, R. I. Laming, X. Gu, M. N. Zervas, M. J. Cole, T. Widdowson, A. D. Ellis, “10 cm chirped fibre Bragg gratings for dispersion compensation at 10 Gbit/s over 400 km of non-dispersion shifted fibre,” Electron. Lett. 31, 2203–2204 (1995).
[CrossRef]

Farley, R. J.

P. E. Dyer, R. J. Farley, R. Giedl, “Analysis of grating formation with excimer-laser irradiated phase masks,” Opt. Commun. 115, 327–334 (1995).
[CrossRef]

P. E. Dyer, R. J. Farley, R. Giedl, K. C. Byron, D. Reid, “High reflectivity fibre gratings produced by incubated damage using a 193 nm ArF laser,” Electron. Lett. 30, 860–862 (1994).
[CrossRef]

Ferguson, R.

G. Wojcik, J. Mould, R. Ferguson, R. Martino, K. K. Low, “Some image modeling issues for I-line, 5× phase shifting masks,” in Optical Laser Microlithography VII, T. A. Brunner, ed., Proc. SPIE2197, 455–465 (1994).
[CrossRef]

Fujii, Y.

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

Gasca, L.

F. Bakhti, P. Sansonetti, C. Sinet, L. Gasca, L. Martineau, S. Lacroix, X. Daxhelet, F. Gonthier, “Optical add/drop multiplexer based on UV-written Bragg grating in a fused 100% coupler,” Electron. Lett. 33, 803–804 (1997).
[CrossRef]

Giedl, R.

P. E. Dyer, R. J. Farley, R. Giedl, “Analysis of grating formation with excimer-laser irradiated phase masks,” Opt. Commun. 115, 327–334 (1995).
[CrossRef]

P. E. Dyer, R. J. Farley, R. Giedl, K. C. Byron, D. Reid, “High reflectivity fibre gratings produced by incubated damage using a 193 nm ArF laser,” Electron. Lett. 30, 860–862 (1994).
[CrossRef]

Glenn, W. H.

Gonthier, F.

F. Bakhti, P. Sansonetti, C. Sinet, L. Gasca, L. Martineau, S. Lacroix, X. Daxhelet, F. Gonthier, “Optical add/drop multiplexer based on UV-written Bragg grating in a fused 100% coupler,” Electron. Lett. 33, 803–804 (1997).
[CrossRef]

Grober, R. D.

K. Karrai, R. D. Grober, “Piezoelectric tip-sample distance control for near field optical microscopes,” Appl. Phys. Lett. 66, 1842–1844 (1995).
[CrossRef]

Gu, X.

W. H. Loh, R. I. Laming, X. Gu, M. N. Zervas, M. J. Cole, T. Widdowson, A. D. Ellis, “10 cm chirped fibre Bragg gratings for dispersion compensation at 10 Gbit/s over 400 km of non-dispersion shifted fibre,” Electron. Lett. 31, 2203–2204 (1995).
[CrossRef]

Hecht, B.

B. Hecht, H. Bielefeldt, Y. Inouye, D. W. Pohl, L. Novotny, “Facts and artifacts in near-field optical microscopy,” J. Appl. Phys. 81, 2492–2498 (1997).
[CrossRef]

Hill, K. O.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, 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]

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

Inouye, Y.

B. Hecht, H. Bielefeldt, Y. Inouye, D. W. Pohl, L. Novotny, “Facts and artifacts in near-field optical microscopy,” J. Appl. Phys. 81, 2492–2498 (1997).
[CrossRef]

Johnson, D. C.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, 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]

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

Karrai, K.

K. Karrai, R. D. Grober, “Piezoelectric tip-sample distance control for near field optical microscopes,” Appl. Phys. Lett. 66, 1842–1844 (1995).
[CrossRef]

Kawasaki, B. S.

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

Kittel, C.

C. Kittel, Introduction to Solid State Physics, 6th ed. (Wiley, New York, 1986).

Kringlebotn, J. T.

A. Asseh, H. Storoy, J. T. Kringlebotn, W. Margulis, B. Sahlgren, S. Sandgren, R. Stubbe, G. Edwall, “10 cm YB3+ DFB fiber laser with permanent phase-shifted grating,” Electron. Lett. 31, 969–970 (1995).
[CrossRef]

Lacroix, S.

F. Bakhti, P. Sansonetti, C. Sinet, L. Gasca, L. Martineau, S. Lacroix, X. Daxhelet, F. Gonthier, “Optical add/drop multiplexer based on UV-written Bragg grating in a fused 100% coupler,” Electron. Lett. 33, 803–804 (1997).
[CrossRef]

Laming, R. I.

M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, S. Barcelos, “Compensation of imperfect phase mask with moving fiber-scanning beam technique for production of fiber gratings,” Electron. Lett. 31, 1483–1485 (1995).
[CrossRef]

W. H. Loh, R. I. Laming, X. Gu, M. N. Zervas, M. J. Cole, T. Widdowson, A. D. Ellis, “10 cm chirped fibre Bragg gratings for dispersion compensation at 10 Gbit/s over 400 km of non-dispersion shifted fibre,” Electron. Lett. 31, 2203–2204 (1995).
[CrossRef]

Loh, W. H.

W. H. Loh, R. I. Laming, X. Gu, M. N. Zervas, M. J. Cole, T. Widdowson, A. D. Ellis, “10 cm chirped fibre Bragg gratings for dispersion compensation at 10 Gbit/s over 400 km of non-dispersion shifted fibre,” Electron. Lett. 31, 2203–2204 (1995).
[CrossRef]

M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, S. Barcelos, “Compensation of imperfect phase mask with moving fiber-scanning beam technique for production of fiber gratings,” Electron. Lett. 31, 1483–1485 (1995).
[CrossRef]

Low, K. K.

G. Wojcik, J. Mould, R. Ferguson, R. Martino, K. K. Low, “Some image modeling issues for I-line, 5× phase shifting masks,” in Optical Laser Microlithography VII, T. A. Brunner, ed., Proc. SPIE2197, 455–465 (1994).
[CrossRef]

Malo, B.

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, 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]

Margulis, W.

A. Asseh, H. Storoy, J. T. Kringlebotn, W. Margulis, B. Sahlgren, S. Sandgren, R. Stubbe, G. Edwall, “10 cm YB3+ DFB fiber laser with permanent phase-shifted grating,” Electron. Lett. 31, 969–970 (1995).
[CrossRef]

Martineau, L.

F. Bakhti, P. Sansonetti, C. Sinet, L. Gasca, L. Martineau, S. Lacroix, X. Daxhelet, F. Gonthier, “Optical add/drop multiplexer based on UV-written Bragg grating in a fused 100% coupler,” Electron. Lett. 33, 803–804 (1997).
[CrossRef]

Martino, R.

G. Wojcik, J. Mould, R. Ferguson, R. Martino, K. K. Low, “Some image modeling issues for I-line, 5× phase shifting masks,” in Optical Laser Microlithography VII, T. A. Brunner, ed., Proc. SPIE2197, 455–465 (1994).
[CrossRef]

Meltz, G.

Morey, W. W.

Mould, J.

G. Wojcik, J. Mould, R. Ferguson, R. Martino, K. K. Low, “Some image modeling issues for I-line, 5× phase shifting masks,” in Optical Laser Microlithography VII, T. A. Brunner, ed., Proc. SPIE2197, 455–465 (1994).
[CrossRef]

Novotny, L.

B. Hecht, H. Bielefeldt, Y. Inouye, D. W. Pohl, L. Novotny, “Facts and artifacts in near-field optical microscopy,” J. Appl. Phys. 81, 2492–2498 (1997).
[CrossRef]

Pohl, D. W.

B. Hecht, H. Bielefeldt, Y. Inouye, D. W. Pohl, L. Novotny, “Facts and artifacts in near-field optical microscopy,” J. Appl. Phys. 81, 2492–2498 (1997).
[CrossRef]

Prohaska, J. D.

Rayleigh, Lord

Lord Rayleigh, “On the manufacture and theory of diffraction grating,” Philos. Mag. 11, 196–205 (1881).

Reid, D.

P. E. Dyer, R. J. Farley, R. Giedl, K. C. Byron, D. Reid, “High reflectivity fibre gratings produced by incubated damage using a 193 nm ArF laser,” Electron. Lett. 30, 860–862 (1994).
[CrossRef]

Rogers, J. K.

R. Toledo-Crow, J. K. Rogers, F. Seiferth, M. Vaez-Iravani, “Contrast mechanisms and imaging modes in near field optical microscopy,” Ultramicroscopy 57, 293–297 (1995).
[CrossRef]

Sahlgren, B.

A. Asseh, H. Storoy, J. T. Kringlebotn, W. Margulis, B. Sahlgren, S. Sandgren, R. Stubbe, G. Edwall, “10 cm YB3+ DFB fiber laser with permanent phase-shifted grating,” Electron. Lett. 31, 969–970 (1995).
[CrossRef]

Sandgren, S.

A. Asseh, H. Storoy, J. T. Kringlebotn, W. Margulis, B. Sahlgren, S. Sandgren, R. Stubbe, G. Edwall, “10 cm YB3+ DFB fiber laser with permanent phase-shifted grating,” Electron. Lett. 31, 969–970 (1995).
[CrossRef]

Sansonetti, P.

F. Bakhti, P. Sansonetti, C. Sinet, L. Gasca, L. Martineau, S. Lacroix, X. Daxhelet, F. Gonthier, “Optical add/drop multiplexer based on UV-written Bragg grating in a fused 100% coupler,” Electron. Lett. 33, 803–804 (1997).
[CrossRef]

Seiferth, F.

R. Toledo-Crow, J. K. Rogers, F. Seiferth, M. Vaez-Iravani, “Contrast mechanisms and imaging modes in near field optical microscopy,” Ultramicroscopy 57, 293–297 (1995).
[CrossRef]

Sinet, C.

F. Bakhti, P. Sansonetti, C. Sinet, L. Gasca, L. Martineau, S. Lacroix, X. Daxhelet, F. Gonthier, “Optical add/drop multiplexer based on UV-written Bragg grating in a fused 100% coupler,” Electron. Lett. 33, 803–804 (1997).
[CrossRef]

Snitzer, E.

Storoy, H.

A. Asseh, H. Storoy, J. T. Kringlebotn, W. Margulis, B. Sahlgren, S. Sandgren, R. Stubbe, G. Edwall, “10 cm YB3+ DFB fiber laser with permanent phase-shifted grating,” Electron. Lett. 31, 969–970 (1995).
[CrossRef]

Stubbe, R.

A. Asseh, H. Storoy, J. T. Kringlebotn, W. Margulis, B. Sahlgren, S. Sandgren, R. Stubbe, G. Edwall, “10 cm YB3+ DFB fiber laser with permanent phase-shifted grating,” Electron. Lett. 31, 969–970 (1995).
[CrossRef]

Talbot, H.

H. Talbot, “Facts relating to optical science,” Philos. Mag. 9, 401–407 (1836).

Toledo-Crow, R.

R. Toledo-Crow, J. K. Rogers, F. Seiferth, M. Vaez-Iravani, “Contrast mechanisms and imaging modes in near field optical microscopy,” Ultramicroscopy 57, 293–297 (1995).
[CrossRef]

Vaez-Iravani, M.

R. Toledo-Crow, J. K. Rogers, F. Seiferth, M. Vaez-Iravani, “Contrast mechanisms and imaging modes in near field optical microscopy,” Ultramicroscopy 57, 293–297 (1995).
[CrossRef]

Widdowson, T.

W. H. Loh, R. I. Laming, X. Gu, M. N. Zervas, M. J. Cole, T. Widdowson, A. D. Ellis, “10 cm chirped fibre Bragg gratings for dispersion compensation at 10 Gbit/s over 400 km of non-dispersion shifted fibre,” Electron. Lett. 31, 2203–2204 (1995).
[CrossRef]

Winthrop, J.

Wojcik, G.

G. Wojcik, J. Mould, R. Ferguson, R. Martino, K. K. Low, “Some image modeling issues for I-line, 5× phase shifting masks,” in Optical Laser Microlithography VII, T. A. Brunner, ed., Proc. SPIE2197, 455–465 (1994).
[CrossRef]

Zervas, M. N.

M. J. Cole, W. H. Loh, R. I. Laming, M. N. Zervas, S. Barcelos, “Compensation of imperfect phase mask with moving fiber-scanning beam technique for production of fiber gratings,” Electron. Lett. 31, 1483–1485 (1995).
[CrossRef]

W. H. Loh, R. I. Laming, X. Gu, M. N. Zervas, M. J. Cole, T. Widdowson, A. D. Ellis, “10 cm chirped fibre Bragg gratings for dispersion compensation at 10 Gbit/s over 400 km of non-dispersion shifted fibre,” Electron. Lett. 31, 2203–2204 (1995).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (3)

K. Karrai, R. D. Grober, “Piezoelectric tip-sample distance control for near field optical microscopes,” Appl. Phys. Lett. 66, 1842–1844 (1995).
[CrossRef]

K. O. Hill, Y. Fujii, D. C. Johnson, B. S. Kawasaki, “Photosensitivity in optical fiber waveguides: application to reflection filter fabrication,” Appl. Phys. Lett. 32, 647–649 (1978).
[CrossRef]

K. O. Hill, B. Malo, F. Bilodeau, D. C. Johnson, 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]

Electron. Lett. (5)

P. E. Dyer, R. J. Farley, R. Giedl, K. C. Byron, D. Reid, “High reflectivity fibre gratings produced by incubated damage using a 193 nm ArF laser,” Electron. Lett. 30, 860–862 (1994).
[CrossRef]

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[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Talbot diffraction pattern from a 1-µm period phase mask with an arbitrary phase shift of 1.47 rad. The images are generated by a strong zeroth diffraction order and first order. Both diagrams show a 5 µm × 5 µm area in space, starting at a height of 5 µm above the mask. The phase mask is along the bottom of the picture in each case, and the propagation of light travels from bottom to top. (a) Experimentally measured data. The centers of the high elevations on the phase mask are positioned directly below the centers of the lowest full row of maxima. (b) Numerical calculation of the expected field distribution with scalar Fresnel–Kirchhoff diffraction theory. In both diagrams, the pattern repeat distance is 2.08 µm, which matches our calculated value.

Fig. 2
Fig. 2

Cross sections of Fig. 1 normal to the phase mask, through sets of Talbot maxima, showing a more detailed comparison of the observed data (open circles) with the numerical model (solid curve).

Fig. 3
Fig. 3

Talbot diffraction patterns across the Gaussian beam shape. The three figures are recorded at relative positions (a) 0, (b) 50 µm, and (c) 120 µm toward the edge of the beam and include a strong zeroth diffraction order and first order. With the same experimental parameters as in Fig. 1, the pattern distortions occur because of the increasing rate of change of phase and amplitude of the wave front of the light incident on the phase mask.

Fig. 4
Fig. 4

Scan of a Talbot diffraction pattern with an induced π rad phase shift. (a) Experimentally acquired data with the scan height above the phase mask running from 3.63 to 7.96 µm and with a lateral width of 4.56 µm. (b) Result of a numerical simulation of (a). The images include a suppressed zeroth diffraction order in addition to the first and second orders.

Fig. 5
Fig. 5

(a) Cross sections of Fig. 4 showing a more detailed comparison of the observed data (dashed curve) with the numerical model (solid curve) at a constant height across two of the circular objects. (b) Compares the normalized sum of all the rows of data from Figs. 4(a) and 4(b) within the range of one Talbot length. The observed data (dashed curve) and numerical model (solid curve) were summed from Z T /2 below the line of data shown in Fig. 5(a) to Z T /2 above.

Fig. 6
Fig. 6

Demonstration of the effect of moving away from the phase-mask surface and out of the range of the second diffracted order. (a) A scan that was run from 5.65 to 12.46 µm from the mask surface and includes a suppressed zeroth order in addition to the first and second orders. (b) The same lateral position as (a) but here the probe was raised to allow the scan to run from 53.4 to 60.21 µm above the mask. With no second order present, the beating between the first order and the weak zeroth order becomes apparent. (c) A simple diffraction numerical simulation of (b).

Fig. 7
Fig. 7

Cross sections of Fig. 6(b) and 6(c) showing a more detailed comparison of the observed data (dashed curve) with the numerical model (solid curve) across a row of several vertical fringes at constant height.

Fig. 8
Fig. 8

Effect on the free-space interference pattern when the incident beam is misaligned from normal incidence to the phase mask by (a) +0.01 deg and (b) -0.01 deg. Both scans include the suppressed zeroth, first, and second diffracted orders.

Fig. 9
Fig. 9

(a) Cross sections of the experimental data shown in Figs. 4(a) and 8(b) taken in each case at a height of 4 µm. The line of data from Fig. 4(a) (solid curve) gives two periods of modulation per 1-µm phase-mask period, and the misaligned beam of Fig. 8(b) (dashed curve) has generated three periods. (b) The modulation depths of a normalized sum of the data from Figs. 4(a) (solid curve) and 8(b) (dashed curve) averaged over one Talbot length can vary by up to 40%.

Equations (4)

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ZT=2a2/λ,
Ex, z=m Cm expimGxexpikmz,
km = k2-m2G21/2.
ZTm, n=2π/k2-m2G21/2-k2-n2G21/2,

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