Abstract

We use a planar linear grating with varied line-space grooves to introduce a tailored one-dimensional phase variation profile that results in an aberrated point-spread function at the focal plane. A design procedure for the period chirp map for such gratings is developed. As an example, we present theoretical and experimental results on a mechanically ruled, varied line-space echelle grating in single-mode fiber-coupled optical multiplexers in the wavelength region of 1545  nm. The varied line-space grating changes the multiplexer's Gaussian spectral response function to a flat-top dependence with reduced sensitivity to source laser wavelength drift.

© 2007 Optical Society of America

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References

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  1. E. G. Loewen and E. Popov, Diffraction Gratings and Applications (Marcel Dekker, 1997).
  2. K. Kudo, "Optical properties of plane-grating monochromator," J. Opt. Soc. Am. 55, 150-161 (1965).
    [CrossRef]
  3. M. V. R. K. Murty, "Theory and principles of monochromators, spectrometers, and spectrographs," Opt. Eng. 13, 23-39 (1974).
  4. J. P. Schwenker, "Astigmatism-corrected gratings for plane grating-spherical mirror spectrographs," Appl. Opt. 31, 6102-6010 (1992).
    [CrossRef] [PubMed]
  5. C. Palmer and W. R. McKinney, "Equivalence of focusing conditions for holographic and varied line-space grating systems," Appl. Opt. 29, 47-51 (1990).
    [CrossRef] [PubMed]
  6. M. C. Hettrick and S. Bowyer, "Variable line-space gratings: new designs for use in grazing incidence spectrometers," Appl. Opt. 22, 3921-3924 (1983).
    [CrossRef] [PubMed]
  7. M. C. Hettrick, "Aberrations of varied line-space grazing incidence gratings in a converging light beam," Appl. Opt. 23, 3221-3235 (1984).
    [CrossRef] [PubMed]
  8. M. Itou, T. Harada, and T. Kita, "Soft x-ray monochromators with a varied-space plane grating for synchrotron radiation: design and evaluation," Appl. Opt. 28, 146-153 (1989).
    [CrossRef] [PubMed]
  9. C. Palmer and W. R. McKinney, "Imaging theory of plane-symmetric varied line-space grating systems," Opt. Eng. 33, 820-829 (1994).
    [CrossRef]
  10. M. Bissen, M. Fisher, and G. Rogers, "Comparison of blazed and laminar profile varied line spacing gratings," in Gratings and Grating Monochromators for Synchrotron Radiation, W. R. McKinney and C. A. Palmer, eds., Proc. SPIE 3150, 130-136 (1997).
    [CrossRef]
  11. M. Koike and T. Namioka, "Plane gratings for high-resolution grazing-incidence monochromators: holographic grating versus mechanically ruled varied-line-spacing grating," Appl. Opt. 36, 6308-6318 (1997).
    [CrossRef]
  12. T. Kita and T. Harada, "Ruling engine using a piezoelectric device for large and high-groove density gratings," Appl. Opt. 31, 1399-1406 (1992).
    [CrossRef] [PubMed]
  13. C. G. Chen, P. T. Konkola, R. K. Heilmann, C. Joo, and M. L. Schattenburg, "Nanometer-accurate grating fabrication with scanning beam interference lithography," in Nano- and Microtechnology: Materials, Processes, Packaging, and Systems, D. K. Sood, A. P. Malshe, and R. Maeda, eds., Proc. SPIE 4936, 126-134 (2002).
    [CrossRef]
  14. Y. Xie, X. Xu, Y. Hong, Y. Liu, S. Fu, S. He, and B. Jin, "Fabrication of varied-line-spacing grating by elastic medium," Opt. Express 12, 3894-3899 (2004).
    [CrossRef] [PubMed]
  15. A. D. Sappey, P. Huang, R. Harr, and G. Murphy, "Echelle grating dense wavelength division multiplexer/demultiplexer," U.S. patent 6,647,182 B2 (11 November 2003).
  16. A. D. Sappey and B. W. Bach, "Apparatus and method for the reduction of polarization sensitivity in diffraction gratings used in fiber optic communications devices," U.S. patent 6,400,509 (4 June 2002).
  17. W. T. Cathey and E. Dowski, "New paradigm for imaging systems," Appl. Opt. 41, 6080-6092 (2002).
    [CrossRef] [PubMed]
  18. S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, "Engineering the pupil phase to improve image quality," in Visual Information Processing XII, Z. Rahman, R. A. Schowengerdt, and S. E. Reichenbach, eds., Proc. SPIE 5108, 1-12 (2003).
  19. R. E. Wagner and W. J. Tomlinson, "Coupling efficiency of optics in single-mode fiber components," Appl. Opt. 21, 2671-2688 (1982).
    [CrossRef] [PubMed]
  20. R. W. Gerchburg and W. O. Saxton, "A practical algorithm for determination of phase from image and diffraction plane pictures," Optik 53, 237-246 (1972).
  21. J. R. Fienup, "Phase retrieval algorithms: a comparison," Appl. Opt. 21, 2758-2769 (1982).
    [CrossRef] [PubMed]
  22. F. Wyrowski, "Diffractive optical elements: iterative calculation of quantized, blazed phase structures," J. Opt. Soc. Am. A 7, 961-969 (1990).
    [CrossRef]
  23. K. Okamoto and H. Yamada, "Arrayed-waveguide grating multiplexer with flat spectral response," Opt. Lett. 20, 43-45 (1995).
    [CrossRef] [PubMed]
  24. D. M. Trouchet, "Multiplexer/demultiplexer with flattened spectral response," U.S. patent 6,141,152 (31 October 2002).
  25. T. Kamalakis and T. Sphicopoulos, "An efficient technique for the design of an array-waveguide grating with flat spectral response," J. Lightwave Technol. 19, 1716-1725 (2001).
    [CrossRef]
  26. G. G. Cappiello and R. H. Dueck, "Wavelength division multiplexing/demultiplexing devices employing patterned optical components," U.S. patent 6,415,073 B1 (2 July 2002).
  27. P. Huang and S. Spuler, "Apparatus and method for producing a flat-topped filter response for (de)multiplexer having a diffraction grating with variable line spacing," U.S. patent 6,754,412 B2 (22 June 2004).

2004

2002

W. T. Cathey and E. Dowski, "New paradigm for imaging systems," Appl. Opt. 41, 6080-6092 (2002).
[CrossRef] [PubMed]

C. G. Chen, P. T. Konkola, R. K. Heilmann, C. Joo, and M. L. Schattenburg, "Nanometer-accurate grating fabrication with scanning beam interference lithography," in Nano- and Microtechnology: Materials, Processes, Packaging, and Systems, D. K. Sood, A. P. Malshe, and R. Maeda, eds., Proc. SPIE 4936, 126-134 (2002).
[CrossRef]

2001

1997

M. Bissen, M. Fisher, and G. Rogers, "Comparison of blazed and laminar profile varied line spacing gratings," in Gratings and Grating Monochromators for Synchrotron Radiation, W. R. McKinney and C. A. Palmer, eds., Proc. SPIE 3150, 130-136 (1997).
[CrossRef]

M. Koike and T. Namioka, "Plane gratings for high-resolution grazing-incidence monochromators: holographic grating versus mechanically ruled varied-line-spacing grating," Appl. Opt. 36, 6308-6318 (1997).
[CrossRef]

1995

1994

C. Palmer and W. R. McKinney, "Imaging theory of plane-symmetric varied line-space grating systems," Opt. Eng. 33, 820-829 (1994).
[CrossRef]

1992

1990

1989

1984

1983

1982

1974

M. V. R. K. Murty, "Theory and principles of monochromators, spectrometers, and spectrographs," Opt. Eng. 13, 23-39 (1974).

1972

R. W. Gerchburg and W. O. Saxton, "A practical algorithm for determination of phase from image and diffraction plane pictures," Optik 53, 237-246 (1972).

1965

Bach, B. W.

A. D. Sappey and B. W. Bach, "Apparatus and method for the reduction of polarization sensitivity in diffraction gratings used in fiber optic communications devices," U.S. patent 6,400,509 (4 June 2002).

Bissen, M.

M. Bissen, M. Fisher, and G. Rogers, "Comparison of blazed and laminar profile varied line spacing gratings," in Gratings and Grating Monochromators for Synchrotron Radiation, W. R. McKinney and C. A. Palmer, eds., Proc. SPIE 3150, 130-136 (1997).
[CrossRef]

Bowyer, S.

Cappiello, G. G.

G. G. Cappiello and R. H. Dueck, "Wavelength division multiplexing/demultiplexing devices employing patterned optical components," U.S. patent 6,415,073 B1 (2 July 2002).

Cathey, W. T.

Chen, C. G.

C. G. Chen, P. T. Konkola, R. K. Heilmann, C. Joo, and M. L. Schattenburg, "Nanometer-accurate grating fabrication with scanning beam interference lithography," in Nano- and Microtechnology: Materials, Processes, Packaging, and Systems, D. K. Sood, A. P. Malshe, and R. Maeda, eds., Proc. SPIE 4936, 126-134 (2002).
[CrossRef]

Dowski, E.

Dueck, R. H.

G. G. Cappiello and R. H. Dueck, "Wavelength division multiplexing/demultiplexing devices employing patterned optical components," U.S. patent 6,415,073 B1 (2 July 2002).

Fienup, J. R.

Fisher, M.

M. Bissen, M. Fisher, and G. Rogers, "Comparison of blazed and laminar profile varied line spacing gratings," in Gratings and Grating Monochromators for Synchrotron Radiation, W. R. McKinney and C. A. Palmer, eds., Proc. SPIE 3150, 130-136 (1997).
[CrossRef]

Fu, S.

Gerchburg, R. W.

R. W. Gerchburg and W. O. Saxton, "A practical algorithm for determination of phase from image and diffraction plane pictures," Optik 53, 237-246 (1972).

Harada, T.

Harr, R.

A. D. Sappey, P. Huang, R. Harr, and G. Murphy, "Echelle grating dense wavelength division multiplexer/demultiplexer," U.S. patent 6,647,182 B2 (11 November 2003).

He, S.

Heilmann, R. K.

C. G. Chen, P. T. Konkola, R. K. Heilmann, C. Joo, and M. L. Schattenburg, "Nanometer-accurate grating fabrication with scanning beam interference lithography," in Nano- and Microtechnology: Materials, Processes, Packaging, and Systems, D. K. Sood, A. P. Malshe, and R. Maeda, eds., Proc. SPIE 4936, 126-134 (2002).
[CrossRef]

Hettrick, M. C.

Hong, Y.

Huang, P.

A. D. Sappey, P. Huang, R. Harr, and G. Murphy, "Echelle grating dense wavelength division multiplexer/demultiplexer," U.S. patent 6,647,182 B2 (11 November 2003).

P. Huang and S. Spuler, "Apparatus and method for producing a flat-topped filter response for (de)multiplexer having a diffraction grating with variable line spacing," U.S. patent 6,754,412 B2 (22 June 2004).

Itou, M.

Joo, C.

C. G. Chen, P. T. Konkola, R. K. Heilmann, C. Joo, and M. L. Schattenburg, "Nanometer-accurate grating fabrication with scanning beam interference lithography," in Nano- and Microtechnology: Materials, Processes, Packaging, and Systems, D. K. Sood, A. P. Malshe, and R. Maeda, eds., Proc. SPIE 4936, 126-134 (2002).
[CrossRef]

Kamalakis, T.

Kita, T.

Koike, M.

Konkola, P. T.

C. G. Chen, P. T. Konkola, R. K. Heilmann, C. Joo, and M. L. Schattenburg, "Nanometer-accurate grating fabrication with scanning beam interference lithography," in Nano- and Microtechnology: Materials, Processes, Packaging, and Systems, D. K. Sood, A. P. Malshe, and R. Maeda, eds., Proc. SPIE 4936, 126-134 (2002).
[CrossRef]

Kudo, K.

Liu, Y.

Loewen, E. G.

E. G. Loewen and E. Popov, Diffraction Gratings and Applications (Marcel Dekker, 1997).

McKinney, W. R.

C. Palmer and W. R. McKinney, "Imaging theory of plane-symmetric varied line-space grating systems," Opt. Eng. 33, 820-829 (1994).
[CrossRef]

C. Palmer and W. R. McKinney, "Equivalence of focusing conditions for holographic and varied line-space grating systems," Appl. Opt. 29, 47-51 (1990).
[CrossRef] [PubMed]

Murphy, G.

A. D. Sappey, P. Huang, R. Harr, and G. Murphy, "Echelle grating dense wavelength division multiplexer/demultiplexer," U.S. patent 6,647,182 B2 (11 November 2003).

Murty, M. V. R. K.

M. V. R. K. Murty, "Theory and principles of monochromators, spectrometers, and spectrographs," Opt. Eng. 13, 23-39 (1974).

Namioka, T.

Okamoto, K.

Palmer, C.

C. Palmer and W. R. McKinney, "Imaging theory of plane-symmetric varied line-space grating systems," Opt. Eng. 33, 820-829 (1994).
[CrossRef]

C. Palmer and W. R. McKinney, "Equivalence of focusing conditions for holographic and varied line-space grating systems," Appl. Opt. 29, 47-51 (1990).
[CrossRef] [PubMed]

Pauca, V. P.

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, "Engineering the pupil phase to improve image quality," in Visual Information Processing XII, Z. Rahman, R. A. Schowengerdt, and S. E. Reichenbach, eds., Proc. SPIE 5108, 1-12 (2003).

Plemmons, R. J.

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, "Engineering the pupil phase to improve image quality," in Visual Information Processing XII, Z. Rahman, R. A. Schowengerdt, and S. E. Reichenbach, eds., Proc. SPIE 5108, 1-12 (2003).

Popov, E.

E. G. Loewen and E. Popov, Diffraction Gratings and Applications (Marcel Dekker, 1997).

Prasad, S.

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, "Engineering the pupil phase to improve image quality," in Visual Information Processing XII, Z. Rahman, R. A. Schowengerdt, and S. E. Reichenbach, eds., Proc. SPIE 5108, 1-12 (2003).

Rogers, G.

M. Bissen, M. Fisher, and G. Rogers, "Comparison of blazed and laminar profile varied line spacing gratings," in Gratings and Grating Monochromators for Synchrotron Radiation, W. R. McKinney and C. A. Palmer, eds., Proc. SPIE 3150, 130-136 (1997).
[CrossRef]

Sappey, A. D.

A. D. Sappey, P. Huang, R. Harr, and G. Murphy, "Echelle grating dense wavelength division multiplexer/demultiplexer," U.S. patent 6,647,182 B2 (11 November 2003).

A. D. Sappey and B. W. Bach, "Apparatus and method for the reduction of polarization sensitivity in diffraction gratings used in fiber optic communications devices," U.S. patent 6,400,509 (4 June 2002).

Saxton, W. O.

R. W. Gerchburg and W. O. Saxton, "A practical algorithm for determination of phase from image and diffraction plane pictures," Optik 53, 237-246 (1972).

Schattenburg, M. L.

C. G. Chen, P. T. Konkola, R. K. Heilmann, C. Joo, and M. L. Schattenburg, "Nanometer-accurate grating fabrication with scanning beam interference lithography," in Nano- and Microtechnology: Materials, Processes, Packaging, and Systems, D. K. Sood, A. P. Malshe, and R. Maeda, eds., Proc. SPIE 4936, 126-134 (2002).
[CrossRef]

Schwenker, J. P.

Sphicopoulos, T.

Spuler, S.

P. Huang and S. Spuler, "Apparatus and method for producing a flat-topped filter response for (de)multiplexer having a diffraction grating with variable line spacing," U.S. patent 6,754,412 B2 (22 June 2004).

Tomlinson, W. J.

Torgersen, T. C.

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, "Engineering the pupil phase to improve image quality," in Visual Information Processing XII, Z. Rahman, R. A. Schowengerdt, and S. E. Reichenbach, eds., Proc. SPIE 5108, 1-12 (2003).

Trouchet, D. M.

D. M. Trouchet, "Multiplexer/demultiplexer with flattened spectral response," U.S. patent 6,141,152 (31 October 2002).

van der Gracht, J.

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, "Engineering the pupil phase to improve image quality," in Visual Information Processing XII, Z. Rahman, R. A. Schowengerdt, and S. E. Reichenbach, eds., Proc. SPIE 5108, 1-12 (2003).

Wagner, R. E.

Wyrowski, F.

Xie, Y.

Xu, X.

Yamada, H.

Appl. Opt.

J. P. Schwenker, "Astigmatism-corrected gratings for plane grating-spherical mirror spectrographs," Appl. Opt. 31, 6102-6010 (1992).
[CrossRef] [PubMed]

C. Palmer and W. R. McKinney, "Equivalence of focusing conditions for holographic and varied line-space grating systems," Appl. Opt. 29, 47-51 (1990).
[CrossRef] [PubMed]

M. C. Hettrick and S. Bowyer, "Variable line-space gratings: new designs for use in grazing incidence spectrometers," Appl. Opt. 22, 3921-3924 (1983).
[CrossRef] [PubMed]

M. C. Hettrick, "Aberrations of varied line-space grazing incidence gratings in a converging light beam," Appl. Opt. 23, 3221-3235 (1984).
[CrossRef] [PubMed]

M. Itou, T. Harada, and T. Kita, "Soft x-ray monochromators with a varied-space plane grating for synchrotron radiation: design and evaluation," Appl. Opt. 28, 146-153 (1989).
[CrossRef] [PubMed]

M. Koike and T. Namioka, "Plane gratings for high-resolution grazing-incidence monochromators: holographic grating versus mechanically ruled varied-line-spacing grating," Appl. Opt. 36, 6308-6318 (1997).
[CrossRef]

T. Kita and T. Harada, "Ruling engine using a piezoelectric device for large and high-groove density gratings," Appl. Opt. 31, 1399-1406 (1992).
[CrossRef] [PubMed]

W. T. Cathey and E. Dowski, "New paradigm for imaging systems," Appl. Opt. 41, 6080-6092 (2002).
[CrossRef] [PubMed]

J. R. Fienup, "Phase retrieval algorithms: a comparison," Appl. Opt. 21, 2758-2769 (1982).
[CrossRef] [PubMed]

R. E. Wagner and W. J. Tomlinson, "Coupling efficiency of optics in single-mode fiber components," Appl. Opt. 21, 2671-2688 (1982).
[CrossRef] [PubMed]

J. Lightwave Technol.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Eng.

M. V. R. K. Murty, "Theory and principles of monochromators, spectrometers, and spectrographs," Opt. Eng. 13, 23-39 (1974).

C. Palmer and W. R. McKinney, "Imaging theory of plane-symmetric varied line-space grating systems," Opt. Eng. 33, 820-829 (1994).
[CrossRef]

Opt. Express

Opt. Lett.

Optik

R. W. Gerchburg and W. O. Saxton, "A practical algorithm for determination of phase from image and diffraction plane pictures," Optik 53, 237-246 (1972).

Proc. SPIE

M. Bissen, M. Fisher, and G. Rogers, "Comparison of blazed and laminar profile varied line spacing gratings," in Gratings and Grating Monochromators for Synchrotron Radiation, W. R. McKinney and C. A. Palmer, eds., Proc. SPIE 3150, 130-136 (1997).
[CrossRef]

C. G. Chen, P. T. Konkola, R. K. Heilmann, C. Joo, and M. L. Schattenburg, "Nanometer-accurate grating fabrication with scanning beam interference lithography," in Nano- and Microtechnology: Materials, Processes, Packaging, and Systems, D. K. Sood, A. P. Malshe, and R. Maeda, eds., Proc. SPIE 4936, 126-134 (2002).
[CrossRef]

Other

D. M. Trouchet, "Multiplexer/demultiplexer with flattened spectral response," U.S. patent 6,141,152 (31 October 2002).

A. D. Sappey, P. Huang, R. Harr, and G. Murphy, "Echelle grating dense wavelength division multiplexer/demultiplexer," U.S. patent 6,647,182 B2 (11 November 2003).

A. D. Sappey and B. W. Bach, "Apparatus and method for the reduction of polarization sensitivity in diffraction gratings used in fiber optic communications devices," U.S. patent 6,400,509 (4 June 2002).

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, "Engineering the pupil phase to improve image quality," in Visual Information Processing XII, Z. Rahman, R. A. Schowengerdt, and S. E. Reichenbach, eds., Proc. SPIE 5108, 1-12 (2003).

G. G. Cappiello and R. H. Dueck, "Wavelength division multiplexing/demultiplexing devices employing patterned optical components," U.S. patent 6,415,073 B1 (2 July 2002).

P. Huang and S. Spuler, "Apparatus and method for producing a flat-topped filter response for (de)multiplexer having a diffraction grating with variable line spacing," U.S. patent 6,754,412 B2 (22 June 2004).

E. G. Loewen and E. Popov, Diffraction Gratings and Applications (Marcel Dekker, 1997).

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Figures (7)

Fig. 1
Fig. 1

One-dimensional wavefront phase variation from a VLS grating.

Fig. 2
Fig. 2

SMF-coupled, telecentric multiplexer–demultiplexer with echelle grating in the Littrow mount (two wavelengths channels λ 1 < λ 2 are shown).

Fig. 3
Fig. 3

Measured filter SRF from a ULS grating (in logarithmic decibel scale) and predicted Gaussian passband for a single fiber channel centered near 1543.7   nm ( 194 .2   THz on the International Telecommunication Union DWDM frequency grid). The predicted passband curve is shifted both in wavelength and amplitude to coincide with the measured passband at the passband peak.

Fig. 4
Fig. 4

Intensity contour of the target PSF of the flattop VLS multiplexer–demultiplexer.

Fig. 5
Fig. 5

(a) Normalized phase variation profile and (b) VLS period chirp map across the grating clear aperture in the dispersion direction.

Fig. 6
Fig. 6

Measured filter SRF from the VLS grating and predicted flattop passband for the channel centered near 1543.7 n m . The predicted passband curve is shifted both in wavelength and amplitude to coincide with the measured passband at the passband peak.

Fig. 7
Fig. 7

Measured filter SRFs of twelve 100- GHz -spaced channels with the prototype VLS grating multiplexer–demultiplexer. Only the main passbands are shown for clarity.

Tables (1)

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Table 1 Specifications of the Echelle Grating Optical Multiplexer and Demultiplexer

Equations (2)

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OPD = n d 0 ( sin θ λ sin θ i ) = m λ
Δ ϕ ( y g ) Δ y g = 2 π λ n [ d ( y g ) d 0 ] d ( y g ) ( sin θ λ sin θ i ) , = 2 π m d 0 Δ d ( y g ) d ( y g ) 2 π m d 0 2 Δ d ( y g ) ,

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