Abstract

It is shown that a recently proposed phase-retrieval technique for Bragg gratings [Opt.  Lett.   22, 93 (1997); J.  Lightwave Technol.    15, 1314 (1997)] is not well suited for gratings with imperfections. The reconstructed group delay is in many cases not a more accurate estimate than the simulated group delay of the perfect, designed grating, independently of how small the errors in the grating structure are. The error in the group delay may be especially large near the zeros in the reflection spectrum.

© 1999 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. M. A. Muriel and A. Carballar, Opt. Lett. 22, 93 (1997).
    [CrossRef] [PubMed]
  2. A. Carballar and M. A. Muriel, J. Lightwave Technol. 15, 1314 (1997).
    [CrossRef]
  3. A. Papoulis, The Fourier Integral and Its Applications (McGraw-Hill, New York, 1962).
  4. H. M. Nussenzveig, Causality and Dispersion Relations (Academic, New York, 1972).
  5. L. Poladian, Opt. Lett. 22, 1571 (1997).
    [CrossRef]
  6. D. Pastor and J. Capmany, Electron. Lett. 34, 1344 (1998).
    [CrossRef]
  7. G. Lenz, B. J. Eggleton, C. R. Giles, C. K. Madsen, and R. E. Slusher, IEEE J. Quantum Electron. 34, 1390 (1998).
    [CrossRef]

1998 (2)

D. Pastor and J. Capmany, Electron. Lett. 34, 1344 (1998).
[CrossRef]

G. Lenz, B. J. Eggleton, C. R. Giles, C. K. Madsen, and R. E. Slusher, IEEE J. Quantum Electron. 34, 1390 (1998).
[CrossRef]

1997 (3)

Capmany, J.

D. Pastor and J. Capmany, Electron. Lett. 34, 1344 (1998).
[CrossRef]

Carballar, A.

M. A. Muriel and A. Carballar, Opt. Lett. 22, 93 (1997).
[CrossRef] [PubMed]

A. Carballar and M. A. Muriel, J. Lightwave Technol. 15, 1314 (1997).
[CrossRef]

Eggleton, B. J.

G. Lenz, B. J. Eggleton, C. R. Giles, C. K. Madsen, and R. E. Slusher, IEEE J. Quantum Electron. 34, 1390 (1998).
[CrossRef]

Giles, C. R.

G. Lenz, B. J. Eggleton, C. R. Giles, C. K. Madsen, and R. E. Slusher, IEEE J. Quantum Electron. 34, 1390 (1998).
[CrossRef]

Lenz, G.

G. Lenz, B. J. Eggleton, C. R. Giles, C. K. Madsen, and R. E. Slusher, IEEE J. Quantum Electron. 34, 1390 (1998).
[CrossRef]

Madsen, C. K.

G. Lenz, B. J. Eggleton, C. R. Giles, C. K. Madsen, and R. E. Slusher, IEEE J. Quantum Electron. 34, 1390 (1998).
[CrossRef]

Muriel, M. A.

A. Carballar and M. A. Muriel, J. Lightwave Technol. 15, 1314 (1997).
[CrossRef]

M. A. Muriel and A. Carballar, Opt. Lett. 22, 93 (1997).
[CrossRef] [PubMed]

Nussenzveig, H. M.

H. M. Nussenzveig, Causality and Dispersion Relations (Academic, New York, 1972).

Papoulis, A.

A. Papoulis, The Fourier Integral and Its Applications (McGraw-Hill, New York, 1962).

Pastor, D.

D. Pastor and J. Capmany, Electron. Lett. 34, 1344 (1998).
[CrossRef]

Poladian, L.

Slusher, R. E.

G. Lenz, B. J. Eggleton, C. R. Giles, C. K. Madsen, and R. E. Slusher, IEEE J. Quantum Electron. 34, 1390 (1998).
[CrossRef]

Electron. Lett. (1)

D. Pastor and J. Capmany, Electron. Lett. 34, 1344 (1998).
[CrossRef]

IEEE J. Quantum Electron. (1)

G. Lenz, B. J. Eggleton, C. R. Giles, C. K. Madsen, and R. E. Slusher, IEEE J. Quantum Electron. 34, 1390 (1998).
[CrossRef]

J. Lightwave Technol. (1)

A. Carballar and M. A. Muriel, J. Lightwave Technol. 15, 1314 (1997).
[CrossRef]

Opt. Lett. (2)

Other (2)

A. Papoulis, The Fourier Integral and Its Applications (McGraw-Hill, New York, 1962).

H. M. Nussenzveig, Causality and Dispersion Relations (Academic, New York, 1972).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

Reflectivity spectrum for the actual grating (solid curve) and the ideal uniform grating (dotted curve).

Fig. 2
Fig. 2

Calculated group delay for the actual grating (solid curve), the reconstructed group delay (dashed curve), and the group delay for the ideal uniform grating (dotted curve).

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

Hs=0htexp-st dt
H˜s=lnHs=lnHs+i arg Hs.
φminω=ωπ-lnHiωω2-ω2dω.
Hmins=Hsσn>0s+sn*s-sn
iω+sn*iω-sn1.
φω=φminω-2σn>0arctanω-ωnσn,
τgω=-dφωdω=τg,minω+2σn>0σnσn2+ω-ωn2.
r2ω=expiar1ω*
τ2ω=-τ1ω,

Metrics