Abstract

Many authors (including this one) have suggested that the problem of synthesizing a grating from its reflection spectrum is significantly more difficult than the direct problem of obtaining the spectrum from the grating. Fortunately, this view is mistaken. One can synthesize a grating from any reflection spectrum by direct solution of the standard coupled-mode equations while simultaneously evaluating a simple integral to obtain the grating strength. This approach has the advantage of being based on a well-understood set of equations, making it amenable to physical interpretation, mathematical approximation, and generalization.

© 2000 Optical Society of America

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Corrections

L. Poladian, "Simple grating synthesis algorithm: errata," Opt. Lett. 25, 1400-1400 (2000)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-25-18-1400

References

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  1. T. Erdogan, J. Lightwave Technol. 15, 1277 (1997).
    [CrossRef]
  2. G.-H. Song and S.-Y. Shin, J. Opt. Soc. Am. A 2, 1905 (1993).
    [CrossRef]
  3. J. E. Roman and K. A. Winick, IEEE J. Quantum Electron. 29, 975 (1993).
    [CrossRef]
  4. L. Poladian, Phys. Rev. E 54, 2963 (1996).
    [CrossRef]
  5. E. Peral, J. Campany, and J. Marti, Electron. Lett. 32, 918 (1996).
    [CrossRef]
  6. M. A. Muriel, J. Azaña, and A. Carballar, in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), pp. 250–251.
  7. R. Feced, M. N. Zervas, and M. A. Muriel, IEEE J. Quantum Electron. 35, 1105 (1999).
    [CrossRef]
  8. L. Poladian, Opt. Lett. 22, 1571 (1997).
    [CrossRef]
  9. L. Poladian, J. Opt. Fiber Technol. 5, 215 (1999).
    [CrossRef]

1999 (2)

R. Feced, M. N. Zervas, and M. A. Muriel, IEEE J. Quantum Electron. 35, 1105 (1999).
[CrossRef]

L. Poladian, J. Opt. Fiber Technol. 5, 215 (1999).
[CrossRef]

1997 (2)

L. Poladian, Opt. Lett. 22, 1571 (1997).
[CrossRef]

T. Erdogan, J. Lightwave Technol. 15, 1277 (1997).
[CrossRef]

1996 (2)

L. Poladian, Phys. Rev. E 54, 2963 (1996).
[CrossRef]

E. Peral, J. Campany, and J. Marti, Electron. Lett. 32, 918 (1996).
[CrossRef]

1993 (2)

G.-H. Song and S.-Y. Shin, J. Opt. Soc. Am. A 2, 1905 (1993).
[CrossRef]

J. E. Roman and K. A. Winick, IEEE J. Quantum Electron. 29, 975 (1993).
[CrossRef]

Azaña, J.

M. A. Muriel, J. Azaña, and A. Carballar, in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), pp. 250–251.

Campany, J.

E. Peral, J. Campany, and J. Marti, Electron. Lett. 32, 918 (1996).
[CrossRef]

Carballar, A.

M. A. Muriel, J. Azaña, and A. Carballar, in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), pp. 250–251.

Erdogan, T.

T. Erdogan, J. Lightwave Technol. 15, 1277 (1997).
[CrossRef]

Feced, R.

R. Feced, M. N. Zervas, and M. A. Muriel, IEEE J. Quantum Electron. 35, 1105 (1999).
[CrossRef]

Marti, J.

E. Peral, J. Campany, and J. Marti, Electron. Lett. 32, 918 (1996).
[CrossRef]

Muriel, M. A.

R. Feced, M. N. Zervas, and M. A. Muriel, IEEE J. Quantum Electron. 35, 1105 (1999).
[CrossRef]

M. A. Muriel, J. Azaña, and A. Carballar, in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), pp. 250–251.

Peral, E.

E. Peral, J. Campany, and J. Marti, Electron. Lett. 32, 918 (1996).
[CrossRef]

Poladian, L.

L. Poladian, J. Opt. Fiber Technol. 5, 215 (1999).
[CrossRef]

L. Poladian, Opt. Lett. 22, 1571 (1997).
[CrossRef]

L. Poladian, Phys. Rev. E 54, 2963 (1996).
[CrossRef]

Roman, J. E.

J. E. Roman and K. A. Winick, IEEE J. Quantum Electron. 29, 975 (1993).
[CrossRef]

Shin, S.-Y.

Song, G.-H.

Winick, K. A.

J. E. Roman and K. A. Winick, IEEE J. Quantum Electron. 29, 975 (1993).
[CrossRef]

Zervas, M. N.

R. Feced, M. N. Zervas, and M. A. Muriel, IEEE J. Quantum Electron. 35, 1105 (1999).
[CrossRef]

Electron. Lett. (1)

E. Peral, J. Campany, and J. Marti, Electron. Lett. 32, 918 (1996).
[CrossRef]

IEEE J. Quantum Electron. (2)

R. Feced, M. N. Zervas, and M. A. Muriel, IEEE J. Quantum Electron. 35, 1105 (1999).
[CrossRef]

J. E. Roman and K. A. Winick, IEEE J. Quantum Electron. 29, 975 (1993).
[CrossRef]

J. Lightwave Technol. (1)

T. Erdogan, J. Lightwave Technol. 15, 1277 (1997).
[CrossRef]

J. Opt. Fiber Technol. (1)

L. Poladian, J. Opt. Fiber Technol. 5, 215 (1999).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Lett. (1)

Phys. Rev. E (1)

L. Poladian, Phys. Rev. E 54, 2963 (1996).
[CrossRef]

Other (1)

M. A. Muriel, J. Azaña, and A. Carballar, in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), pp. 250–251.

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Figures (6)

Fig. 1
Fig. 1

Comparison of the target spectrum (dashed curve and dashed line) and the achieved spectrum (solid curves) for the zero-dispersion design, showing reflectance and dispersion. Note that the dispersion is displayed only over the bandwidth at which the reflection is significant >-20 dB.

Fig. 2
Fig. 2

Comparison of target (dashed line) and achieved (solid curve) dispersion for a target design with constant dispersion of 40 ps/nm over the bandwidth at which the reflection is significant >-20 dB. The results of the comparison are essentially the same for the spectral amplitude as for the zero-dispersion case.

Fig. 3
Fig. 3

Core index-modulation profile of the grating design required for the spectrum in Eq. (5) to be obtained. The grating is unchirped, with a period of 538.2 µm.

Fig. 4
Fig. 4

Core index-modulation profile (solid curve) and average dc index profile (dashed curve) for the constant-dispersion grating design corresponding to the target spectrum in Fig. 2. In addition to the dc profile, the grating period is chirped from 537.95 µm at z=0 to 538.2 µm at z=L.

Fig. 5
Fig. 5

Partial reflectance spectra at z=0, 1, 2, 3 cm obtained during the synthesis procedure.

Fig. 6
Fig. 6

Fourier transforms of the z=0 cm and z=3 cm partial reflectance spectra in Fig. 5. In the absence of numerical error, the final spectrum should still be causal (i.e., zero for negative time).

Equations (6)

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ddzuz,δ=iδuz,δ+iqzvz,δ,
ddzvz,δ=-iδvz,δ-iq*zuz,δ,
rδ=v0,δu0,δ.
rz,δ=vz,δuz,δ,
qz=iπ-r*z,δdδ,
rδ=0.99exp-δ2/200expiϕδ,

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