Abstract

The design of wavelength-division-multiplexed (WDM) filters requires control of both the attributes of the filter within the reflection band and the filter’s effects on adjacent bands. Causality arguments are used to give the minimum dispersion that can be achieved in the transmission of an adjacent channel in terms of the bandwidth, sidelobe suppression, and channel spacing of WDM filters. The ripple in the side-channel dispersion is also related to the sidelobe properties. Results for a synthesized grating design and its calculated spectrum are compared with the theoretical limits on dispersion.

© 2001 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. J. Eggleton, G. Lenz, N. Lichinister, D. B. Patterson, and R. E. Slusher, IEEE Photon. Technol. Lett. 9, 1403 (1997).
    [CrossRef]
  2. G. Lenz, B. J. Eggleton, C. R. Riles, C. K. Madsen, and R. E. Slusher, IEEE J. Quantum. Electron. 34, 1390 (1998).
    [CrossRef]
  3. M. Kuznetsov, N. M. Froberg, S. R. Henion, and K. A. Rauschenbach, IEEE Photon. Technol. Lett. 11, 1411 (1999).
    [CrossRef]
  4. L. Poladian, Opt. Lett. 22, 1571 (1997).
    [CrossRef]
  5. L. Poladian, Opt. Lett. 25, 787 (2000).
    [CrossRef]

2000 (1)

1999 (1)

M. Kuznetsov, N. M. Froberg, S. R. Henion, and K. A. Rauschenbach, IEEE Photon. Technol. Lett. 11, 1411 (1999).
[CrossRef]

1998 (1)

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

1997 (2)

B. J. Eggleton, G. Lenz, N. Lichinister, D. B. Patterson, and R. E. Slusher, IEEE Photon. Technol. Lett. 9, 1403 (1997).
[CrossRef]

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

Eggleton, B. J.

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

B. J. Eggleton, G. Lenz, N. Lichinister, D. B. Patterson, and R. E. Slusher, IEEE Photon. Technol. Lett. 9, 1403 (1997).
[CrossRef]

Froberg, N. M.

M. Kuznetsov, N. M. Froberg, S. R. Henion, and K. A. Rauschenbach, IEEE Photon. Technol. Lett. 11, 1411 (1999).
[CrossRef]

Henion, S. R.

M. Kuznetsov, N. M. Froberg, S. R. Henion, and K. A. Rauschenbach, IEEE Photon. Technol. Lett. 11, 1411 (1999).
[CrossRef]

Kuznetsov, M.

M. Kuznetsov, N. M. Froberg, S. R. Henion, and K. A. Rauschenbach, IEEE Photon. Technol. Lett. 11, 1411 (1999).
[CrossRef]

Lenz, G.

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

B. J. Eggleton, G. Lenz, N. Lichinister, D. B. Patterson, and R. E. Slusher, IEEE Photon. Technol. Lett. 9, 1403 (1997).
[CrossRef]

Lichinister, N.

B. J. Eggleton, G. Lenz, N. Lichinister, D. B. Patterson, and R. E. Slusher, IEEE Photon. Technol. Lett. 9, 1403 (1997).
[CrossRef]

Madsen, C. K.

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

Patterson, D. B.

B. J. Eggleton, G. Lenz, N. Lichinister, D. B. Patterson, and R. E. Slusher, IEEE Photon. Technol. Lett. 9, 1403 (1997).
[CrossRef]

Poladian, L.

Rauschenbach, K. A.

M. Kuznetsov, N. M. Froberg, S. R. Henion, and K. A. Rauschenbach, IEEE Photon. Technol. Lett. 11, 1411 (1999).
[CrossRef]

Riles, C. R.

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

Slusher, R. E.

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

B. J. Eggleton, G. Lenz, N. Lichinister, D. B. Patterson, and R. E. Slusher, IEEE Photon. Technol. Lett. 9, 1403 (1997).
[CrossRef]

IEEE J. Quantum. Electron. (1)

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

IEEE Photon. Technol. Lett. (2)

M. Kuznetsov, N. M. Froberg, S. R. Henion, and K. A. Rauschenbach, IEEE Photon. Technol. Lett. 11, 1411 (1999).
[CrossRef]

B. J. Eggleton, G. Lenz, N. Lichinister, D. B. Patterson, and R. E. Slusher, IEEE Photon. Technol. Lett. 9, 1403 (1997).
[CrossRef]

Opt. Lett. (2)

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 (6)

Fig. 1
Fig. 1

Schematic of a WDM filter shape showing the relevant parameters. The channel spacing is Δωsep=ωs-ωL, the guard bandwidth is Δωguard=ωS-ωR, and the sidelobes have a typical size ΔT.

Fig. 2
Fig. 2

Dispersion limits given by Eq.  (5) for various channel spacings as a function of the guard-band-to-channel spacing ratio, Δωguard/Δωsep. The solid curves are for a -20dB filter, and the dashed curves are for a -30dB filter.

Fig. 3
Fig. 3

Asymmetric quasi-sinc-apodized grating designed as a WDM filter for a 100-GHz channel spacing.

Fig. 4
Fig. 4

Transmission spectrum of the grating shown in Fig.  3. The dashed curve is a piecewise linear filter shape approximating the actual spectrum.

Fig. 5
Fig. 5

The thick solid curve shows the dispersion in transmission for the grating shown in Fig.  3. The dotted curve shows the minimum dispersion limit. The dashed curve gives the dispersion for the linear approximation. The thin solid curve gives the spline approximation.

Fig. 6
Fig. 6

Closeup of the spectrum in Fig.  4, showing the ripples in the transmission of the adjacent side channel.

Equations (12)

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

τω=-12πP-dωω-ωlnTωω,
τω=-12π-ωSdωω-ωlnTωω-12πPωSdωω-ωlnTωω.
τminω=-12π-ωLωRdωω-ω2lnT0=-lnT02π1ω-ωR-1ω-ωL.
Dminω=-lnT04π2cω2ω-ωR2-ω2ω-ωL2.
DminωS=-lnT04π2cωS2Δωguard2-ωS2Δωsep2,
lnTω=lnT0ω-ωSωR-ωS,ωR<ω<ωS.
Dlinearω=-lnT04π2cω2ω-ωSω-ωR-ω2ω-ωL2.
lnTω=lnT03ω-ωSωR-ωS2-2ω-ωSωR-ωS3.
Dsplineω=-lnT04π2c62ω-ωS-ωRω2ωS-ωR3×lnω-ωRω-ωS-12ω2ωS-ωR2-ω2ω-ωL2.
TdBω=ΔTdBsin2πωΩ,
τrippleω=ln1010πΩΔTdBcos2πωΩ,
Drippleω=ln1010πcω2Ω2ΔTdBsin2πωΩ.

Metrics