Abstract

We report on the characterization of single-mode and multimode proton-exchanged periodically segmented waveguides in lithium niobate. Variation of effective indices of different modes for different annealing times as a function of duty cycle and period of segmentation is presented. It is shown that the proton-exchanged periodically segmented waveguide can be modeled by an equivalent z-invariant depth-independent graded-index waveguide with a Gaussian index distribution. Although the depth of the equivalent waveguide is independent of duty cycle, the peak refractive-index change increases almost linearly with the duty cycle and saturates at large duty cycles. The results should benefit the design of linear and nonlinear devices that are based on segmented waveguides.

© 1994 Optical Society of America

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  1. J. D. Bierlien, D. B. Laubacher, J. B. Brown, C. J. van der Poel, Appl. Phys. Lett. 56, 1725 (1990).
    [CrossRef]
  2. C. J. Van der Poel, J. D. Bierlien, J. B. Brown, Appl. Phys. Lett. 57, 2074 (1990).
    [CrossRef]
  3. S. Makio, F. Nitanda, K. Ito, M. Sato, in Conference on Lasers and Electro-Optics, Vol. 11 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 270.
  4. F. Laurell, J. B. Brown, J. D. Bierlien, Appl. Phys. Lett. 62, 1872 (1993).
    [CrossRef]
  5. L. Li, J. J. Burke, Opt. Lett. 17, 1195 (1992).
    [CrossRef] [PubMed]
  6. Z. Weissman, A. Hardy, Electron. Lett. 28, 1514 (1992).
    [CrossRef]
  7. D. Eger, M. Oron, M. Katz, J. Appl. Phys. 74, 4298 (1993).
    [CrossRef]
  8. A. Loni, R. M. De Lu Rue, Appl. Opt. 31, 5096 (1992).
    [CrossRef] [PubMed]
  9. S. T. Vohra, A. R. Mickelson, S. E. Asher, J. Appl. Phys. 66, 5161 (1989).
    [CrossRef]
  10. X. F. Cao, R. V. Ramaswamy, R. Srivastava, J. Lightwave Technol. 10, 1302 (1992).
    [CrossRef]
  11. N. Goto, G. L. Yip, Appl. Opt. 28, 60 (1989).
    [CrossRef] [PubMed]
  12. J. M. Zavada, H. C. Casey, C.-H. Chen, A. Loni, Appl. Phys. Lett. 62, 2769 (1993).
    [CrossRef]
  13. J. Nikolopoulos, G. L. Yip, J. Lightwave Technol. 9, 864 (1991).
    [CrossRef]
  14. P. Suchoski, R. V. Ramaswamy, J. Lightwave Technol. 5, 1246 (1987).
    [CrossRef]

1993

F. Laurell, J. B. Brown, J. D. Bierlien, Appl. Phys. Lett. 62, 1872 (1993).
[CrossRef]

D. Eger, M. Oron, M. Katz, J. Appl. Phys. 74, 4298 (1993).
[CrossRef]

J. M. Zavada, H. C. Casey, C.-H. Chen, A. Loni, Appl. Phys. Lett. 62, 2769 (1993).
[CrossRef]

1992

A. Loni, R. M. De Lu Rue, Appl. Opt. 31, 5096 (1992).
[CrossRef] [PubMed]

X. F. Cao, R. V. Ramaswamy, R. Srivastava, J. Lightwave Technol. 10, 1302 (1992).
[CrossRef]

L. Li, J. J. Burke, Opt. Lett. 17, 1195 (1992).
[CrossRef] [PubMed]

Z. Weissman, A. Hardy, Electron. Lett. 28, 1514 (1992).
[CrossRef]

1991

J. Nikolopoulos, G. L. Yip, J. Lightwave Technol. 9, 864 (1991).
[CrossRef]

1990

J. D. Bierlien, D. B. Laubacher, J. B. Brown, C. J. van der Poel, Appl. Phys. Lett. 56, 1725 (1990).
[CrossRef]

C. J. Van der Poel, J. D. Bierlien, J. B. Brown, Appl. Phys. Lett. 57, 2074 (1990).
[CrossRef]

1989

N. Goto, G. L. Yip, Appl. Opt. 28, 60 (1989).
[CrossRef] [PubMed]

S. T. Vohra, A. R. Mickelson, S. E. Asher, J. Appl. Phys. 66, 5161 (1989).
[CrossRef]

1987

P. Suchoski, R. V. Ramaswamy, J. Lightwave Technol. 5, 1246 (1987).
[CrossRef]

Asher, S. E.

S. T. Vohra, A. R. Mickelson, S. E. Asher, J. Appl. Phys. 66, 5161 (1989).
[CrossRef]

Bierlien, J. D.

F. Laurell, J. B. Brown, J. D. Bierlien, Appl. Phys. Lett. 62, 1872 (1993).
[CrossRef]

C. J. Van der Poel, J. D. Bierlien, J. B. Brown, Appl. Phys. Lett. 57, 2074 (1990).
[CrossRef]

J. D. Bierlien, D. B. Laubacher, J. B. Brown, C. J. van der Poel, Appl. Phys. Lett. 56, 1725 (1990).
[CrossRef]

Brown, J. B.

F. Laurell, J. B. Brown, J. D. Bierlien, Appl. Phys. Lett. 62, 1872 (1993).
[CrossRef]

C. J. Van der Poel, J. D. Bierlien, J. B. Brown, Appl. Phys. Lett. 57, 2074 (1990).
[CrossRef]

J. D. Bierlien, D. B. Laubacher, J. B. Brown, C. J. van der Poel, Appl. Phys. Lett. 56, 1725 (1990).
[CrossRef]

Burke, J. J.

Cao, X. F.

X. F. Cao, R. V. Ramaswamy, R. Srivastava, J. Lightwave Technol. 10, 1302 (1992).
[CrossRef]

Casey, H. C.

J. M. Zavada, H. C. Casey, C.-H. Chen, A. Loni, Appl. Phys. Lett. 62, 2769 (1993).
[CrossRef]

Chen, C.-H.

J. M. Zavada, H. C. Casey, C.-H. Chen, A. Loni, Appl. Phys. Lett. 62, 2769 (1993).
[CrossRef]

De Lu Rue, R. M.

Eger, D.

D. Eger, M. Oron, M. Katz, J. Appl. Phys. 74, 4298 (1993).
[CrossRef]

Goto, N.

Hardy, A.

Z. Weissman, A. Hardy, Electron. Lett. 28, 1514 (1992).
[CrossRef]

Ito, K.

S. Makio, F. Nitanda, K. Ito, M. Sato, in Conference on Lasers and Electro-Optics, Vol. 11 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 270.

Katz, M.

D. Eger, M. Oron, M. Katz, J. Appl. Phys. 74, 4298 (1993).
[CrossRef]

Laubacher, D. B.

J. D. Bierlien, D. B. Laubacher, J. B. Brown, C. J. van der Poel, Appl. Phys. Lett. 56, 1725 (1990).
[CrossRef]

Laurell, F.

F. Laurell, J. B. Brown, J. D. Bierlien, Appl. Phys. Lett. 62, 1872 (1993).
[CrossRef]

Li, L.

Loni, A.

J. M. Zavada, H. C. Casey, C.-H. Chen, A. Loni, Appl. Phys. Lett. 62, 2769 (1993).
[CrossRef]

A. Loni, R. M. De Lu Rue, Appl. Opt. 31, 5096 (1992).
[CrossRef] [PubMed]

Makio, S.

S. Makio, F. Nitanda, K. Ito, M. Sato, in Conference on Lasers and Electro-Optics, Vol. 11 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 270.

Mickelson, A. R.

S. T. Vohra, A. R. Mickelson, S. E. Asher, J. Appl. Phys. 66, 5161 (1989).
[CrossRef]

Nikolopoulos, J.

J. Nikolopoulos, G. L. Yip, J. Lightwave Technol. 9, 864 (1991).
[CrossRef]

Nitanda, F.

S. Makio, F. Nitanda, K. Ito, M. Sato, in Conference on Lasers and Electro-Optics, Vol. 11 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 270.

Oron, M.

D. Eger, M. Oron, M. Katz, J. Appl. Phys. 74, 4298 (1993).
[CrossRef]

Ramaswamy, R. V.

X. F. Cao, R. V. Ramaswamy, R. Srivastava, J. Lightwave Technol. 10, 1302 (1992).
[CrossRef]

P. Suchoski, R. V. Ramaswamy, J. Lightwave Technol. 5, 1246 (1987).
[CrossRef]

Sato, M.

S. Makio, F. Nitanda, K. Ito, M. Sato, in Conference on Lasers and Electro-Optics, Vol. 11 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 270.

Srivastava, R.

X. F. Cao, R. V. Ramaswamy, R. Srivastava, J. Lightwave Technol. 10, 1302 (1992).
[CrossRef]

Suchoski, P.

P. Suchoski, R. V. Ramaswamy, J. Lightwave Technol. 5, 1246 (1987).
[CrossRef]

van der Poel, C. J.

J. D. Bierlien, D. B. Laubacher, J. B. Brown, C. J. van der Poel, Appl. Phys. Lett. 56, 1725 (1990).
[CrossRef]

C. J. Van der Poel, J. D. Bierlien, J. B. Brown, Appl. Phys. Lett. 57, 2074 (1990).
[CrossRef]

Vohra, S. T.

S. T. Vohra, A. R. Mickelson, S. E. Asher, J. Appl. Phys. 66, 5161 (1989).
[CrossRef]

Weissman, Z.

Z. Weissman, A. Hardy, Electron. Lett. 28, 1514 (1992).
[CrossRef]

Yip, G. L.

J. Nikolopoulos, G. L. Yip, J. Lightwave Technol. 9, 864 (1991).
[CrossRef]

N. Goto, G. L. Yip, Appl. Opt. 28, 60 (1989).
[CrossRef] [PubMed]

Zavada, J. M.

J. M. Zavada, H. C. Casey, C.-H. Chen, A. Loni, Appl. Phys. Lett. 62, 2769 (1993).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

J. D. Bierlien, D. B. Laubacher, J. B. Brown, C. J. van der Poel, Appl. Phys. Lett. 56, 1725 (1990).
[CrossRef]

C. J. Van der Poel, J. D. Bierlien, J. B. Brown, Appl. Phys. Lett. 57, 2074 (1990).
[CrossRef]

F. Laurell, J. B. Brown, J. D. Bierlien, Appl. Phys. Lett. 62, 1872 (1993).
[CrossRef]

J. M. Zavada, H. C. Casey, C.-H. Chen, A. Loni, Appl. Phys. Lett. 62, 2769 (1993).
[CrossRef]

Electron. Lett.

Z. Weissman, A. Hardy, Electron. Lett. 28, 1514 (1992).
[CrossRef]

J. Appl. Phys.

D. Eger, M. Oron, M. Katz, J. Appl. Phys. 74, 4298 (1993).
[CrossRef]

S. T. Vohra, A. R. Mickelson, S. E. Asher, J. Appl. Phys. 66, 5161 (1989).
[CrossRef]

J. Lightwave Technol.

X. F. Cao, R. V. Ramaswamy, R. Srivastava, J. Lightwave Technol. 10, 1302 (1992).
[CrossRef]

J. Nikolopoulos, G. L. Yip, J. Lightwave Technol. 9, 864 (1991).
[CrossRef]

P. Suchoski, R. V. Ramaswamy, J. Lightwave Technol. 5, 1246 (1987).
[CrossRef]

Opt. Lett.

Other

S. Makio, F. Nitanda, K. Ito, M. Sato, in Conference on Lasers and Electro-Optics, Vol. 11 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 270.

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Figures (4)

Fig. 1
Fig. 1

Cross section of a periodically segmented waveguide consisting of a periodic array of high-index regions (hatched areas) surrounded by a low-index region.

Fig. 2
Fig. 2

Measured variation of the mode indices of the PEPS waveguide as a function of duty cycle for (a) 3 h, (b) 5 h, and (c) 8 h of annealing. The solid curves correspond to the calculated variation of an equivalent z-invariant graded-index waveguide with a Gaussian index distribution.

Fig. 3
Fig. 3

Variation of Δn at the surface of the equivalent graded-index waveguide as a function of duty cycle.

Fig. 4
Fig. 4

Measured variation of the effective indices of the TM0 and TM1 modes as a function of the period of segmentation of a PEPS waveguide with a duty cycle of 0.5.

Equations (1)

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n ( x ) = n s + Δ n exp ( x 2 / d x 2 ) ,

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