Abstract

We report measurements of the guided-wave reflectivity of a periodic, surface-corrugation, waveguide grating as a function of incidence angle and polarization. We show that the measured response is more accurately described by a coupled-mode theory based on the local-normal-mode expansion of the fields than by that based on the ideal-mode expansion.

© 1987 Optical Society of America

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  1. D. C. Flanders, H. Kogelnik, R. V. Schmidt, C. V. Shank, Appl. Phys. Lett. 24, 194 (1974).
    [CrossRef]
  2. C. S. Hong, J. B. Shellan, A. C. Livanos, A. Yariv, A. Katzir, Appl. Phys. Lett. 31, 276 (1977).
    [CrossRef]
  3. K. S. Pennington, L. Kuhn, Opt. Commun. 3, 357 (1971).
    [CrossRef]
  4. R. C. Alferness, L. L. Buhl, Appl. Phys. Lett. 40, 861 (1982).
    [CrossRef]
  5. P. S. Chung, Opt. Laser Technol. 15, 263 (1983).
    [CrossRef]
  6. A. Yariv, IEEE J. Quantum Electron. QE-9, 919 (1973).
    [CrossRef]
  7. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).
  8. H. Kogelnik, in Integrated Optics, Vol. 7 of Topics in Applied Physics, T. Tamir, ed. (Springer-Verlag, New York, 1975).
    [CrossRef]
  9. K. Wagatsuma, H. Sakaki, S. Saito, IEEE J. Quantum Electron. QE-15, 632 (1979).
    [CrossRef]
  10. J. VanRoey, P. E. Lagasse, Appl. Opt. 20, 423 (1981).
    [CrossRef]
  11. W. Streifer, D. R. Scifres, R. D. Burnham, IEEE J. Quantum Electron. QE-12, 74 (1976).
    [CrossRef]
  12. G. I. Stegeman, D. Sarid, J. J. Burke, D. G. Hall, J. Opt. Soc. Am. 71, 1497 (1981).
    [CrossRef]
  13. R. W. Gruhlke, D. G. Hall, Appl. Opt. 23, 127 (1984).
    [CrossRef] [PubMed]
  14. L. A. Weller-Brophy, D. G. Hall, Proc. Soc. Photo-Opt. Instrum. Eng. 578, 173 (1985).
  15. L. A. Weller-Brophy, D. G. Hall, submitted to IEEE J. Lightwave Technol.—IEEE J. Quantum Electron.

1985

L. A. Weller-Brophy, D. G. Hall, Proc. Soc. Photo-Opt. Instrum. Eng. 578, 173 (1985).

1984

1983

P. S. Chung, Opt. Laser Technol. 15, 263 (1983).
[CrossRef]

1982

R. C. Alferness, L. L. Buhl, Appl. Phys. Lett. 40, 861 (1982).
[CrossRef]

1981

1979

K. Wagatsuma, H. Sakaki, S. Saito, IEEE J. Quantum Electron. QE-15, 632 (1979).
[CrossRef]

1977

C. S. Hong, J. B. Shellan, A. C. Livanos, A. Yariv, A. Katzir, Appl. Phys. Lett. 31, 276 (1977).
[CrossRef]

1976

W. Streifer, D. R. Scifres, R. D. Burnham, IEEE J. Quantum Electron. QE-12, 74 (1976).
[CrossRef]

1974

D. C. Flanders, H. Kogelnik, R. V. Schmidt, C. V. Shank, Appl. Phys. Lett. 24, 194 (1974).
[CrossRef]

1973

A. Yariv, IEEE J. Quantum Electron. QE-9, 919 (1973).
[CrossRef]

1971

K. S. Pennington, L. Kuhn, Opt. Commun. 3, 357 (1971).
[CrossRef]

Alferness, R. C.

R. C. Alferness, L. L. Buhl, Appl. Phys. Lett. 40, 861 (1982).
[CrossRef]

Buhl, L. L.

R. C. Alferness, L. L. Buhl, Appl. Phys. Lett. 40, 861 (1982).
[CrossRef]

Burke, J. J.

Burnham, R. D.

W. Streifer, D. R. Scifres, R. D. Burnham, IEEE J. Quantum Electron. QE-12, 74 (1976).
[CrossRef]

Chung, P. S.

P. S. Chung, Opt. Laser Technol. 15, 263 (1983).
[CrossRef]

Flanders, D. C.

D. C. Flanders, H. Kogelnik, R. V. Schmidt, C. V. Shank, Appl. Phys. Lett. 24, 194 (1974).
[CrossRef]

Gruhlke, R. W.

Hall, D. G.

L. A. Weller-Brophy, D. G. Hall, Proc. Soc. Photo-Opt. Instrum. Eng. 578, 173 (1985).

R. W. Gruhlke, D. G. Hall, Appl. Opt. 23, 127 (1984).
[CrossRef] [PubMed]

G. I. Stegeman, D. Sarid, J. J. Burke, D. G. Hall, J. Opt. Soc. Am. 71, 1497 (1981).
[CrossRef]

L. A. Weller-Brophy, D. G. Hall, submitted to IEEE J. Lightwave Technol.—IEEE J. Quantum Electron.

Hong, C. S.

C. S. Hong, J. B. Shellan, A. C. Livanos, A. Yariv, A. Katzir, Appl. Phys. Lett. 31, 276 (1977).
[CrossRef]

Katzir, A.

C. S. Hong, J. B. Shellan, A. C. Livanos, A. Yariv, A. Katzir, Appl. Phys. Lett. 31, 276 (1977).
[CrossRef]

Kogelnik, H.

D. C. Flanders, H. Kogelnik, R. V. Schmidt, C. V. Shank, Appl. Phys. Lett. 24, 194 (1974).
[CrossRef]

H. Kogelnik, in Integrated Optics, Vol. 7 of Topics in Applied Physics, T. Tamir, ed. (Springer-Verlag, New York, 1975).
[CrossRef]

Kuhn, L.

K. S. Pennington, L. Kuhn, Opt. Commun. 3, 357 (1971).
[CrossRef]

Lagasse, P. E.

Livanos, A. C.

C. S. Hong, J. B. Shellan, A. C. Livanos, A. Yariv, A. Katzir, Appl. Phys. Lett. 31, 276 (1977).
[CrossRef]

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).

Pennington, K. S.

K. S. Pennington, L. Kuhn, Opt. Commun. 3, 357 (1971).
[CrossRef]

Saito, S.

K. Wagatsuma, H. Sakaki, S. Saito, IEEE J. Quantum Electron. QE-15, 632 (1979).
[CrossRef]

Sakaki, H.

K. Wagatsuma, H. Sakaki, S. Saito, IEEE J. Quantum Electron. QE-15, 632 (1979).
[CrossRef]

Sarid, D.

Schmidt, R. V.

D. C. Flanders, H. Kogelnik, R. V. Schmidt, C. V. Shank, Appl. Phys. Lett. 24, 194 (1974).
[CrossRef]

Scifres, D. R.

W. Streifer, D. R. Scifres, R. D. Burnham, IEEE J. Quantum Electron. QE-12, 74 (1976).
[CrossRef]

Shank, C. V.

D. C. Flanders, H. Kogelnik, R. V. Schmidt, C. V. Shank, Appl. Phys. Lett. 24, 194 (1974).
[CrossRef]

Shellan, J. B.

C. S. Hong, J. B. Shellan, A. C. Livanos, A. Yariv, A. Katzir, Appl. Phys. Lett. 31, 276 (1977).
[CrossRef]

Stegeman, G. I.

Streifer, W.

W. Streifer, D. R. Scifres, R. D. Burnham, IEEE J. Quantum Electron. QE-12, 74 (1976).
[CrossRef]

VanRoey, J.

Wagatsuma, K.

K. Wagatsuma, H. Sakaki, S. Saito, IEEE J. Quantum Electron. QE-15, 632 (1979).
[CrossRef]

Weller-Brophy, L. A.

L. A. Weller-Brophy, D. G. Hall, Proc. Soc. Photo-Opt. Instrum. Eng. 578, 173 (1985).

L. A. Weller-Brophy, D. G. Hall, submitted to IEEE J. Lightwave Technol.—IEEE J. Quantum Electron.

Yariv, A.

C. S. Hong, J. B. Shellan, A. C. Livanos, A. Yariv, A. Katzir, Appl. Phys. Lett. 31, 276 (1977).
[CrossRef]

A. Yariv, IEEE J. Quantum Electron. QE-9, 919 (1973).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

D. C. Flanders, H. Kogelnik, R. V. Schmidt, C. V. Shank, Appl. Phys. Lett. 24, 194 (1974).
[CrossRef]

C. S. Hong, J. B. Shellan, A. C. Livanos, A. Yariv, A. Katzir, Appl. Phys. Lett. 31, 276 (1977).
[CrossRef]

R. C. Alferness, L. L. Buhl, Appl. Phys. Lett. 40, 861 (1982).
[CrossRef]

IEEE J. Quantum Electron.

W. Streifer, D. R. Scifres, R. D. Burnham, IEEE J. Quantum Electron. QE-12, 74 (1976).
[CrossRef]

A. Yariv, IEEE J. Quantum Electron. QE-9, 919 (1973).
[CrossRef]

K. Wagatsuma, H. Sakaki, S. Saito, IEEE J. Quantum Electron. QE-15, 632 (1979).
[CrossRef]

J. Opt. Soc. Am.

Opt. Commun.

K. S. Pennington, L. Kuhn, Opt. Commun. 3, 357 (1971).
[CrossRef]

Opt. Laser Technol.

P. S. Chung, Opt. Laser Technol. 15, 263 (1983).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng.

L. A. Weller-Brophy, D. G. Hall, Proc. Soc. Photo-Opt. Instrum. Eng. 578, 173 (1985).

Other

L. A. Weller-Brophy, D. G. Hall, submitted to IEEE J. Lightwave Technol.—IEEE J. Quantum Electron.

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).

H. Kogelnik, in Integrated Optics, Vol. 7 of Topics in Applied Physics, T. Tamir, ed. (Springer-Verlag, New York, 1975).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Diagram of the planar waveguide with surface corrugation. The parameters θi, θr, h, Δh, L, and Λ denote incidence angle, reflected angle, unperturbed film thickness, corrugation depth, grating length, and grating period, respectively.

Fig. 2
Fig. 2

Calculated TM–TM coupling coefficients. A, IM expansion of Wagatsuma et al.9; B, IM expansion of VanRoey and Lagasse10; C, BPT of Stegeman et al.12; D, LNM expansion15; a, modified IM expansion of Streifer for θi = 0° only.11

Tables (2)

Tables Icon

Table 1 Measured and Calculated Grating Reflectivitiesa

Tables Icon

Table 2 Measured and Calculated Bragg-Matched Angles

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