Abstract

Heterostructure GaAs-Al<sub>x</sub>Ga<sub>1-x</sub>As-GaAs waveguides for 10.6 µm wavelength grown by liquid-phase epitaxy have a linear variation of dielectric constant in their substrates. On the basis of their mode equation, a computer program was devised for obtaining optimum values of the six parameters that define the index profiles, given a sufficient number and distribution of mode-angle measurements. The optimized parameters agreed well with the measured values for a variety of waveguides, illustrating the generality of the parameter-optimization procedure. Two types of leaky modes were observed, whose effective index β/<i>k</i> is less than the seed index, (1) Lummer—Gehrcke modes that are incompletely reflected at the substrate-seed interface and (2) low-loss totally reflected modes whose evanescent fields radiate into high-index seeds.

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  1. P. K. Cheo, J. M. Berak, W. Oshinsky, and J. L. Swindal, Appl. Opt. 12, 500 (1973).
  2. J. T. Boyd, IEEE J. Quant. Electron. QE-8, 788 (1972).
  3. R. E. Fern and A. Onton, J. Appl. Phys. 42, 3499 (1971).
  4. P. K. Tien, Appl. Opt. 10, 2395 (1971).
  5. R. Ulrich and R. Torge, Appl. Opt. 12, 2901 (1973).
  6. See, for example, B. S. Gottfried and J. Weisman, Introduction to Optimization Theory (Prenctice—Hall, Englewood Cliffs, N.J., 1973).
  7. R. Ulrich and W. Prettl, Appl. Phys. 1, 55 (1973).
  8. J. H. McFee, J. D. McGee, T. Y. Chang, and V. T. Nguyen, Appl. Phys. Lett. 21, 534 (1972).
  9. E. Garmire, Appl. Phys. Lett. 23, 403 (1973).
  10. G. D. Boyd (private communication, 1971).
  11. J. H. McFee, R. E. Nahory, M. A. Pollack, and R. A. Logan, Appl. Phys. Lett. 23, 571 (1973).
  12. G. Tyras, Radiation and Propagation of Electromagnetic Waves (Academic, New York, 1969), Ch. 4.
  13. J. P. Gordon, Bell Syst. Tech. J. 40, 321 (1966).
  14. Handbook of Mathematical Functions, edited by Milton Abramowitz and Irene Stegun, Natl. Bur. Std. (U. S.) Handbook 55 (U. S. Government Printing Office, Washington, D. C., 1964; Dover, New York, 1965).
  15. D. F. Nelson and J. McKenna, J. Appl. Phys. 38, 4057 (1967).
  16. A. Reisinger, Appl. Opt. 12, 1015 (1973).
  17. C. M. Nagel, Jr. (private communication, 1967).
  18. C. L. Semmelman (private communication, 1970); P. E. FleiScher, in System Analysis by Digital Computer, edited by F. F. Kuo and J. F. Kaiser (Wiley, New York, 1966).
  19. D. W. Marquardt, J. Soc. Indust. Appl. Math. 11, 431 (1963).
  20. P. S. Epstein, Proc. Nat. Acad. Sdi. 16, 627 (1930).

Berak, J. M.

P. K. Cheo, J. M. Berak, W. Oshinsky, and J. L. Swindal, Appl. Opt. 12, 500 (1973).

Boyd, G. D.

G. D. Boyd (private communication, 1971).

Boyd, J. T.

J. T. Boyd, IEEE J. Quant. Electron. QE-8, 788 (1972).

Chang, T. Y.

J. H. McFee, J. D. McGee, T. Y. Chang, and V. T. Nguyen, Appl. Phys. Lett. 21, 534 (1972).

Cheo, P. K.

P. K. Cheo, J. M. Berak, W. Oshinsky, and J. L. Swindal, Appl. Opt. 12, 500 (1973).

Epstein, P. S.

P. S. Epstein, Proc. Nat. Acad. Sdi. 16, 627 (1930).

Fern, R. E.

R. E. Fern and A. Onton, J. Appl. Phys. 42, 3499 (1971).

Garmire, E.

E. Garmire, Appl. Phys. Lett. 23, 403 (1973).

Gordon, J. P.

J. P. Gordon, Bell Syst. Tech. J. 40, 321 (1966).

Gottfried, B. S.

See, for example, B. S. Gottfried and J. Weisman, Introduction to Optimization Theory (Prenctice—Hall, Englewood Cliffs, N.J., 1973).

Logan, R. A.

J. H. McFee, R. E. Nahory, M. A. Pollack, and R. A. Logan, Appl. Phys. Lett. 23, 571 (1973).

Marquardt, D. W.

D. W. Marquardt, J. Soc. Indust. Appl. Math. 11, 431 (1963).

McFee, J. H.

J. H. McFee, R. E. Nahory, M. A. Pollack, and R. A. Logan, Appl. Phys. Lett. 23, 571 (1973).

J. H. McFee, J. D. McGee, T. Y. Chang, and V. T. Nguyen, Appl. Phys. Lett. 21, 534 (1972).

McGee, J. D.

J. H. McFee, J. D. McGee, T. Y. Chang, and V. T. Nguyen, Appl. Phys. Lett. 21, 534 (1972).

McKenna, J.

D. F. Nelson and J. McKenna, J. Appl. Phys. 38, 4057 (1967).

Nagel, Jr., C. M.

C. M. Nagel, Jr. (private communication, 1967).

Nahory, R. E.

J. H. McFee, R. E. Nahory, M. A. Pollack, and R. A. Logan, Appl. Phys. Lett. 23, 571 (1973).

Nelson, D. F.

D. F. Nelson and J. McKenna, J. Appl. Phys. 38, 4057 (1967).

Nguyen, V. T.

J. H. McFee, J. D. McGee, T. Y. Chang, and V. T. Nguyen, Appl. Phys. Lett. 21, 534 (1972).

Onton, A.

R. E. Fern and A. Onton, J. Appl. Phys. 42, 3499 (1971).

Oshinsky, W.

P. K. Cheo, J. M. Berak, W. Oshinsky, and J. L. Swindal, Appl. Opt. 12, 500 (1973).

Pollack, M. A.

J. H. McFee, R. E. Nahory, M. A. Pollack, and R. A. Logan, Appl. Phys. Lett. 23, 571 (1973).

Prettl, W.

R. Ulrich and W. Prettl, Appl. Phys. 1, 55 (1973).

Reisinger, A.

A. Reisinger, Appl. Opt. 12, 1015 (1973).

Semmelman, C. L.

C. L. Semmelman (private communication, 1970); P. E. FleiScher, in System Analysis by Digital Computer, edited by F. F. Kuo and J. F. Kaiser (Wiley, New York, 1966).

Swindal, J. L.

P. K. Cheo, J. M. Berak, W. Oshinsky, and J. L. Swindal, Appl. Opt. 12, 500 (1973).

Tien, P. K.

P. K. Tien, Appl. Opt. 10, 2395 (1971).

Torge, R.

R. Ulrich and R. Torge, Appl. Opt. 12, 2901 (1973).

Tyras, G.

G. Tyras, Radiation and Propagation of Electromagnetic Waves (Academic, New York, 1969), Ch. 4.

Ulrich, R.

R. Ulrich and W. Prettl, Appl. Phys. 1, 55 (1973).

R. Ulrich and R. Torge, Appl. Opt. 12, 2901 (1973).

Weisman, J.

See, for example, B. S. Gottfried and J. Weisman, Introduction to Optimization Theory (Prenctice—Hall, Englewood Cliffs, N.J., 1973).

Other (20)

P. K. Cheo, J. M. Berak, W. Oshinsky, and J. L. Swindal, Appl. Opt. 12, 500 (1973).

J. T. Boyd, IEEE J. Quant. Electron. QE-8, 788 (1972).

R. E. Fern and A. Onton, J. Appl. Phys. 42, 3499 (1971).

P. K. Tien, Appl. Opt. 10, 2395 (1971).

R. Ulrich and R. Torge, Appl. Opt. 12, 2901 (1973).

See, for example, B. S. Gottfried and J. Weisman, Introduction to Optimization Theory (Prenctice—Hall, Englewood Cliffs, N.J., 1973).

R. Ulrich and W. Prettl, Appl. Phys. 1, 55 (1973).

J. H. McFee, J. D. McGee, T. Y. Chang, and V. T. Nguyen, Appl. Phys. Lett. 21, 534 (1972).

E. Garmire, Appl. Phys. Lett. 23, 403 (1973).

G. D. Boyd (private communication, 1971).

J. H. McFee, R. E. Nahory, M. A. Pollack, and R. A. Logan, Appl. Phys. Lett. 23, 571 (1973).

G. Tyras, Radiation and Propagation of Electromagnetic Waves (Academic, New York, 1969), Ch. 4.

J. P. Gordon, Bell Syst. Tech. J. 40, 321 (1966).

Handbook of Mathematical Functions, edited by Milton Abramowitz and Irene Stegun, Natl. Bur. Std. (U. S.) Handbook 55 (U. S. Government Printing Office, Washington, D. C., 1964; Dover, New York, 1965).

D. F. Nelson and J. McKenna, J. Appl. Phys. 38, 4057 (1967).

A. Reisinger, Appl. Opt. 12, 1015 (1973).

C. M. Nagel, Jr. (private communication, 1967).

C. L. Semmelman (private communication, 1970); P. E. FleiScher, in System Analysis by Digital Computer, edited by F. F. Kuo and J. F. Kaiser (Wiley, New York, 1966).

D. W. Marquardt, J. Soc. Indust. Appl. Math. 11, 431 (1963).

P. S. Epstein, Proc. Nat. Acad. Sdi. 16, 627 (1930).

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