Abstract

A new rich family of complex permittivity profiles is obtained by introduction of additional parameters in the Burman and Gould procedure of generating the generalized Epstein profile. As an example of its possible applications, a model of planar-stripe injection lasers is developed. By proper choice of parameters the permittivity profile along the junction plane can be varied in its central part without affecting its tails. Effects of interaction between the optical field and the charge carriers inside the stripe can thus be modeled. An analytical solution of the wave equation is given, and a number of examples of the near-field pattern for the fundamental lateral mode are calculated for (AlGa)As lasers by a self-consistent iterative technique. The influence of asymmetry of the permittivity on near-field shifts is demonstrated.

© 1984 Optical Society of America

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    [CrossRef]
  2. K. Kobayashi et al., IEEE J. Quantum Electron. QE-13, 659 (1977).
    [CrossRef]
  3. P. A. Kirkby, A. R. Goodwin, G. H. B. Thompson, P. R. Selway, IEEE J. Quantum Electron. QE-13, 705 (1977).
    [CrossRef]
  4. N. Chinone, J. Appl. Phys. 48, 3237 (1977).
    [CrossRef]
  5. H. S. Sommers, J. Appl. Phys. 50, 6630 (1979).
    [CrossRef]
  6. D. Kerps, Proc. Inst. Electr. Eng. Part I: Solid-State Electron Devices 127, 94 (1980).
  7. G. H. B. Thompson, D. F. Lovelace, S. E. H. Turley, IEE J. Solid-State Electron Devices 2, 12 (1978).
    [CrossRef]
  8. R. Lang, IEEE J. Quantum Electron. QE-15, 718 (1979).
    [CrossRef]
  9. R. W. Dixon, W. B. Joyce, Bell Syst. Tech. J. 59, 975 (1980).
  10. K. A. Shore, T. E. Rozzi, G. H. in’t Veld, Proc. Inst. Electr. Eng. Part I: Solid-State Electron Devices 127, 221 (1980).
  11. C. B. Su, J. Appl. Phys. 52, 2665 (1981).
    [CrossRef]
  12. K. A. Shore, T. E. Rozzi, Proc. Inst. Electr. Eng. Part I: Solid-State Electron Devices 128, 154 (1981).
  13. J. K. Butler, H. S. Sommers, IEEE J. Quantum Electron. QE-14, 413 (1978).
    [CrossRef]
  14. F. D. Nunes, N. B. Patel, J. G. Mendoza Alvarez, J. E. Ripper, J. Appl. Phys. 50, 3852 (1979).
    [CrossRef]
  15. P. M. Asbeck, D. A. Cammack, J. J. Daniele, Appl. Phys. Lett. 33, 504 (1978).
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  19. W. Streifer, D. R. Scifres, R. D. Burnham, Electron. Lett. 17, 933 (1981).
    [CrossRef]
  20. K. Petermann, Opt. Quantum Electron. 13, 323 (1981).
    [CrossRef]
  21. T. J. S. Mattos, N. B. Patel, F. D. Nunes, J. Appl. Phys. 53, 149 (1982).
    [CrossRef]
  22. J. Pietzsch, Electron. Lett. 18, 1015 (1982).
    [CrossRef]
  23. W. Streifer, R. D. Burnham, D. R. Scifres, IEEE J. Quantum Electron. QE-15, 136 (1979).
    [CrossRef]
  24. H. Namizaki, H. Kan, M. Ishii, A. Ito, J. Appl. Phys. 45, 2785 (1974).
    [CrossRef]
  25. G. H. B. Thompson, D. F. Lovelace, S. E. H. Turley, IEEE J. Quantum Electron. QE-15, 772 (1979).
    [CrossRef]
  26. T. Sugino, K. Itoh, H. Shimizu, M. Wada, I. Teramoto, IEEE J. Quantum Electron. QE-17, 745 (1981).
    [CrossRef]
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  32. M. Osiński, AEU Arch. Elektron. Ubertragungstech. Electron. Commun. 30, 223 (1976).
  33. M. Osiński, Opt. Quantum Electron. 9, 361 (1977).
    [CrossRef]
  34. M. Osiński, Acta Phys. Pol. A 60, 109 (1981).
  35. R. Burman, R. N. Gould, Can. J. Phys. 43, 921 (1965).
    [CrossRef]
  36. T. L. Paoli, IEEE J. Quantum Electron. QE-13, 662 (1977).
    [CrossRef]
  37. W. Streifer, E. Kapon, Appl. Opt. 18, 3724 (1979).
    [CrossRef] [PubMed]
  38. J. Buus, IEEE J. Quantum Electron. QE-18, 1083 (1982).
    [CrossRef]
  39. J. Buus, Opt. Quantum Electron. 10, 459 (1978).
    [CrossRef]
  40. R. Lang, Trans. IECE Jpn. E62, 299 (1979).
  41. P. M. Asbeck, D. A. Cammack, J. J. Daniele, V. Klebanoff, IEEE J. Quantum Electron. QE-15, 727 (1979).
    [CrossRef]
  42. J. Buus, IEEE J. Quantum Electron. QE-19, 953 (1983).
    [CrossRef]
  43. B. W. Hakki, C. J. Hwang, J. Appl. Phys. 45, 2168 (1974).
    [CrossRef]
  44. G. H. B. Thompson, G. D. Henshall, J. E. A. Whiteaway, P. A. Kirkby, J. Appl. Phys. 47, 1501 (1976).
    [CrossRef]
  45. D. Botez, G. J. Herskowitz, Proc. IEEE 68, 689 (1980).
    [CrossRef]

1983

J. Buus, IEEE J. Quantum Electron. QE-19, 953 (1983).
[CrossRef]

1982

T. J. S. Mattos, N. B. Patel, F. D. Nunes, J. Appl. Phys. 53, 149 (1982).
[CrossRef]

J. Pietzsch, Electron. Lett. 18, 1015 (1982).
[CrossRef]

J. Buus, IEEE J. Quantum Electron. QE-18, 1083 (1982).
[CrossRef]

1981

M. Osiński, Acta Phys. Pol. A 60, 109 (1981).

T. Sugino, K. Itoh, H. Shimizu, M. Wada, I. Teramoto, IEEE J. Quantum Electron. QE-17, 745 (1981).
[CrossRef]

C. B. Su, J. Appl. Phys. 52, 2665 (1981).
[CrossRef]

K. A. Shore, T. E. Rozzi, Proc. Inst. Electr. Eng. Part I: Solid-State Electron Devices 128, 154 (1981).

W. Streifer, D. R. Scifres, R. D. Burnham, Electron. Lett. 17, 933 (1981).
[CrossRef]

K. Petermann, Opt. Quantum Electron. 13, 323 (1981).
[CrossRef]

1980

D. Kerps, Proc. Inst. Electr. Eng. Part I: Solid-State Electron Devices 127, 94 (1980).

R. W. Dixon, W. B. Joyce, Bell Syst. Tech. J. 59, 975 (1980).

K. A. Shore, T. E. Rozzi, G. H. in’t Veld, Proc. Inst. Electr. Eng. Part I: Solid-State Electron Devices 127, 221 (1980).

P. G. Eliseev, M. Osiński, Kvantovaya Elektron. (Moscow) 7, 1407 (1980) [Sov. J. Quantum Electron. 10, 811 (1980)].

D. Botez, G. J. Herskowitz, Proc. IEEE 68, 689 (1980).
[CrossRef]

1979

W. Streifer, E. Kapon, Appl. Opt. 18, 3724 (1979).
[CrossRef] [PubMed]

R. Lang, Trans. IECE Jpn. E62, 299 (1979).

P. M. Asbeck, D. A. Cammack, J. J. Daniele, V. Klebanoff, IEEE J. Quantum Electron. QE-15, 727 (1979).
[CrossRef]

G. H. B. Thompson, D. F. Lovelace, S. E. H. Turley, IEEE J. Quantum Electron. QE-15, 772 (1979).
[CrossRef]

W. Streifer, R. D. Burnham, D. R. Scifres, IEEE J. Quantum Electron. QE-15, 136 (1979).
[CrossRef]

H. S. Sommers, J. Appl. Phys. 50, 6630 (1979).
[CrossRef]

R. Lang, IEEE J. Quantum Electron. QE-15, 718 (1979).
[CrossRef]

M. Osiński, P. G. Eliseev, IEE J. Solid-State Electron Devices 3, 215 (1979).
[CrossRef]

F. D. Nunes, N. B. Patel, J. G. Mendoza Alvarez, J. E. Ripper, J. Appl. Phys. 50, 3852 (1979).
[CrossRef]

1978

P. M. Asbeck, D. A. Cammack, J. J. Daniele, Appl. Phys. Lett. 33, 504 (1978).
[CrossRef]

W. Streifer, D. R. Scifres, R. D. Burnham, IEEE J. Quantum Electron. QE-14, 418 (1978).
[CrossRef]

J. K. Butler, H. S. Sommers, IEEE J. Quantum Electron. QE-14, 413 (1978).
[CrossRef]

G. H. B. Thompson, D. F. Lovelace, S. E. H. Turley, IEE J. Solid-State Electron Devices 2, 12 (1978).
[CrossRef]

J. Buus, Opt. Quantum Electron. 10, 459 (1978).
[CrossRef]

1977

M. Osiński, Opt. Quantum Electron. 9, 361 (1977).
[CrossRef]

T. L. Paoli, IEEE J. Quantum Electron. QE-13, 662 (1977).
[CrossRef]

K. Kobayashi et al., IEEE J. Quantum Electron. QE-13, 659 (1977).
[CrossRef]

P. A. Kirkby, A. R. Goodwin, G. H. B. Thompson, P. R. Selway, IEEE J. Quantum Electron. QE-13, 705 (1977).
[CrossRef]

N. Chinone, J. Appl. Phys. 48, 3237 (1977).
[CrossRef]

1976

T. L. Paoli, IEEE J. Quantum Electron. QE-12, 770 (1976).
[CrossRef]

M. Osiński, AEU Arch. Elektron. Ubertragungstech. Electron. Commun. 30, 223 (1976).

G. H. B. Thompson, G. D. Henshall, J. E. A. Whiteaway, P. A. Kirkby, J. Appl. Phys. 47, 1501 (1976).
[CrossRef]

1974

B. W. Hakki, C. J. Hwang, J. Appl. Phys. 45, 2168 (1974).
[CrossRef]

H. Namizaki, H. Kan, M. Ishii, A. Ito, J. Appl. Phys. 45, 2785 (1974).
[CrossRef]

1972

S. N. Stolyarov, Kvantovaya Elektron. No. 8, 69 (1972) [Sov. J. Quantum Electron. 2, 144 (1972)].

1965

R. Burman, R. N. Gould, Can. J. Phys. 43, 921 (1965).
[CrossRef]

1930

P. S. Epstein, Proc. Natl. Acad. Sci. USA 16, 627 (1930).
[CrossRef] [PubMed]

Asbeck, P. M.

P. M. Asbeck, D. A. Cammack, J. J. Daniele, V. Klebanoff, IEEE J. Quantum Electron. QE-15, 727 (1979).
[CrossRef]

P. M. Asbeck, D. A. Cammack, J. J. Daniele, Appl. Phys. Lett. 33, 504 (1978).
[CrossRef]

Botez, D.

D. Botez, G. J. Herskowitz, Proc. IEEE 68, 689 (1980).
[CrossRef]

Brekhovskikh, L. M.

L. M. Brekhovskikh, Waves in Layered Media (Academic, New York, 1980). Note that in formula (20.11) on p. 166 the factor ½(γ − α − β − 1) should read as an exponent of (1 − ζ).

Burman, R.

R. Burman, R. N. Gould, Can. J. Phys. 43, 921 (1965).
[CrossRef]

Burnham, R. D.

W. Streifer, D. R. Scifres, R. D. Burnham, Electron. Lett. 17, 933 (1981).
[CrossRef]

W. Streifer, R. D. Burnham, D. R. Scifres, IEEE J. Quantum Electron. QE-15, 136 (1979).
[CrossRef]

W. Streifer, D. R. Scifres, R. D. Burnham, IEEE J. Quantum Electron. QE-14, 418 (1978).
[CrossRef]

Butler, J. K.

J. K. Butler, H. S. Sommers, IEEE J. Quantum Electron. QE-14, 413 (1978).
[CrossRef]

Buus, J.

J. Buus, IEEE J. Quantum Electron. QE-19, 953 (1983).
[CrossRef]

J. Buus, IEEE J. Quantum Electron. QE-18, 1083 (1982).
[CrossRef]

J. Buus, Opt. Quantum Electron. 10, 459 (1978).
[CrossRef]

Cammack, D. A.

P. M. Asbeck, D. A. Cammack, J. J. Daniele, V. Klebanoff, IEEE J. Quantum Electron. QE-15, 727 (1979).
[CrossRef]

P. M. Asbeck, D. A. Cammack, J. J. Daniele, Appl. Phys. Lett. 33, 504 (1978).
[CrossRef]

Chinone, N.

N. Chinone, J. Appl. Phys. 48, 3237 (1977).
[CrossRef]

Choros, T.

T. Choroś, M. Osiński, in Proceedings, International Conference Radiative Recombination and Related Phenomena in III–V Compound Semiconductors RECON-79, Prague, 4–7 Sept. 1979, p. 32.

Daniele, J. J.

P. M. Asbeck, D. A. Cammack, J. J. Daniele, V. Klebanoff, IEEE J. Quantum Electron. QE-15, 727 (1979).
[CrossRef]

P. M. Asbeck, D. A. Cammack, J. J. Daniele, Appl. Phys. Lett. 33, 504 (1978).
[CrossRef]

Dixon, R. W.

R. W. Dixon, W. B. Joyce, Bell Syst. Tech. J. 59, 975 (1980).

Dziewiecka, T.

T. Dziewiecka, M. Osiński, in Proceedings, International Workshop on the Physics of Semiconductor Devices, Delhi, India, 23–28 Nov. 1981, p. 60.

Eliseev, P. G.

P. G. Eliseev, M. Osiński, Kvantovaya Elektron. (Moscow) 7, 1407 (1980) [Sov. J. Quantum Electron. 10, 811 (1980)].

M. Osiński, P. G. Eliseev, IEE J. Solid-State Electron Devices 3, 215 (1979).
[CrossRef]

Epstein, P. S.

P. S. Epstein, Proc. Natl. Acad. Sci. USA 16, 627 (1930).
[CrossRef] [PubMed]

Goodwin, A. R.

P. A. Kirkby, A. R. Goodwin, G. H. B. Thompson, P. R. Selway, IEEE J. Quantum Electron. QE-13, 705 (1977).
[CrossRef]

Gould, R. N.

R. Burman, R. N. Gould, Can. J. Phys. 43, 921 (1965).
[CrossRef]

Hakki, B. W.

B. W. Hakki, C. J. Hwang, J. Appl. Phys. 45, 2168 (1974).
[CrossRef]

Henshall, G. D.

G. H. B. Thompson, G. D. Henshall, J. E. A. Whiteaway, P. A. Kirkby, J. Appl. Phys. 47, 1501 (1976).
[CrossRef]

Herskowitz, G. J.

D. Botez, G. J. Herskowitz, Proc. IEEE 68, 689 (1980).
[CrossRef]

Hwang, C. J.

B. W. Hakki, C. J. Hwang, J. Appl. Phys. 45, 2168 (1974).
[CrossRef]

Ishii, M.

H. Namizaki, H. Kan, M. Ishii, A. Ito, J. Appl. Phys. 45, 2785 (1974).
[CrossRef]

Ito, A.

H. Namizaki, H. Kan, M. Ishii, A. Ito, J. Appl. Phys. 45, 2785 (1974).
[CrossRef]

Itoh, K.

T. Sugino, K. Itoh, H. Shimizu, M. Wada, I. Teramoto, IEEE J. Quantum Electron. QE-17, 745 (1981).
[CrossRef]

Joyce, W. B.

R. W. Dixon, W. B. Joyce, Bell Syst. Tech. J. 59, 975 (1980).

Kan, H.

H. Namizaki, H. Kan, M. Ishii, A. Ito, J. Appl. Phys. 45, 2785 (1974).
[CrossRef]

Kapon, E.

Kerps, D.

D. Kerps, Proc. Inst. Electr. Eng. Part I: Solid-State Electron Devices 127, 94 (1980).

Kirkby, P. A.

P. A. Kirkby, A. R. Goodwin, G. H. B. Thompson, P. R. Selway, IEEE J. Quantum Electron. QE-13, 705 (1977).
[CrossRef]

G. H. B. Thompson, G. D. Henshall, J. E. A. Whiteaway, P. A. Kirkby, J. Appl. Phys. 47, 1501 (1976).
[CrossRef]

Klebanoff, V.

P. M. Asbeck, D. A. Cammack, J. J. Daniele, V. Klebanoff, IEEE J. Quantum Electron. QE-15, 727 (1979).
[CrossRef]

Kobayashi, K.

K. Kobayashi et al., IEEE J. Quantum Electron. QE-13, 659 (1977).
[CrossRef]

Lang, R.

R. Lang, Trans. IECE Jpn. E62, 299 (1979).

R. Lang, IEEE J. Quantum Electron. QE-15, 718 (1979).
[CrossRef]

Lovelace, D. F.

G. H. B. Thompson, D. F. Lovelace, S. E. H. Turley, IEEE J. Quantum Electron. QE-15, 772 (1979).
[CrossRef]

G. H. B. Thompson, D. F. Lovelace, S. E. H. Turley, IEE J. Solid-State Electron Devices 2, 12 (1978).
[CrossRef]

Mattos, T. J. S.

T. J. S. Mattos, N. B. Patel, F. D. Nunes, J. Appl. Phys. 53, 149 (1982).
[CrossRef]

Mendoza Alvarez, J. G.

F. D. Nunes, N. B. Patel, J. G. Mendoza Alvarez, J. E. Ripper, J. Appl. Phys. 50, 3852 (1979).
[CrossRef]

Namizaki, H.

H. Namizaki, H. Kan, M. Ishii, A. Ito, J. Appl. Phys. 45, 2785 (1974).
[CrossRef]

Nunes, F. D.

T. J. S. Mattos, N. B. Patel, F. D. Nunes, J. Appl. Phys. 53, 149 (1982).
[CrossRef]

F. D. Nunes, N. B. Patel, J. G. Mendoza Alvarez, J. E. Ripper, J. Appl. Phys. 50, 3852 (1979).
[CrossRef]

Osinski, M.

M. Osiński, Acta Phys. Pol. A 60, 109 (1981).

P. G. Eliseev, M. Osiński, Kvantovaya Elektron. (Moscow) 7, 1407 (1980) [Sov. J. Quantum Electron. 10, 811 (1980)].

M. Osiński, P. G. Eliseev, IEE J. Solid-State Electron Devices 3, 215 (1979).
[CrossRef]

M. Osiński, Opt. Quantum Electron. 9, 361 (1977).
[CrossRef]

M. Osiński, AEU Arch. Elektron. Ubertragungstech. Electron. Commun. 30, 223 (1976).

T. Choroś, M. Osiński, in Proceedings, International Conference Radiative Recombination and Related Phenomena in III–V Compound Semiconductors RECON-79, Prague, 4–7 Sept. 1979, p. 32.

T. Dziewiecka, M. Osiński, in Proceedings, International Workshop on the Physics of Semiconductor Devices, Delhi, India, 23–28 Nov. 1981, p. 60.

Paoli, T. L.

T. L. Paoli, IEEE J. Quantum Electron. QE-13, 662 (1977).
[CrossRef]

T. L. Paoli, IEEE J. Quantum Electron. QE-12, 770 (1976).
[CrossRef]

Patel, N. B.

T. J. S. Mattos, N. B. Patel, F. D. Nunes, J. Appl. Phys. 53, 149 (1982).
[CrossRef]

F. D. Nunes, N. B. Patel, J. G. Mendoza Alvarez, J. E. Ripper, J. Appl. Phys. 50, 3852 (1979).
[CrossRef]

Petermann, K.

K. Petermann, Opt. Quantum Electron. 13, 323 (1981).
[CrossRef]

Pietzsch, J.

J. Pietzsch, Electron. Lett. 18, 1015 (1982).
[CrossRef]

Ripper, J. E.

F. D. Nunes, N. B. Patel, J. G. Mendoza Alvarez, J. E. Ripper, J. Appl. Phys. 50, 3852 (1979).
[CrossRef]

Rozzi, T. E.

K. A. Shore, T. E. Rozzi, Proc. Inst. Electr. Eng. Part I: Solid-State Electron Devices 128, 154 (1981).

K. A. Shore, T. E. Rozzi, G. H. in’t Veld, Proc. Inst. Electr. Eng. Part I: Solid-State Electron Devices 127, 221 (1980).

Scifres, D. R.

W. Streifer, D. R. Scifres, R. D. Burnham, Electron. Lett. 17, 933 (1981).
[CrossRef]

W. Streifer, R. D. Burnham, D. R. Scifres, IEEE J. Quantum Electron. QE-15, 136 (1979).
[CrossRef]

W. Streifer, D. R. Scifres, R. D. Burnham, IEEE J. Quantum Electron. QE-14, 418 (1978).
[CrossRef]

Selway, P. R.

P. A. Kirkby, A. R. Goodwin, G. H. B. Thompson, P. R. Selway, IEEE J. Quantum Electron. QE-13, 705 (1977).
[CrossRef]

Shimizu, H.

T. Sugino, K. Itoh, H. Shimizu, M. Wada, I. Teramoto, IEEE J. Quantum Electron. QE-17, 745 (1981).
[CrossRef]

Shore, K. A.

K. A. Shore, T. E. Rozzi, Proc. Inst. Electr. Eng. Part I: Solid-State Electron Devices 128, 154 (1981).

K. A. Shore, T. E. Rozzi, G. H. in’t Veld, Proc. Inst. Electr. Eng. Part I: Solid-State Electron Devices 127, 221 (1980).

Sommers, H. S.

H. S. Sommers, J. Appl. Phys. 50, 6630 (1979).
[CrossRef]

J. K. Butler, H. S. Sommers, IEEE J. Quantum Electron. QE-14, 413 (1978).
[CrossRef]

Stolyarov, S. N.

S. N. Stolyarov, Kvantovaya Elektron. No. 8, 69 (1972) [Sov. J. Quantum Electron. 2, 144 (1972)].

Streifer, W.

W. Streifer, D. R. Scifres, R. D. Burnham, Electron. Lett. 17, 933 (1981).
[CrossRef]

W. Streifer, R. D. Burnham, D. R. Scifres, IEEE J. Quantum Electron. QE-15, 136 (1979).
[CrossRef]

W. Streifer, E. Kapon, Appl. Opt. 18, 3724 (1979).
[CrossRef] [PubMed]

W. Streifer, D. R. Scifres, R. D. Burnham, IEEE J. Quantum Electron. QE-14, 418 (1978).
[CrossRef]

Su, C. B.

C. B. Su, J. Appl. Phys. 52, 2665 (1981).
[CrossRef]

Sugino, T.

T. Sugino, K. Itoh, H. Shimizu, M. Wada, I. Teramoto, IEEE J. Quantum Electron. QE-17, 745 (1981).
[CrossRef]

Teramoto, I.

T. Sugino, K. Itoh, H. Shimizu, M. Wada, I. Teramoto, IEEE J. Quantum Electron. QE-17, 745 (1981).
[CrossRef]

Thompson, G. H. B.

G. H. B. Thompson, D. F. Lovelace, S. E. H. Turley, IEEE J. Quantum Electron. QE-15, 772 (1979).
[CrossRef]

G. H. B. Thompson, D. F. Lovelace, S. E. H. Turley, IEE J. Solid-State Electron Devices 2, 12 (1978).
[CrossRef]

P. A. Kirkby, A. R. Goodwin, G. H. B. Thompson, P. R. Selway, IEEE J. Quantum Electron. QE-13, 705 (1977).
[CrossRef]

G. H. B. Thompson, G. D. Henshall, J. E. A. Whiteaway, P. A. Kirkby, J. Appl. Phys. 47, 1501 (1976).
[CrossRef]

Turley, S. E. H.

G. H. B. Thompson, D. F. Lovelace, S. E. H. Turley, IEEE J. Quantum Electron. QE-15, 772 (1979).
[CrossRef]

G. H. B. Thompson, D. F. Lovelace, S. E. H. Turley, IEE J. Solid-State Electron Devices 2, 12 (1978).
[CrossRef]

Veld, G. H. in’t

K. A. Shore, T. E. Rozzi, G. H. in’t Veld, Proc. Inst. Electr. Eng. Part I: Solid-State Electron Devices 127, 221 (1980).

Wada, M.

T. Sugino, K. Itoh, H. Shimizu, M. Wada, I. Teramoto, IEEE J. Quantum Electron. QE-17, 745 (1981).
[CrossRef]

Whiteaway, J. E. A.

G. H. B. Thompson, G. D. Henshall, J. E. A. Whiteaway, P. A. Kirkby, J. Appl. Phys. 47, 1501 (1976).
[CrossRef]

Acta Phys. Pol. A

M. Osiński, Acta Phys. Pol. A 60, 109 (1981).

AEU Arch. Elektron. Ubertragungstech. Electron. Commun.

M. Osiński, AEU Arch. Elektron. Ubertragungstech. Electron. Commun. 30, 223 (1976).

Appl. Opt.

Appl. Phys. Lett.

P. M. Asbeck, D. A. Cammack, J. J. Daniele, Appl. Phys. Lett. 33, 504 (1978).
[CrossRef]

Bell Syst. Tech. J.

R. W. Dixon, W. B. Joyce, Bell Syst. Tech. J. 59, 975 (1980).

Can. J. Phys.

R. Burman, R. N. Gould, Can. J. Phys. 43, 921 (1965).
[CrossRef]

Electron. Lett.

W. Streifer, D. R. Scifres, R. D. Burnham, Electron. Lett. 17, 933 (1981).
[CrossRef]

J. Pietzsch, Electron. Lett. 18, 1015 (1982).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Transverse cross section of a planar stripe-geometry heterojunction laser. The active region is confined within |x| < d/2 and |y| < s/2. The injection current flows along the x axis.

Fig. 2
Fig. 2

Profiles of real (top) and imaginary (bottom) parts of permittivity for stripe lasers with generalized Epstein layer in the junction plane (parameters given in Table I).

Fig. 3
Fig. 3

Another set of examples of generalized Epstein profiles for stripe lasers with parameters given in Table I.

Fig. 4
Fig. 4

Distribution of lateral near-field intensity for the fundamental mode for six cases corresponding to respective generalized Epstein profiles from Fig. 2.

Fig. 5
Fig. 5

Near-field patterns for the fundamental lateral mode calculated for respective generalized Epstein profiles from Fig. 3.

Tables (2)

Tables Icon

Table I Parameters Used in Calculations of Generalized Epstein Profiles and Fundamental-Mode Near Fields

Tables Icon

Table II Position of Near-Field Maximum yF and of Minimum of Imaginary Part of Permittivity yG Relative to Stripe Center and Stripe Width s

Equations (32)

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{ v ( 1 - v ) d 2 d v 2 + [ γ - ( α + β + 1 ) v ] d d v - α β } F ( α , β , γ ; v ) = 0 ,
[ d 2 d x 2 + K 2 ( x ) ] ψ ( x ) = 0 ,
F ( α , β , γ ; v ) = θ ( x ) ψ ( x )
θ ( x ) = v - γ / 2 ( 1 - v ) ( γ - α - β - 1 ) / 2 ( d v d x ) 1 / 2 ,
K 2 ( x ) = ½ d 2 d x 2 ( ln d v d x ) - ¼ [ d d x ( ln d v d x ) ] 2 - ( d d x ln v ) 2 [ K 1 + K 2 v ( 1 - v ) 2 + K 3 v 1 - v ] ,
( x ) = 1 + 2 exp ( x / l ) [ 1 + exp ( x / l ) ] 2 + ( 3 - 1 ) exp ( x / l ) 1 + exp ( x / l )
v ( x ) = - ½ exp ( x / a ) - ½ exp ( x / b ) ,
v ( x ) = - u ( x ) - w ( x ) ,
u ( x ) = ξ exp ( x / a ) ,
w ( x ) = ζ exp ( x / b ) .
k 0 2 ( x ) = K 2 ( x ) = ( b - a ) 2 u w 2 a b ( b u + a w ) 2 - [ b 2 u + a 2 w 2 a b ( b u + a w ) ] 2 + [ b u + a w a b ( u + w ) ] 2 [ K 1 + K 2 u + w ( 1 + u + w ) 2 + K 3 u + w 1 + u + w ] .
( x , y ) = ¯ ( x ) + ˜ ( x , y ) ,
˜ ( x , y ) = { 0 x > d / 2 , ( y ) x d / 2 ,
˜ ( x , y ) ¯ ( x ) .
Δ 2 E ( x , y ) + [ k 0 2 ( x , y ) - q 2 ] E ( x , y ) = 0
d 2 Y ( y ) d y 2 + [ k 0 2 Γ E ( y ) - p 2 ] Y ( y ) = 0 ,
E x ( x , y ) = X ( x ) Y ( y ) .
( y ) = [ K 2 ( y ) + p 2 ] / ( k 0 2 Γ E ) ,
Y ( y ) 2 y 0.
Y Q ( y ) = A Q v 1 - γ / 2 ( 1 - v ) ( α + β + 1 - γ ) / 2 ( b u + a w ) - 1 / 2 × d Q d v Q [ v γ + Q + 1 ( 1 - v ) - β ] ,
γ - α = - Q
α = [ 1 + 1 - 4 A + 1 + 4 B - 1 - 4 ( A + C ) ] / 2 ;
β = [ 1 + 1 - 4 A + 1 + 4 B + 1 - 4 ( A + C ) ] / 2 ;
γ = 1 + 1 - 4 A ;
A = 0.25 + [ max ( a , b ) ] 2 ( k 0 2 Γ E 1 - p 2 ) ,
C = [ min ( a , b ) ] 2 ( k 0 2 Γ E 3 - p 2 ) - [ max ( a , b ) ] 2 × ( k 0 2 Γ E 1 - p 2 ) ,
B = ( 1 + ξ + ζ ) 2 ξ + ζ ( ( ξ + ζ ξ b + ζ a ) 2 { a 2 b 2 [ k 0 2 Γ E ( 0 ) - p 2 ] - 2 ξ ζ a b ( b - a ) 2 - ( ξ b 2 + ζ a 2 ) 2 4 ( ξ b + ζ a ) 2 } - A - C ξ + ζ 1 + ξ + ζ ) ,
1 = lim y - ( y ) ,
3 = lim y ( y ) .
Y 0 ( y ) = A 0 v γ / 2 ( 1 - v ) ( 1 - β ) / 2 ( b u + a w ) - 1 / 2 ,
Y 1 ( y ) = A 1 v γ / 2 ( 1 - v ) - β / 2 ( b u + a w ) - 1 / 2 [ v ( β - γ ) + γ ] ,
Y 2 ( y ) = A 2 v γ / 2 ( 1 - v ) ( - 1 - β ) / 2 ( b u + a w ) - 1 / 2 [ v 2 ( γ - β ) × ( γ + 1 - β ) + 2 v ( β - γ ) ( γ + 1 ) + γ ( γ + 1 ) ] .

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