Abstract

It is shown theoretically that the relaxation oscillation in the direct modulation of the injection laser is reduced by transverse carrier diffusion when the stripe width is comparable to the carrier diffusion length. Modified rate equations are derived by considering the distribution of the light intensity, the carrier density, and the diffusion of the carrier. By small-signal analysis of the rate equations it is found that the height of the resonancelike peak in the modulation characteristics is a minimum when the transverse width in which both the light and the carriers are confined is around the diffusion length.

© 1978 Optical Society of America

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References

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  1. T. Ikegami, Y. Suematsu, J. Inst. Elect. Commun. Eng. Jpn. 51-B, 57 (1968).
  2. T. Ikegami, K. Kobayashi, Y. Suematsu, J. Inst. Elect. Commun. Eng. Jpn. 53-B, 246 (1970).
  3. N. G. Basov, V. V. Nikitin, A. S. Semenov, Usp. Fiz. Nauk. 97, 561 (1969);M. J. Adams, Opto-electronics 5, 201 (1973).
    [CrossRef]
  4. K. Saito, N. Shige, T. Kajimura, T. Tsukada, M. Maeda, T. Ito, 1977 International Conference on Integrated Optics and Optical Fiber Communication, Tokyo (1977) A5-1;H. Nishi, H. Kuwahara, K. Hanamitsu, M. Takusagawa, T. Kudo, in 1977 International Conference on Integrated Optics and Optical Fiber Communication, Tokyo (1977) A6-2;H. Kawaguchi, T. Kawakami, in 1976 IEEE International Semiconductor Laser Conference, Nemu-no-sato (1976) L-11-7;M. Nagano, K. Kasahara, T. Hashimoto, in 1976 IEEE International Semiconductor Laser Conference, Nemu-no-sato (1976) L-IV-7.
  5. T. Kobayashi, H. Kawaguchi, Y. Furukawa, Jpn. J. Appl. Phys. 16, 601 (1977).
    [CrossRef]
  6. K. Kumabe, Jpn. J. Appl. Phys. 15, 2249 (1976).
    [CrossRef]
  7. T. Ikegami, in 1st European Conference on Optical Fiber Communication, London (1975), p. 111.
  8. N. Chinone, Central Laboratory of Hitachi Ltd.; private communication.
  9. W. Streifer, R. D. Burnham, D. R. Scifres, IEEE J. Quantum Electron. QE-13, 403 (1977).
    [CrossRef]
  10. M. Danielsen, The Electromagnetics Institute, Technical University of Denmark; private communication.
  11. Y. Suematsu, S. Akiba, T. Hong, IEEE J. Quantum Electron. QE-13, 596 (1977).
    [CrossRef]
  12. Y. Suematsu, K. Furuya, Trans. IECE Jpn. E60, 467 (1977).
  13. H. C. Casey, B. I. Miller, E. Pinkas, J. Appl. Phys. 44, 1281 (1973).
    [CrossRef]
  14. T. Hong, Y. Suematsu, in 1977 International Conference on Integrated Optics and Optical Fiber Communication, Tokyo (1977), A5-2
  15. K. Nagano, M. Maeda, M. Tanaka, K. Saito, R. Ito, Paper of Technical Group on Optical and Quantum Electronics of Japan, OQE77-19 (1977) (in Japanese).

1977 (5)

T. Kobayashi, H. Kawaguchi, Y. Furukawa, Jpn. J. Appl. Phys. 16, 601 (1977).
[CrossRef]

W. Streifer, R. D. Burnham, D. R. Scifres, IEEE J. Quantum Electron. QE-13, 403 (1977).
[CrossRef]

Y. Suematsu, S. Akiba, T. Hong, IEEE J. Quantum Electron. QE-13, 596 (1977).
[CrossRef]

Y. Suematsu, K. Furuya, Trans. IECE Jpn. E60, 467 (1977).

K. Nagano, M. Maeda, M. Tanaka, K. Saito, R. Ito, Paper of Technical Group on Optical and Quantum Electronics of Japan, OQE77-19 (1977) (in Japanese).

1976 (1)

K. Kumabe, Jpn. J. Appl. Phys. 15, 2249 (1976).
[CrossRef]

1973 (1)

H. C. Casey, B. I. Miller, E. Pinkas, J. Appl. Phys. 44, 1281 (1973).
[CrossRef]

1970 (1)

T. Ikegami, K. Kobayashi, Y. Suematsu, J. Inst. Elect. Commun. Eng. Jpn. 53-B, 246 (1970).

1969 (1)

N. G. Basov, V. V. Nikitin, A. S. Semenov, Usp. Fiz. Nauk. 97, 561 (1969);M. J. Adams, Opto-electronics 5, 201 (1973).
[CrossRef]

1968 (1)

T. Ikegami, Y. Suematsu, J. Inst. Elect. Commun. Eng. Jpn. 51-B, 57 (1968).

Akiba, S.

Y. Suematsu, S. Akiba, T. Hong, IEEE J. Quantum Electron. QE-13, 596 (1977).
[CrossRef]

Basov, N. G.

N. G. Basov, V. V. Nikitin, A. S. Semenov, Usp. Fiz. Nauk. 97, 561 (1969);M. J. Adams, Opto-electronics 5, 201 (1973).
[CrossRef]

Burnham, R. D.

W. Streifer, R. D. Burnham, D. R. Scifres, IEEE J. Quantum Electron. QE-13, 403 (1977).
[CrossRef]

Casey, H. C.

H. C. Casey, B. I. Miller, E. Pinkas, J. Appl. Phys. 44, 1281 (1973).
[CrossRef]

Chinone, N.

N. Chinone, Central Laboratory of Hitachi Ltd.; private communication.

Danielsen, M.

M. Danielsen, The Electromagnetics Institute, Technical University of Denmark; private communication.

Furukawa, Y.

T. Kobayashi, H. Kawaguchi, Y. Furukawa, Jpn. J. Appl. Phys. 16, 601 (1977).
[CrossRef]

Furuya, K.

Y. Suematsu, K. Furuya, Trans. IECE Jpn. E60, 467 (1977).

Hong, T.

Y. Suematsu, S. Akiba, T. Hong, IEEE J. Quantum Electron. QE-13, 596 (1977).
[CrossRef]

T. Hong, Y. Suematsu, in 1977 International Conference on Integrated Optics and Optical Fiber Communication, Tokyo (1977), A5-2

Ikegami, T.

T. Ikegami, K. Kobayashi, Y. Suematsu, J. Inst. Elect. Commun. Eng. Jpn. 53-B, 246 (1970).

T. Ikegami, Y. Suematsu, J. Inst. Elect. Commun. Eng. Jpn. 51-B, 57 (1968).

T. Ikegami, in 1st European Conference on Optical Fiber Communication, London (1975), p. 111.

Ito, R.

K. Nagano, M. Maeda, M. Tanaka, K. Saito, R. Ito, Paper of Technical Group on Optical and Quantum Electronics of Japan, OQE77-19 (1977) (in Japanese).

Ito, T.

K. Saito, N. Shige, T. Kajimura, T. Tsukada, M. Maeda, T. Ito, 1977 International Conference on Integrated Optics and Optical Fiber Communication, Tokyo (1977) A5-1;H. Nishi, H. Kuwahara, K. Hanamitsu, M. Takusagawa, T. Kudo, in 1977 International Conference on Integrated Optics and Optical Fiber Communication, Tokyo (1977) A6-2;H. Kawaguchi, T. Kawakami, in 1976 IEEE International Semiconductor Laser Conference, Nemu-no-sato (1976) L-11-7;M. Nagano, K. Kasahara, T. Hashimoto, in 1976 IEEE International Semiconductor Laser Conference, Nemu-no-sato (1976) L-IV-7.

Kajimura, T.

K. Saito, N. Shige, T. Kajimura, T. Tsukada, M. Maeda, T. Ito, 1977 International Conference on Integrated Optics and Optical Fiber Communication, Tokyo (1977) A5-1;H. Nishi, H. Kuwahara, K. Hanamitsu, M. Takusagawa, T. Kudo, in 1977 International Conference on Integrated Optics and Optical Fiber Communication, Tokyo (1977) A6-2;H. Kawaguchi, T. Kawakami, in 1976 IEEE International Semiconductor Laser Conference, Nemu-no-sato (1976) L-11-7;M. Nagano, K. Kasahara, T. Hashimoto, in 1976 IEEE International Semiconductor Laser Conference, Nemu-no-sato (1976) L-IV-7.

Kawaguchi, H.

T. Kobayashi, H. Kawaguchi, Y. Furukawa, Jpn. J. Appl. Phys. 16, 601 (1977).
[CrossRef]

Kobayashi, K.

T. Ikegami, K. Kobayashi, Y. Suematsu, J. Inst. Elect. Commun. Eng. Jpn. 53-B, 246 (1970).

Kobayashi, T.

T. Kobayashi, H. Kawaguchi, Y. Furukawa, Jpn. J. Appl. Phys. 16, 601 (1977).
[CrossRef]

Kumabe, K.

K. Kumabe, Jpn. J. Appl. Phys. 15, 2249 (1976).
[CrossRef]

Maeda, M.

K. Nagano, M. Maeda, M. Tanaka, K. Saito, R. Ito, Paper of Technical Group on Optical and Quantum Electronics of Japan, OQE77-19 (1977) (in Japanese).

K. Saito, N. Shige, T. Kajimura, T. Tsukada, M. Maeda, T. Ito, 1977 International Conference on Integrated Optics and Optical Fiber Communication, Tokyo (1977) A5-1;H. Nishi, H. Kuwahara, K. Hanamitsu, M. Takusagawa, T. Kudo, in 1977 International Conference on Integrated Optics and Optical Fiber Communication, Tokyo (1977) A6-2;H. Kawaguchi, T. Kawakami, in 1976 IEEE International Semiconductor Laser Conference, Nemu-no-sato (1976) L-11-7;M. Nagano, K. Kasahara, T. Hashimoto, in 1976 IEEE International Semiconductor Laser Conference, Nemu-no-sato (1976) L-IV-7.

Miller, B. I.

H. C. Casey, B. I. Miller, E. Pinkas, J. Appl. Phys. 44, 1281 (1973).
[CrossRef]

Nagano, K.

K. Nagano, M. Maeda, M. Tanaka, K. Saito, R. Ito, Paper of Technical Group on Optical and Quantum Electronics of Japan, OQE77-19 (1977) (in Japanese).

Nikitin, V. V.

N. G. Basov, V. V. Nikitin, A. S. Semenov, Usp. Fiz. Nauk. 97, 561 (1969);M. J. Adams, Opto-electronics 5, 201 (1973).
[CrossRef]

Pinkas, E.

H. C. Casey, B. I. Miller, E. Pinkas, J. Appl. Phys. 44, 1281 (1973).
[CrossRef]

Saito, K.

K. Nagano, M. Maeda, M. Tanaka, K. Saito, R. Ito, Paper of Technical Group on Optical and Quantum Electronics of Japan, OQE77-19 (1977) (in Japanese).

K. Saito, N. Shige, T. Kajimura, T. Tsukada, M. Maeda, T. Ito, 1977 International Conference on Integrated Optics and Optical Fiber Communication, Tokyo (1977) A5-1;H. Nishi, H. Kuwahara, K. Hanamitsu, M. Takusagawa, T. Kudo, in 1977 International Conference on Integrated Optics and Optical Fiber Communication, Tokyo (1977) A6-2;H. Kawaguchi, T. Kawakami, in 1976 IEEE International Semiconductor Laser Conference, Nemu-no-sato (1976) L-11-7;M. Nagano, K. Kasahara, T. Hashimoto, in 1976 IEEE International Semiconductor Laser Conference, Nemu-no-sato (1976) L-IV-7.

Scifres, D. R.

W. Streifer, R. D. Burnham, D. R. Scifres, IEEE J. Quantum Electron. QE-13, 403 (1977).
[CrossRef]

Semenov, A. S.

N. G. Basov, V. V. Nikitin, A. S. Semenov, Usp. Fiz. Nauk. 97, 561 (1969);M. J. Adams, Opto-electronics 5, 201 (1973).
[CrossRef]

Shige, N.

K. Saito, N. Shige, T. Kajimura, T. Tsukada, M. Maeda, T. Ito, 1977 International Conference on Integrated Optics and Optical Fiber Communication, Tokyo (1977) A5-1;H. Nishi, H. Kuwahara, K. Hanamitsu, M. Takusagawa, T. Kudo, in 1977 International Conference on Integrated Optics and Optical Fiber Communication, Tokyo (1977) A6-2;H. Kawaguchi, T. Kawakami, in 1976 IEEE International Semiconductor Laser Conference, Nemu-no-sato (1976) L-11-7;M. Nagano, K. Kasahara, T. Hashimoto, in 1976 IEEE International Semiconductor Laser Conference, Nemu-no-sato (1976) L-IV-7.

Streifer, W.

W. Streifer, R. D. Burnham, D. R. Scifres, IEEE J. Quantum Electron. QE-13, 403 (1977).
[CrossRef]

Suematsu, Y.

Y. Suematsu, K. Furuya, Trans. IECE Jpn. E60, 467 (1977).

Y. Suematsu, S. Akiba, T. Hong, IEEE J. Quantum Electron. QE-13, 596 (1977).
[CrossRef]

T. Ikegami, K. Kobayashi, Y. Suematsu, J. Inst. Elect. Commun. Eng. Jpn. 53-B, 246 (1970).

T. Ikegami, Y. Suematsu, J. Inst. Elect. Commun. Eng. Jpn. 51-B, 57 (1968).

T. Hong, Y. Suematsu, in 1977 International Conference on Integrated Optics and Optical Fiber Communication, Tokyo (1977), A5-2

Tanaka, M.

K. Nagano, M. Maeda, M. Tanaka, K. Saito, R. Ito, Paper of Technical Group on Optical and Quantum Electronics of Japan, OQE77-19 (1977) (in Japanese).

Tsukada, T.

K. Saito, N. Shige, T. Kajimura, T. Tsukada, M. Maeda, T. Ito, 1977 International Conference on Integrated Optics and Optical Fiber Communication, Tokyo (1977) A5-1;H. Nishi, H. Kuwahara, K. Hanamitsu, M. Takusagawa, T. Kudo, in 1977 International Conference on Integrated Optics and Optical Fiber Communication, Tokyo (1977) A6-2;H. Kawaguchi, T. Kawakami, in 1976 IEEE International Semiconductor Laser Conference, Nemu-no-sato (1976) L-11-7;M. Nagano, K. Kasahara, T. Hashimoto, in 1976 IEEE International Semiconductor Laser Conference, Nemu-no-sato (1976) L-IV-7.

IEEE J. Quantum Electron. (2)

W. Streifer, R. D. Burnham, D. R. Scifres, IEEE J. Quantum Electron. QE-13, 403 (1977).
[CrossRef]

Y. Suematsu, S. Akiba, T. Hong, IEEE J. Quantum Electron. QE-13, 596 (1977).
[CrossRef]

J. Appl. Phys. (1)

H. C. Casey, B. I. Miller, E. Pinkas, J. Appl. Phys. 44, 1281 (1973).
[CrossRef]

J. Inst. Elect. Commun. Eng. Jpn. (2)

T. Ikegami, Y. Suematsu, J. Inst. Elect. Commun. Eng. Jpn. 51-B, 57 (1968).

T. Ikegami, K. Kobayashi, Y. Suematsu, J. Inst. Elect. Commun. Eng. Jpn. 53-B, 246 (1970).

Jpn. J. Appl. Phys. (2)

T. Kobayashi, H. Kawaguchi, Y. Furukawa, Jpn. J. Appl. Phys. 16, 601 (1977).
[CrossRef]

K. Kumabe, Jpn. J. Appl. Phys. 15, 2249 (1976).
[CrossRef]

Paper of Technical Group on Optical and Quantum Electronics of Japan (1)

K. Nagano, M. Maeda, M. Tanaka, K. Saito, R. Ito, Paper of Technical Group on Optical and Quantum Electronics of Japan, OQE77-19 (1977) (in Japanese).

Trans. IECE Jpn. (1)

Y. Suematsu, K. Furuya, Trans. IECE Jpn. E60, 467 (1977).

Usp. Fiz. Nauk. (1)

N. G. Basov, V. V. Nikitin, A. S. Semenov, Usp. Fiz. Nauk. 97, 561 (1969);M. J. Adams, Opto-electronics 5, 201 (1973).
[CrossRef]

Other (5)

K. Saito, N. Shige, T. Kajimura, T. Tsukada, M. Maeda, T. Ito, 1977 International Conference on Integrated Optics and Optical Fiber Communication, Tokyo (1977) A5-1;H. Nishi, H. Kuwahara, K. Hanamitsu, M. Takusagawa, T. Kudo, in 1977 International Conference on Integrated Optics and Optical Fiber Communication, Tokyo (1977) A6-2;H. Kawaguchi, T. Kawakami, in 1976 IEEE International Semiconductor Laser Conference, Nemu-no-sato (1976) L-11-7;M. Nagano, K. Kasahara, T. Hashimoto, in 1976 IEEE International Semiconductor Laser Conference, Nemu-no-sato (1976) L-IV-7.

T. Ikegami, in 1st European Conference on Optical Fiber Communication, London (1975), p. 111.

N. Chinone, Central Laboratory of Hitachi Ltd.; private communication.

M. Danielsen, The Electromagnetics Institute, Technical University of Denmark; private communication.

T. Hong, Y. Suematsu, in 1977 International Conference on Integrated Optics and Optical Fiber Communication, Tokyo (1977), A5-2

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Figures (4)

Fig. 1
Fig. 1

Structure of stripe-laser and transverse distributions of light and carrier concentration.

Fig. 2
Fig. 2

Modulated light intensity normalized by that of the low frequency limit vs the frequency normalized by the inverse of carrier lifetime 1/τs. The parameter is the stripe width normalized by the carrier diffusion length.

Fig. 3
Fig. 3

Height of resonancelike peak vs stripe width. L is the carrier diffusion length.

Fig. 4
Fig. 4

Modulation characteristics measured and calculated. Discrete points indicate data; lines are theoretical. Experimental data were reported in Ref. 15.

Equations (10)

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d S / d t = ( g S + C / τ s ) F 2 ( r ) N ( x , t ) d υ S / τ p ,
d N ( x , t ) / d t = J / ( e a ) + D 2 / x 2 N ( x , t ) N ( x , t ) / τ s g V S F 2 ( r ) N ( x , t ) ,
F ( r ) = 2 2 / ( l w a ) 1 / 2 cos ( π x / w ) cos ( π y / a ) sin ( m π z / l ) ,
N ( x , t ) N 0 ( t ) N 1 ( t ) cos ( 2 π x / w ) ,
d S / d t = [ g ( N 0 N 1 / 2 ) 1 / τ p ] S + C ( N 0 N 1 / 2 ) / τ s , d N 0 / d t = J / ( e a ) N 0 / τ s g S ( N 0 N 1 / 2 ) , d N 1 / d t = N 1 / τ s + g S ( N 0 N 1 ) h N 1 / τ s , }
h = ( 2 π L / w ) 2 ,
N e 0 = [ 1 C ( J / J t h + 2 h + 2 ) / ( J / J t h + 2 h + 1 ) / ( J / J t h 1 ) ] / ( g τ p ) .
Δ f = ( 1 N e 0 g τ p ) / ( 2 π τ p ) .
f 0 = [ ( J / J t h 1 ) / ( τ s τ p ) ] 1 / 2 .
( w / L ) opt = 5.0 / [ ( J / J t h 1 ) τ s / τ p ] 1 / 4 .

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