Abstract

Switching between linearly polarized states of slightly different optical frequencies with the same transverse-mode pattern is found, as the injection current is increased. Switchings found here for semiconductor rate-equation models incorporating a vector electric field, birefringence, and the α factor are similar to previously reported experimental results.

© 1996 Optical Society of America

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  1. C. J. Chang-Hasnain, J. P. Harbison, G Hasnain, A. C. Von Lehmen, L. T. Florez, N. G. StoffelIEEE J. Quantum Electron. 27, 1402 (1991).
  2. K. D. Choquette, R. E. LeibenguthIEEE Photon. Technol. Lett. 6, 40 (1994).
  3. K. D. Choquette, D. A. Richie, R. E. LeibenguthAppl. Phys. Lett. 64, 2062(1994).
  4. H Li, T. L. Lucas, J. G. McInerney, R. A. MorganChaos Solitons Fractals 4, 1619 (1994).
  5. Z. G. Pan, S Jiang, M DegenaisAppl. Phys. Lett. 63, 2999(1993).
  6. A Chavez-Pirson, H Ando, H Saito, H KanbeAppl. Phys. Lett. 62, 3082 (1993).
  7. K. D. Choquette, K. L. Lear, R. E. Leibenguth, M. T. AsomAppl. Phys. Lett. 64, 2767 (1994).
  8. A. K. Jansen van Doorn, M. P. van Exter, J. P. WoerdmanElectron. Lett. 30, 1941 (1994).
  9. S Jiang, Z Pan, M Dagenais, R. A. Morgan, K KojimaAppl. Phys. Lett. 63, 3545 (1993).
  10. C. J. Chang-Hasnain, J. P. Harbison, L. T. Florez, N. G. StoffelElectron. Lett. 27, 163 (1991).
  11. M San Miguel, Q Feng, J. V. MoloneyPhys. Rev. A 52, 1728 (1995).
  12. F Meier, B. P. Zachachrenyaeds., Optical Orientation(North-Holland, Amsterdam, 1984).
  13. T. C. Damen, L Vina, J. E. Cunningham, J Shah, L. J. ShamPhys. Rev. Lett. 67, 3432(1991);S. Bar-Ad, I. Bar-Joseph, Phys. Rev. Lett. 68, 349(1992).
  14. W Van HaeringenPhys. Rev. 158, 256 (1967);D. Lenstra, Phys. Rep. 59, 299 (1980).
  15. M. P. van Exter, A. K. Jansen van Doorn, R. F. M. Hendriks, J. P. WoerdmanProc. SPIE2693(1996);A. K. Jansen van Doorn, M. P. van Exter, M. Travagnin, J. P. Woerdman (personal communication, 1996).

1995

M San Miguel, Q Feng, J. V. MoloneyPhys. Rev. A 52, 1728 (1995).

1994

K. D. Choquette, R. E. LeibenguthIEEE Photon. Technol. Lett. 6, 40 (1994).

K. D. Choquette, D. A. Richie, R. E. LeibenguthAppl. Phys. Lett. 64, 2062(1994).

H Li, T. L. Lucas, J. G. McInerney, R. A. MorganChaos Solitons Fractals 4, 1619 (1994).

K. D. Choquette, K. L. Lear, R. E. Leibenguth, M. T. AsomAppl. Phys. Lett. 64, 2767 (1994).

A. K. Jansen van Doorn, M. P. van Exter, J. P. WoerdmanElectron. Lett. 30, 1941 (1994).

1993

S Jiang, Z Pan, M Dagenais, R. A. Morgan, K KojimaAppl. Phys. Lett. 63, 3545 (1993).

Z. G. Pan, S Jiang, M DegenaisAppl. Phys. Lett. 63, 2999(1993).

A Chavez-Pirson, H Ando, H Saito, H KanbeAppl. Phys. Lett. 62, 3082 (1993).

1991

C. J. Chang-Hasnain, J. P. Harbison, L. T. Florez, N. G. StoffelElectron. Lett. 27, 163 (1991).

T. C. Damen, L Vina, J. E. Cunningham, J Shah, L. J. ShamPhys. Rev. Lett. 67, 3432(1991);S. Bar-Ad, I. Bar-Joseph, Phys. Rev. Lett. 68, 349(1992).

C. J. Chang-Hasnain, J. P. Harbison, G Hasnain, A. C. Von Lehmen, L. T. Florez, N. G. StoffelIEEE J. Quantum Electron. 27, 1402 (1991).

1967

W Van HaeringenPhys. Rev. 158, 256 (1967);D. Lenstra, Phys. Rep. 59, 299 (1980).

Ando, H

A Chavez-Pirson, H Ando, H Saito, H KanbeAppl. Phys. Lett. 62, 3082 (1993).

Asom, M. T.

K. D. Choquette, K. L. Lear, R. E. Leibenguth, M. T. AsomAppl. Phys. Lett. 64, 2767 (1994).

Chang-Hasnain, C. J.

C. J. Chang-Hasnain, J. P. Harbison, L. T. Florez, N. G. StoffelElectron. Lett. 27, 163 (1991).

C. J. Chang-Hasnain, J. P. Harbison, G Hasnain, A. C. Von Lehmen, L. T. Florez, N. G. StoffelIEEE J. Quantum Electron. 27, 1402 (1991).

Chavez-Pirson, A

A Chavez-Pirson, H Ando, H Saito, H KanbeAppl. Phys. Lett. 62, 3082 (1993).

Choquette, K. D.

K. D. Choquette, K. L. Lear, R. E. Leibenguth, M. T. AsomAppl. Phys. Lett. 64, 2767 (1994).

K. D. Choquette, R. E. LeibenguthIEEE Photon. Technol. Lett. 6, 40 (1994).

K. D. Choquette, D. A. Richie, R. E. LeibenguthAppl. Phys. Lett. 64, 2062(1994).

Cunningham, J. E.

T. C. Damen, L Vina, J. E. Cunningham, J Shah, L. J. ShamPhys. Rev. Lett. 67, 3432(1991);S. Bar-Ad, I. Bar-Joseph, Phys. Rev. Lett. 68, 349(1992).

Dagenais, M

S Jiang, Z Pan, M Dagenais, R. A. Morgan, K KojimaAppl. Phys. Lett. 63, 3545 (1993).

Damen, T. C.

T. C. Damen, L Vina, J. E. Cunningham, J Shah, L. J. ShamPhys. Rev. Lett. 67, 3432(1991);S. Bar-Ad, I. Bar-Joseph, Phys. Rev. Lett. 68, 349(1992).

Degenais, M

Z. G. Pan, S Jiang, M DegenaisAppl. Phys. Lett. 63, 2999(1993).

Feng, Q

M San Miguel, Q Feng, J. V. MoloneyPhys. Rev. A 52, 1728 (1995).

Florez, L. T.

C. J. Chang-Hasnain, J. P. Harbison, L. T. Florez, N. G. StoffelElectron. Lett. 27, 163 (1991).

C. J. Chang-Hasnain, J. P. Harbison, G Hasnain, A. C. Von Lehmen, L. T. Florez, N. G. StoffelIEEE J. Quantum Electron. 27, 1402 (1991).

Harbison, J. P.

C. J. Chang-Hasnain, J. P. Harbison, G Hasnain, A. C. Von Lehmen, L. T. Florez, N. G. StoffelIEEE J. Quantum Electron. 27, 1402 (1991).

C. J. Chang-Hasnain, J. P. Harbison, L. T. Florez, N. G. StoffelElectron. Lett. 27, 163 (1991).

Hasnain, G

C. J. Chang-Hasnain, J. P. Harbison, G Hasnain, A. C. Von Lehmen, L. T. Florez, N. G. StoffelIEEE J. Quantum Electron. 27, 1402 (1991).

Hendriks, R. F. M.

M. P. van Exter, A. K. Jansen van Doorn, R. F. M. Hendriks, J. P. WoerdmanProc. SPIE2693(1996);A. K. Jansen van Doorn, M. P. van Exter, M. Travagnin, J. P. Woerdman (personal communication, 1996).

Jansen van Doorn, A. K.

A. K. Jansen van Doorn, M. P. van Exter, J. P. WoerdmanElectron. Lett. 30, 1941 (1994).

M. P. van Exter, A. K. Jansen van Doorn, R. F. M. Hendriks, J. P. WoerdmanProc. SPIE2693(1996);A. K. Jansen van Doorn, M. P. van Exter, M. Travagnin, J. P. Woerdman (personal communication, 1996).

Jiang, S

S Jiang, Z Pan, M Dagenais, R. A. Morgan, K KojimaAppl. Phys. Lett. 63, 3545 (1993).

Z. G. Pan, S Jiang, M DegenaisAppl. Phys. Lett. 63, 2999(1993).

Kanbe, H

A Chavez-Pirson, H Ando, H Saito, H KanbeAppl. Phys. Lett. 62, 3082 (1993).

Kojima, K

S Jiang, Z Pan, M Dagenais, R. A. Morgan, K KojimaAppl. Phys. Lett. 63, 3545 (1993).

Lear, K. L.

K. D. Choquette, K. L. Lear, R. E. Leibenguth, M. T. AsomAppl. Phys. Lett. 64, 2767 (1994).

Leibenguth, R. E.

K. D. Choquette, K. L. Lear, R. E. Leibenguth, M. T. AsomAppl. Phys. Lett. 64, 2767 (1994).

K. D. Choquette, D. A. Richie, R. E. LeibenguthAppl. Phys. Lett. 64, 2062(1994).

K. D. Choquette, R. E. LeibenguthIEEE Photon. Technol. Lett. 6, 40 (1994).

Li, H

H Li, T. L. Lucas, J. G. McInerney, R. A. MorganChaos Solitons Fractals 4, 1619 (1994).

Lucas, T. L.

H Li, T. L. Lucas, J. G. McInerney, R. A. MorganChaos Solitons Fractals 4, 1619 (1994).

McInerney, J. G.

H Li, T. L. Lucas, J. G. McInerney, R. A. MorganChaos Solitons Fractals 4, 1619 (1994).

Moloney, J. V.

M San Miguel, Q Feng, J. V. MoloneyPhys. Rev. A 52, 1728 (1995).

Morgan, R. A.

H Li, T. L. Lucas, J. G. McInerney, R. A. MorganChaos Solitons Fractals 4, 1619 (1994).

S Jiang, Z Pan, M Dagenais, R. A. Morgan, K KojimaAppl. Phys. Lett. 63, 3545 (1993).

Pan, Z

S Jiang, Z Pan, M Dagenais, R. A. Morgan, K KojimaAppl. Phys. Lett. 63, 3545 (1993).

Pan, Z. G.

Z. G. Pan, S Jiang, M DegenaisAppl. Phys. Lett. 63, 2999(1993).

Richie, D. A.

K. D. Choquette, D. A. Richie, R. E. LeibenguthAppl. Phys. Lett. 64, 2062(1994).

Saito, H

A Chavez-Pirson, H Ando, H Saito, H KanbeAppl. Phys. Lett. 62, 3082 (1993).

San Miguel, M

M San Miguel, Q Feng, J. V. MoloneyPhys. Rev. A 52, 1728 (1995).

Shah, J

T. C. Damen, L Vina, J. E. Cunningham, J Shah, L. J. ShamPhys. Rev. Lett. 67, 3432(1991);S. Bar-Ad, I. Bar-Joseph, Phys. Rev. Lett. 68, 349(1992).

Sham, L. J.

T. C. Damen, L Vina, J. E. Cunningham, J Shah, L. J. ShamPhys. Rev. Lett. 67, 3432(1991);S. Bar-Ad, I. Bar-Joseph, Phys. Rev. Lett. 68, 349(1992).

Stoffel, N. G.

C. J. Chang-Hasnain, J. P. Harbison, L. T. Florez, N. G. StoffelElectron. Lett. 27, 163 (1991).

C. J. Chang-Hasnain, J. P. Harbison, G Hasnain, A. C. Von Lehmen, L. T. Florez, N. G. StoffelIEEE J. Quantum Electron. 27, 1402 (1991).

van Exter, M. P.

A. K. Jansen van Doorn, M. P. van Exter, J. P. WoerdmanElectron. Lett. 30, 1941 (1994).

M. P. van Exter, A. K. Jansen van Doorn, R. F. M. Hendriks, J. P. WoerdmanProc. SPIE2693(1996);A. K. Jansen van Doorn, M. P. van Exter, M. Travagnin, J. P. Woerdman (personal communication, 1996).

Van Haeringen, W

W Van HaeringenPhys. Rev. 158, 256 (1967);D. Lenstra, Phys. Rep. 59, 299 (1980).

Vina, L

T. C. Damen, L Vina, J. E. Cunningham, J Shah, L. J. ShamPhys. Rev. Lett. 67, 3432(1991);S. Bar-Ad, I. Bar-Joseph, Phys. Rev. Lett. 68, 349(1992).

Von Lehmen, A. C.

C. J. Chang-Hasnain, J. P. Harbison, G Hasnain, A. C. Von Lehmen, L. T. Florez, N. G. StoffelIEEE J. Quantum Electron. 27, 1402 (1991).

Woerdman, J. P.

A. K. Jansen van Doorn, M. P. van Exter, J. P. WoerdmanElectron. Lett. 30, 1941 (1994).

M. P. van Exter, A. K. Jansen van Doorn, R. F. M. Hendriks, J. P. WoerdmanProc. SPIE2693(1996);A. K. Jansen van Doorn, M. P. van Exter, M. Travagnin, J. P. Woerdman (personal communication, 1996).

Appl. Phys. Lett.

K. D. Choquette, D. A. Richie, R. E. LeibenguthAppl. Phys. Lett. 64, 2062(1994).

Z. G. Pan, S Jiang, M DegenaisAppl. Phys. Lett. 63, 2999(1993).

A Chavez-Pirson, H Ando, H Saito, H KanbeAppl. Phys. Lett. 62, 3082 (1993).

K. D. Choquette, K. L. Lear, R. E. Leibenguth, M. T. AsomAppl. Phys. Lett. 64, 2767 (1994).

S Jiang, Z Pan, M Dagenais, R. A. Morgan, K KojimaAppl. Phys. Lett. 63, 3545 (1993).

Chaos Solitons Fractals

H Li, T. L. Lucas, J. G. McInerney, R. A. MorganChaos Solitons Fractals 4, 1619 (1994).

Electron. Lett.

A. K. Jansen van Doorn, M. P. van Exter, J. P. WoerdmanElectron. Lett. 30, 1941 (1994).

C. J. Chang-Hasnain, J. P. Harbison, L. T. Florez, N. G. StoffelElectron. Lett. 27, 163 (1991).

IEEE J. Quantum Electron

C. J. Chang-Hasnain, J. P. Harbison, G Hasnain, A. C. Von Lehmen, L. T. Florez, N. G. StoffelIEEE J. Quantum Electron. 27, 1402 (1991).

IEEE Photon. Technol. Lett.

K. D. Choquette, R. E. LeibenguthIEEE Photon. Technol. Lett. 6, 40 (1994).

Phys. Rev.

W Van HaeringenPhys. Rev. 158, 256 (1967);D. Lenstra, Phys. Rep. 59, 299 (1980).

Phys. Rev. A

M San Miguel, Q Feng, J. V. MoloneyPhys. Rev. A 52, 1728 (1995).

Phys. Rev. Lett.

T. C. Damen, L Vina, J. E. Cunningham, J Shah, L. J. ShamPhys. Rev. Lett. 67, 3432(1991);S. Bar-Ad, I. Bar-Joseph, Phys. Rev. Lett. 68, 349(1992).

Other

M. P. van Exter, A. K. Jansen van Doorn, R. F. M. Hendriks, J. P. WoerdmanProc. SPIE2693(1996);A. K. Jansen van Doorn, M. P. van Exter, M. Travagnin, J. P. Woerdman (personal communication, 1996).

F Meier, B. P. Zachachrenyaeds., Optical Orientation(North-Holland, Amsterdam, 1984).

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Figures (3)

Fig. 1
Fig. 1

Stability diagram of the linearly polarized solutions for the parameters κ = 300 ns−1, γ = 1 ns−1, γs = 50 ns−1, and α = 3.

Fig. 2
Fig. 2

Time-averaged (20-ns) power of the x ^-polarized (filled circles) and ŷ-polarized (open circles) field components and their total (solid lines) for γp = 2γ, showing switching in (a) the absence (γa = 0) and (b) the presence (γa = −0.1γ) of linear amplitude anisotropy. For selected (indicated) currents, Re(Eγ) versus Re(Ex) is shown at the top of the figure, and the optical spectra are shown in (c), in which x ^- and ŷ-polarized field spectra are indicated by solid and dashed curves, respectively.

Fig. 3
Fig. 3

Time-averaged power for γp = 10γ in (a) the absence (γa = 0) and (b) the presence (γa = 0.1γ) of linear amplitude anisotropy. Other details as in Fig. 2.

Equations (8)

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d E ± d t = κ E ± i ω 0 E ± + κ ( 1 + i α ) ( N ± n ) E ± i γ p E γ a E ,
d N d t = γ ( N μ ) γ ( N + n ) | E + | 2 γ ( N n ) | E | 2 ,
d n d t = γ s n γ ( N + n ) | E + | 2 + γ ( N n ) | E | 2 ,
d E ± d t = ( κ + γ a ) E x i ( ω 0 + γ p ) E x + κ ( 1 + i α ) ( N E x + i n E y ) ,
d E y d t = ( κ γ a ) E y i ( ω 0 γ p ) E y + κ ( 1 + i α ) ( N E y + i n E x ) .
P ( λ ) = λ 3 + ( γ s γ + μ 1 ) λ 2 + [ 2 κ γ ( μ 1 ) + 4 ( γ p γ ) 2 ] λ 4 κ γ p γ 2 × α ( μ 1 ) + 4 ( γ p γ ) 2 ( γ s γ + μ 1 ) ,
( γ p γ ) x > [ κ γ α ( μ 1 ) ] / ( γ s γ + μ 1 )
( γ p γ ) y < ( γ s γ + μ 1 ) / 2 α

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