Abstract

Polarization-resolved dynamics of mutually coupled vertical-cavity surface-emitting lasers with asymmetrical injections is studied. For one laser, the injection parameters, such as injection rate, lasing frequency, and propagation phase, are set to fixed values, while for the other laser these parameters are taken as variables. The results show that asymmetrical injections have great influence on the dynamics and polarization state of the system. Subjected to injections with different degrees of asymmetry, the lasers can experience bifurcations in the original polarization, polarization switching to the orthogonal direction, or emission with both of the two linearly polarized modes.

© 2008 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  28. R. Vicente, J. Mulet, C. R. Mirasso, and M. Sciamanna, "Bistable polarization switching in mutually coupled vertical-cavity surface-emitting lasers," Opt. Lett. 31, 996-998 (2006).
    [CrossRef] [PubMed]
  29. W. L. Zhang, W. Pan, B. Luo, X. F. Li, X. H. Zou, and M. Y. Wang, "Polarization switching of mutually coupled vertical-cavity surface-emitting lasers," J. Opt. Soc. Am. B 24, 1276-1282 (2007).
    [CrossRef]
  30. W. L. Zhang, W. Pan, B. Luo, X. F. Li, X. H. Zou, and M. Y. Wang, "Influence of mutual injection on the polarization switching dynamics of vertical-cavity surface-emitting lasers," J. Opt. Soc. Am. B 24, 2472-2478 (2007).
    [CrossRef]
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    [CrossRef]

2007 (3)

2006 (8)

R. Vicente, J. Mulet, C. R. Mirasso, and M. Sciamanna, "Polarization switching dynamics and bistability in mutually coupled vertical-cavity surface-emitting lasers," Proc. SPIE 6184, 618413 (2006).
[CrossRef]

R. Vicente, J. Mulet, C. R. Mirasso, and M. Sciamanna, "Bistable polarization switching in mutually coupled vertical-cavity surface-emitting lasers," Opt. Lett. 31, 996-998 (2006).
[CrossRef] [PubMed]

X. F. Li, W. Pan, B. Luo, and D. Ma, "Multi-transverse-mode dynamics of vertical-cavity surface-emitting lasers with external optical injection," J. Opt. Soc. Am. B 23, 1292-1301 (2006).
[CrossRef]

M. Sciamanna and K. Panajotov, "Route to polarization switching induced by optical injection in vertical-cavity surface-emitting lasers," Phys. Rev. A 73, 023811 (2006).
[CrossRef]

I. Gatare, M. Sciamanna, J. Buesa, T. Hhienpont, and K. Panajotov, "Nonlinear dynamics accompanying polarization switching in vertical-cavity surface-emitting lasers with orthogonal optical injection," Appl. Phys. Lett. 88, 101106 (2006).
[CrossRef]

C. Masoller, M. S. Torre, and P. Mandel, "Influence of the injection current sweep rate on the polarization switching of vertical-cavity surface-emitting lasers," J. Appl. Phys. 99, 026108 (2006).
[CrossRef]

J. Paul, C. Masoller, Y. Hong, P. S. Spencer, and K. A. Shore, "Experimental study of polarization switching of vertical-cavity surface-emitting lasers as a dynamical bifurcation," Opt. Lett. 33, 748-750 (2006).
[CrossRef]

M. A. Arteaga, H. J. Unold, J. M. Ostermann, R. Michalzik, H. Thienpont, and K. Panajotov, "Investigation of polarization properties of VCSELs subject to optical feedback from an extremely short external cavity—part I: theoretical analysis," IEEE J. Quantum Electron. 42, 89-101 (2006).
[CrossRef]

2005 (3)

C. Masoller and M. S. Torre, "Influence of optical feedback on the polarization switching of vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 41, 483-489 (2005).
[CrossRef]

H. Erzgräber, D. Lenstra, B. Krauskopf, E. Wille, M. Peil, I. Fischer, and W. Elsäßer, "Mutually delay-coupled semiconductor lasers: mode bifurcation scenarios," Opt. Commun. 255, 286-296 (2005).
[CrossRef]

Y. Hong, R. Ju, P. S. Spencer, and K. A. Shore, "Investigation of polarization bistability in vertical-cavity surface-emitting lasers subjected to optical feedback," IEEE J. Quantum Electron. 41, 619-624 (2005).
[CrossRef]

2004 (2)

S. Tang, R. Vicente, M. C. Chiang, C. R. Mirasso, and J. M. Liu, "Nonlinear dynamics of semiconductor lasers with mutual optoelectronic coupling," IEEE J. Sel. Top. Quantum Electron. 10, 936-943 (2004).
[CrossRef]

M. C. Soriano, M. Yousefi, J. Danckaert, S. Barland, M. Romanelli, G. Giacomelli, and F. Marin, "Low-frequency fluctuations in vertical-cavity surface-emitting lasers with polarization selective feedback: experiment and theory," IEEE J. Sel. Top. Quantum Electron. 10, 998-1005 (2004).
[CrossRef]

2003 (4)

2002 (1)

J. Danckaert, B. Nagler, J. Albert, K. Panajotov, I. Veretennicoff, and T. Erneux, "Minimal rate equations describing polarization switching in vertical-cavity surface-emitting lasers," Opt. Commun. 201, 129-137 (2002).
[CrossRef]

2001 (3)

J. Mulet, C. R. Mirasso, and M. S. Miguel, "Polarization resolved intensity noise in vertical-cavity surface-emitting lasers," Phys. Rev. A 64, 023817 (2001).
[CrossRef]

T. Heil, I. Fischer, and W. Elsässer, "Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers," Phys. Rev. Lett. 86, 795-798 (2001).
[CrossRef] [PubMed]

C. R. Mirasso, M. Kolesik, M. Matus, J. K. White, and J. V. Moloney, "Synchronization and multimode dynamics of mutually coupled semiconductor lasers," Phys. Rev. A 65, 013805 (2001).
[CrossRef]

2000 (1)

K. Iga, "Surface-emitting laser—its birth and generation of new optoelectronics field," IEEE J. Sel. Top. Quantum Electron. 6, 1201-1215 (2000).
[CrossRef]

1999 (1)

C. Masoller and N. B. Abraham, "Low-frequency fluctuation in vertical-cavity surface-emitting semiconductor lasers with optical feedback," Phys. Rev. A 59, 3021-3031 (1999).
[CrossRef]

1998 (1)

A. Valle, L. Pesquera, and K. A. Shore, "Polarization selection and sensitivity of external cavity vertical-cavity surface-emitting laser diodes," IEEE Photon. Technol. Lett. 10, 639-641 (1998).
[CrossRef]

1997 (1)

T. H. Russell and T. D. Milster, "Polarization switching control in vertical-cavity surface-emitting laser," Appl. Phys. Lett. 70, 2520-2522 (1997).
[CrossRef]

1995 (1)

M. S. Miguel, Q. Feng, and J. V. Moloney, "Light-polarization dynamics in surface-emitting semiconductor lasers," Phys. Rev. A 52, 1728-1739 (1995).
[CrossRef]

1993 (1)

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, "Optical injection induced polarization bistability in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 63, 2999-3001 (1993).
[CrossRef]

Appl. Phys. Lett. (3)

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, "Optical injection induced polarization bistability in vertical-cavity surface-emitting lasers," Appl. Phys. Lett. 63, 2999-3001 (1993).
[CrossRef]

T. H. Russell and T. D. Milster, "Polarization switching control in vertical-cavity surface-emitting laser," Appl. Phys. Lett. 70, 2520-2522 (1997).
[CrossRef]

I. Gatare, M. Sciamanna, J. Buesa, T. Hhienpont, and K. Panajotov, "Nonlinear dynamics accompanying polarization switching in vertical-cavity surface-emitting lasers with orthogonal optical injection," Appl. Phys. Lett. 88, 101106 (2006).
[CrossRef]

IEEE J. Quantum Electron. (4)

A. Valle, I. Gatare, K. Panajotov, and M. Sciamanna, "Transverse mode switching and locking in vertical-cavity surface-emitting lasers subject to orthogonal optical injection," IEEE J. Quantum Electron. 43, 322-333 (2007).
[CrossRef]

Y. Hong, R. Ju, P. S. Spencer, and K. A. Shore, "Investigation of polarization bistability in vertical-cavity surface-emitting lasers subjected to optical feedback," IEEE J. Quantum Electron. 41, 619-624 (2005).
[CrossRef]

M. A. Arteaga, H. J. Unold, J. M. Ostermann, R. Michalzik, H. Thienpont, and K. Panajotov, "Investigation of polarization properties of VCSELs subject to optical feedback from an extremely short external cavity—part I: theoretical analysis," IEEE J. Quantum Electron. 42, 89-101 (2006).
[CrossRef]

C. Masoller and M. S. Torre, "Influence of optical feedback on the polarization switching of vertical-cavity surface-emitting lasers," IEEE J. Quantum Electron. 41, 483-489 (2005).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (3)

M. C. Soriano, M. Yousefi, J. Danckaert, S. Barland, M. Romanelli, G. Giacomelli, and F. Marin, "Low-frequency fluctuations in vertical-cavity surface-emitting lasers with polarization selective feedback: experiment and theory," IEEE J. Sel. Top. Quantum Electron. 10, 998-1005 (2004).
[CrossRef]

S. Tang, R. Vicente, M. C. Chiang, C. R. Mirasso, and J. M. Liu, "Nonlinear dynamics of semiconductor lasers with mutual optoelectronic coupling," IEEE J. Sel. Top. Quantum Electron. 10, 936-943 (2004).
[CrossRef]

K. Iga, "Surface-emitting laser—its birth and generation of new optoelectronics field," IEEE J. Sel. Top. Quantum Electron. 6, 1201-1215 (2000).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

A. Valle, L. Pesquera, and K. A. Shore, "Polarization selection and sensitivity of external cavity vertical-cavity surface-emitting laser diodes," IEEE Photon. Technol. Lett. 10, 639-641 (1998).
[CrossRef]

J. Appl. Phys. (1)

C. Masoller, M. S. Torre, and P. Mandel, "Influence of the injection current sweep rate on the polarization switching of vertical-cavity surface-emitting lasers," J. Appl. Phys. 99, 026108 (2006).
[CrossRef]

J. Opt. Soc. Am. B (3)

Opt. Commun. (3)

J. Danckaert, B. Nagler, J. Albert, K. Panajotov, I. Veretennicoff, and T. Erneux, "Minimal rate equations describing polarization switching in vertical-cavity surface-emitting lasers," Opt. Commun. 201, 129-137 (2002).
[CrossRef]

H. Erzgräber, D. Lenstra, B. Krauskopf, E. Wille, M. Peil, I. Fischer, and W. Elsäßer, "Mutually delay-coupled semiconductor lasers: mode bifurcation scenarios," Opt. Commun. 255, 286-296 (2005).
[CrossRef]

Y. Hong, P. S. Spencer, S. Bandyopadhyay, P. Rees, and K. A. Shore, "Polarization-resolved chaos and instabilities in a vertical-cavity surface-emitting laser subject to optical injection," Opt. Commun. 216, 185-189 (2003).
[CrossRef]

Opt. Lett. (5)

Phys. Rev. A (5)

C. R. Mirasso, M. Kolesik, M. Matus, J. K. White, and J. V. Moloney, "Synchronization and multimode dynamics of mutually coupled semiconductor lasers," Phys. Rev. A 65, 013805 (2001).
[CrossRef]

M. S. Miguel, Q. Feng, and J. V. Moloney, "Light-polarization dynamics in surface-emitting semiconductor lasers," Phys. Rev. A 52, 1728-1739 (1995).
[CrossRef]

J. Mulet, C. R. Mirasso, and M. S. Miguel, "Polarization resolved intensity noise in vertical-cavity surface-emitting lasers," Phys. Rev. A 64, 023817 (2001).
[CrossRef]

M. Sciamanna and K. Panajotov, "Route to polarization switching induced by optical injection in vertical-cavity surface-emitting lasers," Phys. Rev. A 73, 023811 (2006).
[CrossRef]

C. Masoller and N. B. Abraham, "Low-frequency fluctuation in vertical-cavity surface-emitting semiconductor lasers with optical feedback," Phys. Rev. A 59, 3021-3031 (1999).
[CrossRef]

Phys. Rev. Lett. (1)

T. Heil, I. Fischer, and W. Elsässer, "Chaos synchronization and spontaneous symmetry-breaking in symmetrically delay-coupled semiconductor lasers," Phys. Rev. Lett. 86, 795-798 (2001).
[CrossRef] [PubMed]

Proc. SPIE (1)

R. Vicente, J. Mulet, C. R. Mirasso, and M. Sciamanna, "Polarization switching dynamics and bistability in mutually coupled vertical-cavity surface-emitting lasers," Proc. SPIE 6184, 618413 (2006).
[CrossRef]

Other (1)

W. L. Zhang, W. Pan, B. Luo, M. Y. Wang, and X. H. Zou, "Polarization switching and hysteresis of VCSELs with time-varying optical injection," IEEE J. Sel. Top. Quantum Electron. (to be published).

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Figures (10)

Fig. 1
Fig. 1

Average intensities of the XP and YP modes of laser 1 in the parameter space of injection rate and delay, with Δ ω = 0 and ϕ 1 = ϕ 2 = 0 .

Fig. 2
Fig. 2

(a) Bifurcation diagram of output intensity of laser 1 as a function of η. (b) Values of N for the CLMs at which the system operates. Dark (light) gray corresponds to the XP (YP) mode.

Fig. 3
Fig. 3

Average intensities of the XP and YP modes in the parameter space of ε and τ, with Δ ω = 0 , η 1 = 15 ns 1 , and ϕ 1 = ϕ 2 = 0 . (a) XP and (b) YP modes of laser 1; (c) XP and (d) YP modes of laser 2.

Fig. 4
Fig. 4

As in Fig. 3 except that Δ ω = 20 rad ns .

Fig. 5
Fig. 5

Bifurcation diagram of output intensity as a function of ε, with Δ ω = 0 , τ = 0.2 ns , η 1 = 15 ns 1 , and ϕ 1 = ϕ 2 = 0 . Output of laser 1 for (a) increasing and (b) decreasing ε; output of laser 2 with (c) increasing and (d) decreasing ε.

Fig. 6
Fig. 6

Output intensity of laser 1 in the time and frequency domains. From (a) to (f), ε = 0.05 , 0.15 , 0.3 , 0.35 , 0.5 , 0.9 ; other conditions are the same as in Fig. 4.

Fig. 7
Fig. 7

Cross correlation of the two lasers as a function of ε. Values of parameters are same as in Fig. 4. Solid, dotted, and dashed–dotted curves correspond to Δ t = 0.2 , 0, 0.2 ns , respectively.

Fig. 8
Fig. 8

Bifurcation diagram of output intensity as a function of Δ ω , with τ = 0.2 ns , ϕ 1 = ϕ 2 = 0 , η 1 = η 2 = 15 ns 1 . Output of laser 1 with (a) increasing and (b) decreasing Δ ω ; output of laser 2 with (c) increasing and (d) decreasing Δ ω .

Fig. 9
Fig. 9

Cross correlation of the two lasers as a function of Δ ω . Values of parameters are same as in Fig. 7. Solid, dotted, and dashed–dotted curves correspond to Δ t = 0.2 , 0, 0.2 ns , respectively.

Fig. 10
Fig. 10

Bifurcation diagram of output intensity as a function of Δ ϕ , with τ = 0.2 ns , ϕ 1 = 0 , Δ ω = 0 , and η 1 = η 2 = 15 ns 1 . Output of laser 1 with (a) increasing and (b) decreasing Δ ϕ ; output of laser 2 with (c) increasing and (d) decreasing Δ ϕ .

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

d E X , i d t = k ( 1 + j α ) ( N i E X , i E X , i + j n i E Y , i ) ( γ a + j γ p ) E X , i + j ( 1 ) i Δ ω E X , i + η i exp ( i ϕ i ) E X , 3 i ( t τ ) ,
d E Y , i d t = k ( 1 + j α ) ( N i E Y , i E Y , i j n i E X , i ) + ( γ a + j γ p ) E Y , i + j ( 1 ) i Δ ω E Y , i + η i exp ( i ϕ i ) E Y , 3 i ( t τ ) ,
d N i d t = γ e N i ( 1 + E X , i 2 + E Y , i 2 ) + γ e μ i j γ e n i ( E Y , i E X , i * E X , i E Y , i * ) ,
d n i d t = γ s n i γ e n i ( E X , i 2 + E Y , i 2 ) j γ e N i ( E Y , i E X , i * E X , i E Y , i * ) ,
C ( Δ t ) = ( P 1 ( t ) P 1 ) ( P 2 ( t + Δ t ) P 2 ) ( P 1 ( t ) P 1 ) 2 ( P 2 ( t + Δ t ) P 2 ) 2 ,

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