Abstract

The effects of unpredictability degree on the chaos synchronization properties of vertical-cavity surface-emitting lasers with variable-polarization optical feedback are investigated numerically. For variable-polarization optical injection, only low-unpredictability chaos can be well synchronized, while high-unpredictability chaos cannot be synchronized even with large injection strength. On the other hand, for the polarization-preserved optical injection, the synchronization quality is hardly affected by the unpredictability degree, and high-quality synchronization can be achieved for both low- and high-unpredictability chaos due to injection locking.

© 2011 Optical Society of America

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2011 (3)

2010 (3)

S. Xiang, W. Pan, L. Yan, B. Luo, N. Jiang, K. Wen, X. Zou, and L. Yang, J. Opt. Soc. Am. B 27, 476 (2010).
[CrossRef]

J. Tiana-Alsina, M. C. Torrent, O. A. Rosso, C. Masoller, and J. Garcia-Ojalvo, Phys. Rev. A 82, 013819 (2010).
[CrossRef]

M. C. Soriano, L. Zunino, O. A. Rosso, and C. R. Mirasso, Proc. SPIE 7720, 77202G_1 (2010).

2009 (2)

2008 (3)

2007 (2)

M. Sciamanna, I. Gatare, A. Locquet, and K. Panajotov, Phys. Rev. E 75, 056213 (2007).
[CrossRef]

I. Gatare, M. Sciamanna, A. Locquet, and K. Panajotov, Opt. Lett. 32, 1629 (2007).
[CrossRef] [PubMed]

2005 (2)

R. Ju, P. S. Spencer, and K. A. Shore, IEEE J. Quantum Electron. 41, 1461 (2005).
[CrossRef]

R. Vicente, J. Daudén, P. Colet, and R. Toral, IEEE J. Quantum Electron. 41, 541 (2005).
[CrossRef]

2003 (1)

A. Scire, J. Mulet, C. R. Mirasso, J. Danckaert, and M. S. Miguel, Phys. Rev. Lett. 90, 113901 (2003).
[CrossRef] [PubMed]

2002 (1)

C. Bandt and B. Pompe, Phys. Rev. Lett. 88, 174102 (2002).
[CrossRef] [PubMed]

1997 (1)

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, IEEE J. Quantum Electron. 33, 765 (1997).
[CrossRef]

1996 (1)

S. Ramanujan, G. P. Agrawal, J. M. Chwalek, H. Winful, IEEE J. Quantum Electron. 32, 213 (1996).
[CrossRef]

1995 (1)

M. San Miguel, Q. Feng, and J. V. Moloney, Phys. Rev. A 52, 1728 (1995).
[CrossRef] [PubMed]

Abraham, N. B.

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, IEEE J. Quantum Electron. 33, 765 (1997).
[CrossRef]

Agrawal, G. P.

S. Ramanujan, G. P. Agrawal, J. M. Chwalek, H. Winful, IEEE J. Quantum Electron. 32, 213 (1996).
[CrossRef]

Bandt, C.

C. Bandt and B. Pompe, Phys. Rev. Lett. 88, 174102 (2002).
[CrossRef] [PubMed]

Chwalek, J. M.

S. Ramanujan, G. P. Agrawal, J. M. Chwalek, H. Winful, IEEE J. Quantum Electron. 32, 213 (1996).
[CrossRef]

Colet, P.

R. Vicente, J. Daudén, P. Colet, and R. Toral, IEEE J. Quantum Electron. 41, 541 (2005).
[CrossRef]

Danckaert, J.

A. Scire, J. Mulet, C. R. Mirasso, J. Danckaert, and M. S. Miguel, Phys. Rev. Lett. 90, 113901 (2003).
[CrossRef] [PubMed]

Daudén, J.

R. Vicente, J. Daudén, P. Colet, and R. Toral, IEEE J. Quantum Electron. 41, 541 (2005).
[CrossRef]

Feng, Q.

M. San Miguel, Q. Feng, and J. V. Moloney, Phys. Rev. A 52, 1728 (1995).
[CrossRef] [PubMed]

Fischer, I.

M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, and C. R. Mirasso, IEEE J. Quantum Electron. 47, 252 (2011).
[CrossRef]

Garcia-Ojalvo, J.

J. Tiana-Alsina, M. C. Torrent, O. A. Rosso, C. Masoller, and J. Garcia-Ojalvo, Phys. Rev. A 82, 013819 (2010).
[CrossRef]

Gatare, I.

I. Gatare, M. Sciamanna, A. Locquet, and K. Panajotov, Opt. Lett. 32, 1629 (2007).
[CrossRef] [PubMed]

M. Sciamanna, I. Gatare, A. Locquet, and K. Panajotov, Phys. Rev. E 75, 056213 (2007).
[CrossRef]

Hong, Y.

Jiang, N.

Ju, R.

R. Ju, P. S. Spencer, and K. A. Shore, IEEE J. Quantum Electron. 41, 1461 (2005).
[CrossRef]

Lee, M. W.

Liu, J.

Locquet, A.

M. Sciamanna, I. Gatare, A. Locquet, and K. Panajotov, Phys. Rev. E 75, 056213 (2007).
[CrossRef]

I. Gatare, M. Sciamanna, A. Locquet, and K. Panajotov, Opt. Lett. 32, 1629 (2007).
[CrossRef] [PubMed]

Luo, B.

Martin-Regalado, J.

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, IEEE J. Quantum Electron. 33, 765 (1997).
[CrossRef]

Masoller, C.

J. Tiana-Alsina, M. C. Torrent, O. A. Rosso, C. Masoller, and J. Garcia-Ojalvo, Phys. Rev. A 82, 013819 (2010).
[CrossRef]

Miguel, M. S.

A. Scire, J. Mulet, C. R. Mirasso, J. Danckaert, and M. S. Miguel, Phys. Rev. Lett. 90, 113901 (2003).
[CrossRef] [PubMed]

Mirasso, C. R.

M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, and C. R. Mirasso, IEEE J. Quantum Electron. 47, 252 (2011).
[CrossRef]

M. C. Soriano, L. Zunino, O. A. Rosso, and C. R. Mirasso, Proc. SPIE 7720, 77202G_1 (2010).

O. A. Rosso, R. Vicente, C. R. Mirasso, Phys. Lett. A 372, 1018 (2008).
[CrossRef]

A. Scire, J. Mulet, C. R. Mirasso, J. Danckaert, and M. S. Miguel, Phys. Rev. Lett. 90, 113901 (2003).
[CrossRef] [PubMed]

Moloney, J. V.

M. San Miguel, Q. Feng, and J. V. Moloney, Phys. Rev. A 52, 1728 (1995).
[CrossRef] [PubMed]

Mulet, J.

A. Scire, J. Mulet, C. R. Mirasso, J. Danckaert, and M. S. Miguel, Phys. Rev. Lett. 90, 113901 (2003).
[CrossRef] [PubMed]

Pan, W.

Panajotov, K.

Paul, J.

Pompe, B.

C. Bandt and B. Pompe, Phys. Rev. Lett. 88, 174102 (2002).
[CrossRef] [PubMed]

Prati, F.

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, IEEE J. Quantum Electron. 33, 765 (1997).
[CrossRef]

Ramanujan, S.

S. Ramanujan, G. P. Agrawal, J. M. Chwalek, H. Winful, IEEE J. Quantum Electron. 32, 213 (1996).
[CrossRef]

Rosso, O. A.

M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, and C. R. Mirasso, IEEE J. Quantum Electron. 47, 252 (2011).
[CrossRef]

J. Tiana-Alsina, M. C. Torrent, O. A. Rosso, C. Masoller, and J. Garcia-Ojalvo, Phys. Rev. A 82, 013819 (2010).
[CrossRef]

M. C. Soriano, L. Zunino, O. A. Rosso, and C. R. Mirasso, Proc. SPIE 7720, 77202G_1 (2010).

O. A. Rosso, R. Vicente, C. R. Mirasso, Phys. Lett. A 372, 1018 (2008).
[CrossRef]

San Miguel, M.

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, IEEE J. Quantum Electron. 33, 765 (1997).
[CrossRef]

M. San Miguel, Q. Feng, and J. V. Moloney, Phys. Rev. A 52, 1728 (1995).
[CrossRef] [PubMed]

Sciamanna, M.

Scire, A.

A. Scire, J. Mulet, C. R. Mirasso, J. Danckaert, and M. S. Miguel, Phys. Rev. Lett. 90, 113901 (2003).
[CrossRef] [PubMed]

Shore, K. A.

Soriano, M. C.

M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, and C. R. Mirasso, IEEE J. Quantum Electron. 47, 252 (2011).
[CrossRef]

M. C. Soriano, L. Zunino, O. A. Rosso, and C. R. Mirasso, Proc. SPIE 7720, 77202G_1 (2010).

Spencer, P. S.

Thienpont, H.

Tiana-Alsina, J.

J. Tiana-Alsina, M. C. Torrent, O. A. Rosso, C. Masoller, and J. Garcia-Ojalvo, Phys. Rev. A 82, 013819 (2010).
[CrossRef]

Toral, R.

R. Vicente, J. Daudén, P. Colet, and R. Toral, IEEE J. Quantum Electron. 41, 541 (2005).
[CrossRef]

Torrent, M. C.

J. Tiana-Alsina, M. C. Torrent, O. A. Rosso, C. Masoller, and J. Garcia-Ojalvo, Phys. Rev. A 82, 013819 (2010).
[CrossRef]

Uchida, A.

Vicente, R.

O. A. Rosso, R. Vicente, C. R. Mirasso, Phys. Lett. A 372, 1018 (2008).
[CrossRef]

R. Vicente, J. Daudén, P. Colet, and R. Toral, IEEE J. Quantum Electron. 41, 541 (2005).
[CrossRef]

Wen, K.

Winful, H.

S. Ramanujan, G. P. Agrawal, J. M. Chwalek, H. Winful, IEEE J. Quantum Electron. 32, 213 (1996).
[CrossRef]

Wu, Z. M.

Xia, G. Q.

Xiang, S.

Yan, L.

Yang, L.

Zhu, H.

Zou, X.

Zunino, L.

M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, and C. R. Mirasso, IEEE J. Quantum Electron. 47, 252 (2011).
[CrossRef]

M. C. Soriano, L. Zunino, O. A. Rosso, and C. R. Mirasso, Proc. SPIE 7720, 77202G_1 (2010).

IEEE J. Quantum Electron. (5)

R. Ju, P. S. Spencer, and K. A. Shore, IEEE J. Quantum Electron. 41, 1461 (2005).
[CrossRef]

R. Vicente, J. Daudén, P. Colet, and R. Toral, IEEE J. Quantum Electron. 41, 541 (2005).
[CrossRef]

J. Martin-Regalado, F. Prati, M. San Miguel, and N. B. Abraham, IEEE J. Quantum Electron. 33, 765 (1997).
[CrossRef]

S. Ramanujan, G. P. Agrawal, J. M. Chwalek, H. Winful, IEEE J. Quantum Electron. 32, 213 (1996).
[CrossRef]

M. C. Soriano, L. Zunino, O. A. Rosso, I. Fischer, and C. R. Mirasso, IEEE J. Quantum Electron. 47, 252 (2011).
[CrossRef]

J. Lightwave Technol. (2)

J. Opt. Soc. Am. B (1)

Opt. Express (1)

Opt. Lett. (4)

Phys. Lett. A (1)

O. A. Rosso, R. Vicente, C. R. Mirasso, Phys. Lett. A 372, 1018 (2008).
[CrossRef]

Phys. Rev. A (2)

J. Tiana-Alsina, M. C. Torrent, O. A. Rosso, C. Masoller, and J. Garcia-Ojalvo, Phys. Rev. A 82, 013819 (2010).
[CrossRef]

M. San Miguel, Q. Feng, and J. V. Moloney, Phys. Rev. A 52, 1728 (1995).
[CrossRef] [PubMed]

Phys. Rev. E (1)

M. Sciamanna, I. Gatare, A. Locquet, and K. Panajotov, Phys. Rev. E 75, 056213 (2007).
[CrossRef]

Phys. Rev. Lett. (2)

A. Scire, J. Mulet, C. R. Mirasso, J. Danckaert, and M. S. Miguel, Phys. Rev. Lett. 90, 113901 (2003).
[CrossRef] [PubMed]

C. Bandt and B. Pompe, Phys. Rev. Lett. 88, 174102 (2002).
[CrossRef] [PubMed]

Proc. SPIE (1)

M. C. Soriano, L. Zunino, O. A. Rosso, and C. R. Mirasso, Proc. SPIE 7720, 77202G_1 (2010).

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Figures (5)

Fig. 1
Fig. 1

Schematic illustration of VCSELs with RP in the external cavity. VCSEL: vertical-cavity surface- emitting laser; ML: microscopic lens; BS: beam splitter; RP: rotating polarizer; M: mirror; NDF: neutral density filter; ISO: optical isolator. The red dashed line represents the injection path, and RP2 is inserted in the injection path.

Fig. 2
Fig. 2

(a) Polarization-resolved intensities for VCSEL1 as functions of θ p , (b) PE for the total output of VCSEL1 as a function of θ p , (c)  C T T as functions of θ ps (with θ p = θ ps ) for γ = 10 ns 1 and μ = 1.5 , and (d) for different γ when μ = 1.5 , and (e) for different μ when γ = 20 ns 1 , with γ v / γ = 10 .

Fig. 3
Fig. 3

2D maps of C T T in the parameter space of (a)  θ p and γ v / γ , (b)  Δ f and γ v / γ with θ p = θ ps = 20 o , (c)  θ p and θ ps with γ v / γ = 10 , with γ = 10 ns 1 .

Fig. 4
Fig. 4

The C T T as a function of θ p (a) and γ v / γ (b), with γ = 10 ns 1 for PPOI scheme.

Fig. 5
Fig. 5

(a) The total output for VCSEL1, (b) for VCSEL2 with VPOI, and (c) with PPOI, (d) the correlation plot for VPOI, and (e) for PPOI, with γ = 10 ns 1 , θ p = 60 , and γ v / γ = 10 .

Equations (5)

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

d E 1 x / d t = k ( 1 + i α ) [ ( N 1 1 ) E 1 x + i n 1 E 1 y ] ( γ a + i γ p ) E 1 x + β sp ξ 1 x + γ E 1 x ( t τ ) cos 2 ( θ p ) e i ω τ + γ E 1 y ( t τ ) cos ( θ p ) sin ( θ p ) e i ω τ ,
d E 1 y / d t = k ( 1 + i α ) [ ( N 1 1 ) E 1 y i n 1 E 1 x ] + ( γ a + i γ p ) E 1 y + β sp ξ 1 y + γ E 1 x ( t τ ) sin ( θ p ) cos ( θ p ) e i ω τ + γ E 1 y ( t τ ) sin 2 ( θ p ) e i ω τ ,
d N 1 / d t = γ N [ μ N 1 ( 1 + | E 1 x | 2 + | E 1 y | 2 ) + i n 1 ( E 1 x E 1 y * E 1 y E 1 x * ) ] ,
d n 1 / d t = γ s n 1 γ N [ n 1 ( | E 1 x | 2 + | E 1 y | 2 ) + i N 1 ( E 1 y E 1 x * E 1 x E 1 y * ) ] .
C T T = [ I 1 T ( t τ r ) I 1 T ( t τ r ) ] [ I 2 T ( t ) I 2 T ( t ) ] [ I 1 T ( t τ r ) I 1 T ( t τ r ) ] 2 [ I 2 T ( t ) I 2 T ( t ) ] 2 .

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