Abstract

The square-wave response of edge-emitting diode lasers subject to a delayed polarization-rotated optical feedback is studied in detail. Specifically, the polarization state of the feedback is rotated such that the natural laser mode is coupled into the orthogonal, unsupported mode. Square-wave self-modulated polarization intensities oscillating in antiphase are observed experimentally. We find numerically that these oscillations naturally appear for a broad range of values of parameters, provided that the feedback is sufficiently strong and the differential losses in the normally unsupported polarization mode are small. We then investigate the laser equations analytically and find that the square-wave oscillations are the result of a bifurcation phenomenon.

© 2006 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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2006

A. Gavrielides, T. Erneux, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonette, in Proc. SPIE 6115, 60 (2006).

2005

D. W. Sukow, A. Gavrielides, T. Erneux, M. J. Baracco, Z. A. Parmenter, and K. L. Blackburn, Phys. Rev. A 72, 043818 (2005).
[CrossRef]

2003

T. Heil, A. Uchida, P. Davis, and T. Aida, Phys. Rev. A 68, 033811 (2003).
[CrossRef]

2002

J. M. Saucedo Solorio, D. W. Sukow, D. R. Hicks, and A. Gavrielides, Opt. Commun. 214, 327 (2002).
[CrossRef]

M. Sciamanna, T. Erneux, F. Rogister, O. Deparis, P. Megret, and M. Blondel, Phys. Rev. A 65, 041801(R) (2002).
[CrossRef]

2001

1999

1998

T. C. Yen, J. W. Chang, J. M. Lin, and R. J. Chen, Opt. Commun. 150, 159 (1998).
[CrossRef]

H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. Choquette, Appl. Phys. Lett. 72, 2355 (1998).
[CrossRef]

1997

F. Robert, P. Besnard, M. L. Charles, and G. M. Stephan, IEEE J. Quantum Electron. 33, 2231 (1997).
[CrossRef]

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

G. Ropars, P. Langot, M. Brunel, M. Vallet, F. Bretenaker, A. Le Floch, and K. D. Choquette, Appl. Phys. Lett. 70, 2661 (1997).
[CrossRef]

P. Saboureau, J.-P. Foing, and P. Schanne, IEEE J. Quantum Electron. 33, 1582 (1997).
[CrossRef]

1993

T. B. Simpson and J. M. Liu, J. Appl. Phys. 73, 2587 (1993).
[CrossRef]

1991

1990

W. H. Loh, Y. Ozeki, and C. L. Tang, Appl. Phys. Lett. 56, 2613 (1990).
[CrossRef]

W. H. Loh, A. T. Schremer, and C. L. Tang, IEEE Photon. Technol. Lett. 2, 467 (1990).
[CrossRef]

Abraham, N. B.

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

Ackemann, T.

Aida, T.

T. Heil, A. Uchida, P. Davis, and T. Aida, Phys. Rev. A 68, 033811 (2003).
[CrossRef]

Amonette, J.

A. Gavrielides, T. Erneux, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonette, in Proc. SPIE 6115, 60 (2006).

Balle, S.

Baracco, M. J.

D. W. Sukow, A. Gavrielides, T. Erneux, M. J. Baracco, Z. A. Parmenter, and K. L. Blackburn, Phys. Rev. A 72, 043818 (2005).
[CrossRef]

Barland, S.

Besnard, P.

F. Robert, P. Besnard, M. L. Charles, and G. M. Stephan, IEEE J. Quantum Electron. 33, 2231 (1997).
[CrossRef]

Blackburn, K. L.

D. W. Sukow, A. Gavrielides, T. Erneux, M. J. Baracco, Z. A. Parmenter, and K. L. Blackburn, Phys. Rev. A 72, 043818 (2005).
[CrossRef]

Blondel, M.

M. Sciamanna, T. Erneux, F. Rogister, O. Deparis, P. Megret, and M. Blondel, Phys. Rev. A 65, 041801(R) (2002).
[CrossRef]

F. Rogister, A. Locquet, D. Pieroux, M. Sciamanna, O. Deparis, P. Megret, and M. Blondel, Opt. Lett. 26, 1486 (2001).
[CrossRef]

Bretenaker, F.

G. Ropars, P. Langot, M. Brunel, M. Vallet, F. Bretenaker, A. Le Floch, and K. D. Choquette, Appl. Phys. Lett. 70, 2661 (1997).
[CrossRef]

Brunel, M.

G. Ropars, P. Langot, M. Brunel, M. Vallet, F. Bretenaker, A. Le Floch, and K. D. Choquette, Appl. Phys. Lett. 70, 2661 (1997).
[CrossRef]

Burner, G.

A. Gavrielides, T. Erneux, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonette, in Proc. SPIE 6115, 60 (2006).

Chang, J. W.

T. C. Yen, J. W. Chang, J. M. Lin, and R. J. Chen, Opt. Commun. 150, 159 (1998).
[CrossRef]

Charles, M. L.

F. Robert, P. Besnard, M. L. Charles, and G. M. Stephan, IEEE J. Quantum Electron. 33, 2231 (1997).
[CrossRef]

Chen, R. J.

T. C. Yen, J. W. Chang, J. M. Lin, and R. J. Chen, Opt. Commun. 150, 159 (1998).
[CrossRef]

Chern, J.-K.

Choquette, K.

H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. Choquette, Appl. Phys. Lett. 72, 2355 (1998).
[CrossRef]

Choquette, K. D.

G. Ropars, P. Langot, M. Brunel, M. Vallet, F. Bretenaker, A. Le Floch, and K. D. Choquette, Appl. Phys. Lett. 70, 2661 (1997).
[CrossRef]

Davis, P.

T. Heil, A. Uchida, P. Davis, and T. Aida, Phys. Rev. A 68, 033811 (2003).
[CrossRef]

Deparis, O.

M. Sciamanna, T. Erneux, F. Rogister, O. Deparis, P. Megret, and M. Blondel, Phys. Rev. A 65, 041801(R) (2002).
[CrossRef]

F. Rogister, A. Locquet, D. Pieroux, M. Sciamanna, O. Deparis, P. Megret, and M. Blondel, Opt. Lett. 26, 1486 (2001).
[CrossRef]

Erneux, T.

A. Gavrielides, T. Erneux, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonette, in Proc. SPIE 6115, 60 (2006).

D. W. Sukow, A. Gavrielides, T. Erneux, M. J. Baracco, Z. A. Parmenter, and K. L. Blackburn, Phys. Rev. A 72, 043818 (2005).
[CrossRef]

M. Sciamanna, T. Erneux, F. Rogister, O. Deparis, P. Megret, and M. Blondel, Phys. Rev. A 65, 041801(R) (2002).
[CrossRef]

Foing, J.-P.

P. Saboureau, J.-P. Foing, and P. Schanne, IEEE J. Quantum Electron. 33, 1582 (1997).
[CrossRef]

Gavrielides, A.

A. Gavrielides, T. Erneux, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonette, in Proc. SPIE 6115, 60 (2006).

D. W. Sukow, A. Gavrielides, T. Erneux, M. J. Baracco, Z. A. Parmenter, and K. L. Blackburn, Phys. Rev. A 72, 043818 (2005).
[CrossRef]

J. M. Saucedo Solorio, D. W. Sukow, D. R. Hicks, and A. Gavrielides, Opt. Commun. 214, 327 (2002).
[CrossRef]

H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. Choquette, Appl. Phys. Lett. 72, 2355 (1998).
[CrossRef]

Giudici, M.

Heil, T.

T. Heil, A. Uchida, P. Davis, and T. Aida, Phys. Rev. A 68, 033811 (2003).
[CrossRef]

Hicks, D. R.

J. M. Saucedo Solorio, D. W. Sukow, D. R. Hicks, and A. Gavrielides, Opt. Commun. 214, 327 (2002).
[CrossRef]

Hohl, A.

H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. Choquette, Appl. Phys. Lett. 72, 2355 (1998).
[CrossRef]

Hou, H.

H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. Choquette, Appl. Phys. Lett. 72, 2355 (1998).
[CrossRef]

Houlihan, J.

J. Houlihan, G. Huyet, and J. G. McInerney, Opt. Commun. 199, 175 (2001).
[CrossRef]

Huyet, G.

J. Houlihan, G. Huyet, and J. G. McInerney, Opt. Commun. 199, 175 (2001).
[CrossRef]

Langot, P.

G. Ropars, P. Langot, M. Brunel, M. Vallet, F. Bretenaker, A. Le Floch, and K. D. Choquette, Appl. Phys. Lett. 70, 2661 (1997).
[CrossRef]

Le Floch, A.

G. Ropars, P. Langot, M. Brunel, M. Vallet, F. Bretenaker, A. Le Floch, and K. D. Choquette, Appl. Phys. Lett. 70, 2661 (1997).
[CrossRef]

Li, H.

H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. Choquette, Appl. Phys. Lett. 72, 2355 (1998).
[CrossRef]

Lin, J. M.

T. C. Yen, J. W. Chang, J. M. Lin, and R. J. Chen, Opt. Commun. 150, 159 (1998).
[CrossRef]

Liu, J. M.

T. B. Simpson and J. M. Liu, J. Appl. Phys. 73, 2587 (1993).
[CrossRef]

Locquet, A.

Loh, W. H.

W. H. Loh, Y. Ozeki, and C. L. Tang, Appl. Phys. Lett. 56, 2613 (1990).
[CrossRef]

W. H. Loh, A. T. Schremer, and C. L. Tang, IEEE Photon. Technol. Lett. 2, 467 (1990).
[CrossRef]

Martin-Regalado, J.

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

McInerney, J. G.

J. Houlihan, G. Huyet, and J. G. McInerney, Opt. Commun. 199, 175 (2001).
[CrossRef]

McLachlan, T.

A. Gavrielides, T. Erneux, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonette, in Proc. SPIE 6115, 60 (2006).

Megret, P.

M. Sciamanna, T. Erneux, F. Rogister, O. Deparis, P. Megret, and M. Blondel, Phys. Rev. A 65, 041801(R) (2002).
[CrossRef]

F. Rogister, A. Locquet, D. Pieroux, M. Sciamanna, O. Deparis, P. Megret, and M. Blondel, Opt. Lett. 26, 1486 (2001).
[CrossRef]

Miller, J.

A. Gavrielides, T. Erneux, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonette, in Proc. SPIE 6115, 60 (2006).

Otsuka, K.

Ozeki, Y.

W. H. Loh, Y. Ozeki, and C. L. Tang, Appl. Phys. Lett. 56, 2613 (1990).
[CrossRef]

Parmenter, Z. A.

D. W. Sukow, A. Gavrielides, T. Erneux, M. J. Baracco, Z. A. Parmenter, and K. L. Blackburn, Phys. Rev. A 72, 043818 (2005).
[CrossRef]

Pieroux, D.

Prati, F.

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

Robert, F.

F. Robert, P. Besnard, M. L. Charles, and G. M. Stephan, IEEE J. Quantum Electron. 33, 2231 (1997).
[CrossRef]

Rogister, F.

M. Sciamanna, T. Erneux, F. Rogister, O. Deparis, P. Megret, and M. Blondel, Phys. Rev. A 65, 041801(R) (2002).
[CrossRef]

F. Rogister, A. Locquet, D. Pieroux, M. Sciamanna, O. Deparis, P. Megret, and M. Blondel, Opt. Lett. 26, 1486 (2001).
[CrossRef]

Ropars, G.

G. Ropars, P. Langot, M. Brunel, M. Vallet, F. Bretenaker, A. Le Floch, and K. D. Choquette, Appl. Phys. Lett. 70, 2661 (1997).
[CrossRef]

Saboureau, P.

P. Saboureau, J.-P. Foing, and P. Schanne, IEEE J. Quantum Electron. 33, 1582 (1997).
[CrossRef]

San Miguel, M.

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

Saucedo Solorio, J. M.

J. M. Saucedo Solorio, D. W. Sukow, D. R. Hicks, and A. Gavrielides, Opt. Commun. 214, 327 (2002).
[CrossRef]

Schanne, P.

P. Saboureau, J.-P. Foing, and P. Schanne, IEEE J. Quantum Electron. 33, 1582 (1997).
[CrossRef]

Schremer, A. T.

W. H. Loh, A. T. Schremer, and C. L. Tang, IEEE Photon. Technol. Lett. 2, 467 (1990).
[CrossRef]

Sciamanna, M.

M. Sciamanna, T. Erneux, F. Rogister, O. Deparis, P. Megret, and M. Blondel, Phys. Rev. A 65, 041801(R) (2002).
[CrossRef]

F. Rogister, A. Locquet, D. Pieroux, M. Sciamanna, O. Deparis, P. Megret, and M. Blondel, Opt. Lett. 26, 1486 (2001).
[CrossRef]

Simpson, T. B.

T. B. Simpson and J. M. Liu, J. Appl. Phys. 73, 2587 (1993).
[CrossRef]

Stephan, G. M.

F. Robert, P. Besnard, M. L. Charles, and G. M. Stephan, IEEE J. Quantum Electron. 33, 2231 (1997).
[CrossRef]

Sukow, D. W.

A. Gavrielides, T. Erneux, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonette, in Proc. SPIE 6115, 60 (2006).

D. W. Sukow, A. Gavrielides, T. Erneux, M. J. Baracco, Z. A. Parmenter, and K. L. Blackburn, Phys. Rev. A 72, 043818 (2005).
[CrossRef]

J. M. Saucedo Solorio, D. W. Sukow, D. R. Hicks, and A. Gavrielides, Opt. Commun. 214, 327 (2002).
[CrossRef]

Tang, C. L.

W. H. Loh, A. T. Schremer, and C. L. Tang, IEEE Photon. Technol. Lett. 2, 467 (1990).
[CrossRef]

W. H. Loh, Y. Ozeki, and C. L. Tang, Appl. Phys. Lett. 56, 2613 (1990).
[CrossRef]

Tredicce, and J. R.

Uchida, A.

T. Heil, A. Uchida, P. Davis, and T. Aida, Phys. Rev. A 68, 033811 (2003).
[CrossRef]

Vallet, M.

G. Ropars, P. Langot, M. Brunel, M. Vallet, F. Bretenaker, A. Le Floch, and K. D. Choquette, Appl. Phys. Lett. 70, 2661 (1997).
[CrossRef]

Yen, T. C.

T. C. Yen, J. W. Chang, J. M. Lin, and R. J. Chen, Opt. Commun. 150, 159 (1998).
[CrossRef]

Appl. Phys. Lett.

H. Li, A. Hohl, A. Gavrielides, H. Hou, and K. Choquette, Appl. Phys. Lett. 72, 2355 (1998).
[CrossRef]

G. Ropars, P. Langot, M. Brunel, M. Vallet, F. Bretenaker, A. Le Floch, and K. D. Choquette, Appl. Phys. Lett. 70, 2661 (1997).
[CrossRef]

W. H. Loh, Y. Ozeki, and C. L. Tang, Appl. Phys. Lett. 56, 2613 (1990).
[CrossRef]

IEEE J. Quantum Electron.

P. Saboureau, J.-P. Foing, and P. Schanne, IEEE J. Quantum Electron. 33, 1582 (1997).
[CrossRef]

F. Robert, P. Besnard, M. L. Charles, and G. M. Stephan, IEEE J. Quantum Electron. 33, 2231 (1997).
[CrossRef]

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

IEEE Photon. Technol. Lett.

W. H. Loh, A. T. Schremer, and C. L. Tang, IEEE Photon. Technol. Lett. 2, 467 (1990).
[CrossRef]

J. Appl. Phys.

T. B. Simpson and J. M. Liu, J. Appl. Phys. 73, 2587 (1993).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

T. C. Yen, J. W. Chang, J. M. Lin, and R. J. Chen, Opt. Commun. 150, 159 (1998).
[CrossRef]

J. Houlihan, G. Huyet, and J. G. McInerney, Opt. Commun. 199, 175 (2001).
[CrossRef]

J. M. Saucedo Solorio, D. W. Sukow, D. R. Hicks, and A. Gavrielides, Opt. Commun. 214, 327 (2002).
[CrossRef]

Opt. Lett.

Phys. Rev. A

M. Sciamanna, T. Erneux, F. Rogister, O. Deparis, P. Megret, and M. Blondel, Phys. Rev. A 65, 041801(R) (2002).
[CrossRef]

D. W. Sukow, A. Gavrielides, T. Erneux, M. J. Baracco, Z. A. Parmenter, and K. L. Blackburn, Phys. Rev. A 72, 043818 (2005).
[CrossRef]

T. Heil, A. Uchida, P. Davis, and T. Aida, Phys. Rev. A 68, 033811 (2003).
[CrossRef]

Proc. SPIE

A. Gavrielides, T. Erneux, D. W. Sukow, G. Burner, T. McLachlan, J. Miller, and J. Amonette, in Proc. SPIE 6115, 60 (2006).

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram of the experimental system. ND, neutral density filter; PD1, PD2, photodetectors; AMP, amplifiers. Other abbreviations defined in text.

Fig. 2
Fig. 2

Experimental time series of the square-wave self-modulated oscillations. Top and bottom, TE and TM mode intensities, respectively. (a) and (b) τ = 2.60 ns , (c) and (d) τ = 6.92 ns .

Fig. 3
Fig. 3

Long-time numerical solution of Eqs. (1, 2, 3). The values of the parameters are P = 0.5 , α = 2 , T = 150 , τ = 10 3 , η = 0.35 , k = 1 3 , and β = 0.09 . The horizontal broken lines emphasize the plateaus of the square-wave oscillations: E 1 0.7 and E 2 1.1 .

Fig. 4
Fig. 4

Bifurcation diagram of the square-wave self-modulated solutions. P = 0.5 , α = 2 , η = 0.35 , and k = 1 3 . The figure represents the difference between the values of E 2 E 1 for each plateau of the square wave as a function of β. If β > β c , chaotic oscillations appear.

Equations (10)

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

d E 1 d t = ( 1 + i α ) N E 1 ,
d E 2 d t = ( 1 + i α ) k ( N β ) E 2 + η E 1 ( t τ ) ,
T d N d t = P N ( 1 + 2 N ) ( E 1 2 + E 2 2 ) .
N A 1 = 0 ,
k ( N β ) A 2 + η A 1 ( s 1 ) cos ( Φ ) = 0 ,
α [ N ( s 1 ) k ( N β ) ] A 2 η A 1 ( s 1 ) sin ( Φ ) = 0 ,
P N ( 1 + 2 N ) ( A 1 2 + A 2 2 ) = 0 ,
k ( N β ) A 2 + η P 1 + α 2 = 0 .
A 2 2 = P N 1 + 2 N .
β β c = η k ( 1 + α 2 ) .

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