Abstract

Vertical-cavity surface-emitting lasers subjected to weak polarization-insensitive optical feedback are studied experimentally and theoretically. We find that the feedback induces random anticorrelated hopping between the two orthogonal linearly polarized modes. This polarization mode hopping is accompanied by rapid anticorrelated oscillations in the linearly polarized intensities at the external-cavity frequency. The study of a simple stochastic delay differential equation suggests that these oscillations generated by the delay are typical of any hopping phenomenon between states.

© 2003 Optical Society of America

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  1. K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, IEEE Photon. Technol. Lett. 10, 6 (1998).
    [CrossRef]
  2. T. H. Russell and T. D. Milster, Appl. Phys. Lett. 70, 2520 (1997).
    [CrossRef]
  3. A. Valle, L. Pesquera, and K. A. Shore, IEEE Photon. Technol. Lett. 10, 639 (1998).
    [CrossRef]
  4. M. Sciamanna, T. Erneux, F. Rogister, O. Deparis, P. Mégret, and M. Blondel, Phys. Rev. A 65, 041801(R) (2002).
    [CrossRef]
  5. G. Giacomelli, F. Marin, and I. Rabbiosi, Phys. Rev. Lett. 82, 675 (1999).
    [CrossRef]
  6. T. Ohira and Y. Sato, Phys. Rev. Lett. 82, 2811 (1999).
    [CrossRef]
  7. L. S. Tsimring and A. Pikovsky, Phys. Rev. Lett. 87, 250602 (2001).
    [CrossRef]
  8. M. Giudici, S. Balle, T. Ackemann, S. Barland, and J. R. Tredicce, J. Opt. Soc. Am. B 11, 2114 (1999).
    [CrossRef]
  9. M. Sondermann, H. Bohnet, and T. Ackemann, Phys. Rev. A 67, 021802 (2003).
    [CrossRef]
  10. J. Mork, M. Semkow, and B. Tromborg, Electron. Lett. 26, 609 (1990).
    [CrossRef]

2003

M. Sondermann, H. Bohnet, and T. Ackemann, Phys. Rev. A 67, 021802 (2003).
[CrossRef]

2002

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

2001

L. S. Tsimring and A. Pikovsky, Phys. Rev. Lett. 87, 250602 (2001).
[CrossRef]

1999

M. Giudici, S. Balle, T. Ackemann, S. Barland, and J. R. Tredicce, J. Opt. Soc. Am. B 11, 2114 (1999).
[CrossRef]

G. Giacomelli, F. Marin, and I. Rabbiosi, Phys. Rev. Lett. 82, 675 (1999).
[CrossRef]

T. Ohira and Y. Sato, Phys. Rev. Lett. 82, 2811 (1999).
[CrossRef]

1998

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, IEEE Photon. Technol. Lett. 10, 6 (1998).
[CrossRef]

A. Valle, L. Pesquera, and K. A. Shore, IEEE Photon. Technol. Lett. 10, 639 (1998).
[CrossRef]

1997

T. H. Russell and T. D. Milster, Appl. Phys. Lett. 70, 2520 (1997).
[CrossRef]

1990

J. Mork, M. Semkow, and B. Tromborg, Electron. Lett. 26, 609 (1990).
[CrossRef]

Ackemann, T.

M. Sondermann, H. Bohnet, and T. Ackemann, Phys. Rev. A 67, 021802 (2003).
[CrossRef]

M. Giudici, S. Balle, T. Ackemann, S. Barland, and J. R. Tredicce, J. Opt. Soc. Am. B 11, 2114 (1999).
[CrossRef]

Balle, S.

M. Giudici, S. Balle, T. Ackemann, S. Barland, and J. R. Tredicce, J. Opt. Soc. Am. B 11, 2114 (1999).
[CrossRef]

Barland, S.

M. Giudici, S. Balle, T. Ackemann, S. Barland, and J. R. Tredicce, J. Opt. Soc. Am. B 11, 2114 (1999).
[CrossRef]

Blondel, M.

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

Bohnet, H.

M. Sondermann, H. Bohnet, and T. Ackemann, Phys. Rev. A 67, 021802 (2003).
[CrossRef]

Danckaert, J.

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, IEEE Photon. Technol. Lett. 10, 6 (1998).
[CrossRef]

Deparis, O.

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

Erneux, T.

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

Giacomelli, G.

G. Giacomelli, F. Marin, and I. Rabbiosi, Phys. Rev. Lett. 82, 675 (1999).
[CrossRef]

Giudici, M.

M. Giudici, S. Balle, T. Ackemann, S. Barland, and J. R. Tredicce, J. Opt. Soc. Am. B 11, 2114 (1999).
[CrossRef]

Marin, F.

G. Giacomelli, F. Marin, and I. Rabbiosi, Phys. Rev. Lett. 82, 675 (1999).
[CrossRef]

Mégret, P.

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

Milster, T. D.

T. H. Russell and T. D. Milster, Appl. Phys. Lett. 70, 2520 (1997).
[CrossRef]

Mork, J.

J. Mork, M. Semkow, and B. Tromborg, Electron. Lett. 26, 609 (1990).
[CrossRef]

Ohira, T.

T. Ohira and Y. Sato, Phys. Rev. Lett. 82, 2811 (1999).
[CrossRef]

Panajotov, K.

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, IEEE Photon. Technol. Lett. 10, 6 (1998).
[CrossRef]

Peeters, M.

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, IEEE Photon. Technol. Lett. 10, 6 (1998).
[CrossRef]

Pesquera, L.

A. Valle, L. Pesquera, and K. A. Shore, IEEE Photon. Technol. Lett. 10, 639 (1998).
[CrossRef]

Pikovsky, A.

L. S. Tsimring and A. Pikovsky, Phys. Rev. Lett. 87, 250602 (2001).
[CrossRef]

Rabbiosi, I.

G. Giacomelli, F. Marin, and I. Rabbiosi, Phys. Rev. Lett. 82, 675 (1999).
[CrossRef]

Rogister, F.

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

Russell, T. H.

T. H. Russell and T. D. Milster, Appl. Phys. Lett. 70, 2520 (1997).
[CrossRef]

Ryvkin, B.

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, IEEE Photon. Technol. Lett. 10, 6 (1998).
[CrossRef]

Sato, Y.

T. Ohira and Y. Sato, Phys. Rev. Lett. 82, 2811 (1999).
[CrossRef]

Sciamanna, M.

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

Semkow, M.

J. Mork, M. Semkow, and B. Tromborg, Electron. Lett. 26, 609 (1990).
[CrossRef]

Shore, K. A.

A. Valle, L. Pesquera, and K. A. Shore, IEEE Photon. Technol. Lett. 10, 639 (1998).
[CrossRef]

Sondermann, M.

M. Sondermann, H. Bohnet, and T. Ackemann, Phys. Rev. A 67, 021802 (2003).
[CrossRef]

Thienpont, H.

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, IEEE Photon. Technol. Lett. 10, 6 (1998).
[CrossRef]

Tredicce, J. R.

M. Giudici, S. Balle, T. Ackemann, S. Barland, and J. R. Tredicce, J. Opt. Soc. Am. B 11, 2114 (1999).
[CrossRef]

Tromborg, B.

J. Mork, M. Semkow, and B. Tromborg, Electron. Lett. 26, 609 (1990).
[CrossRef]

Tsimring, L. S.

L. S. Tsimring and A. Pikovsky, Phys. Rev. Lett. 87, 250602 (2001).
[CrossRef]

Valle, A.

A. Valle, L. Pesquera, and K. A. Shore, IEEE Photon. Technol. Lett. 10, 639 (1998).
[CrossRef]

Veretennicoff, I.

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, IEEE Photon. Technol. Lett. 10, 6 (1998).
[CrossRef]

Appl. Phys. Lett.

T. H. Russell and T. D. Milster, Appl. Phys. Lett. 70, 2520 (1997).
[CrossRef]

Electron. Lett.

J. Mork, M. Semkow, and B. Tromborg, Electron. Lett. 26, 609 (1990).
[CrossRef]

IEEE Photon. Technol. Lett.

A. Valle, L. Pesquera, and K. A. Shore, IEEE Photon. Technol. Lett. 10, 639 (1998).
[CrossRef]

IEEE Photon. Technol. Lett.

K. Panajotov, B. Ryvkin, J. Danckaert, M. Peeters, H. Thienpont, and I. Veretennicoff, IEEE Photon. Technol. Lett. 10, 6 (1998).
[CrossRef]

J. Opt. Soc. Am. B

M. Giudici, S. Balle, T. Ackemann, S. Barland, and J. R. Tredicce, J. Opt. Soc. Am. B 11, 2114 (1999).
[CrossRef]

Phys. Rev. A

M. Sondermann, H. Bohnet, and T. Ackemann, Phys. Rev. A 67, 021802 (2003).
[CrossRef]

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

Phys. Rev. Lett.

G. Giacomelli, F. Marin, and I. Rabbiosi, Phys. Rev. Lett. 82, 675 (1999).
[CrossRef]

T. Ohira and Y. Sato, Phys. Rev. Lett. 82, 2811 (1999).
[CrossRef]

L. S. Tsimring and A. Pikovsky, Phys. Rev. Lett. 87, 250602 (2001).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

LP-resolved LI curve. Thin black curve, x-LP mode in the solitary VCSEL. Thick black (gray) curve x- (y)-LP mode in the VCSEL subject to weak PIOF. The inset shows an enlargement in the channelled region.

Fig. 2
Fig. 2

(a) Polarization mode hopping for J=1.86Jth close to a switching point in the LI curve. (b) Anticorrelated oscillations at the EC frequency in the x- (black) and y-LP mode (gray). (c) Total intensity (dotted curve) and x-LP mode intensity (solid curve).

Fig. 3
Fig. 3

(a) Optical spectrum in the y-LP mode for J=1.93Jth. (b) Same as (a) but at different times.

Fig. 4
Fig. 4

Numerical simulations of Eqs. (1)–(4). (a), (b) Time traces of Ix (black) and Iy (gray) for βsp=10-6 ns-1 and βsp=5×10-8 ns-1, respectively. See the different time scales. (c) Enlargement of (a). The total intensity Itot is plotted by the dotted curve. (d) x-LP mode frequency versus time for the case in (a).

Fig. 5
Fig. 5

Numerical simulation of Eq. (5) for τ=1 ns, =2 ns-1, and D=1 ns-1. (b) Enlargement of (a).

Equations (5)

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

E·x,y=121+jαGx,y-γEx,y+κEx,yt-τexp-jΩx,yτ+βspNξx,y,
N·=JeV-Nτe-GxΓEx2-GyΓEy2,
Ωx,y=mπcn0x,yLc1-1ndndJJ,
Gx,y=ax,yN-Ntr1-s,cEx2-c,sEy2.
x·=xt-x3t+xt-τ+2Dξt,

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