Abstract

We report on the prediction of stable self-starting pulses in a GaAs bulk semiconductor microring laser with terahertz repetition rate. The pulses are obtained without active or passive mode locking. Especially interesting for practical applications is the bistability between pulses and continuous waves.

© 2010 Optical Society of America

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References

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  1. J. C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Elsevier, 2006).
  2. U. Keller, Nature 424, 831 (2003).
    [CrossRef] [PubMed]
  3. C. Z. Ning, R. A. Indik, and J. V. Moloney, IEEE J. Quantum Electron. 33, 1543 (1997).
    [CrossRef]
  4. W. W. Chow, S. W. Koch, and M. Sargent, Semiconductor Laser Physics (Springer-Verlag, 1994).
    [CrossRef]
  5. J. Yao, G. P. Agrawal, P. Gallion and C. M. Bowden, Opt. Commun. 119, 246 (1995).
    [CrossRef]
  6. J. Javaloyes and S. Balle, IEEE J. Quantum Electron. 45, 431 (2009).
    [CrossRef]
  7. T. B. Benjamin and J. E. Feir, J. Fluid Mech. 27, 417 (1967).
    [CrossRef]
  8. Y. Nomura, S. Ochi, N. Tomita, K. Akiyama, T. Isu, T. Takiguchi and H. Higuchi, Phys. Rev. A 65, 043807 (2002).
    [CrossRef]
  9. C. Gosset, K. Merghem, A. Martinez, G. Moreau, G. Patriarche, G. Aubin, A. Ramdane, J. Landreau and F. Lelarge, Appl. Phys. Lett. 88, 241105 (2006).
    [CrossRef]

2009 (1)

J. Javaloyes and S. Balle, IEEE J. Quantum Electron. 45, 431 (2009).
[CrossRef]

2006 (1)

C. Gosset, K. Merghem, A. Martinez, G. Moreau, G. Patriarche, G. Aubin, A. Ramdane, J. Landreau and F. Lelarge, Appl. Phys. Lett. 88, 241105 (2006).
[CrossRef]

2003 (1)

U. Keller, Nature 424, 831 (2003).
[CrossRef] [PubMed]

2002 (1)

Y. Nomura, S. Ochi, N. Tomita, K. Akiyama, T. Isu, T. Takiguchi and H. Higuchi, Phys. Rev. A 65, 043807 (2002).
[CrossRef]

1997 (1)

C. Z. Ning, R. A. Indik, and J. V. Moloney, IEEE J. Quantum Electron. 33, 1543 (1997).
[CrossRef]

1995 (1)

J. Yao, G. P. Agrawal, P. Gallion and C. M. Bowden, Opt. Commun. 119, 246 (1995).
[CrossRef]

1967 (1)

T. B. Benjamin and J. E. Feir, J. Fluid Mech. 27, 417 (1967).
[CrossRef]

Agrawal, G. P.

J. Yao, G. P. Agrawal, P. Gallion and C. M. Bowden, Opt. Commun. 119, 246 (1995).
[CrossRef]

Akiyama, K.

Y. Nomura, S. Ochi, N. Tomita, K. Akiyama, T. Isu, T. Takiguchi and H. Higuchi, Phys. Rev. A 65, 043807 (2002).
[CrossRef]

Aubin, G.

C. Gosset, K. Merghem, A. Martinez, G. Moreau, G. Patriarche, G. Aubin, A. Ramdane, J. Landreau and F. Lelarge, Appl. Phys. Lett. 88, 241105 (2006).
[CrossRef]

Balle, S.

J. Javaloyes and S. Balle, IEEE J. Quantum Electron. 45, 431 (2009).
[CrossRef]

Benjamin, T. B.

T. B. Benjamin and J. E. Feir, J. Fluid Mech. 27, 417 (1967).
[CrossRef]

Bowden, C. M.

J. Yao, G. P. Agrawal, P. Gallion and C. M. Bowden, Opt. Commun. 119, 246 (1995).
[CrossRef]

Chow, W. W.

W. W. Chow, S. W. Koch, and M. Sargent, Semiconductor Laser Physics (Springer-Verlag, 1994).
[CrossRef]

Diels, J. C.

J. C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Elsevier, 2006).

Feir, J. E.

T. B. Benjamin and J. E. Feir, J. Fluid Mech. 27, 417 (1967).
[CrossRef]

Gallion, P.

J. Yao, G. P. Agrawal, P. Gallion and C. M. Bowden, Opt. Commun. 119, 246 (1995).
[CrossRef]

Gosset, C.

C. Gosset, K. Merghem, A. Martinez, G. Moreau, G. Patriarche, G. Aubin, A. Ramdane, J. Landreau and F. Lelarge, Appl. Phys. Lett. 88, 241105 (2006).
[CrossRef]

Higuchi, H.

Y. Nomura, S. Ochi, N. Tomita, K. Akiyama, T. Isu, T. Takiguchi and H. Higuchi, Phys. Rev. A 65, 043807 (2002).
[CrossRef]

Indik, R. A.

C. Z. Ning, R. A. Indik, and J. V. Moloney, IEEE J. Quantum Electron. 33, 1543 (1997).
[CrossRef]

Isu, T.

Y. Nomura, S. Ochi, N. Tomita, K. Akiyama, T. Isu, T. Takiguchi and H. Higuchi, Phys. Rev. A 65, 043807 (2002).
[CrossRef]

Javaloyes, J.

J. Javaloyes and S. Balle, IEEE J. Quantum Electron. 45, 431 (2009).
[CrossRef]

Keller, U.

U. Keller, Nature 424, 831 (2003).
[CrossRef] [PubMed]

Koch, S. W.

W. W. Chow, S. W. Koch, and M. Sargent, Semiconductor Laser Physics (Springer-Verlag, 1994).
[CrossRef]

Landreau, J.

C. Gosset, K. Merghem, A. Martinez, G. Moreau, G. Patriarche, G. Aubin, A. Ramdane, J. Landreau and F. Lelarge, Appl. Phys. Lett. 88, 241105 (2006).
[CrossRef]

Lelarge, F.

C. Gosset, K. Merghem, A. Martinez, G. Moreau, G. Patriarche, G. Aubin, A. Ramdane, J. Landreau and F. Lelarge, Appl. Phys. Lett. 88, 241105 (2006).
[CrossRef]

Martinez, A.

C. Gosset, K. Merghem, A. Martinez, G. Moreau, G. Patriarche, G. Aubin, A. Ramdane, J. Landreau and F. Lelarge, Appl. Phys. Lett. 88, 241105 (2006).
[CrossRef]

Merghem, K.

C. Gosset, K. Merghem, A. Martinez, G. Moreau, G. Patriarche, G. Aubin, A. Ramdane, J. Landreau and F. Lelarge, Appl. Phys. Lett. 88, 241105 (2006).
[CrossRef]

Moloney, J. V.

C. Z. Ning, R. A. Indik, and J. V. Moloney, IEEE J. Quantum Electron. 33, 1543 (1997).
[CrossRef]

Moreau, G.

C. Gosset, K. Merghem, A. Martinez, G. Moreau, G. Patriarche, G. Aubin, A. Ramdane, J. Landreau and F. Lelarge, Appl. Phys. Lett. 88, 241105 (2006).
[CrossRef]

Ning, C. Z.

C. Z. Ning, R. A. Indik, and J. V. Moloney, IEEE J. Quantum Electron. 33, 1543 (1997).
[CrossRef]

Nomura, Y.

Y. Nomura, S. Ochi, N. Tomita, K. Akiyama, T. Isu, T. Takiguchi and H. Higuchi, Phys. Rev. A 65, 043807 (2002).
[CrossRef]

Ochi, S.

Y. Nomura, S. Ochi, N. Tomita, K. Akiyama, T. Isu, T. Takiguchi and H. Higuchi, Phys. Rev. A 65, 043807 (2002).
[CrossRef]

Patriarche, G.

C. Gosset, K. Merghem, A. Martinez, G. Moreau, G. Patriarche, G. Aubin, A. Ramdane, J. Landreau and F. Lelarge, Appl. Phys. Lett. 88, 241105 (2006).
[CrossRef]

Ramdane, A.

C. Gosset, K. Merghem, A. Martinez, G. Moreau, G. Patriarche, G. Aubin, A. Ramdane, J. Landreau and F. Lelarge, Appl. Phys. Lett. 88, 241105 (2006).
[CrossRef]

Rudolph, W.

J. C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Elsevier, 2006).

Sargent, M.

W. W. Chow, S. W. Koch, and M. Sargent, Semiconductor Laser Physics (Springer-Verlag, 1994).
[CrossRef]

Takiguchi, T.

Y. Nomura, S. Ochi, N. Tomita, K. Akiyama, T. Isu, T. Takiguchi and H. Higuchi, Phys. Rev. A 65, 043807 (2002).
[CrossRef]

Tomita, N.

Y. Nomura, S. Ochi, N. Tomita, K. Akiyama, T. Isu, T. Takiguchi and H. Higuchi, Phys. Rev. A 65, 043807 (2002).
[CrossRef]

Yao, J.

J. Yao, G. P. Agrawal, P. Gallion and C. M. Bowden, Opt. Commun. 119, 246 (1995).
[CrossRef]

Appl. Phys. Lett. (1)

C. Gosset, K. Merghem, A. Martinez, G. Moreau, G. Patriarche, G. Aubin, A. Ramdane, J. Landreau and F. Lelarge, Appl. Phys. Lett. 88, 241105 (2006).
[CrossRef]

IEEE J. Quantum Electron. (2)

J. Javaloyes and S. Balle, IEEE J. Quantum Electron. 45, 431 (2009).
[CrossRef]

C. Z. Ning, R. A. Indik, and J. V. Moloney, IEEE J. Quantum Electron. 33, 1543 (1997).
[CrossRef]

J. Fluid Mech. (1)

T. B. Benjamin and J. E. Feir, J. Fluid Mech. 27, 417 (1967).
[CrossRef]

Nature (1)

U. Keller, Nature 424, 831 (2003).
[CrossRef] [PubMed]

Opt. Commun. (1)

J. Yao, G. P. Agrawal, P. Gallion and C. M. Bowden, Opt. Commun. 119, 246 (1995).
[CrossRef]

Phys. Rev. A (1)

Y. Nomura, S. Ochi, N. Tomita, K. Akiyama, T. Isu, T. Takiguchi and H. Higuchi, Phys. Rev. A 65, 043807 (2002).
[CrossRef]

Other (2)

J. C. Diels and W. Rudolph, Ultrashort Laser Pulse Phenomena (Elsevier, 2006).

W. W. Chow, S. W. Koch, and M. Sargent, Semiconductor Laser Physics (Springer-Verlag, 1994).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Parametric set: δ 0 = 0 , D = 0 , γ = 2 10 5 , ρ = 0.99 , θ = 3.47 and I p = 1.44 , L = 136.5 . Linear stability analysis of the CW solutions.

Fig. 2
Fig. 2

Phase diagram of Eq. (2) in the θ L plane for I p = 1.44 . The other parameters are the same as in Fig. 1. The wave vectors K + k ± 1 are linearly unstable above the dashed line and K + k ± 2 above the continuous one. Both lines are analytically computed.

Fig. 3
Fig. 3

Normalized amplitude of the side modes K + k ± 1 versus L. I p = 2.06 , θ = 3.47 , ρ = 0.99 , γ = 2 × 10 5 , D = 1.2 , δ 0 = 0 .

Equations (22)

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E = 1 2 ( E + e i ( k r z ω r t ) + E e i ( k r z ω r t ) + cc ) ,
P = 1 2 ( P + e i ( k r z ω r t ) + P e i ( k r z ω r t ) + cc ) ,
E ± t = i ω r Γ c 2 ϵ 0 n g n b P ± + i ω r χ 0 ( N ) n b Γ c 2 n g E ± ± c n g E ± z ,
P ± t = [ Γ 0 ( N ) + i ( δ 0 δ ( N ) ) ] P ± i ϵ 0 ϵ b A ( N ) E ± ,
N t = D 2 N z 2 γ ( N N p ) + i 4 [ ϵ 0 ϵ b ( χ 0 ( N ) ¯ χ 0 ( N ) ) ( | E + | 2 + | E | 2 ) + P + ¯ E + P + E + ¯ + P ¯ E P E ¯ ] ,
ν = ω r χ 0 r n b 2 n g , E r 2 = 4 N 0 γ ϵ 0 ϵ b , N = N 0 N ,
t = ν t , E ± = E r E ± , D = D ν 2 n g 2 c 2 γ ,
z = ν n g c z , P ± = ϵ 0 ϵ b E r P ± , I p = N p N 0 ,
Γ 0 ( N ) = ν Γ 0 ( N ) , L = c ν n g L , γ = γ ν ,
δ 0 = ν δ 0 , δ ( N ) = ν δ ( N ) , A ( N ) = ν A ( N ) ,
t E ± = i χ 0 r P ± + [ i χ 0 ( N ) χ 0 r ] E ± z E ± ,
t P ± = [ Γ 0 ( N ) + i ( δ 0 δ ( N ) ) ] P ± i A ( N ) E ± ,
t N = γ [ N I p D z z N 2 χ 0 i ( N ) ( | E + | 2 + | E | 2 ) i ( P + ¯ E + P + E + ¯ + P ¯ E P E ¯ ) ] ,
E ± ( L 2 ) = E ± ( ± L 2 ) ρ e i θ .
t E ± = i χ 0 r P ± + [ i χ 0 ( N ) χ 0 r + a ] E ± z E ± ,
t P ± = [ Γ 0 ( N ) + i ( δ 0 δ ( N ) ) ] P ± i A ( N ) E ± ,
t N = γ [ N I p D z z N 2 χ 0 i ( N ) ( e 2 ln ( ρ ) z | E + | 2 + e + 2 ln ( ρ ) z | E | 2 ) i e 2 ln ( ρ ) z ( P + ¯ E + P + E + ¯ ) i e + 2 ln ( ρ ) z ( P ¯ E P E ¯ ) ] ,
E + ( L 2 ) = E + ( + L 2 ) , E ( + L 2 ) = E ( L 2 ) .
t N = γ [ N I p D z z N 2 χ 0 i ( N ) ( | E + | 2 + | E | 2 ) i ( P + ¯ E + P + E + ¯ + P ¯ E P E ¯ ) ] .
K = 2 π n L , Ω = Ω ( N s , K ) , E Q ( N s , K ) = 0 ,
| E s + | 2 + | E s | 2 = L ρ ( I p N s ) χ 0 r ( 1 ρ 2 ) ,
P s ± = i A ( N s ) E s ± i Ω + Γ 0 ( N s ) + i [ δ ( N s ) δ 0 ] .

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