Abstract

A semiconductor laser including two laterally coupled waveguides, in which one of the waveguides includes a partially reflecting surface (an internal mirror) between its facets, is analyzed. The internal mirror inserts longitudinal coupling into the system. The spectrum of the Fabry–Perot modes exhibits modulation in the gain required for lasing threshold, with a periodicity that depends on the longitudinal position of the internal mirror. The combined coupled-cavity effect may explain the observed gain spectrum in GaN lasers.

© 2003 Optical Society of America

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References

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  1. R. Lang, A. Yariv, and J. Salzman, IEEE J. Quantum Electron. QE-23, 395 (1987).
    [CrossRef]
  2. I. A. Avrutsky, R. Gordon, R. Clayton, and J. M. Xu, IEEE J. Quantum Electron. 33, 1801 (1997).
    [CrossRef]
  3. C. H. Henry and R. F. Kazarinov, IEEE J. Quantum Electron. QE-20, 733 (1984).
    [CrossRef]
  4. K. J. Ebeling and L. A. Coldren, J. Appl. Phys. 54, 2962 (1983).
    [CrossRef]
  5. L. A. Coldren and T. L. Koch, IEEE J. Quantum Electron. QE-20, 659 (1984).
    [CrossRef]
  6. S. Nakamura and G. Fasol, The Blue Laser Diode (Springer-Verlag, Berlin, 1997).
    [CrossRef]
  7. U. Tisch, B. Meyler, O. Katz, E. Finkman, and J. Salzman, J. Appl. Phys. 89, 2676 (2001).
    [CrossRef]
  8. S. Nakamura, J. Electron. Mater. 27, 160 (1998).
    [CrossRef]

2001 (1)

U. Tisch, B. Meyler, O. Katz, E. Finkman, and J. Salzman, J. Appl. Phys. 89, 2676 (2001).
[CrossRef]

1998 (1)

S. Nakamura, J. Electron. Mater. 27, 160 (1998).
[CrossRef]

1997 (1)

I. A. Avrutsky, R. Gordon, R. Clayton, and J. M. Xu, IEEE J. Quantum Electron. 33, 1801 (1997).
[CrossRef]

1987 (1)

R. Lang, A. Yariv, and J. Salzman, IEEE J. Quantum Electron. QE-23, 395 (1987).
[CrossRef]

1984 (2)

L. A. Coldren and T. L. Koch, IEEE J. Quantum Electron. QE-20, 659 (1984).
[CrossRef]

C. H. Henry and R. F. Kazarinov, IEEE J. Quantum Electron. QE-20, 733 (1984).
[CrossRef]

1983 (1)

K. J. Ebeling and L. A. Coldren, J. Appl. Phys. 54, 2962 (1983).
[CrossRef]

Avrutsky, I. A.

I. A. Avrutsky, R. Gordon, R. Clayton, and J. M. Xu, IEEE J. Quantum Electron. 33, 1801 (1997).
[CrossRef]

Clayton, R.

I. A. Avrutsky, R. Gordon, R. Clayton, and J. M. Xu, IEEE J. Quantum Electron. 33, 1801 (1997).
[CrossRef]

Coldren, L. A.

L. A. Coldren and T. L. Koch, IEEE J. Quantum Electron. QE-20, 659 (1984).
[CrossRef]

K. J. Ebeling and L. A. Coldren, J. Appl. Phys. 54, 2962 (1983).
[CrossRef]

Ebeling, K. J.

K. J. Ebeling and L. A. Coldren, J. Appl. Phys. 54, 2962 (1983).
[CrossRef]

Fasol, G.

S. Nakamura and G. Fasol, The Blue Laser Diode (Springer-Verlag, Berlin, 1997).
[CrossRef]

Finkman, E.

U. Tisch, B. Meyler, O. Katz, E. Finkman, and J. Salzman, J. Appl. Phys. 89, 2676 (2001).
[CrossRef]

Gordon, R.

I. A. Avrutsky, R. Gordon, R. Clayton, and J. M. Xu, IEEE J. Quantum Electron. 33, 1801 (1997).
[CrossRef]

Henry, C. H.

C. H. Henry and R. F. Kazarinov, IEEE J. Quantum Electron. QE-20, 733 (1984).
[CrossRef]

Katz, O.

U. Tisch, B. Meyler, O. Katz, E. Finkman, and J. Salzman, J. Appl. Phys. 89, 2676 (2001).
[CrossRef]

Kazarinov, R. F.

C. H. Henry and R. F. Kazarinov, IEEE J. Quantum Electron. QE-20, 733 (1984).
[CrossRef]

Koch, T. L.

L. A. Coldren and T. L. Koch, IEEE J. Quantum Electron. QE-20, 659 (1984).
[CrossRef]

Lang, R.

R. Lang, A. Yariv, and J. Salzman, IEEE J. Quantum Electron. QE-23, 395 (1987).
[CrossRef]

Meyler, B.

U. Tisch, B. Meyler, O. Katz, E. Finkman, and J. Salzman, J. Appl. Phys. 89, 2676 (2001).
[CrossRef]

Nakamura, S.

S. Nakamura, J. Electron. Mater. 27, 160 (1998).
[CrossRef]

S. Nakamura and G. Fasol, The Blue Laser Diode (Springer-Verlag, Berlin, 1997).
[CrossRef]

Salzman, J.

U. Tisch, B. Meyler, O. Katz, E. Finkman, and J. Salzman, J. Appl. Phys. 89, 2676 (2001).
[CrossRef]

R. Lang, A. Yariv, and J. Salzman, IEEE J. Quantum Electron. QE-23, 395 (1987).
[CrossRef]

Tisch, U.

U. Tisch, B. Meyler, O. Katz, E. Finkman, and J. Salzman, J. Appl. Phys. 89, 2676 (2001).
[CrossRef]

Xu, J. M.

I. A. Avrutsky, R. Gordon, R. Clayton, and J. M. Xu, IEEE J. Quantum Electron. 33, 1801 (1997).
[CrossRef]

Yariv, A.

R. Lang, A. Yariv, and J. Salzman, IEEE J. Quantum Electron. QE-23, 395 (1987).
[CrossRef]

IEEE J. Quantum Electron. (4)

R. Lang, A. Yariv, and J. Salzman, IEEE J. Quantum Electron. QE-23, 395 (1987).
[CrossRef]

I. A. Avrutsky, R. Gordon, R. Clayton, and J. M. Xu, IEEE J. Quantum Electron. 33, 1801 (1997).
[CrossRef]

C. H. Henry and R. F. Kazarinov, IEEE J. Quantum Electron. QE-20, 733 (1984).
[CrossRef]

L. A. Coldren and T. L. Koch, IEEE J. Quantum Electron. QE-20, 659 (1984).
[CrossRef]

J. Appl. Phys. (2)

U. Tisch, B. Meyler, O. Katz, E. Finkman, and J. Salzman, J. Appl. Phys. 89, 2676 (2001).
[CrossRef]

K. J. Ebeling and L. A. Coldren, J. Appl. Phys. 54, 2962 (1983).
[CrossRef]

J. Electron. Mater. (1)

S. Nakamura, J. Electron. Mater. 27, 160 (1998).
[CrossRef]

Other (1)

S. Nakamura and G. Fasol, The Blue Laser Diode (Springer-Verlag, Berlin, 1997).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Schematic of the coupled-cavity laser formed by the two parallel waveguides, WG-I and WG-II, with an internal mirror in WG-II.

Fig. 2
Fig. 2

Material gain versus wavelength at wavelengths for which the eigenvalue condition, Eq. (10), is fulfilled. The calculation parameters appear in Table 2.

Fig. 3
Fig. 3

a, material gain modulation depth versus internal reflectivity. b, periodicity of the modulated gain spectrum versus 1/L2.

Tables (2)

Tables Icon

Table 1 Layers of the Laser Used for the Calculations

Tables Icon

Table 2 Parameters Used in the Calculation

Equations (13)

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

afz=aIfzaIIfz,  abz=aIbzaIIbz.
R̲̲z=rIz00rIIz,  T̲̲z=tIz00tIIz.
P̲̲Δz=p11p12p21p22,
a̲f0+=R̲̲0+ab0+.
a̲fL1-=P̲̲L1a̲f0+.
a̲bL1-=R̲̲L1-a̲fL1-+T̲̲L1+a̲bL1+.
a̲b0+=P̲̲L1a̲bL1-.
a̲bL1+=S̲̲a̲f0+,
a̲fL1+=R̲̲L1+a̲bL1++T̲̲L1-a̲fL1-.
a̲bL1+=M̲̲ a̲f0+,
S̲̲-1M̲̲-I̲̲=0.
σ˜s=σs,Re+jσs,Im,
σs,Im=12ΓsλFPgmλFP+1-ΓsλFPαm.

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