Abstract

It has been shown that strong optical injection locking can significantly enhance the resonance frequency of semiconductor lasers. In this Letter, we describe the trade-off between the maximum resonance frequency enhancement and the quality factor (Q) of the lossless laser cavity and show that the time–bandwidth product (product of photon lifetime and maximum resonance frequency) is equal to one half the square root of the external power injection ratio. The theoretical model agrees well with our experimental data.

© 2007 Optical Society of America

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References

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  1. T. B. Simpson and J. M. Liu, IEEE Photon. Technol. Lett. 9, 1322 (1997).
    [CrossRef]
  2. X. J. Meng, T. Chau, and M. C. Wu, Electron. Lett. 34, 2031 (1998).
    [CrossRef]
  3. L. Chrostowski, X. Zhao, C. J. Chang-Hasnain, R. Shau, M. Ortsiefer, and M. C. Amann, IEEE Photon. Technol. Lett. 18, 367 (2006).
    [CrossRef]
  4. R. Lang, IEEE J. Quantum Electron. 18, 976 (1982).
    [CrossRef]
  5. A. Murakami, K. Kawashima, and K. Atsuki, IEEE J. Quantum Electron. 39, 1196 (2003).
    [CrossRef]
  6. C. H. Henry, N. A. Olsson, and N. K. Dutta, IEEE J. Quantum Electron. 21, 1152 (1985).
    [CrossRef]
  7. F. Mogensen, H. Olesen, and G. Jacobsen, IEEE J. Quantum Electron. 21, 784 (1985).
    [CrossRef]
  8. A. Yariv, Optical Electronics in Modern Communications (Oxford U. Press, 1997).
  9. E. K. Lau, H. K. Sung, and M. C. Wu, "Frequency response enhancement of optical injection-locked lasers," IEEE J. Quantum Electron. (to be published).
  10. R. Adler, Proc. IRE 34, 351 (1946).
    [CrossRef]
  11. J. C. Slater, Microwave Electronics (Van Nostrand, 1950).

2006 (1)

L. Chrostowski, X. Zhao, C. J. Chang-Hasnain, R. Shau, M. Ortsiefer, and M. C. Amann, IEEE Photon. Technol. Lett. 18, 367 (2006).
[CrossRef]

2003 (1)

A. Murakami, K. Kawashima, and K. Atsuki, IEEE J. Quantum Electron. 39, 1196 (2003).
[CrossRef]

1998 (1)

X. J. Meng, T. Chau, and M. C. Wu, Electron. Lett. 34, 2031 (1998).
[CrossRef]

1997 (1)

T. B. Simpson and J. M. Liu, IEEE Photon. Technol. Lett. 9, 1322 (1997).
[CrossRef]

1985 (2)

C. H. Henry, N. A. Olsson, and N. K. Dutta, IEEE J. Quantum Electron. 21, 1152 (1985).
[CrossRef]

F. Mogensen, H. Olesen, and G. Jacobsen, IEEE J. Quantum Electron. 21, 784 (1985).
[CrossRef]

1982 (1)

R. Lang, IEEE J. Quantum Electron. 18, 976 (1982).
[CrossRef]

1946 (1)

R. Adler, Proc. IRE 34, 351 (1946).
[CrossRef]

Electron. Lett. (1)

X. J. Meng, T. Chau, and M. C. Wu, Electron. Lett. 34, 2031 (1998).
[CrossRef]

IEEE J. Quantum Electron. (4)

R. Lang, IEEE J. Quantum Electron. 18, 976 (1982).
[CrossRef]

A. Murakami, K. Kawashima, and K. Atsuki, IEEE J. Quantum Electron. 39, 1196 (2003).
[CrossRef]

C. H. Henry, N. A. Olsson, and N. K. Dutta, IEEE J. Quantum Electron. 21, 1152 (1985).
[CrossRef]

F. Mogensen, H. Olesen, and G. Jacobsen, IEEE J. Quantum Electron. 21, 784 (1985).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

L. Chrostowski, X. Zhao, C. J. Chang-Hasnain, R. Shau, M. Ortsiefer, and M. C. Amann, IEEE Photon. Technol. Lett. 18, 367 (2006).
[CrossRef]

T. B. Simpson and J. M. Liu, IEEE Photon. Technol. Lett. 9, 1322 (1997).
[CrossRef]

Proc. IRE (1)

R. Adler, Proc. IRE 34, 351 (1946).
[CrossRef]

Other (3)

J. C. Slater, Microwave Electronics (Van Nostrand, 1950).

A. Yariv, Optical Electronics in Modern Communications (Oxford U. Press, 1997).

E. K. Lau, H. K. Sung, and M. C. Wu, "Frequency response enhancement of optical injection-locked lasers," IEEE J. Quantum Electron. (to be published).

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Figures (4)

Fig. 1
Fig. 1

Injection locking of various laser structures: (a) VCSEL, (b) Fabry–Perot, (c) DFB.

Fig. 2
Fig. 2

Ratio of internal and external injection ratios for different mirror reflectivities.

Fig. 3
Fig. 3

Frequency responses for two different lasers: (a) Q = 13,320 , (b) Q = 3330 . The curves in each set are the maximum resonance frequency at a given injection ratio. Light to dark curves correspond to R ext = 10 , 5 , 0, 5, and 10 dB , respectively. Dotted curves correspond to the free-running response.

Fig. 4
Fig. 4

Comparison of theory with experimental data for maximum resonance frequency enhancement. The points are sets of Δ ω R , max at different injection ratios, for two different lasers. Solid lines, fits of Eq. (11); dotted lines, calculated Δ ω R , max based on DFB stop-band width.

Equations (15)

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d A ( t ) d t = 1 2 g [ N ( t ) N th ] A ( t ) + κ A inj cos ϕ ( t ) ,
d ϕ ( t ) d t = α 2 g [ N ( t ) N th ] + κ A inj A ( t ) sin ϕ ( t ) Δ ω ,
R int = ( A inj A 0 ) 2 = P inj , int P 0 ,
R ext = P inj , ext P out ,
R int R ext = ( 1 r ) 2 r .
κ = 1 τ rt = v g 2 L ,
Δ ω R = κ R int sin ϕ 0 ,
κ R int 1 + α 2 < Δ ω < κ R int .
Δ ω R , max = κ R int = v g 2 L R int .
Δ ω R , max = v g 2 L 1 r r R ext .
Q ω 0 ω 1 2 = ω 0 L v g r 1 r ,
Δ ω R , max = ω 0 2 Q R ext .
ω R 2 = ω R 0 2 + Δ ω R 2 .
τ c Δ ω R , max = 1 2 R ext .
Δ ω = ω 0 2 Q P i P 0 .

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