Abstract

Fixation of the optical frequency of slave laser to the frequencies between two adjacent modes by multiple optical injection locking is investigated. Numerical simulation suggests that the frequency pulling among many four wave mixing tones is the origin of the locking mechanism.

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References

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  1. H. L. Stover and W. H. Steier, “Locking of laser oscillators by light injection,” Appl. Phys. Lett. 8(4), 91–93 (1966).
    [CrossRef]
  2. R. Adler, “A study of locking phenomena in oscillators, “A study of locking phenomena in oscillators,” Proc. IRE, Vol.34, No.10, pp.351–357, Oct. 1946.
  3. R. Lang and K. Kobayashi, “Suppression of the relaxation oscillation in the modulated output of semiconductor lasers,” IEEE J. Quantum Electron. 12(3), 194–199 (1976).
    [CrossRef]
  4. C. H. Henry, N. A. Olsson, and N. K. Dutta, “Locking range and stability of injection locked 1.54 μm InGaAsP semiconductor lasers,” IEEE J. Quantum Electron. 21(8), 1152–1156 (1985).
    [CrossRef]
  5. R. Hui, A. D’Ottavi, A. Mecozzi, and P. Spano, “Injection locking in distributed feedback semiconductor lasers,” IEEE J. Quantum Electron. 27(6), 1688–1695 (1991).
    [CrossRef]
  6. X. Jin and S. L. Chuang, “Relative intensity noise characteristics of injection-locked semiconductor lasers,” Appl. Phys. Lett. 77(9), 1250–1252 (2000).
    [CrossRef]
  7. J. Pezeshki, M. Saylors, H. Mandelberg, and J. Goldhar, “Generation of a CW laser oscillator signal using a stabilized injection locked semiconductor laser,” J. Lightwave Technol. 26(5), 588–599 (2008).
    [CrossRef]
  8. H. Y. Ryu, S. H. Lee, W. K. Lee, H. S. Moon, and H. S. Suh, “Absolute frequency measurement of an acetylene stabilized laser using a selected single mode from a femtosecond fiber laser comb,” Opt. Express 16(5), 2867–2873 (2008).
    [CrossRef] [PubMed]
  9. L. Siegman, (University Science Books, 1986), Chap. 27, ISBN 0–935702–11–5.
  10. S. Kobayashi and T. Kimura, “Injection locking in AlGaAs semiconductor laser,” IEEE J. Quantum Electron. 17(5), 681–689 (1981).
    [CrossRef]
  11. J. Troger, L. Thevenaz, P.-A. Nicati, and P. A. Robert, “Theory and experiment of a single-mode diode laser subject to external light injection from several lasers,” J. Lightwave Technol. 17(4), 629–636 (1999).
    [CrossRef]
  12. R. Lang, “Injection locking properties of a semiconductor lasr,” IEEE J. Quantum Electron. 18(6), 976–983 (1982).
    [CrossRef]
  13. W. Robert, Boyd, Nonlinear Optics (Academic Press, Inc., 1992), ISBN 0–12–121680–2.

2008 (2)

J. Pezeshki, M. Saylors, H. Mandelberg, and J. Goldhar, “Generation of a CW laser oscillator signal using a stabilized injection locked semiconductor laser,” J. Lightwave Technol. 26(5), 588–599 (2008).
[CrossRef]

H. Y. Ryu, S. H. Lee, W. K. Lee, H. S. Moon, and H. S. Suh, “Absolute frequency measurement of an acetylene stabilized laser using a selected single mode from a femtosecond fiber laser comb,” Opt. Express 16(5), 2867–2873 (2008).
[CrossRef] [PubMed]

2000 (1)

X. Jin and S. L. Chuang, “Relative intensity noise characteristics of injection-locked semiconductor lasers,” Appl. Phys. Lett. 77(9), 1250–1252 (2000).
[CrossRef]

1999 (1)

J. Troger, L. Thevenaz, P.-A. Nicati, and P. A. Robert, “Theory and experiment of a single-mode diode laser subject to external light injection from several lasers,” J. Lightwave Technol. 17(4), 629–636 (1999).
[CrossRef]

1991 (1)

R. Hui, A. D’Ottavi, A. Mecozzi, and P. Spano, “Injection locking in distributed feedback semiconductor lasers,” IEEE J. Quantum Electron. 27(6), 1688–1695 (1991).
[CrossRef]

1985 (1)

C. H. Henry, N. A. Olsson, and N. K. Dutta, “Locking range and stability of injection locked 1.54 μm InGaAsP semiconductor lasers,” IEEE J. Quantum Electron. 21(8), 1152–1156 (1985).
[CrossRef]

1982 (1)

R. Lang, “Injection locking properties of a semiconductor lasr,” IEEE J. Quantum Electron. 18(6), 976–983 (1982).
[CrossRef]

1981 (1)

S. Kobayashi and T. Kimura, “Injection locking in AlGaAs semiconductor laser,” IEEE J. Quantum Electron. 17(5), 681–689 (1981).
[CrossRef]

1976 (1)

R. Lang and K. Kobayashi, “Suppression of the relaxation oscillation in the modulated output of semiconductor lasers,” IEEE J. Quantum Electron. 12(3), 194–199 (1976).
[CrossRef]

1966 (1)

H. L. Stover and W. H. Steier, “Locking of laser oscillators by light injection,” Appl. Phys. Lett. 8(4), 91–93 (1966).
[CrossRef]

Chuang, S. L.

X. Jin and S. L. Chuang, “Relative intensity noise characteristics of injection-locked semiconductor lasers,” Appl. Phys. Lett. 77(9), 1250–1252 (2000).
[CrossRef]

D’Ottavi, A.

R. Hui, A. D’Ottavi, A. Mecozzi, and P. Spano, “Injection locking in distributed feedback semiconductor lasers,” IEEE J. Quantum Electron. 27(6), 1688–1695 (1991).
[CrossRef]

Dutta, N. K.

C. H. Henry, N. A. Olsson, and N. K. Dutta, “Locking range and stability of injection locked 1.54 μm InGaAsP semiconductor lasers,” IEEE J. Quantum Electron. 21(8), 1152–1156 (1985).
[CrossRef]

Goldhar, J.

J. Pezeshki, M. Saylors, H. Mandelberg, and J. Goldhar, “Generation of a CW laser oscillator signal using a stabilized injection locked semiconductor laser,” J. Lightwave Technol. 26(5), 588–599 (2008).
[CrossRef]

Henry, C. H.

C. H. Henry, N. A. Olsson, and N. K. Dutta, “Locking range and stability of injection locked 1.54 μm InGaAsP semiconductor lasers,” IEEE J. Quantum Electron. 21(8), 1152–1156 (1985).
[CrossRef]

Hui, R.

R. Hui, A. D’Ottavi, A. Mecozzi, and P. Spano, “Injection locking in distributed feedback semiconductor lasers,” IEEE J. Quantum Electron. 27(6), 1688–1695 (1991).
[CrossRef]

Jin, X.

X. Jin and S. L. Chuang, “Relative intensity noise characteristics of injection-locked semiconductor lasers,” Appl. Phys. Lett. 77(9), 1250–1252 (2000).
[CrossRef]

Kimura, T.

S. Kobayashi and T. Kimura, “Injection locking in AlGaAs semiconductor laser,” IEEE J. Quantum Electron. 17(5), 681–689 (1981).
[CrossRef]

Kobayashi, K.

R. Lang and K. Kobayashi, “Suppression of the relaxation oscillation in the modulated output of semiconductor lasers,” IEEE J. Quantum Electron. 12(3), 194–199 (1976).
[CrossRef]

Kobayashi, S.

S. Kobayashi and T. Kimura, “Injection locking in AlGaAs semiconductor laser,” IEEE J. Quantum Electron. 17(5), 681–689 (1981).
[CrossRef]

Lang, R.

R. Lang, “Injection locking properties of a semiconductor lasr,” IEEE J. Quantum Electron. 18(6), 976–983 (1982).
[CrossRef]

R. Lang and K. Kobayashi, “Suppression of the relaxation oscillation in the modulated output of semiconductor lasers,” IEEE J. Quantum Electron. 12(3), 194–199 (1976).
[CrossRef]

Lee, S. H.

H. Y. Ryu, S. H. Lee, W. K. Lee, H. S. Moon, and H. S. Suh, “Absolute frequency measurement of an acetylene stabilized laser using a selected single mode from a femtosecond fiber laser comb,” Opt. Express 16(5), 2867–2873 (2008).
[CrossRef] [PubMed]

Lee, W. K.

H. Y. Ryu, S. H. Lee, W. K. Lee, H. S. Moon, and H. S. Suh, “Absolute frequency measurement of an acetylene stabilized laser using a selected single mode from a femtosecond fiber laser comb,” Opt. Express 16(5), 2867–2873 (2008).
[CrossRef] [PubMed]

Mandelberg, H.

J. Pezeshki, M. Saylors, H. Mandelberg, and J. Goldhar, “Generation of a CW laser oscillator signal using a stabilized injection locked semiconductor laser,” J. Lightwave Technol. 26(5), 588–599 (2008).
[CrossRef]

Mecozzi, A.

R. Hui, A. D’Ottavi, A. Mecozzi, and P. Spano, “Injection locking in distributed feedback semiconductor lasers,” IEEE J. Quantum Electron. 27(6), 1688–1695 (1991).
[CrossRef]

Moon, H. S.

H. Y. Ryu, S. H. Lee, W. K. Lee, H. S. Moon, and H. S. Suh, “Absolute frequency measurement of an acetylene stabilized laser using a selected single mode from a femtosecond fiber laser comb,” Opt. Express 16(5), 2867–2873 (2008).
[CrossRef] [PubMed]

Nicati, P.-A.

J. Troger, L. Thevenaz, P.-A. Nicati, and P. A. Robert, “Theory and experiment of a single-mode diode laser subject to external light injection from several lasers,” J. Lightwave Technol. 17(4), 629–636 (1999).
[CrossRef]

Olsson, N. A.

C. H. Henry, N. A. Olsson, and N. K. Dutta, “Locking range and stability of injection locked 1.54 μm InGaAsP semiconductor lasers,” IEEE J. Quantum Electron. 21(8), 1152–1156 (1985).
[CrossRef]

Pezeshki, J.

J. Pezeshki, M. Saylors, H. Mandelberg, and J. Goldhar, “Generation of a CW laser oscillator signal using a stabilized injection locked semiconductor laser,” J. Lightwave Technol. 26(5), 588–599 (2008).
[CrossRef]

Robert, P. A.

J. Troger, L. Thevenaz, P.-A. Nicati, and P. A. Robert, “Theory and experiment of a single-mode diode laser subject to external light injection from several lasers,” J. Lightwave Technol. 17(4), 629–636 (1999).
[CrossRef]

Ryu, H. Y.

H. Y. Ryu, S. H. Lee, W. K. Lee, H. S. Moon, and H. S. Suh, “Absolute frequency measurement of an acetylene stabilized laser using a selected single mode from a femtosecond fiber laser comb,” Opt. Express 16(5), 2867–2873 (2008).
[CrossRef] [PubMed]

Saylors, M.

J. Pezeshki, M. Saylors, H. Mandelberg, and J. Goldhar, “Generation of a CW laser oscillator signal using a stabilized injection locked semiconductor laser,” J. Lightwave Technol. 26(5), 588–599 (2008).
[CrossRef]

Spano, P.

R. Hui, A. D’Ottavi, A. Mecozzi, and P. Spano, “Injection locking in distributed feedback semiconductor lasers,” IEEE J. Quantum Electron. 27(6), 1688–1695 (1991).
[CrossRef]

Steier, W. H.

H. L. Stover and W. H. Steier, “Locking of laser oscillators by light injection,” Appl. Phys. Lett. 8(4), 91–93 (1966).
[CrossRef]

Stover, H. L.

H. L. Stover and W. H. Steier, “Locking of laser oscillators by light injection,” Appl. Phys. Lett. 8(4), 91–93 (1966).
[CrossRef]

Suh, H. S.

H. Y. Ryu, S. H. Lee, W. K. Lee, H. S. Moon, and H. S. Suh, “Absolute frequency measurement of an acetylene stabilized laser using a selected single mode from a femtosecond fiber laser comb,” Opt. Express 16(5), 2867–2873 (2008).
[CrossRef] [PubMed]

Thevenaz, L.

J. Troger, L. Thevenaz, P.-A. Nicati, and P. A. Robert, “Theory and experiment of a single-mode diode laser subject to external light injection from several lasers,” J. Lightwave Technol. 17(4), 629–636 (1999).
[CrossRef]

Troger, J.

J. Troger, L. Thevenaz, P.-A. Nicati, and P. A. Robert, “Theory and experiment of a single-mode diode laser subject to external light injection from several lasers,” J. Lightwave Technol. 17(4), 629–636 (1999).
[CrossRef]

Appl. Phys. Lett. (2)

H. L. Stover and W. H. Steier, “Locking of laser oscillators by light injection,” Appl. Phys. Lett. 8(4), 91–93 (1966).
[CrossRef]

X. Jin and S. L. Chuang, “Relative intensity noise characteristics of injection-locked semiconductor lasers,” Appl. Phys. Lett. 77(9), 1250–1252 (2000).
[CrossRef]

IEEE J. Quantum Electron. (5)

R. Lang and K. Kobayashi, “Suppression of the relaxation oscillation in the modulated output of semiconductor lasers,” IEEE J. Quantum Electron. 12(3), 194–199 (1976).
[CrossRef]

C. H. Henry, N. A. Olsson, and N. K. Dutta, “Locking range and stability of injection locked 1.54 μm InGaAsP semiconductor lasers,” IEEE J. Quantum Electron. 21(8), 1152–1156 (1985).
[CrossRef]

R. Hui, A. D’Ottavi, A. Mecozzi, and P. Spano, “Injection locking in distributed feedback semiconductor lasers,” IEEE J. Quantum Electron. 27(6), 1688–1695 (1991).
[CrossRef]

S. Kobayashi and T. Kimura, “Injection locking in AlGaAs semiconductor laser,” IEEE J. Quantum Electron. 17(5), 681–689 (1981).
[CrossRef]

R. Lang, “Injection locking properties of a semiconductor lasr,” IEEE J. Quantum Electron. 18(6), 976–983 (1982).
[CrossRef]

J. Lightwave Technol. (2)

J. Troger, L. Thevenaz, P.-A. Nicati, and P. A. Robert, “Theory and experiment of a single-mode diode laser subject to external light injection from several lasers,” J. Lightwave Technol. 17(4), 629–636 (1999).
[CrossRef]

J. Pezeshki, M. Saylors, H. Mandelberg, and J. Goldhar, “Generation of a CW laser oscillator signal using a stabilized injection locked semiconductor laser,” J. Lightwave Technol. 26(5), 588–599 (2008).
[CrossRef]

Opt. Express (1)

H. Y. Ryu, S. H. Lee, W. K. Lee, H. S. Moon, and H. S. Suh, “Absolute frequency measurement of an acetylene stabilized laser using a selected single mode from a femtosecond fiber laser comb,” Opt. Express 16(5), 2867–2873 (2008).
[CrossRef] [PubMed]

Other (3)

L. Siegman, (University Science Books, 1986), Chap. 27, ISBN 0–935702–11–5.

R. Adler, “A study of locking phenomena in oscillators, “A study of locking phenomena in oscillators,” Proc. IRE, Vol.34, No.10, pp.351–357, Oct. 1946.

W. Robert, Boyd, Nonlinear Optics (Academic Press, Inc., 1992), ISBN 0–12–121680–2.

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Figures (11)

Fig. 1
Fig. 1

Schematic diagram of the experimental setup. PC: polarization controller, OC: optical circulator, VA: variable optical attenuator, PD: photodetector, OSA: optical spectrum analyzer, and RFSA: RF spectrum analyzer.

Fig. 2
Fig. 2

Optical spectra of the master and the slave laser. Dotted line: the master laser output, dashed line: free running slave laser output, and solid line: injection locked slave laser output.

Fig. 3
Fig. 3

RF spectra of the slave laser: (a) unlocked case, and (b) locked case.

Fig. 4
Fig. 4

Optical spectra of the master and the slave laser. Dotted line: the master laser output, dashed line: free running slave laser output, and solid line: injection locked slave laser output.

Fig. 5
Fig. 5

RF spectra of the slave laser: (a) unlocked case, and (b) locked case.

Fig. 6
Fig. 6

Optical spectra of the master and the slave laser. Dotted line: the master laser output, dashed line: free running slave laser output, and solid line: injection locked slave laser output.

Fig. 7
Fig. 7

RF spectra of the slave laser at a trisecting point between two neighboring master laser modes.

Fig. 8
Fig. 8

Simulated optical spectra of two mode injection: (a) free running slave laser (solid line), master laser (dotted line), (b) slave laser output after injection locking. (Insets are zoom-in of slave laser output)

Fig. 9
Fig. 9

Simulated optical spectra of two mode injection: (a) free running slave laser (solid line), master laser (dotted line), (b) slave laser output after injection locking. (Insets are zoom-in of slave laser output).

Fig. 10
Fig. 10

Simulated slave laser frequency offset from injection locking frequency vs. injected optical power. Solid line: locking to the bisecting point, dotted line: locking to the trisecting point, and dashed line: locking to the quartering point.

Fig. 11
Fig. 11

Simulated optical spectra of two mode injection for various injection power level: (a) PMaster/PSlave = 1.87 × 10−4, (b) PMaster/PSlave = 8.60 × 10−4, (c) PMaster/PSlave = 2.78 × 10−3, and (d) PMaster/PSlave = 3.29 × 10−3. (Insets are zoom-in of slave laser output).

Tables (1)

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Table 1 Simulation Parameters

Equations (7)

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Δ ν L o c k = ν 0 P M a s t e r / P S l a v e .
ε ( t ) = E ( t ) exp [ i ( ω S t + φ ( t ) ) ] ,
ε m ( t ) = E m ( t ) exp [ i ( ω m t + φ m ) ] .
d P d t = ( G γ ) P + 2 τ L m = 1 l P P m cos ( φ m φ ) + R s p ,
d φ d t = 1 2 α ( G γ ) + 1 τ L m = 1 l P m P sin ( φ m φ ) ,
G = Γ g 0 v g 1 + P P s log ( N + N s N t r + N s ) ,
d N d t = η i I q γ e N G P ,

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