Abstract

We investigate theoretically the tuning characteristics of a diode with an external grating cavity for which one of the external-cavity modes and the peak of the grating reflection scan synchronously. We show that the tuning curve is hysteretic. Moreover, the theoretical analysis reveals that frequencies at turning points of the hysteretic tuning curve are related to the external cavity mode spacing, the reflectivity of the front facet, and the linewidth enhancement factor α of the laser diode. A method for achieving an overlap of the peak of the reflection profile of the grating with one of the external-cavity modes is described. Experimentally, by measuring the hysteretic tuning curve, we observed the predicted effect and found the reflectivity of the front facet and the α value for a Toshiba TOLD 9215 visible diode to be 2.9 ± 1.6% and 5.1 ∓ 1.3, respectively.

© 1992 Optical Society of America

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References

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  1. C. E. Wieman, L. Hollberg, “Using diode lasers for atomic physics,” Rev. Sci. Instrum. 62, 1–19 (1991).
    [CrossRef]
  2. P. Zorabedian, W. R. Trutra, L. S. Cutler, “Bistability in grating-tuned external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 23, 1855–1860 (1987).
    [CrossRef]
  3. J. O. Binder, G. D. Cormack, A. Somani, “Intermode tuning characteristics of an InGaAsP laser with optical feedback from an external grating reflector,” in Proceedings of the IEEE Pacific Rim Conference on Communications, Computers, and Signal Processing (Institute of Electric and Electronics Engineers, New York, 1989), pp. 22–26.
    [CrossRef]
  4. K. C. Harvey, C. J. Myatt, “External-cavity diode laser using a grazing-incidence diffraction grating,” Opt. Lett. 16, 910–912 (1991).
    [CrossRef] [PubMed]
  5. Z. M. Chuang, D. A. Cohen, L. A. Coldren, “Tuning characteristics of a tunable-single-frequency external-cavity laser,” IEEE J. Quantum Electron. 26, 1200–1205 (1990).
    [CrossRef]
  6. P. W. A. Mcllroy, “Calculation of mode suppression ratio in Fabry–Perot, DBR, and external cavity lasers,” J. Quantum Electron. 26, 991–997 (1990).
    [CrossRef]
  7. K. Vahala, L. C. Chiu, S. Margalit, A. Yariv, “On the linewidth enhancement factor α in semiconductor injection lasers,” Appl. Phys. Lett. 42, 631–633 (1983).
    [CrossRef]
  8. I. D. Henning, J. V. Collins, “Measurement of the semiconductor laser linewidth broadening factor,” Electron. Lett. 27, 927–929 (1983).
    [CrossRef]
  9. B. Tromborg, J. H. Osmundsen, H. Olesen, “Stability analysis for a semiconductor laser in an external cavity,” IEEE J. Quantum Electron. 20, 1023–1032 (1984).
    [CrossRef]
  10. H. Sato, T. Fujita, J. Ohya, “Theoretical analysis of longitudinal mode coupling in external cavity semiconductor lasers,” IEEE J. Quantum Electron. 21, 284–291 (1985).
    [CrossRef]
  11. A. Olsson, C. L. Tang, “Coherent optical interference effects in external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 17, 1320–1323 (1981).
    [CrossRef]

1991 (2)

1990 (2)

Z. M. Chuang, D. A. Cohen, L. A. Coldren, “Tuning characteristics of a tunable-single-frequency external-cavity laser,” IEEE J. Quantum Electron. 26, 1200–1205 (1990).
[CrossRef]

P. W. A. Mcllroy, “Calculation of mode suppression ratio in Fabry–Perot, DBR, and external cavity lasers,” J. Quantum Electron. 26, 991–997 (1990).
[CrossRef]

1987 (1)

P. Zorabedian, W. R. Trutra, L. S. Cutler, “Bistability in grating-tuned external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 23, 1855–1860 (1987).
[CrossRef]

1985 (1)

H. Sato, T. Fujita, J. Ohya, “Theoretical analysis of longitudinal mode coupling in external cavity semiconductor lasers,” IEEE J. Quantum Electron. 21, 284–291 (1985).
[CrossRef]

1984 (1)

B. Tromborg, J. H. Osmundsen, H. Olesen, “Stability analysis for a semiconductor laser in an external cavity,” IEEE J. Quantum Electron. 20, 1023–1032 (1984).
[CrossRef]

1983 (2)

K. Vahala, L. C. Chiu, S. Margalit, A. Yariv, “On the linewidth enhancement factor α in semiconductor injection lasers,” Appl. Phys. Lett. 42, 631–633 (1983).
[CrossRef]

I. D. Henning, J. V. Collins, “Measurement of the semiconductor laser linewidth broadening factor,” Electron. Lett. 27, 927–929 (1983).
[CrossRef]

1981 (1)

A. Olsson, C. L. Tang, “Coherent optical interference effects in external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 17, 1320–1323 (1981).
[CrossRef]

Binder, J. O.

J. O. Binder, G. D. Cormack, A. Somani, “Intermode tuning characteristics of an InGaAsP laser with optical feedback from an external grating reflector,” in Proceedings of the IEEE Pacific Rim Conference on Communications, Computers, and Signal Processing (Institute of Electric and Electronics Engineers, New York, 1989), pp. 22–26.
[CrossRef]

Chiu, L. C.

K. Vahala, L. C. Chiu, S. Margalit, A. Yariv, “On the linewidth enhancement factor α in semiconductor injection lasers,” Appl. Phys. Lett. 42, 631–633 (1983).
[CrossRef]

Chuang, Z. M.

Z. M. Chuang, D. A. Cohen, L. A. Coldren, “Tuning characteristics of a tunable-single-frequency external-cavity laser,” IEEE J. Quantum Electron. 26, 1200–1205 (1990).
[CrossRef]

Cohen, D. A.

Z. M. Chuang, D. A. Cohen, L. A. Coldren, “Tuning characteristics of a tunable-single-frequency external-cavity laser,” IEEE J. Quantum Electron. 26, 1200–1205 (1990).
[CrossRef]

Coldren, L. A.

Z. M. Chuang, D. A. Cohen, L. A. Coldren, “Tuning characteristics of a tunable-single-frequency external-cavity laser,” IEEE J. Quantum Electron. 26, 1200–1205 (1990).
[CrossRef]

Collins, J. V.

I. D. Henning, J. V. Collins, “Measurement of the semiconductor laser linewidth broadening factor,” Electron. Lett. 27, 927–929 (1983).
[CrossRef]

Cormack, G. D.

J. O. Binder, G. D. Cormack, A. Somani, “Intermode tuning characteristics of an InGaAsP laser with optical feedback from an external grating reflector,” in Proceedings of the IEEE Pacific Rim Conference on Communications, Computers, and Signal Processing (Institute of Electric and Electronics Engineers, New York, 1989), pp. 22–26.
[CrossRef]

Cutler, L. S.

P. Zorabedian, W. R. Trutra, L. S. Cutler, “Bistability in grating-tuned external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 23, 1855–1860 (1987).
[CrossRef]

Fujita, T.

H. Sato, T. Fujita, J. Ohya, “Theoretical analysis of longitudinal mode coupling in external cavity semiconductor lasers,” IEEE J. Quantum Electron. 21, 284–291 (1985).
[CrossRef]

Harvey, K. C.

Henning, I. D.

I. D. Henning, J. V. Collins, “Measurement of the semiconductor laser linewidth broadening factor,” Electron. Lett. 27, 927–929 (1983).
[CrossRef]

Hollberg, L.

C. E. Wieman, L. Hollberg, “Using diode lasers for atomic physics,” Rev. Sci. Instrum. 62, 1–19 (1991).
[CrossRef]

Margalit, S.

K. Vahala, L. C. Chiu, S. Margalit, A. Yariv, “On the linewidth enhancement factor α in semiconductor injection lasers,” Appl. Phys. Lett. 42, 631–633 (1983).
[CrossRef]

Mcllroy, P. W. A.

P. W. A. Mcllroy, “Calculation of mode suppression ratio in Fabry–Perot, DBR, and external cavity lasers,” J. Quantum Electron. 26, 991–997 (1990).
[CrossRef]

Myatt, C. J.

Ohya, J.

H. Sato, T. Fujita, J. Ohya, “Theoretical analysis of longitudinal mode coupling in external cavity semiconductor lasers,” IEEE J. Quantum Electron. 21, 284–291 (1985).
[CrossRef]

Olesen, H.

B. Tromborg, J. H. Osmundsen, H. Olesen, “Stability analysis for a semiconductor laser in an external cavity,” IEEE J. Quantum Electron. 20, 1023–1032 (1984).
[CrossRef]

Olsson, A.

A. Olsson, C. L. Tang, “Coherent optical interference effects in external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 17, 1320–1323 (1981).
[CrossRef]

Osmundsen, J. H.

B. Tromborg, J. H. Osmundsen, H. Olesen, “Stability analysis for a semiconductor laser in an external cavity,” IEEE J. Quantum Electron. 20, 1023–1032 (1984).
[CrossRef]

Sato, H.

H. Sato, T. Fujita, J. Ohya, “Theoretical analysis of longitudinal mode coupling in external cavity semiconductor lasers,” IEEE J. Quantum Electron. 21, 284–291 (1985).
[CrossRef]

Somani, A.

J. O. Binder, G. D. Cormack, A. Somani, “Intermode tuning characteristics of an InGaAsP laser with optical feedback from an external grating reflector,” in Proceedings of the IEEE Pacific Rim Conference on Communications, Computers, and Signal Processing (Institute of Electric and Electronics Engineers, New York, 1989), pp. 22–26.
[CrossRef]

Tang, C. L.

A. Olsson, C. L. Tang, “Coherent optical interference effects in external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 17, 1320–1323 (1981).
[CrossRef]

Tromborg, B.

B. Tromborg, J. H. Osmundsen, H. Olesen, “Stability analysis for a semiconductor laser in an external cavity,” IEEE J. Quantum Electron. 20, 1023–1032 (1984).
[CrossRef]

Trutra, W. R.

P. Zorabedian, W. R. Trutra, L. S. Cutler, “Bistability in grating-tuned external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 23, 1855–1860 (1987).
[CrossRef]

Vahala, K.

K. Vahala, L. C. Chiu, S. Margalit, A. Yariv, “On the linewidth enhancement factor α in semiconductor injection lasers,” Appl. Phys. Lett. 42, 631–633 (1983).
[CrossRef]

Wieman, C. E.

C. E. Wieman, L. Hollberg, “Using diode lasers for atomic physics,” Rev. Sci. Instrum. 62, 1–19 (1991).
[CrossRef]

Yariv, A.

K. Vahala, L. C. Chiu, S. Margalit, A. Yariv, “On the linewidth enhancement factor α in semiconductor injection lasers,” Appl. Phys. Lett. 42, 631–633 (1983).
[CrossRef]

Zorabedian, P.

P. Zorabedian, W. R. Trutra, L. S. Cutler, “Bistability in grating-tuned external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 23, 1855–1860 (1987).
[CrossRef]

Appl. Phys. Lett. (1)

K. Vahala, L. C. Chiu, S. Margalit, A. Yariv, “On the linewidth enhancement factor α in semiconductor injection lasers,” Appl. Phys. Lett. 42, 631–633 (1983).
[CrossRef]

Electron. Lett. (1)

I. D. Henning, J. V. Collins, “Measurement of the semiconductor laser linewidth broadening factor,” Electron. Lett. 27, 927–929 (1983).
[CrossRef]

IEEE J. Quantum Electron. (5)

B. Tromborg, J. H. Osmundsen, H. Olesen, “Stability analysis for a semiconductor laser in an external cavity,” IEEE J. Quantum Electron. 20, 1023–1032 (1984).
[CrossRef]

H. Sato, T. Fujita, J. Ohya, “Theoretical analysis of longitudinal mode coupling in external cavity semiconductor lasers,” IEEE J. Quantum Electron. 21, 284–291 (1985).
[CrossRef]

A. Olsson, C. L. Tang, “Coherent optical interference effects in external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 17, 1320–1323 (1981).
[CrossRef]

P. Zorabedian, W. R. Trutra, L. S. Cutler, “Bistability in grating-tuned external-cavity semiconductor lasers,” IEEE J. Quantum Electron. 23, 1855–1860 (1987).
[CrossRef]

Z. M. Chuang, D. A. Cohen, L. A. Coldren, “Tuning characteristics of a tunable-single-frequency external-cavity laser,” IEEE J. Quantum Electron. 26, 1200–1205 (1990).
[CrossRef]

J. Quantum Electron. (1)

P. W. A. Mcllroy, “Calculation of mode suppression ratio in Fabry–Perot, DBR, and external cavity lasers,” J. Quantum Electron. 26, 991–997 (1990).
[CrossRef]

Opt. Lett. (1)

Rev. Sci. Instrum. (1)

C. E. Wieman, L. Hollberg, “Using diode lasers for atomic physics,” Rev. Sci. Instrum. 62, 1–19 (1991).
[CrossRef]

Other (1)

J. O. Binder, G. D. Cormack, A. Somani, “Intermode tuning characteristics of an InGaAsP laser with optical feedback from an external grating reflector,” in Proceedings of the IEEE Pacific Rim Conference on Communications, Computers, and Signal Processing (Institute of Electric and Electronics Engineers, New York, 1989), pp. 22–26.
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Stability related to relative positions between the intrinsic mode and the external-cavity mode.

Fig. 2
Fig. 2

Relevant modes’ positions when an external cavity scans.

Fig. 3
Fig. 3

Calculated tuning curve of a diode with an external-grating cavity.

Fig. 4
Fig. 4

Hysteresis characteristics of the tuning curve.

Fig. 5
Fig. 5

Relevant turning points of the tuning curve.

Fig. 6
Fig. 6

Experimental setup.

Fig. 7
Fig. 7

Measured positions and frequencies of the turning points.

Equations (7)

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r eff = r 1 + r e exp ( i ϕ e ) 1 + r 1 r e exp ( i ϕ e ) ,
r e = r g exp [ ln 2 ( ν ν g ) 2 Δ ν g 2 ] ,
g = α l ( 1 / l ) ln ( r 2 | r eff | ) ,
ν ν i = Δ ν i Arg ( r eff ) 2 π ,
ν i ν i 0 = α Δ ν i 2 π ln ( r m | r eff | ) .
Δ ν c < Δ ν g < Δ ν i .
d ν = d ν i Δ ν i [ Arg ( r eff ) / 2 π ] , d ν n = d ν Δ ν c ( ϕ e / 2 π ) , d ν n 1 = d ν n Δ ν c .

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