Abstract

We demonstrate the characterization of fiber distributed-feedback lasers by scanning a heat-induced index perturbation along the cavity and by measuring the induced laser frequency shift. The measured shift is shown to be a good indicator for the intensity distribution in the cavity, and the experimental results reveal that the sensitivity of fiber distributed-feedback laser sensors with frequency readout is highly localized near the grating phase-shift position. Use of the characterization data to determine the grating coupling parameter κ, the polarization dependence of κ, and birefringence nonuniformities as well as for identification of the order of longitudinal mode operation are discussed and demonstrated experimentally. Asymmetrically phase-shifted lasers with highly directional output are also investigated.

© 1999 Optical Society of America

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References

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  1. L. J. P. Ketelsen, I. Hoshino, D. A. Ackerman, “The role of axially nonuniform carrier density in altering the TE–TE gain margin in InGaAsP-InP DFB lasers,” IEEE J. Quantum Electron. 27, 957–964 (1991).
    [CrossRef]
  2. M. R. Phillips, T. E. Darchie, E. J. Flynn, “Experimental measure of dynamic spatial-hole burning in DFB lasers,” IEEE Photon. Technol. Lett. 4, 1201–1203 (1992).
    [CrossRef]
  3. W. H. Loh, B. N. Samson, J. P. de Sandro, “Intensity profile in a distributed feedback fibre laser characterized by a green fluorescence scanning technique,” Appl. Phys. Lett. 69, 3773–3775 (1996).
    [CrossRef]
  4. E. Brinkmeyer, G. Stolze, D. Johlen, “Optical space domain reflectometry (OSDR) for determination of strength and chirp distribution along optical fiber gratings,” in Photosensitivity in Glasses, Vol. 17 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997).
  5. A. Cunliffe, L. E. S. Mathias, “Some perturbation effects in cavity resonators,” Proc. Inst. Electron. Eng. 97, 367–376 (1950).
  6. H. B. G. Casimir, “On the theory of electromagnetic waves in resonant cavities,” Phillips Res. Rep. 6, 162–182 (1951).
  7. E. Rønnekleiv, M. Ibsen, M. N. Zervas, R. I. Laming, “Characterization of intensity distribution in symmetric and asymmetric fiber DFB lasers,” in Conference on Lasers and Electro-Optics, Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 80.
  8. J. T. Kringlebotn, J. L. Archambault, L. Reekie, D. N. Payne, “Er3+:Yb3+-codoped fiber distributed-feedback laser,” Opt. Lett. 19, 2101–2103 (1994).
    [CrossRef] [PubMed]
  9. V. C. Lauridsen, T. Søndergaard, P. Varming, J. H. Povlsen, “Design of distributed feedback fibre lasers,” in Proceedings of the European Conference on Optical Communications ’97, (Institution of Electrical Engineers, London, 1997), Vol. 3, pp. 39–42.
  10. H. Soda, Y. Kotaki, H. Sudo, H. Ishikava, S. Yamakoshi, H. Imai, “Stability in single longitudinal mode operation in GaInAsP/InP phase-adjusted DFB lasers,” IEEE J. Quantum Electron. QE-23, 804–814 (1987).
    [CrossRef]
  11. E. Rønnekleiv, O. Hadeler, “Stability of an Er–Yb-doped fiber distributed-feedback laser with external reflections,” Opt. Lett. 24, 617–619 (1999).
    [CrossRef]
  12. G. A. Ball, C. G. Hull-Allen, J. Livas, “Frequency noise of a Bragg grating fibre laser,” Electron. Lett. 30, 1229–1230 (1994).
    [CrossRef]
  13. E. Rønnekleiv, M. N. Zervas, J. T. Kringlebotn, “Modelling of polarization mode competition in fiber DFB lasers,” IEEE J. Quantum Electron. 34, 1559–1569 (1998).
    [CrossRef]
  14. L. Dong, W. H. Loh, J. E. Caplen, J. D. Minelly, L. Reekie, “Efficient single-frequency fiber-lasers with novel photosensitive Er/Yb optical fibers,” Opt. Lett. 22, 694–669 (1997).
    [CrossRef] [PubMed]
  15. J. I. Sakai, T. Kimura, “Birefringence caused by thermal stress in elliptically deformed core optical fibers,” IEEE J. Quantum Electron. QE-18, 1899–1909 (1982).
    [CrossRef]
  16. A. Simon, R. Ulrich, “Evolution of polarization along a single-mode fiber,” Appl. Phys. Lett. 31, 517–521 (1977).
    [CrossRef]
  17. T. Erdogan, V. Mizrahi, “Characterization of UV-induced birefringence in photosensitive Ge-doped silica optical fibers,” J. Opt. Soc. Am. B 10, 2100–2105 (1994).
    [CrossRef]
  18. O. Hadeler, E. Rønnekleiv, M. Ibsen, R. I. Laming, “Polarimetric distributed feedback fiber laser sensor for simultaneous strain and temperature measurements,” Appl. Opt. 38, 1953–1959 (1999).
    [CrossRef]

1999 (2)

1998 (1)

E. Rønnekleiv, M. N. Zervas, J. T. Kringlebotn, “Modelling of polarization mode competition in fiber DFB lasers,” IEEE J. Quantum Electron. 34, 1559–1569 (1998).
[CrossRef]

1997 (1)

1996 (1)

W. H. Loh, B. N. Samson, J. P. de Sandro, “Intensity profile in a distributed feedback fibre laser characterized by a green fluorescence scanning technique,” Appl. Phys. Lett. 69, 3773–3775 (1996).
[CrossRef]

1994 (3)

1992 (1)

M. R. Phillips, T. E. Darchie, E. J. Flynn, “Experimental measure of dynamic spatial-hole burning in DFB lasers,” IEEE Photon. Technol. Lett. 4, 1201–1203 (1992).
[CrossRef]

1991 (1)

L. J. P. Ketelsen, I. Hoshino, D. A. Ackerman, “The role of axially nonuniform carrier density in altering the TE–TE gain margin in InGaAsP-InP DFB lasers,” IEEE J. Quantum Electron. 27, 957–964 (1991).
[CrossRef]

1987 (1)

H. Soda, Y. Kotaki, H. Sudo, H. Ishikava, S. Yamakoshi, H. Imai, “Stability in single longitudinal mode operation in GaInAsP/InP phase-adjusted DFB lasers,” IEEE J. Quantum Electron. QE-23, 804–814 (1987).
[CrossRef]

1982 (1)

J. I. Sakai, T. Kimura, “Birefringence caused by thermal stress in elliptically deformed core optical fibers,” IEEE J. Quantum Electron. QE-18, 1899–1909 (1982).
[CrossRef]

1977 (1)

A. Simon, R. Ulrich, “Evolution of polarization along a single-mode fiber,” Appl. Phys. Lett. 31, 517–521 (1977).
[CrossRef]

1951 (1)

H. B. G. Casimir, “On the theory of electromagnetic waves in resonant cavities,” Phillips Res. Rep. 6, 162–182 (1951).

1950 (1)

A. Cunliffe, L. E. S. Mathias, “Some perturbation effects in cavity resonators,” Proc. Inst. Electron. Eng. 97, 367–376 (1950).

Ackerman, D. A.

L. J. P. Ketelsen, I. Hoshino, D. A. Ackerman, “The role of axially nonuniform carrier density in altering the TE–TE gain margin in InGaAsP-InP DFB lasers,” IEEE J. Quantum Electron. 27, 957–964 (1991).
[CrossRef]

Archambault, J. L.

Ball, G. A.

G. A. Ball, C. G. Hull-Allen, J. Livas, “Frequency noise of a Bragg grating fibre laser,” Electron. Lett. 30, 1229–1230 (1994).
[CrossRef]

Brinkmeyer, E.

E. Brinkmeyer, G. Stolze, D. Johlen, “Optical space domain reflectometry (OSDR) for determination of strength and chirp distribution along optical fiber gratings,” in Photosensitivity in Glasses, Vol. 17 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997).

Caplen, J. E.

Casimir, H. B. G.

H. B. G. Casimir, “On the theory of electromagnetic waves in resonant cavities,” Phillips Res. Rep. 6, 162–182 (1951).

Cunliffe, A.

A. Cunliffe, L. E. S. Mathias, “Some perturbation effects in cavity resonators,” Proc. Inst. Electron. Eng. 97, 367–376 (1950).

Darchie, T. E.

M. R. Phillips, T. E. Darchie, E. J. Flynn, “Experimental measure of dynamic spatial-hole burning in DFB lasers,” IEEE Photon. Technol. Lett. 4, 1201–1203 (1992).
[CrossRef]

de Sandro, J. P.

W. H. Loh, B. N. Samson, J. P. de Sandro, “Intensity profile in a distributed feedback fibre laser characterized by a green fluorescence scanning technique,” Appl. Phys. Lett. 69, 3773–3775 (1996).
[CrossRef]

Dong, L.

Erdogan, T.

Flynn, E. J.

M. R. Phillips, T. E. Darchie, E. J. Flynn, “Experimental measure of dynamic spatial-hole burning in DFB lasers,” IEEE Photon. Technol. Lett. 4, 1201–1203 (1992).
[CrossRef]

Hadeler, O.

Hoshino, I.

L. J. P. Ketelsen, I. Hoshino, D. A. Ackerman, “The role of axially nonuniform carrier density in altering the TE–TE gain margin in InGaAsP-InP DFB lasers,” IEEE J. Quantum Electron. 27, 957–964 (1991).
[CrossRef]

Hull-Allen, C. G.

G. A. Ball, C. G. Hull-Allen, J. Livas, “Frequency noise of a Bragg grating fibre laser,” Electron. Lett. 30, 1229–1230 (1994).
[CrossRef]

Ibsen, M.

O. Hadeler, E. Rønnekleiv, M. Ibsen, R. I. Laming, “Polarimetric distributed feedback fiber laser sensor for simultaneous strain and temperature measurements,” Appl. Opt. 38, 1953–1959 (1999).
[CrossRef]

E. Rønnekleiv, M. Ibsen, M. N. Zervas, R. I. Laming, “Characterization of intensity distribution in symmetric and asymmetric fiber DFB lasers,” in Conference on Lasers and Electro-Optics, Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 80.

Imai, H.

H. Soda, Y. Kotaki, H. Sudo, H. Ishikava, S. Yamakoshi, H. Imai, “Stability in single longitudinal mode operation in GaInAsP/InP phase-adjusted DFB lasers,” IEEE J. Quantum Electron. QE-23, 804–814 (1987).
[CrossRef]

Ishikava, H.

H. Soda, Y. Kotaki, H. Sudo, H. Ishikava, S. Yamakoshi, H. Imai, “Stability in single longitudinal mode operation in GaInAsP/InP phase-adjusted DFB lasers,” IEEE J. Quantum Electron. QE-23, 804–814 (1987).
[CrossRef]

Johlen, D.

E. Brinkmeyer, G. Stolze, D. Johlen, “Optical space domain reflectometry (OSDR) for determination of strength and chirp distribution along optical fiber gratings,” in Photosensitivity in Glasses, Vol. 17 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997).

Ketelsen, L. J. P.

L. J. P. Ketelsen, I. Hoshino, D. A. Ackerman, “The role of axially nonuniform carrier density in altering the TE–TE gain margin in InGaAsP-InP DFB lasers,” IEEE J. Quantum Electron. 27, 957–964 (1991).
[CrossRef]

Kimura, T.

J. I. Sakai, T. Kimura, “Birefringence caused by thermal stress in elliptically deformed core optical fibers,” IEEE J. Quantum Electron. QE-18, 1899–1909 (1982).
[CrossRef]

Kotaki, Y.

H. Soda, Y. Kotaki, H. Sudo, H. Ishikava, S. Yamakoshi, H. Imai, “Stability in single longitudinal mode operation in GaInAsP/InP phase-adjusted DFB lasers,” IEEE J. Quantum Electron. QE-23, 804–814 (1987).
[CrossRef]

Kringlebotn, J. T.

E. Rønnekleiv, M. N. Zervas, J. T. Kringlebotn, “Modelling of polarization mode competition in fiber DFB lasers,” IEEE J. Quantum Electron. 34, 1559–1569 (1998).
[CrossRef]

J. T. Kringlebotn, J. L. Archambault, L. Reekie, D. N. Payne, “Er3+:Yb3+-codoped fiber distributed-feedback laser,” Opt. Lett. 19, 2101–2103 (1994).
[CrossRef] [PubMed]

Laming, R. I.

O. Hadeler, E. Rønnekleiv, M. Ibsen, R. I. Laming, “Polarimetric distributed feedback fiber laser sensor for simultaneous strain and temperature measurements,” Appl. Opt. 38, 1953–1959 (1999).
[CrossRef]

E. Rønnekleiv, M. Ibsen, M. N. Zervas, R. I. Laming, “Characterization of intensity distribution in symmetric and asymmetric fiber DFB lasers,” in Conference on Lasers and Electro-Optics, Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 80.

Lauridsen, V. C.

V. C. Lauridsen, T. Søndergaard, P. Varming, J. H. Povlsen, “Design of distributed feedback fibre lasers,” in Proceedings of the European Conference on Optical Communications ’97, (Institution of Electrical Engineers, London, 1997), Vol. 3, pp. 39–42.

Livas, J.

G. A. Ball, C. G. Hull-Allen, J. Livas, “Frequency noise of a Bragg grating fibre laser,” Electron. Lett. 30, 1229–1230 (1994).
[CrossRef]

Loh, W. H.

L. Dong, W. H. Loh, J. E. Caplen, J. D. Minelly, L. Reekie, “Efficient single-frequency fiber-lasers with novel photosensitive Er/Yb optical fibers,” Opt. Lett. 22, 694–669 (1997).
[CrossRef] [PubMed]

W. H. Loh, B. N. Samson, J. P. de Sandro, “Intensity profile in a distributed feedback fibre laser characterized by a green fluorescence scanning technique,” Appl. Phys. Lett. 69, 3773–3775 (1996).
[CrossRef]

Mathias, L. E. S.

A. Cunliffe, L. E. S. Mathias, “Some perturbation effects in cavity resonators,” Proc. Inst. Electron. Eng. 97, 367–376 (1950).

Minelly, J. D.

Mizrahi, V.

Payne, D. N.

Phillips, M. R.

M. R. Phillips, T. E. Darchie, E. J. Flynn, “Experimental measure of dynamic spatial-hole burning in DFB lasers,” IEEE Photon. Technol. Lett. 4, 1201–1203 (1992).
[CrossRef]

Povlsen, J. H.

V. C. Lauridsen, T. Søndergaard, P. Varming, J. H. Povlsen, “Design of distributed feedback fibre lasers,” in Proceedings of the European Conference on Optical Communications ’97, (Institution of Electrical Engineers, London, 1997), Vol. 3, pp. 39–42.

Reekie, L.

Rønnekleiv, E.

E. Rønnekleiv, O. Hadeler, “Stability of an Er–Yb-doped fiber distributed-feedback laser with external reflections,” Opt. Lett. 24, 617–619 (1999).
[CrossRef]

O. Hadeler, E. Rønnekleiv, M. Ibsen, R. I. Laming, “Polarimetric distributed feedback fiber laser sensor for simultaneous strain and temperature measurements,” Appl. Opt. 38, 1953–1959 (1999).
[CrossRef]

E. Rønnekleiv, M. N. Zervas, J. T. Kringlebotn, “Modelling of polarization mode competition in fiber DFB lasers,” IEEE J. Quantum Electron. 34, 1559–1569 (1998).
[CrossRef]

E. Rønnekleiv, M. Ibsen, M. N. Zervas, R. I. Laming, “Characterization of intensity distribution in symmetric and asymmetric fiber DFB lasers,” in Conference on Lasers and Electro-Optics, Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 80.

Sakai, J. I.

J. I. Sakai, T. Kimura, “Birefringence caused by thermal stress in elliptically deformed core optical fibers,” IEEE J. Quantum Electron. QE-18, 1899–1909 (1982).
[CrossRef]

Samson, B. N.

W. H. Loh, B. N. Samson, J. P. de Sandro, “Intensity profile in a distributed feedback fibre laser characterized by a green fluorescence scanning technique,” Appl. Phys. Lett. 69, 3773–3775 (1996).
[CrossRef]

Simon, A.

A. Simon, R. Ulrich, “Evolution of polarization along a single-mode fiber,” Appl. Phys. Lett. 31, 517–521 (1977).
[CrossRef]

Soda, H.

H. Soda, Y. Kotaki, H. Sudo, H. Ishikava, S. Yamakoshi, H. Imai, “Stability in single longitudinal mode operation in GaInAsP/InP phase-adjusted DFB lasers,” IEEE J. Quantum Electron. QE-23, 804–814 (1987).
[CrossRef]

Søndergaard, T.

V. C. Lauridsen, T. Søndergaard, P. Varming, J. H. Povlsen, “Design of distributed feedback fibre lasers,” in Proceedings of the European Conference on Optical Communications ’97, (Institution of Electrical Engineers, London, 1997), Vol. 3, pp. 39–42.

Stolze, G.

E. Brinkmeyer, G. Stolze, D. Johlen, “Optical space domain reflectometry (OSDR) for determination of strength and chirp distribution along optical fiber gratings,” in Photosensitivity in Glasses, Vol. 17 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997).

Sudo, H.

H. Soda, Y. Kotaki, H. Sudo, H. Ishikava, S. Yamakoshi, H. Imai, “Stability in single longitudinal mode operation in GaInAsP/InP phase-adjusted DFB lasers,” IEEE J. Quantum Electron. QE-23, 804–814 (1987).
[CrossRef]

Ulrich, R.

A. Simon, R. Ulrich, “Evolution of polarization along a single-mode fiber,” Appl. Phys. Lett. 31, 517–521 (1977).
[CrossRef]

Varming, P.

V. C. Lauridsen, T. Søndergaard, P. Varming, J. H. Povlsen, “Design of distributed feedback fibre lasers,” in Proceedings of the European Conference on Optical Communications ’97, (Institution of Electrical Engineers, London, 1997), Vol. 3, pp. 39–42.

Yamakoshi, S.

H. Soda, Y. Kotaki, H. Sudo, H. Ishikava, S. Yamakoshi, H. Imai, “Stability in single longitudinal mode operation in GaInAsP/InP phase-adjusted DFB lasers,” IEEE J. Quantum Electron. QE-23, 804–814 (1987).
[CrossRef]

Zervas, M. N.

E. Rønnekleiv, M. N. Zervas, J. T. Kringlebotn, “Modelling of polarization mode competition in fiber DFB lasers,” IEEE J. Quantum Electron. 34, 1559–1569 (1998).
[CrossRef]

E. Rønnekleiv, M. Ibsen, M. N. Zervas, R. I. Laming, “Characterization of intensity distribution in symmetric and asymmetric fiber DFB lasers,” in Conference on Lasers and Electro-Optics, Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 80.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

W. H. Loh, B. N. Samson, J. P. de Sandro, “Intensity profile in a distributed feedback fibre laser characterized by a green fluorescence scanning technique,” Appl. Phys. Lett. 69, 3773–3775 (1996).
[CrossRef]

A. Simon, R. Ulrich, “Evolution of polarization along a single-mode fiber,” Appl. Phys. Lett. 31, 517–521 (1977).
[CrossRef]

Electron. Lett. (1)

G. A. Ball, C. G. Hull-Allen, J. Livas, “Frequency noise of a Bragg grating fibre laser,” Electron. Lett. 30, 1229–1230 (1994).
[CrossRef]

IEEE J. Quantum Electron. (4)

E. Rønnekleiv, M. N. Zervas, J. T. Kringlebotn, “Modelling of polarization mode competition in fiber DFB lasers,” IEEE J. Quantum Electron. 34, 1559–1569 (1998).
[CrossRef]

H. Soda, Y. Kotaki, H. Sudo, H. Ishikava, S. Yamakoshi, H. Imai, “Stability in single longitudinal mode operation in GaInAsP/InP phase-adjusted DFB lasers,” IEEE J. Quantum Electron. QE-23, 804–814 (1987).
[CrossRef]

J. I. Sakai, T. Kimura, “Birefringence caused by thermal stress in elliptically deformed core optical fibers,” IEEE J. Quantum Electron. QE-18, 1899–1909 (1982).
[CrossRef]

L. J. P. Ketelsen, I. Hoshino, D. A. Ackerman, “The role of axially nonuniform carrier density in altering the TE–TE gain margin in InGaAsP-InP DFB lasers,” IEEE J. Quantum Electron. 27, 957–964 (1991).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

M. R. Phillips, T. E. Darchie, E. J. Flynn, “Experimental measure of dynamic spatial-hole burning in DFB lasers,” IEEE Photon. Technol. Lett. 4, 1201–1203 (1992).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Lett. (3)

Phillips Res. Rep. (1)

H. B. G. Casimir, “On the theory of electromagnetic waves in resonant cavities,” Phillips Res. Rep. 6, 162–182 (1951).

Proc. Inst. Electron. Eng. (1)

A. Cunliffe, L. E. S. Mathias, “Some perturbation effects in cavity resonators,” Proc. Inst. Electron. Eng. 97, 367–376 (1950).

Other (3)

E. Rønnekleiv, M. Ibsen, M. N. Zervas, R. I. Laming, “Characterization of intensity distribution in symmetric and asymmetric fiber DFB lasers,” in Conference on Lasers and Electro-Optics, Vol. 6 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 80.

V. C. Lauridsen, T. Søndergaard, P. Varming, J. H. Povlsen, “Design of distributed feedback fibre lasers,” in Proceedings of the European Conference on Optical Communications ’97, (Institution of Electrical Engineers, London, 1997), Vol. 3, pp. 39–42.

E. Brinkmeyer, G. Stolze, D. Johlen, “Optical space domain reflectometry (OSDR) for determination of strength and chirp distribution along optical fiber gratings,” in Photosensitivity in Glasses, Vol. 17 of 1997 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1997).

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Figures (6)

Fig. 1
Fig. 1

Theoretical intensity distribution |E 0|2 in a 60-mm laser with κ = 230 m-1 for the fundamental and first and second higher-order modes.

Fig. 2
Fig. 2

Theoretical distributions of |E +|2, |E -|2, |E + E -|, and |E 0|2 = |E +|2 + |E -|2, calculated by the T-matrix approach, for an asymmetric laser with κL = 8 and κΔL = 2.

Fig. 3
Fig. 3

Setup for characterizing the phase perturbation sensitivity distribution: WDM, wavelength-division multiplexer; FP, Fabry–Perot interferometer; Det., detector; Sig. gen., signal generator.

Fig. 4
Fig. 4

Laser frequency responses to heat scans measured for symmetric laser #1 (squares) and asymmetric laser #2 (circles), both with 40-mm gratings. The curves show calculated responses for δϕ = 0.53 rad and κ = 230 m-1.

Fig. 5
Fig. 5

(a) Laser frequency and polarization beat frequency responses to heat scans measured for dual-polarization 50-mm DFB laser #3. Upper curve, the calculated laser frequency response δν. The other curves show calculated beat frequency responses δν B for three values of Δκ/κ, assuming z independence of B. Dashed curve indicates -δν B < 0. (b) Measured (circles) and calculated (lines) beat-frequency responses δν B for two distributions of B(z) when Δκ = 0. For all calculations in both (a) and (b) δϕ = 0.53 rad and κ = 230 m-1 were assumed.

Fig. 6
Fig. 6

(a) Laser frequency response (squares) to heat scans measured for 60-mm DFB laser #4 with grating parameters similar to those characterized in Fig. 3 and 4. Calculated responses of the +1- and -1-order modes with δϕ = 0.2 rad are also shown. (b) Measured output power from the left end P left (crosses) and calculated threshold gain for the +1- (solid curve) and -1- (dotted curve) order modes plotted versus heating position when δϕ = 0.2 rad.

Tables (1)

Tables Icon

Table 1 Overview of the Lasers Characterized in This Paper

Equations (5)

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

|Elocz|2=|E0|2+2|E+E-|cos2πznν/c+θ,
|E0|2P0cosh κL±2zcosh κLΔL,
2|E+E-|P0sinh κL±2zcosh κLΔL,
PleftPright=|E-L/2|2|EL/2|2exp2κΔL.
δνν=-δnδz|Elocz|2Cavity nzˆ|Eloczˆ|2dzˆ.

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