Abstract

An ultrashort composite cavity (≤10 µm in length) laser diode was used to verify experimentally a butt-coupling model that considers interference inside the external cavity and its influence on laser operation. The fine structure of an experimental coupled power versus laser-to-fiber separation curve is explained when a complex coupling coefficient is introduced into the model. The importance of the phase term of this coefficient and regions of validity of the modified butt-coupling model are also discussed.

© 1997 Optical Society of America

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References

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  1. H. Kogelnik, “Coupling and conversion coefficients for optical modes,” in Microwave Research Institute Symposia Series, J. Fox, ed. (Polytechnic Institute of Brooklyn, N.Y., 1964), pp. 333–347.
  2. W. B. Joyce, B. C. DeLoach, “Alignment of Gaussian beams,” Appl. Opt. 23, 4187–4196 (1984).
    [CrossRef] [PubMed]
  3. R. G. Hunsperger, A. Yariv, A. Lee, “Parallel end-butt-coupling for optical integrated circuits,” Appl. Opt. 16, 1026–1032 (1977).
    [CrossRef] [PubMed]
  4. C. Voumard, R. Salathe, H. Weber, “Resonance amplifier model describing diode lasers coupled to short external cavity resonator,” Appl. Phys. 12, 369–378 (1977).
    [CrossRef]
  5. J.-Y. Kim, H. C. Hsieh, “An open-resonator model for the analysis of a short external-cavity laser diode and its application to the optical disk head,” J. Lightwave Technol. 10, 439–447 (1992).
    [CrossRef]
  6. H. Ukita, Y. Uenishi, Y. Katagiri, “Applications of an extremely short strong-feedback configuration of an external-cavity laser diode system fabricated with GaAs-based integration technology,” Appl. Opt. 33, 5557–5563 (1994).
    [CrossRef] [PubMed]
  7. P. Karioja, D. Howe, “Diode-laser-to-waveguide butt-coupling,” Appl. Opt. 35, 404–416 (1996).
    [CrossRef] [PubMed]
  8. L. A. Vainstein, “Open resonators for lasers,” Sov. Phys. JETP 17, 709–719 (1963).
  9. M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, N.Y., 1965).
  10. T. D. Milster, E. R. Walker, “Figures of merit for laser beam quality,” in Laser Energy Distribution Profiles: Measurement and Applications, J. M. Darchuk, ed., Proc. SPIE1834, 79–85 (1993).
  11. K. Kinosita, “Numerical evaluation of the intensity curve of a multiple-beam Fizeau fringe,” J. Phys. Soc. Jpn. 8, 219–225 (1953).
    [CrossRef]
  12. J. H. Osmundsen, N. Gade, “Influence of optical feedback on laser frequency spectrum and threshold conditions,” IEEE J. Quantum Electron. QE-19, 465–469 (1983).
    [CrossRef]

1996 (1)

1994 (1)

1992 (1)

J.-Y. Kim, H. C. Hsieh, “An open-resonator model for the analysis of a short external-cavity laser diode and its application to the optical disk head,” J. Lightwave Technol. 10, 439–447 (1992).
[CrossRef]

1984 (1)

1983 (1)

J. H. Osmundsen, N. Gade, “Influence of optical feedback on laser frequency spectrum and threshold conditions,” IEEE J. Quantum Electron. QE-19, 465–469 (1983).
[CrossRef]

1977 (2)

R. G. Hunsperger, A. Yariv, A. Lee, “Parallel end-butt-coupling for optical integrated circuits,” Appl. Opt. 16, 1026–1032 (1977).
[CrossRef] [PubMed]

C. Voumard, R. Salathe, H. Weber, “Resonance amplifier model describing diode lasers coupled to short external cavity resonator,” Appl. Phys. 12, 369–378 (1977).
[CrossRef]

1963 (1)

L. A. Vainstein, “Open resonators for lasers,” Sov. Phys. JETP 17, 709–719 (1963).

1953 (1)

K. Kinosita, “Numerical evaluation of the intensity curve of a multiple-beam Fizeau fringe,” J. Phys. Soc. Jpn. 8, 219–225 (1953).
[CrossRef]

Abramowitz, M.

M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, N.Y., 1965).

DeLoach, B. C.

Gade, N.

J. H. Osmundsen, N. Gade, “Influence of optical feedback on laser frequency spectrum and threshold conditions,” IEEE J. Quantum Electron. QE-19, 465–469 (1983).
[CrossRef]

Howe, D.

Hsieh, H. C.

J.-Y. Kim, H. C. Hsieh, “An open-resonator model for the analysis of a short external-cavity laser diode and its application to the optical disk head,” J. Lightwave Technol. 10, 439–447 (1992).
[CrossRef]

Hunsperger, R. G.

Joyce, W. B.

Karioja, P.

Katagiri, Y.

Kim, J.-Y.

J.-Y. Kim, H. C. Hsieh, “An open-resonator model for the analysis of a short external-cavity laser diode and its application to the optical disk head,” J. Lightwave Technol. 10, 439–447 (1992).
[CrossRef]

Kinosita, K.

K. Kinosita, “Numerical evaluation of the intensity curve of a multiple-beam Fizeau fringe,” J. Phys. Soc. Jpn. 8, 219–225 (1953).
[CrossRef]

Kogelnik, H.

H. Kogelnik, “Coupling and conversion coefficients for optical modes,” in Microwave Research Institute Symposia Series, J. Fox, ed. (Polytechnic Institute of Brooklyn, N.Y., 1964), pp. 333–347.

Lee, A.

Milster, T. D.

T. D. Milster, E. R. Walker, “Figures of merit for laser beam quality,” in Laser Energy Distribution Profiles: Measurement and Applications, J. M. Darchuk, ed., Proc. SPIE1834, 79–85 (1993).

Osmundsen, J. H.

J. H. Osmundsen, N. Gade, “Influence of optical feedback on laser frequency spectrum and threshold conditions,” IEEE J. Quantum Electron. QE-19, 465–469 (1983).
[CrossRef]

Salathe, R.

C. Voumard, R. Salathe, H. Weber, “Resonance amplifier model describing diode lasers coupled to short external cavity resonator,” Appl. Phys. 12, 369–378 (1977).
[CrossRef]

Stegun, I.

M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, N.Y., 1965).

Uenishi, Y.

Ukita, H.

Vainstein, L. A.

L. A. Vainstein, “Open resonators for lasers,” Sov. Phys. JETP 17, 709–719 (1963).

Voumard, C.

C. Voumard, R. Salathe, H. Weber, “Resonance amplifier model describing diode lasers coupled to short external cavity resonator,” Appl. Phys. 12, 369–378 (1977).
[CrossRef]

Walker, E. R.

T. D. Milster, E. R. Walker, “Figures of merit for laser beam quality,” in Laser Energy Distribution Profiles: Measurement and Applications, J. M. Darchuk, ed., Proc. SPIE1834, 79–85 (1993).

Weber, H.

C. Voumard, R. Salathe, H. Weber, “Resonance amplifier model describing diode lasers coupled to short external cavity resonator,” Appl. Phys. 12, 369–378 (1977).
[CrossRef]

Yariv, A.

Appl. Opt. (4)

Appl. Phys. (1)

C. Voumard, R. Salathe, H. Weber, “Resonance amplifier model describing diode lasers coupled to short external cavity resonator,” Appl. Phys. 12, 369–378 (1977).
[CrossRef]

IEEE J. Quantum Electron. (1)

J. H. Osmundsen, N. Gade, “Influence of optical feedback on laser frequency spectrum and threshold conditions,” IEEE J. Quantum Electron. QE-19, 465–469 (1983).
[CrossRef]

J. Lightwave Technol. (1)

J.-Y. Kim, H. C. Hsieh, “An open-resonator model for the analysis of a short external-cavity laser diode and its application to the optical disk head,” J. Lightwave Technol. 10, 439–447 (1992).
[CrossRef]

J. Phys. Soc. Jpn. (1)

K. Kinosita, “Numerical evaluation of the intensity curve of a multiple-beam Fizeau fringe,” J. Phys. Soc. Jpn. 8, 219–225 (1953).
[CrossRef]

Sov. Phys. JETP (1)

L. A. Vainstein, “Open resonators for lasers,” Sov. Phys. JETP 17, 709–719 (1963).

Other (3)

M. Abramowitz, I. Stegun, Handbook of Mathematical Functions (Dover, N.Y., 1965).

T. D. Milster, E. R. Walker, “Figures of merit for laser beam quality,” in Laser Energy Distribution Profiles: Measurement and Applications, J. M. Darchuk, ed., Proc. SPIE1834, 79–85 (1993).

H. Kogelnik, “Coupling and conversion coefficients for optical modes,” in Microwave Research Institute Symposia Series, J. Fox, ed. (Polytechnic Institute of Brooklyn, N.Y., 1964), pp. 333–347.

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Figures (5)

Fig. 1
Fig. 1

(a) Field overlap geometry; (b) equivalent scheme.

Fig. 2
Fig. 2

Model prediction and experimental data for misalignments: angular (a) 10 mrad, (b) 50 mrad; transverse, ≈20 nm both (a) and (b).

Fig. 3
Fig. 3

Comparison between modified model predictions and experimental results for misalignments: angular, 10 mrad; transverse, ≈20 nm. The complex coupling coefficient introduces a characteristic asymmetry into the theoretical curve.

Fig. 4
Fig. 4

Butt-coupling model prediction: real coupling coefficient (solid curve), complex coupling coefficient (dashed curve). Misalignments: angular, 10 mrad; transverse, 20 nm.

Fig. 5
Fig. 5

Amplitude parameter and phase-modification factor (for n = 1) versus the separation between the laser and fiber facets.

Equations (9)

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

Cn=γn exp-iΔn,
Ψx, z=A exp-x-δ2wx2zexp-ik x-δ22Rxz×expikΘx-δexp-ikz-φz,
c12Xz=-dxΨ1x, zΨ2*x, z,
c12=2/w1zw2z1/21/a1/2 expb2/a-c,
a=w1-2z+w2-2z+ikR1-1z-R2-1z/2; b=-δ/w22z+ikδ/R2z+Θ/2; c=δ/w2z2-ikδ2/R2z+2Θδ/2.
reff=RL1/2-1-RL/RL1/2p=1CLL2pz×RLRF1/2 exp(-iΦp,
τeff=p=1 CLF2p-1zRLRF1/2 exp-iΦp-1,
ζrLreff=ζ0 expiϕζ,
expg-αd=expiϕDr1rL ζ,

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