Abstract

We demonstrate that the transverse eigenmodes in a waveguide that combines a parabolic index guide with a Gaussian gain guide can be highly nonorthogonal. The excess-noise factor K that arises from this nonorthogonality exhibits resonant features with maximum values that can easily reach K400. This simple model applies directly to stable-cavity microchip lasers with focused gain.

© 2001 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. E. Siegman, Phys. Rev. A 39, 1253 (1989).
    [CrossRef] [PubMed]
  2. A. E. Siegman, Phys. Rev. A 39, 1264 (1989).
    [CrossRef] [PubMed]
  3. K. Petermann, IEEE J. Quantum Electron. QE-15, 566 (1979).
    [CrossRef]
  4. Y.-J. Cheng, C. G. Fanning, and A. E. Siegman, Phys. Rev. Lett. 77, 627 (1996).
    [CrossRef] [PubMed]
  5. M. A. van Eijkelenborg, Å. M. Lindberg, M. S. Thijssen, and J. P. Woerdman, Phys. Rev. Lett. 77, 4314 (1996).
    [CrossRef] [PubMed]
  6. M. P. van Exter, N. J. van Druten, A. M. van der Lee, S. M. Dutra, G. Nienhuis, and J. P. Woerdman, Phys. Rev. A 63, 043801 (2001).
    [CrossRef]
  7. G. P. Karman, G. S. McDonald, G. H. C. New, and J. P. Woerdman, Nature 402, 138 (1999).
    [CrossRef]
  8. C. Serrat, M. P. van Exter, N. J. van Druten, and J. P. Woerdman, IEEE J. Quantum Electron. 35, 1314 (1999).
    [CrossRef]
  9. N. J. van Druten, S. S. Oemrawsingh, Y. Lien, C. Serrat, M. P. van Exter, and J. P. Woerdman submitted a paper called “Observation of transverse modes in a microchip laser with combined gain and index guiding” to J. Opt. Soc. B.
  10. N. J. van Druten, M. P. van Exter, and J. P. Woerdman, “Equivalence of transverse modes in Raman amplifiers and microchip lasers,” submitted to Opt. Commun.
  11. B. N. Perry, P. Rabinowitz, and M. Newstein, Phys. Rev. Lett. 49, 1921 (1982).
    [CrossRef]

2001 (1)

M. P. van Exter, N. J. van Druten, A. M. van der Lee, S. M. Dutra, G. Nienhuis, and J. P. Woerdman, Phys. Rev. A 63, 043801 (2001).
[CrossRef]

1999 (2)

G. P. Karman, G. S. McDonald, G. H. C. New, and J. P. Woerdman, Nature 402, 138 (1999).
[CrossRef]

C. Serrat, M. P. van Exter, N. J. van Druten, and J. P. Woerdman, IEEE J. Quantum Electron. 35, 1314 (1999).
[CrossRef]

1996 (2)

Y.-J. Cheng, C. G. Fanning, and A. E. Siegman, Phys. Rev. Lett. 77, 627 (1996).
[CrossRef] [PubMed]

M. A. van Eijkelenborg, Å. M. Lindberg, M. S. Thijssen, and J. P. Woerdman, Phys. Rev. Lett. 77, 4314 (1996).
[CrossRef] [PubMed]

1989 (2)

A. E. Siegman, Phys. Rev. A 39, 1253 (1989).
[CrossRef] [PubMed]

A. E. Siegman, Phys. Rev. A 39, 1264 (1989).
[CrossRef] [PubMed]

1982 (1)

B. N. Perry, P. Rabinowitz, and M. Newstein, Phys. Rev. Lett. 49, 1921 (1982).
[CrossRef]

1979 (1)

K. Petermann, IEEE J. Quantum Electron. QE-15, 566 (1979).
[CrossRef]

Cheng, Y.-J.

Y.-J. Cheng, C. G. Fanning, and A. E. Siegman, Phys. Rev. Lett. 77, 627 (1996).
[CrossRef] [PubMed]

Dutra, S. M.

M. P. van Exter, N. J. van Druten, A. M. van der Lee, S. M. Dutra, G. Nienhuis, and J. P. Woerdman, Phys. Rev. A 63, 043801 (2001).
[CrossRef]

Fanning, C. G.

Y.-J. Cheng, C. G. Fanning, and A. E. Siegman, Phys. Rev. Lett. 77, 627 (1996).
[CrossRef] [PubMed]

Karman, G. P.

G. P. Karman, G. S. McDonald, G. H. C. New, and J. P. Woerdman, Nature 402, 138 (1999).
[CrossRef]

Lien, Y.

N. J. van Druten, S. S. Oemrawsingh, Y. Lien, C. Serrat, M. P. van Exter, and J. P. Woerdman submitted a paper called “Observation of transverse modes in a microchip laser with combined gain and index guiding” to J. Opt. Soc. B.

Lindberg, Å. M.

M. A. van Eijkelenborg, Å. M. Lindberg, M. S. Thijssen, and J. P. Woerdman, Phys. Rev. Lett. 77, 4314 (1996).
[CrossRef] [PubMed]

McDonald, G. S.

G. P. Karman, G. S. McDonald, G. H. C. New, and J. P. Woerdman, Nature 402, 138 (1999).
[CrossRef]

New, G. H. C.

G. P. Karman, G. S. McDonald, G. H. C. New, and J. P. Woerdman, Nature 402, 138 (1999).
[CrossRef]

Newstein, M.

B. N. Perry, P. Rabinowitz, and M. Newstein, Phys. Rev. Lett. 49, 1921 (1982).
[CrossRef]

Nienhuis, G.

M. P. van Exter, N. J. van Druten, A. M. van der Lee, S. M. Dutra, G. Nienhuis, and J. P. Woerdman, Phys. Rev. A 63, 043801 (2001).
[CrossRef]

Oemrawsingh, S. S.

N. J. van Druten, S. S. Oemrawsingh, Y. Lien, C. Serrat, M. P. van Exter, and J. P. Woerdman submitted a paper called “Observation of transverse modes in a microchip laser with combined gain and index guiding” to J. Opt. Soc. B.

Perry, B. N.

B. N. Perry, P. Rabinowitz, and M. Newstein, Phys. Rev. Lett. 49, 1921 (1982).
[CrossRef]

Petermann, K.

K. Petermann, IEEE J. Quantum Electron. QE-15, 566 (1979).
[CrossRef]

Rabinowitz, P.

B. N. Perry, P. Rabinowitz, and M. Newstein, Phys. Rev. Lett. 49, 1921 (1982).
[CrossRef]

Serrat, C.

C. Serrat, M. P. van Exter, N. J. van Druten, and J. P. Woerdman, IEEE J. Quantum Electron. 35, 1314 (1999).
[CrossRef]

N. J. van Druten, S. S. Oemrawsingh, Y. Lien, C. Serrat, M. P. van Exter, and J. P. Woerdman submitted a paper called “Observation of transverse modes in a microchip laser with combined gain and index guiding” to J. Opt. Soc. B.

Siegman, A. E.

Y.-J. Cheng, C. G. Fanning, and A. E. Siegman, Phys. Rev. Lett. 77, 627 (1996).
[CrossRef] [PubMed]

A. E. Siegman, Phys. Rev. A 39, 1253 (1989).
[CrossRef] [PubMed]

A. E. Siegman, Phys. Rev. A 39, 1264 (1989).
[CrossRef] [PubMed]

Thijssen, M. S.

M. A. van Eijkelenborg, Å. M. Lindberg, M. S. Thijssen, and J. P. Woerdman, Phys. Rev. Lett. 77, 4314 (1996).
[CrossRef] [PubMed]

van der Lee, A. M.

M. P. van Exter, N. J. van Druten, A. M. van der Lee, S. M. Dutra, G. Nienhuis, and J. P. Woerdman, Phys. Rev. A 63, 043801 (2001).
[CrossRef]

van Druten, N. J.

M. P. van Exter, N. J. van Druten, A. M. van der Lee, S. M. Dutra, G. Nienhuis, and J. P. Woerdman, Phys. Rev. A 63, 043801 (2001).
[CrossRef]

C. Serrat, M. P. van Exter, N. J. van Druten, and J. P. Woerdman, IEEE J. Quantum Electron. 35, 1314 (1999).
[CrossRef]

N. J. van Druten, S. S. Oemrawsingh, Y. Lien, C. Serrat, M. P. van Exter, and J. P. Woerdman submitted a paper called “Observation of transverse modes in a microchip laser with combined gain and index guiding” to J. Opt. Soc. B.

N. J. van Druten, M. P. van Exter, and J. P. Woerdman, “Equivalence of transverse modes in Raman amplifiers and microchip lasers,” submitted to Opt. Commun.

van Eijkelenborg, M. A.

M. A. van Eijkelenborg, Å. M. Lindberg, M. S. Thijssen, and J. P. Woerdman, Phys. Rev. Lett. 77, 4314 (1996).
[CrossRef] [PubMed]

van Exter, M. P.

M. P. van Exter, N. J. van Druten, A. M. van der Lee, S. M. Dutra, G. Nienhuis, and J. P. Woerdman, Phys. Rev. A 63, 043801 (2001).
[CrossRef]

C. Serrat, M. P. van Exter, N. J. van Druten, and J. P. Woerdman, IEEE J. Quantum Electron. 35, 1314 (1999).
[CrossRef]

N. J. van Druten, M. P. van Exter, and J. P. Woerdman, “Equivalence of transverse modes in Raman amplifiers and microchip lasers,” submitted to Opt. Commun.

N. J. van Druten, S. S. Oemrawsingh, Y. Lien, C. Serrat, M. P. van Exter, and J. P. Woerdman submitted a paper called “Observation of transverse modes in a microchip laser with combined gain and index guiding” to J. Opt. Soc. B.

Woerdman, J. P.

M. P. van Exter, N. J. van Druten, A. M. van der Lee, S. M. Dutra, G. Nienhuis, and J. P. Woerdman, Phys. Rev. A 63, 043801 (2001).
[CrossRef]

C. Serrat, M. P. van Exter, N. J. van Druten, and J. P. Woerdman, IEEE J. Quantum Electron. 35, 1314 (1999).
[CrossRef]

G. P. Karman, G. S. McDonald, G. H. C. New, and J. P. Woerdman, Nature 402, 138 (1999).
[CrossRef]

M. A. van Eijkelenborg, Å. M. Lindberg, M. S. Thijssen, and J. P. Woerdman, Phys. Rev. Lett. 77, 4314 (1996).
[CrossRef] [PubMed]

N. J. van Druten, S. S. Oemrawsingh, Y. Lien, C. Serrat, M. P. van Exter, and J. P. Woerdman submitted a paper called “Observation of transverse modes in a microchip laser with combined gain and index guiding” to J. Opt. Soc. B.

N. J. van Druten, M. P. van Exter, and J. P. Woerdman, “Equivalence of transverse modes in Raman amplifiers and microchip lasers,” submitted to Opt. Commun.

IEEE J. Quantum Electron. (2)

K. Petermann, IEEE J. Quantum Electron. QE-15, 566 (1979).
[CrossRef]

C. Serrat, M. P. van Exter, N. J. van Druten, and J. P. Woerdman, IEEE J. Quantum Electron. 35, 1314 (1999).
[CrossRef]

Nature (1)

G. P. Karman, G. S. McDonald, G. H. C. New, and J. P. Woerdman, Nature 402, 138 (1999).
[CrossRef]

Phys. Rev. A (3)

M. P. van Exter, N. J. van Druten, A. M. van der Lee, S. M. Dutra, G. Nienhuis, and J. P. Woerdman, Phys. Rev. A 63, 043801 (2001).
[CrossRef]

A. E. Siegman, Phys. Rev. A 39, 1253 (1989).
[CrossRef] [PubMed]

A. E. Siegman, Phys. Rev. A 39, 1264 (1989).
[CrossRef] [PubMed]

Phys. Rev. Lett. (3)

Y.-J. Cheng, C. G. Fanning, and A. E. Siegman, Phys. Rev. Lett. 77, 627 (1996).
[CrossRef] [PubMed]

M. A. van Eijkelenborg, Å. M. Lindberg, M. S. Thijssen, and J. P. Woerdman, Phys. Rev. Lett. 77, 4314 (1996).
[CrossRef] [PubMed]

B. N. Perry, P. Rabinowitz, and M. Newstein, Phys. Rev. Lett. 49, 1921 (1982).
[CrossRef]

Other (2)

N. J. van Druten, S. S. Oemrawsingh, Y. Lien, C. Serrat, M. P. van Exter, and J. P. Woerdman submitted a paper called “Observation of transverse modes in a microchip laser with combined gain and index guiding” to J. Opt. Soc. B.

N. J. van Druten, M. P. van Exter, and J. P. Woerdman, “Equivalence of transverse modes in Raman amplifiers and microchip lasers,” submitted to Opt. Commun.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1
Fig. 1

Eigenvalues μ and excess-noise factors K of the two lowest-loss transverse modes for ρg=0.315. The real part of the eigenvalue corresponds to the phase shift per Rayleigh range; the imaginary part, to the modal gain. For fixed gain width ρg and gain strength g00, the modes are adiabatically connected to mode u2 (solid curves) and u3 (dashed curves) of the parabolic index guide; see also Fig.  2.

Fig. 2
Fig. 2

Adiabatic trajectories in eigenvalue space for fixed values of the gain width ρg and various values of gain strength g0. The solid curves have been labeled with the corresponding values of ρg. The dashed curves correspond to intermediate values. For those connected to mode u1 of the purely parabolic index guide at g0=0μ=6, ρg=0.42, 0.38; for mode u2μ=10, ρg=0.42,0.38,0.35,0.32,0.31; for mode u3μ=14, ρg=0.32,0.31,0.29,0.27; and for mode u4μ=18ρg=0.27,0.26.

Equations (4)

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

-12ρ2+2ρ2+igρu=μu,
gρ=g0exp-2ρ2/ρg2
aρ|bρ2π0ρa*ρbρdρ.
arai=2-K2K-1.

Metrics