Excess Quantum Noise in Nonnormal Oscillators

  • A. E. Siegman
Conference paper


The eigenmodes or “normal modes” of many common laser cavities are in fact eigensolutions of nonhermitian or non-self-adjoint operators, and this unfamiliar circumstance leads to distinctly “nonnormal” behavior for such lasers. Elementary examples include the transverse modes in gain-guided diode lasers and geometrically unstable optical resonators, the longitudinal modes in lasers with large output coupling at one end, and the polarization modes of twisted birefringent cavities. The modes of these systems are all nonorthogonal in the usual power-orthogonal or energy-orthogonal sense, and as a consequence many of the conventional conclusions of classical and quantum noise theory must be substantially modified. Laser oscillators having nonnormal cavity modes are subject in particular to a so-called Petermann excess noise factor or a large excess spontaneous emission per mode. These excess noise properties have been decisively confirmed by observations of greatly increased Schawlow-Townes linewidths in such lasers.


Spontaneous Emission Output Coupling Excess Noise Laser Oscillator Laser Resonator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. L. Schawlow and C. H. Townes: Infrared and optical masers. Phys. Rev. 112, 1940–1949 (1958).ADSCrossRefGoogle Scholar
  2. 2.
    M. Sargent, III, M. O. Scully, W. E. Lamb, Jr.: Laser Physics. Addison-Wesley Publishing Company (1972).Google Scholar
  3. 3.
    K. Petermann: Calculated spontaneous emission factor for double heterostructure injection lasers with gain-induced waveguiding. IEEE J. Quantum Electron. QE-15, 566–570 (1979).Google Scholar
  4. 4.
    H. A. Haus and S. Kawakami: On the excess spontaneous emission factor in gain-guided laser amplifiers. IEEE J. Quantum Electron. QE-21, 63–69 (1985).Google Scholar
  5. 5.
    A. E. Siegman: Excess spontaneous emission in nonhermitian optical systems. I. Laser amplifiers. II. Laser oscillators. Phys. Rev. A 39, 1253–1268 (1989).Google Scholar
  6. 6.
    W. A. Hamel and J. P. Woerdman: Nonorthogonality of the longitudinal modes of a laser. Phys. Rev. A 40, 2785–2791 (1989); also W. A. Hamel and J. P. Woerdman: Observation of enhanced fundamental linewidth of a laser due to nonorthogonality of its longitudinal eigenmodes. Phys. Rev. Lett. 64, 1506–1509 (1990).Google Scholar
  7. 7.
    Y.-J. Cheng, P. L. Mussche, A. E. Siegman: Measurement of laser quantum frequency fluctuations using a Pound-Drever stabilization system. IEEE J. Quantum Electron. QE-30, 1498–1504 (J1994); and Y.-J. Cheng, G. Fanning, A. E. Siegman: Experimental observation of a large excess quantum noise factor in the linewidth of a laser oscillator using nonorthogonal modes. Phys. Rev. Lett. 77, 627–630 (1996).Google Scholar
  8. 8.
    M. A. van Eijkelenborg, A. M. Lindberg, M. S. Thijssen, J. P. Woerdman. Resonance of quantum noise in an unstable cavity laser. Phys. Rev. Lett. 77, 43144317 (18 November 1996); and M. A. Van Eijkelenburg, A. M. Lindberg, M. S. Thijssen, J. P. Woerdman. Higher order transverse modes of an unstable-cavity laser. IEEE J. Quantum Electron. QE-34, 955–965 (1998).Google Scholar
  9. 9.
    O. Emile, M. Brunel, F. Bretenaker, A. Le Floch: Direct measurement of the excess noise factor in a geometrically stable laser resonator. Phys. Rev. A 57, 4889–4893 (1998).ADSCrossRefGoogle Scholar
  10. 10.
    I. H. Deutsch, J. C. Garrison and E. M. Wright: Excess noise in gain-guided amplifiers. J. Opt. Soc. Am. B 8, 1244–1251 (1991).ADSCrossRefGoogle Scholar
  11. 11.
    P. Goldberg, P. W. Milonni, B. Sundaram: Theory of the fundamental laser linewidth. Phys. Rev. A 44, 1969–1985 (1 August 1991); also P. Goldberg, P. W. Milonni, B. Sundaram: Laser linewidth: amplification of vacuum fluctuations and effects of spatial hole burning. J. Modern Opt. 38, 1421–1427 (1991).ADSGoogle Scholar
  12. 12.
    H. Wenzel and H.-J. Wunsche: An equation for the amplitudes of the modes in semiconductor lasers. IEEE J. Quantum. Electron. QE-30, 2073–2080 (1994).Google Scholar
  13. 13.
    P. Grangier and J.-P. Poizat: A simple quantum picture for the Petermann excess noise factor. Eur. Phys. J. D 1, 97–104 (1998).ADSCrossRefGoogle Scholar
  14. 14.
    K. C. Ho, P. T. Leung, A. M. Vandenbrink, K. Young: 2nd quantization of open systems using quasi-normal modes. Phys. Rev. E 58, 2965–2978 (1998).ADSCrossRefGoogle Scholar
  15. 15.
    C. Lamprecht and H. Ritsch: Quantized atom-field dynamics in unstable cavities. Phys. Rev. Lett. 82, 3787–3790 (1999).ADSCrossRefGoogle Scholar
  16. 16.
    P. J. Bardroff and S. Stenholm: Quantum theory of excess noise. Private communication (1999).Google Scholar
  17. 17.
    A. N. van der Lee et al.: Excess quantum noise due to nonorthogonal polarization modes. Phys. Rev. Lett. 79, 4357–4360 (1997).ADSCrossRefGoogle Scholar
  18. 18.
    O. Emile, M. Brunel, A. Le Floch, F. Bretenaker: Vectorial excess noise factor in common lasers. Europhys. Lett. 43, 153–157 (1998).ADSCrossRefGoogle Scholar
  19. 19.
    A. E. Siegman: Lasers without photons — or should it be lasers with too many photons? Appl. Phys. B 60, 247–257 (1995).Google Scholar
  20. 20.
    A. E. Siegman: Lasers Without Photons. In Coherence and Quantum Optics VII, J. H. Eberly, L. Mandel, E. Wolf (Eds.) ( Plenum Press, University of Rochester, New York 1995 ); pp. 229–238.Google Scholar
  21. 21.
    A. Kostenbauder, Y. Sun, A. E. Siegman: Eigenmode expansions using biorthogonal eigenfunctions: complex-valued Hermite gaussians. J. Opt. Soc. Amer. A 14, 1780–1790 (1997).MathSciNetADSCrossRefGoogle Scholar
  22. 22.
    A. E. Siegman: Nyquist noise formulation for nonhermitian linear systems. Manuscript in preparation (1999).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • A. E. Siegman
    • 1
  1. 1.Ginzton LaboratoryStanford UniversityUSA

Personalised recommendations