Excess quantum noise due to nonorthogonal polarization modes van der Lee, A.M.; van Druten, N.J.; Mieremet, A.L.; van Eijkelenborg, M.A.; Lindberg, Å.M.; van Exter, M.P.; Woerdman, J.P.

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Semi-classical dynamics of excess quantum noisevan Exter, M.P.; van Druten, N.J.; van der Lee, A.M.; Dutra, S.M.; Nienhuis, G.; Woerdman, J.P. Published in:Physical Review A Link to publication Citation for published version (APA):van Exter, M. P., van Druten, N. J., van der Lee, A. M., Dutra, S. M., Nienhuis, G., & Woerdman, J. P. (2001). Semi-classical dynamics of excess quantum noise. Physical Review A, 63(043801). General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. A semiclassical theoretical framework is presented to describe the essential features of the excess quantum noise that occurs in systems with nonorthogonal eigenmodes. Excess noise is shown to be always spectrally colored, instead of white, so that the Petermann excess noise factor is best written as K() instead of K. The consequences of this spectral coloring are analyzed for lasers, both below and above the lasing threshold. DOI: 10.1103/PhysRevA.63.043801 PACS number͑s͒: 42.50.Lc, 42.60.Da I. INTRODUCTIONThe fluctuation-dissipation theorem states that noise and damping go together and that systems that are open to the outside world will inevitably experience noise input from this outside world. This also applies to quantum-mechanical systems, where the fluctuation-dissipation theorem is linked to the discrete nature of the excitation or, equivalently, the commutation behavior of the creation and annihilation operators ͓1͔. A well-studied example of quantum noise is the spontaneous-emission noise in lasers ͓2,3͔. When the optical modes in the laser are orthogonal, this noise amounts effectively to ''one photon per mode.'' When the modes are nonorthogonal the amount of noise will be enhanced by the excess noise factor K, which expresses that there are effectively ''K noise photons'' in the lasing mode ͓3͔. The reason for this noise enhancement is purely geometrical; the noise projection into each mode may be enhanced, but the integrated spontaneous-emission rate will not change, as the noise inputs in these nonorthogonal modes are correlated ͓4͔.Experimentally the existence of excess quantum noise is well established. For lasers with nonorthogonal eigenmodes, several studies ͓5-11͔ have shown how the fundamental laser linewidth, which is due to laser phase diffusion, is enhanced by an excess noise fac...

Threshold behavior of a laser with nonorthogonal polarization modes van der Lee, A.M.; van Exter, M.P.; Assadian, H.A.; van Druten, N.J.; Woerdman, J.P. General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. We investigate experimentally and theoretically the influence of the excess quantum noise in a laser on the laser's input-output curve near threshold. As an experimental system we use a He-Xe gas laser with nonorthogonal polarization modes. We observe that the excess quantum noise is absent far below threshold and steadily builds up as threshold is approached. The excess noise is fully developed when the mode that (above threshold) becomes the lasing mode dominates in power the other, nonlasing, modes. This situation may already occur considerably below threshold, namely, when the hot-cavity photon lifetime of the dominant mode exceeds the coloring time of the excess noise.