Passive Optical Resonators



This chapter deals with the theory of passive optical resonators i.e. where no active medium is present within the cavity. The most widely used laser resonators have either plane or spherical mirrors of rectangular (or, more often, circular) shape, separated by some distance L. Typically, L may range from a few centimeters to a few tens of centimeters, while the mirror dimensions range from a fraction of a centimeter to a few centimeters. Laser resonators thus differ from those used in the microwave field (see e.g. Sect. 2.2.1) in two main respects: (1) The resonator dimensions are much greater than the laser wavelength. (2) Resonators are usually open, i.e. no lateral surfaces are used. The resonator length is usually much greater than the laser wavelength because this wavelength usually ranges from a fraction of a micrometer to a few tens of micrometers. A laser cavity with length comparable to the wavelength would then generally have too low a gain to allow laser oscillation. Laser resonators are usually open because this drastically reduces the number of modes which can oscillate with low loss. In fact, with reference to example 5.1 to be considered below, it is seen that even a narrow linewidth laser such as a He-Ne laser would have a very large number of modes ( ≈ 109) if the resonator were closed. By contrast, on removing the lateral surfaces, the number of low-loss modes reduces to just a few ( ≈ 6 in the example). In these open resonators, in fact, only the very few modes corresponding to a superposition of waves traveling nearly parallel to the resonator axis will have low enough losses to allow laser oscillation.


Geometrical Optic Round Trip Spherical Wave Laser Resonator Open Resonator 
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  1. 1.
    A.E. Siegman, Lasers (University Science Books, Mill Valley, California, 1986) sect. 14.2Google Scholar
  2. 2.
    M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon Press, London 1980) sect. 1.6.5Google Scholar
  3. 3.
    H. Kogelnik and T. Li, Laser Beams and Resonators, Appl. Opt. 5, 1550 (1966)CrossRefADSGoogle Scholar
  4. 4.
    Reference [1], Chap. 19Google Scholar
  5. 5.
    A.G. Fox and T. Li, Resonant Modes in a Maser Interferometer, Bell. Syst. Tech. J. 40, 453 (1961)CrossRefGoogle Scholar
  6. 6.
    T. Li, Diffraction Loss and Selection of Modes in Maser Resonators with Circular Mirrors, Bell. Syst.Tech. J. 44, 917 (1965)Google Scholar
  7. 7.
    V. Magni, Resonators for Solid-State Lasers with Large-Volume Fundamental Mode and High Alignment Stability, Appl. Opt., 25, 107–117 (1986). See also erratum Appl. Opt., 25, 2039 (1986)Google Scholar
  8. 8.
    Reference [1], p. 666Google Scholar
  9. 9.
    W. Koechner, Solid-State Laser Engineering, Vol. 1, Springer Series in Optical Sciences, fourth edition (Springer, New York, 1996)Google Scholar
  10. 10.
    Reference [1], Chap. 22Google Scholar
  11. 11.
    A.E. Siegman, Unstable Optical Resonators for Laser Applications, Proc. IEEE 53, 277–287 (1965)Google Scholar
  12. 12.
    D.B. Rensch and A.N. Chester, Iterative Diffraction Calculations of Transverse Mode Distributions in Confocal Unstable Laser Resonators, Appl. Opt. 12, 997 (1973)CrossRefADSGoogle Scholar
  13. 13.
    A.E. Siegman, Stabilizing Output with Unstable Resonators, Laser Focus 7, 42 (1971)Google Scholar
  14. 14.
    H. Zucker, Optical Resonators with Variable Reflectivity Mirrors, Bell. Syst. Tech. J. 49, 2349 (1970)CrossRefGoogle Scholar
  15. 15.
    A.N. Chester, Mode Selectivity and Mirror Misalignment Effects in Unstable Laser Resonators, Appl. Opt. 11, 2584 (1972)CrossRefADSGoogle Scholar
  16. 16.
    Ref. [1], sect. 23.3Google Scholar
  17. 17.
    S. De Silvestri, P. Laporta, V. Magni and O. Svelto, Solid-State Unstable Resonators with Tapered Reflectivity Mirrors: The super-Gaussian Approach, IEEE J. Quant. Electr. QE-24, 1172 (1988)Google Scholar
  18. 18.
    G. Cerullo et al., Diffraction-Limited Solid State Lasers with Supergaussian Mirror, In: OSA Proc. on Tunable Solid-State Lasers, Vol. 5 ed. by M. Shand and H. Jenssen (Optical Society of America, Washington 1989) pp. 378–384Google Scholar

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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Dipto. FisicaPolitecnico di MilanoMilanoItaly

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