Ring Resonators

  • Norman Hodgson
  • Horst Weber

Abstract

In linear resonators, the interference of the two counterpropagating waves generates a modulation of the intensity along the optical axis. As discussed in Sec. 9.5.2, the intracavity intensity distribution of an axial mode of order q outside the active medium reads:
$$ I\left( z \right) = {I_0}\left[ {1 - \frac{{2R}}{{1 + {R^2}}}\cos \left( {2\pi qz/L} \right)} \right]$$
(20.1)
(20.1) where L is the resonator length, R is the reflectance of the output coupling mirror, and z is the coordinate along the optical axis, starting at a mirror surface. The intensity minima exhibit a periodicity of half the wavelength of the axial mode λ q =2L/q Due to gain saturation this results in a modulated axial gain distribution, referred to as spatial holeburning. The modulation frequency depends on the axial mode order.

Keywords

Burning Coupler Astigmatism 

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References

  1. 5.152
    C.L. Tang, H. Statz, G. deMars, Jr., Spectral output and spiking behavior of solid-state lasers, J. Appl. Phys. 34, 2289, 1963CrossRefGoogle Scholar
  2. 5.153
    M. Hercher, M. Young, C.B. Smoyer, Traveling-wave ruby laser with a passive optical oscillator, J. Appl. Phys. 36, 3351, 1965CrossRefGoogle Scholar
  3. 5.154
    Yu. A. Anan’ev, N.A. Sventsitskaya, V.E. Sherstobitov, Properties of a laser with an unstable resonator, Sov. Phys. JETP 28, 69, 1969Google Scholar
  4. 5.155
    F.P. Schäfer, H. Müller, Tunable dye ring-laser, Opt. Commun. 2, 407, 1971CrossRefGoogle Scholar
  5. 5.156
    A.R. Clobes, M.J. Brienza, Single-frequency traveling-wave Nd.YAG lasers, Appl. Phys. Lett. 21, 265, 1972Google Scholar
  6. 5.157
    H.W. Kogelnik, E.P. Ippen, A. Dienes, C.V. Shank, Astigmatically compensated cavities for cw dye lasers, IEEE J. Quantum Electron. QE-8, 373, 1972CrossRefGoogle Scholar
  7. 5.158
    J.M. Green, J.P. Hohimer, F.K. Tittel, Traveling-wave operation of a tunable cw dye laser, Opt. Commun. 7, 349, 1973CrossRefGoogle Scholar
  8. 5.159
    P. dal Pozzo, & Polloni, O. Svelto, F. Zaraga, An unstable ring resonator, IEEE J. Quantum Electron. 9, 1061, 1973CrossRefGoogle Scholar
  9. 5.160
    R.J. Freiberg, P.P. Chenausky, C.J. Buczek, Unidirectional unstable ring lasers, Appl. Opt. 12, 1140, 1973CrossRefGoogle Scholar
  10. 5.161
    R.J. Freiberg, P.P. Chenausky, C.J. Buczek, Asymmetric unstable traveling-wave resonators, IEEE J. Quantum Electron. QE-10, 279, 1974CrossRefGoogle Scholar
  11. 5.162
    P. del Pozzo, & Pollini, O., Svelto, F. Zaraga, A doubly-confocal unstable ring resonator, Opt. Commun. 11, 115, 1974CrossRefGoogle Scholar
  12. 5.163
    G. Marowsky, R. Kaufman, Influence of spatial hole burning on the output power of a cw dye ring laser, IEEE J. Quantum Electron. QE-12, 207, 1976CrossRefGoogle Scholar
  13. 5.164
    AH Paxton, T.C. Sarvi, Unstable optical resonator with self-imaging aperture, Opt. Commun. 26, 305, 1978CrossRefGoogle Scholar
  14. 5.165
    S.M. Jarrett, J.F. Young, High-efficiency single-frequency cw ring dye laser, Opt. Lett. 4, 176, 1979CrossRefGoogle Scholar
  15. 5.166
    E.F. Ichshenko, E.F. Reshetin, Sensitivity to misalignment of an optical ring resonator with a focusing element, Opt. and Spectrosc. 46, 202, 1979Google Scholar
  16. 5.167
    Yu. A. Anan’ev, V.I. Kuprenyuk, V.E. Sherstobitov, Properties of unstable resonators with field rotation. I. Theoretical principles, Sov. J. Quantum Electron. 9, 1105, 1979CrossRefGoogle Scholar
  17. 5.168
    T.F. Johnston Jr., W. Proffitt, Design and performance of a broad-band optical diode to enforce one-direction traveling-wave operation of a ring laser, IEEE J. Quantum Electron. QE-16, 483, 1980CrossRefGoogle Scholar
  18. 5.169
    F.R. Faxvog, Modes of unidirectional ring laser, Opt. Lett. 5, 285, 1980CrossRefGoogle Scholar
  19. 5.170
    O. Teschke, S. R Teixeira, Unstable ring resonator nitrogen pumped dye laser, Opt. Commun. 32, 287, 1980CrossRefGoogle Scholar
  20. 5.171
    K.E. Oughstun, P.A. Slaymaker, K.A. Bush, Intracavity spatial filtering in unstable ring resonator geometries, Part I — Passive cavity mode theory, IEEE J. Quantum Electron. 19, 1558, 1983CrossRefGoogle Scholar
  21. 5.172
    E. Sklar, Fourier-transform ring laser, J. Opt. Soc. Am A 1, 537, 1984CrossRefGoogle Scholar
  22. 5.173
    E.M. Wright, D.P. O’Brein, W.J. Firth, Reciprocity and orthogonality relations for ring resonators, IEEE J. Quantum Electron. 20, 1307, 1984CrossRefGoogle Scholar
  23. 5.174
    H.A. Haus, H. Statz, I.W. Smith, Frequency locking of modes in a ring laser, IEEE J. Quantum Electron. QE-21, 78, 1985CrossRefGoogle Scholar
  24. 5.175
    T.J. Kane, R.L. Byer, Monolithic, unidirectional single-mode Nd:YAG ring laser, Opt. Lett. 10, 65, 1985CrossRefGoogle Scholar
  25. 5.176
    G.L. Lippi, J.R. Tredicce, N.B. Abraham, F.T. Arecchi, Deterministic mode alternation, gaint pulses and chaos in a bidirectional CO2 ring laser, Opt. Commun. 53, 129, 1985CrossRefGoogle Scholar
  26. 5.177
    V.N. Smirnov, G.A. Strokovskii, Transverse mode formation in a ring laser with a 1-D diaphragm, Opt. Spectrosc. (USSR) 60, 652, 1986Google Scholar
  27. 5.178
    J.S. Uppal, J.C. Monga, D.D. Bhawalkar, Performance of a general asymmetric unstable Nd:glass ring laser, Appl. Opt. 25, 97, 1986CrossRefGoogle Scholar
  28. 5.179
    J.S. Uppal, J. C. Monga, D.D. Bhahvalkar, Analysis of an unstable confocal ring laser with a thermally induced active medium, Appl. Opt. 25(9), 389, 1986CrossRefGoogle Scholar
  29. 5.180
    P. Ru, L.M. Narducci, J.R. Tredicce, D.K. Bandy, L.A. Lugiato, The Gauss-Laguerre modes of a ring resonator, Opt. Commun. 63(5), 310, 1987CrossRefGoogle Scholar
  30. 5.181
    T.J. Kane, A.C. Nilsson, R.L. Byer, Frequency stability and offset locking of a laser-diode-pumped Nd:YAG monolithic nonplanar ring oscillatior, Opt. Lett. 12, 175, 1987CrossRefGoogle Scholar
  31. 5.182
    A.H. Paxton, Unstable ring resonator with an intracavity prism expander, IEEE J. Quantum Electron. QE-23, 241, 1987CrossRefGoogle Scholar
  32. 5.183
    T.J. Kane, E. A. P. Cheng, Fast frequency tuning and phase locking of a diode pumped Nd: YAG ring laser, Opt. Lett. 13, 970, 1988CrossRefGoogle Scholar
  33. 5.184
    K.R. Calahan, C.M. Clayton, A.H. Paxton, Unstable ring resonator with a compact output beam: description and experimental evaluation, Appl. Opt. 27(13), 2694, 1988CrossRefGoogle Scholar
  34. 5.185
    I. Schütz, S. Wiegand, R Wallenstein, Diode-pumped solid state lasers, Laser und Optoelektronik 20(3), 39–45, 1988Google Scholar
  35. 5.186
    A.C. Nilsson, T. Day, A.D. Farinas, E.K. Gustafson, R.L. Byer, Narrow linewidth operation of diode-laser-pumped nonplanar ring oscillators, Springer Verlag Topics in Physics: Proceedings of the Fourth Symposium onm Frequency and Metrology, Ancona, Italy, 1988Google Scholar
  36. 5.187
    T. Day, A.C. Nilsson, M.M. Fejer, A.D. Farinas, E.K. Gustafson, C.D. Nabors, R.L. Byer, 30-Hz linewidth, diode-laser-pumped, Nd:GGG nonplanar ring oscillators by active frequency stabilization, Electron. Lett. 25, 810, 1989CrossRefGoogle Scholar
  37. 5.188
    A.C. Nilsson, E.K. Gustafson, R.L. Byer, Eigenpolarization theory of monolithic nonplanar ring oscillators, J. Quantum Electron. 25, 767, 1989CrossRefGoogle Scholar
  38. 5.189
    P. Fritschel, A Jeffries, T. Kane, Frequency fluctuations of a diode-pumped Nd:YAG ring laser, Opt. Lett. 14, 993, 1989CrossRefGoogle Scholar
  39. 5.190
    T. A. King, Ring laser resonators, in D.R. Hall, P.E. Jackson (eds.): Physics and technology of laser resonators. London: Adam Hilger 1989, pp. 62–79Google Scholar
  40. 5.191
    F. Bretenaker, A le Foch, J.P. Tache, Theoretical and experimental study of elliptical Gaussian-mode size dynamics in ring lasers, Phys. Rev. A 41, 3792, 1990CrossRefGoogle Scholar
  41. 5.192
    T. Day, E.K. Gustafson, R.L. Byer, Active frequency stabilization of a 1.062-um, Nd: GGG, diode-laser-pumped non-planar ring oscillator to less than 3 Hz of relative linewidth, Opt. Lett. 15, 221, 1990CrossRefGoogle Scholar
  42. 5.193
    W.R. Trutna Jr., D.K. Donald, Two-piece, piezo-electrically tuned, single-mode Nd: YAG ring laser, Opt. Lett. 15, 369, 1990CrossRefGoogle Scholar
  43. 5.194
    E.A.P. Cheng, T.J. Kane, High-power single-mode diode-pumped Nd.YAG laser using a monolithic nonplanar ring resonator, Opt. Lett. 16, 478, 1991CrossRefGoogle Scholar
  44. 5.195
    T. Day, E.K. Gustafson, R.L. Byer, Sub-hertz relative frequency stabilization of two diode-laser-pumped Nd: YAG lasers locked to a Fabry-Perot interferometer, IEEE J. Quantum Electron. 28, 1106, 1992CrossRefGoogle Scholar
  45. 5.196
    J. Harrison, A. Finch, J.H. Flint, P.F. Moulton, Broad-band rapid tuning of a single-frequency diode-pumped neodymium laser, IEEE J. Quantum Electron. 28(4), 1123, 1992CrossRefGoogle Scholar
  46. 5.197
    K.I. Martin, W.A. Clarkson, D.C. Hanna, 3W of single frequency output at 532 nm by intracavity doubling of a diode-bar-pumped Nd:YAG ring laser, Opt. Lett. 21(12), 875, 1996CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London 1997

Authors and Affiliations

  • Norman Hodgson
    • 1
  • Horst Weber
    • 2
  1. 1.Humphrey InstrumentsCarl Zeiss Inc.San LeandroUSA
  2. 2.Optisches InstitutTechnische Universität BerlinBerlinGermany

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