Ray splitting in paraxial optical cavities

G. Puentes; A. Aiello; J. P. Woerdman

doi:10.1103/PhysRevE.69.036209

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Ray splitting in paraxial optical cavities

G. Puentes, A. Aiello, and J. P. Woerdman

Huygens Laboratory, Leiden University, P.O. Box 9504, Leiden, The Netherlands

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Phys. Rev. E 69, 036209 – Published 30 March, 2004

DOI: https://doi.org/10.1103/PhysRevE.69.036209

Abstract

We present a numerical investigation of the ray dynamics in a paraxial optical cavity when a ray-splitting mechanism is present. The cavity is a conventional two-mirror stable resonator and the ray splitting is achieved by inserting an optical beam splitter perpendicular to the cavity axis. We show that depending on the position of the beam splitter the optical resonator can become unstable and the ray dynamics displays a positive Lyapunov exponent.

References (18)

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L. Couchman, E. Ott, and T.M. Antonsen, Jr., Phys. Rev. A 46, 6193 (1992).
J. Jensen, J. Opt. Soc. Am. A 10, 1204 (1993).
M. Hentschel and K. Richter, Phys. Rev. E 66, 056207 (2002).
J. Nöckel and R. Chang, in 2D-Microcavities: Theory and Experiments, Experimental Methods in the Physical Sciences, Vol. 40, edited by R.D. van Zee and J.P. Looney (Academic Press, San Diego, 2002), pp. 185–226.
G. Puentes, A. Aiello, and J.P. Woerdman (unpublished).
A.E. Siegman, Lasers (University Science Books, Mill Valley, CA, 1996).
P. Cvitanović et al., www.nbi.bk/ChaosBook/
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S. Bleher, C. Grebogi, E. Ott, and R. Brown, Phys. Rev. A 38, 930 (1988).
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G. Benettin and J.M. Strelcyn, Phys. Rev. A 17, 773 (1978).
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[c1] A. Kohler, G.H. Killesreiter, and R. Blümel, Phys. Rev. E 56, 2691 (1997).

[c2] L. Couchman, E. Ott, and T.M. Antonsen, Jr., Phys. Rev. A 46, 6193 (1992).

[c3] J. Jensen, J. Opt. Soc. Am. A 10, 1204 (1993).

[c4] M. Hentschel and K. Richter, Phys. Rev. E 66, 056207 (2002).

[c5] J. Nöckel and R. Chang, in 2D-Microcavities: Theory and Experiments, Experimental Methods in the Physical Sciences, Vol. 40, edited by R.D. van Zee and J.P. Looney (Academic Press, San Diego, 2002), pp. 185–226.

[c6] G. Puentes, A. Aiello, and J.P. Woerdman (unpublished).

[c7] A.E. Siegman, Lasers (University Science Books, Mill Valley, CA, 1996).

[c8] P. Cvitanović et al., www.nbi.bk/ChaosBook/

[c9] S. Longhi, Phys. Rev. E 65, 027601 (2002).

[c10] E. Ott, Chaos in Dynamical Systems, 2nd ed. (Cambridge University Press, Cambridge, 2002).

[c11] J. Schneider, T. Tél, and Z. Neufeld, Phys. Rev. E 66, 066218 (2002).

[c12] S. Bleher, C. Grebogi, E. Ott, and R. Brown, Phys. Rev. A 38, 930 (1988).

[c13] J. Aguirre and M.A.F. Sanjuán, Phys. Rev. E 67, 056201 (2003).

[c14] G. Benettin and J.M. Strelcyn, Phys. Rev. A 17, 773 (1978).

[c15] H. Furstenberg, Trans. Am. Math. Soc. 108, 377 (1963).

[c16] A. Crisanti, G. Paladin, and A. Vulpiani, Products of Random Matrices (Springer-Verlag, Berlin, 1993).

[c17] P. Gaspard and G. Nicolis, Phys. Rev. Lett. 65, 1693 (1990).

[c18] P. Gaspard, Chaos, Scattering and Statistical Mechanics, 1st ed. (Cambridge University Press, Cambridge, 1998).

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