LettersNo Access

Modding Out a Continuous Rotation Symmetry for Disentangling a Laser Dynamics

Christophe Letellier

CORIA UMR 6614–Université de Rouen, Av. de l'Université, BP 12, F-76801 Saint-Etienne du Rouvray Cedex, France

https://doi.org/10.1142/S0218127403007424Cited by:5 (Source: Crossref)

Abstract

When a laser system is studied, the time evolution of the light intensity emitted by the laser cavity is recorded. The phase portrait reconstructed from that time series never presents symmetry although the amplitude equations always generate phase portraits with symmetry properties. It is shown that the detuning between the normalized steady-state laser frequency and the molecular resonance frequency induces a continuous rotation symmetry. This equivariant dynamics is linked with the dynamics underlying the experimental observations of the light intensity through a system for which the symmetry properties are modded out.

Keywords:

References

A. Arnéodo, P. H. Coullet and E. A. Spiegel, Phys. Lett. A 94, 1 (1983). Crossref, Web of Science, Google Scholar
L. Cao, Physica D 110(1/2), 43 (1997). Crossref, Web of Science, Google Scholar
P. Collet and J. P. Eckmann , Iterated Maps on the Interval as Dynamical Systems , Progress in Physics , eds. A. Jaffe and D. Ruelle ( Birkhäuser , Boston , 1980 ) . Google Scholar
dos Santos, E. P., Caldas, I. L. & Baptista, M. S. [2002] "Two-frequency torus breakdown in the driven Matsumoto–Chua electronic circuit," Nonlinear Dynamics, Chaos, Control and their Applications to Engineering Sciences, Chaos, Control and Time Series, Vol.5, eds. Balthazar, J. M. et al., pp.38–46 . Google Scholar
H. Haken, Phys. Lett. A 53, 77 (1975). Crossref, Web of Science, Google Scholar
U. Hübneret al., Time Series Prediction, Santa Fe Proc. XV, eds. Gershenfeld and Weigend (Addison Wesley, 1994) pp. 73–104, DOI: 10.1142/S021812740000116X. Google Scholar
C. Letellier and R. Gilmore, Phys. Rev. E 63, 016206 (2001). Crossref, Web of Science, Google Scholar
R. Miranda and E. Stone, Phys. Lett. A 178, 105 (1993). Crossref, Web of Science, Google Scholar
H. Zeghlache and P. Mandel, J. Opt. Soc. Am. B 2, 18 (1985). Crossref, Web of Science, Google Scholar