ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Izmailov I. V., Ljachin A. V., Poizner B. N., Shergin D. A. Simulation of field nonlinear phase shift dynamics in ring interferometer in case of two-frequency influence. Izvestiya VUZ. Applied Nonlinear Dynamics, 2005, vol. 13, iss. 1, pp. 137-151. DOI: 10.18500/0869-6632-2005-13-1-137-151

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Full text PDF(Ru):
(downloads: 138)
Article type: 
535:530.182 + 519.713

Simulation of field nonlinear phase shift dynamics in ring interferometer in case of two-frequency influence

Izmailov Igor Valerevich, National Research Tomsk State University
Ljachin Aleksandr Vladimirovich, National Research Tomsk State University
Poizner Boris Nikolaevich, National Research Tomsk State University
Shergin Denis Aleksandrovich, National Research Tomsk State University

Families of initial-final maps, bifucation lines, maps of Lyapunov’s characterictic exponents and fractal dimentionality D0 are constructed for a model of nonlinear pphase shift dynamics for ont- and two-frequency field in a ring interferometer. The influence of a spectrum form of two-frequency radiation to a structure of mentioned maps is clarified.Ways of maps quantitative analysis are suggested and realized. Two languages of nonlinear dynamics description in the ring interferometer are compared: with the help of ordinary differential equations and of the discrete map. The peculiarity of spatial deterministic chaos was pointed: this state is stable to initial-conditions variation but it is not stable to parameters variation of the model.

Key words: 
  1. Ikeda K. Multiple-valued stationary state and its instability of the transmitted light by ring cavity system. Opt. Commun. 1979;30(2):257–261. DOI: 10.1016/0030-4018(79)90090-7.
  2. Akhmanov SA, Vorontsov MA. Instabilities and structures in coherent nonlinear optical systems covered by two-dimensional feedback. In: Nonlinear Waves: Dynamics and Evolution: Collection of Articles. Moscow: Nauka; 1989. P. 228–237 (in Russian).
  3. Rozanov NN. Optical Bistability and Hysteresis in Distributed Nonlinear Systems. Moscow: Nauka; 1997. 336 p. (in Russian).
  4. Izmailov IV, Magazinnikov AL, Poizner BN. Modeling processes in a ring interferometer with nonlinearity, delay and diffusion under nonmonochromatic radiation. Russian Physics Journal. 2000;43(2):29–35 (in Russian).
  5. Balyakin AA, Ryskin NM. Transition to chaos in a nonlinear ring resonator upon excitation by an external multifrequency signal. Bulletin of the Russian Academy of Sciences: Physics. 2001;65(12):1739–1742 (in Russian).
  6. Balyakin AA. Investigation of the chaotic dynamics of a ring nonlinear resonator under a two-frequency external action. Izvestiya VUZ. Applied Nonlinear Dynamics. 2003;11(4–5):3–15 (in Russian).
  7. Dmitriev AS. Dynamic chaos as a carrier of information. In: New in Synergetics: A Look into the Third Millennium. Moscow: Nauka; 2002. P. 82–122 (in Russian).
  8. Izmailov IV, Poizner BN. Implementation options for a nonlinear optical device for covert information transmission. Atmospheric and Oceanic Optics. 2001;14(11):1074–1086 (in Russian).
  9. Izmailov IV, Lyachin AV, Poizner BN, Shergin DA. Spatial deterministic chaos and the transition from ordinary differential equations to mappings. Izvestiya VUZ. Applied Nonlinear Dynamics. 2004;13(1–2):123 (in Russian).
  10. Shergin DA, Izmailov IV. Discrete mappings as a means of describing deterministic spatial chaos. In: Collection of Abstracts of the 9th All-Russian Scientific Conference of Physics Students and Young Scientists: In 2 Volumes. Vol. 2. Ekaterinburg-Krasnoyarsk: Russian ERT; 2003. P. 90–93 (in Russian).
  11. Shergin DA, Izmailov IV, Poizner BN. Discrete mappings as a language for describing spatial deterministic chaos. In: Modern Problems of Physics and High Technologies: Proceedings of the International Conference. September 29 - October 4, 2003, Tomsk. Tomsk: STL Publishing; 2003. P. 186–189 (in Russian).
  12. Izmailov IV, Ravodin IN. Influence of nonlinearity and delay in a ring interferometer on bifurcations (calculation and modeling). Russian Physics Journal. 1999;1:126 (in Russian).
  13. Shergin DA, Izmailov IV. Nonlinear ring interferometer through the prism of Lyapunov exponents for discrete display. In: Kozlova SA, editor. Optics-2003. Proceedings of the Third International Conference of Young Scientists and Specialists «Optics-2003». St. Petersburg, October 20-23, 2003. St. Petersburg: ITMO University; 2003. P. 104–105 (in Russian).
  14. Kuznetsov SP. Dynamic Chaos. Lecture Course. Textbook for University Students Enrolled in Physical Specialties. Moscow: Fizmatlit; 2001. 296 p. (in Russian).
  15. Izmailov IV, Poizner BN, Ravodin VO. A model of interaction between two scientific directions, one of which or both are "fading", taking into account the limitation of the growth of achievements and lag. Izvestiya VUZ. Applied Nonlinear Dynamics. 2001;9(4–5):119–139 (in Russian).
  16. Izmailov IV, Poizner BN, Shergin DA. Processes in ring interferometer: a problem of description by discrete maps. In: The 6th International Conference «Atomic and Molecular Pulsed Lasers» Conference Proceedings. Tomsk, Institute of Atmospheric Optics SB RAS; 2003. P. 98.  
Short text (in English):
(downloads: 98)