- 51 Downloads
We consider the problem of the wave propagation through a nonlinear medium. We derive a dynamic system that governs the behavior of standing (or solitary) waves. The form of this system alone suffices to understand the qualitative dependence of solutions of the original equation on the intensity of the incident wave. We solve this dynamical system in the leading order in the nonlinearity strength. We find multiple solutions of the original problem for a given incoming wave and turning points of these solutions as a function of the wave intensity. We briefly investigate stability of different branches. Our results yield an analytic description of the optical bistability phenomenon.
KeywordsSpectroscopy Dynamic System State Physics Field Theory Elementary Particle
Unable to display preview. Download preview PDF.
- 11.C. M. de Sterke and J. E. Sipe, in Progress in Optics XXXIII, Ed. by E. Wolf (North-Holland, Amsterdam, 1994), p. 203.Google Scholar
- 12.S. Dutta Gupta, in Progress in Optics XXXIII, Ed. by E. Wolf (North-Holland, Amsterdam, 1998).Google Scholar
- 14.G. P. Agrawal, Nonlinear Fiber Optics (Academic, Boston, 1989; Mir, Moscow, 1996).Google Scholar
- 15.N. Bloembergen, Nonlinear Optics: a Lecture Note and Reprint Volum (W. A. Benjamin, New York, 1965; Mir, Moscow, 1966).Google Scholar
- 16.H. M. Gibbs, Optical Bistability: Controlling Light with Light (Academic, New York, 1985; Mir, Moscow, 1988).Google Scholar
- 17.D. L. Mills, Nonlinear Optics: Basic Concepts (Springer-Verlag, New York, 1991).Google Scholar
- 18.Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984; Nauka, Moscow, 1989).Google Scholar
- 19.W. A. Strauss, Nonlinear Wave Equations (American Mathematical Society, Providence, 1989), CBMS Regional Conference Series in Mathematics, No. 73, 1987.Google Scholar