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23 September 2015 Analytical new method to generation of nonlinear optical pulses in wave guides and analysis of its stability
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We have developed a analitical method based on the general theory of modulation of Whitham7 where the variational method is a particular case to generate nonlinear optical pulses and Optical Solitons. We show the equivalence of the solutions of the Nonlinear Schrödinger Equation (NLS) and the solutions derived from the method proposed here, demonstrating that these solutions lead to the Optical Solitons. We developed a new method to check the stability of the NLS equations. We show that the Optical Solitons obtained from a Lagrangian density can propagate through a waveguide such as an optical fiber, and are equivalent to Optical Solitons guided by an optical fiber. To analyze the stability of system solutions we have expanded the Lagrangian density and from the expanded Lagrangian we obtain the system equations of motion and restrict the solutions that have oscillating behavior when disturbed. The stability analysis can also be performed by expansion of the optical field as it is presented in section 4. Thus obtain a self-value equation whose spectrum is positive indicating that the solutions with the characteristics of reproducing the NLS solutions are stable. This method can be used and implemented computationally for linear stability analysis of any optical system or any NLS solution. Another important aspect of our research has been the discovery of a relationship between the Lagrangian of optical system and the optical pulse propagating through a waveguide. The paper is organized as follows. Section 1 is devoted to a quick presentation of NLS systems. The section 2 provides a description of modeling of an optical network. Section 3 and 4 are devoted to the presentation of the proposed method for obtaining this class of solutions and their stability analysis. Section 5 presents conclusions and comments and section 6 provides references.
© (2015) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
A. C. Amaro de Faria Júnior "Analytical new method to generation of nonlinear optical pulses in wave guides and analysis of its stability", Proc. SPIE 9626, Optical Systems Design 2015: Optical Design and Engineering VI, 96263G (23 September 2015);


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