Theoretical Framework of Fuzzy Set-Based Analysis of Chaos in Nonlinear Optics

Abstract

Chaos analysis in nonlinear optical systems is essential for understanding and harnessing their complex behavior. This study explores the application of fuzzy set-based analysis as a novel approach to detect and quantify chaos in a periodically poled lithium niobate (PPLN) waveguide used for second-harmonic generation. We present a comprehensive framework that includes data collection, fuzzy set-based chaos analysis, and comparative assessments with traditional methods. Visual representations of chaotic behavior, such as phase portraits and bifurcation diagrams, are provided to illustrate our findings. Comparative analysis highlights the advantages of fuzzy set-based analysis in handling noisy data and characterizing irregular dynamics. Our research reveals the potential of this approach in controlling chaotic optical systems and advancing secure optical communication technologies. Moreover, it emphasizes the practical implications of chaos analysis in nonlinear optics, offering insights for diverse applications across various industries.