Nonlinear Harmonic Response in Microwave and Photonic Devices, and Waveguides

In the present paper, we have analyzed nonlinear harmonic response in microwave, photonic devices, and waveguides, applications. Based on Frobenius power series expansions, a special software has been cast and applied with very small truncation error (less than 10 -8 ). Four basic sets of nonlinear harmonic response systems have been processed: i) New algorithms for computing twelve Jacobian elliptic functions are built on the basis of transformation of Jacobian elliptic integrals to nonlinear differential equations of second order, where each function has its generating recurrence formula., ii) Selftrapping (paraxial propagation) in W-shaped refractive index fibers are parametrically investigated, iii) Implementation of the Frobenius method for the numerical solution of initial value problems involving second order nonlinear differential equations with or without arbitrary forced functions under the forms: ) t ( f y y y m / n 2 γ = β + ′ α + ′ ′ , ) t ( f y y y y 2 m / n γ = β + ′ α + ′ ′ , and 0 . 0 y y y 3 = β + α + ′ ′ , are discussed, where α, β, and γ are physical parameters; both m and n are positive solid integers, and f(t) is an arbitrary exciting function, and finally iv) waveguides and multiplexers. A novel software program has been designed and processed to handle the above problems.