Accurate design and modeling of Χ(2) nonlinear processes in periodic waveguides by hertzian potential method

We present in this work the scalar potential formulation of second harmonic generation process in Χ(2) nonlinear analysis. This approach is intrinsically well suited to the application of the concept of circuit analysis and synthesis to nonlinear optical problems, and represents a novel alternative method in the analysis of nonlinear optical waveguide, by providing a good convergent numerical solution. The time domain modeling is applied to nonlinear waveguide with dielectric discontinuities in the hypothesis of quasi phase matching condition in order to evaluate the conversion efficiency of the second harmonic signal. With the introduction of the presented rigorous time domain method it is possible to represent the physical phenomena such as light propagation and second harmonic generation process inside a nonlinear optical device with a good convergent solution and low computational cost. Moreover, this powerful approach minimizes the numerical error of the second derivatives of the Helmholtz wave equation through the generator modeling. The novel simulation algorithm is based on nonlinear wave equations associated to the circuital approach which considers the time-domain wave propagating in nonlinear transmission lines. The transmission lines represent the propagating modes of the nonlinear optical waveguide. The application of quasi phase matching in high efficiency second harmonic generation process is analyzed in this work. In particular we model the Χ(2) non linear process in an asymmetrical GaAs slab waveguide with nonlinear core and dielectric discontinuities: in the nonlinear planar waveguides a fundamental mode at λ=1.55 μm is coupled to a second-harmonic mode (λ=0.775 μm) through an appropriate nonlinear susceptibility coefficient. The novel method is also applied to three dimensional structures such as ridge waveguides.