Using the Complex Jacobi Method to Simulate Kerr Non-linear Photonic Components

Abstract

Optical and Quantum Electronics (2006) 38:35-44 © Springer 2006 Using the complex Jacobi method to simulate Kerr non-linear photonic components p e t e r va n d e r s t e e g e n * , b j o r n m a e s, p e t e r b i e n s t m a n a n d r o e l b a e t s

Advances in Iterative Methods and Preconditioners for the Helmholtz Equation

“…The largest convergence rate is reached if ω r,1 = √ 3 −ĵ . While the resulting algorithm is very simple, the convergence, however, is still considered somewhat slow; see numerical examples in [68,132,133].…”

The complex Jacobi iterative method for non-paraxial beam propagation in nonlinear optical waveguides

“…The resulting operators not only give evanescent waves a desired damping, but also allow more accurate approximations to the Helmholtz equation than real Padé(m,n) approximant operators. In this work, rather than using real Padé approximant operators as the existing approaches the beam propagation the equation for the analysis of non-paraxial propagation in nonlinear waveguides is based on the modified Padé(1,1) approximant operator as follows: [4] Furthermore, by adding an extra calculation step for dealing with nonlinear effects as well-done for a different method in [5] and using PMLs to absorb incident radiation without any additional parasitic reflections, regardless of wavelength, incident angle or polarization as boundary conditions, the CJI method is thus a promising technique to solve the nonlinear beam propagation equation quickly and effectively.…”

“…Furthermore, by introducing an extra calculation step the CJI method has been successfully employed to simulate photonic components consisting of materials with nonlinear Kerr effects [5].…”

Non-paraxial beam propagation in nonlinear optical waveguides using complex Jacobi iteration

“…Therefore, at each propagation step the beam propagation equation will be solved effectively by the CJI method with adding an extra calculation step for dealing with nonlinear effect [5].…”

“…Furthermore, by introducing an extra calculation step the CJI method has been successful employed to simulate photonic components composed by materials with nonlinear Kerr effects [5]. Therefore, by doing the same procedure for dealing with nonlinear effects at each propagation step, our recently proposed iterative BPM is extended and is very competitive for modeling optical propagation in nonlinear optical waveguides.…”