Simulations of Kerr based non linear optical components with the Complex Jacobi iteration

Summary form only given. We present several non-linear structures simulated with the non-linear complex Jacobi iteration. This method numerically integrates the fields of the Helmholtz equation for points located on a grid. Because the fields are calculated on each grid point this results in a very flexible method. This iterative method refines each iteration step the calculated fields until a desired error has been achieved. The first structure under discussion is a one dimensional study of a cavity surrounded by two Bragg gratings. These two Bragg gratings create a photonic band gap. The introduced cavity creates a resonance wavelength in the middle of this band gap. All light with this resonance wavelength will be transmitted by this structure. Introducing a non-linear material in the cavity will shift the resonance peak to higher wavelengths. A comparison with non-linear eigenmode expansion confirms the accuracy of our simulation tool. We have also shown that the numerical dispersion introduced by a discrete mesh can be controlled if the discretization step Deltax < lambda/20. We will also present preliminary simulation results from a 2 dimensional vertical coupler. Light coupled vertically in the coupler is symmetrically injected in a left and right waveguide. Injection efficiency in one waveguide reaches a maximum for a certain wavelength. Adding non-linearity in the grating material will hopefully result in a shift of this maximum. Parts of this work has been performed in the context of the Belgian IAP photon network