A complex Jacobi Iteration method for passive wavelength scale devices
Main Researcher: Peter Vandersteegen
Recently -on the conference OWTNM 2004- a new simulation method, called the complex Jacobi Iteration method was introduced. This method numerically integrates the laws of Maxwell in the frequency domain. It accomplishes this with an iterative proces. Each iteration the calculated fields are further refined until a desired relative error is achieved.
We have implemented several extensions: sources, efficient boundary conditions and non-linear Kerr effect. This so called Kerr effect with its intensity dependent index change is considered a promising route to achieve fast optical switching functionality. Achieving all-optical functionality in integrated components indeed requires materials which exhibit non-linear effects.
Injecting a field with gaussian profile in a linear material
Both figures show the absolute E-field in a uniform medium. The used field-source has a Gaussian profile.
In the non-linear uniform medium a propagating soliton is formed.The maximum relative index change - caused by the increased field intensity at the center of this soliton - is 15%. The use of a material with high non-linear Kerr effect only results in a slight increase of iteration steps. Good absorption
at the boundaries is achieved by using perfectly matched layers (PML). The implementation of these PML is done with complex coordinate stretching .
Injecting a field with gaussian profile in a non-linear Kerr material can result in formation of a soliton
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