User:Drjbischoff/sandbox

Coordinate transformation method (C-method) a.k.a. Chandezon method (first suggested by Jean Chandezon) like Rigorous coupled-wave analysis is a semi-analytical method in computational electromagnetics to solve diffraction from periodic structures. It is a Fourier-space or modal method where the fields are represented as a sum of spatial harmonics. The C-method relies on the formulation of Maxwell’s equation in generic curvilinear coordinates that are adapted to the grating profile. Thus, the staircase approximation (slicing) of the RCWA can be avoided and the index distribution has not to be Fourier transformed explicitly. In this way, issues due to the Gibb’s phenomena are alleviated. Moreover, this formulation results in just one differential equation system (DES) per interface between different materials rather than multiple DES (one per slice) as in RCWA. The electromagnetic modes at each interface are calculated and analytically propagated from interface to interface. Like in other differential modal methods, the overall problem is solved by matching boundary conditions at each of the interfaces using a technique like scattering matrices. The resulting infinitely large algebraic equations have then to be truncated depending on accuracy and convergence speed requirements to make it solvable for computers. The C-method inherently conserves the exact boundary conditions for both polarization cases. Thus it shows a superior and widely polarization independent convergence in most cases. Some of the drawbacks of the C-method are that it starts to fail for very steep profiles (which can be relieved by applying the adaptive resolution schema) and does not work for overhanging profiles (though there are exceptions).

Example Implementations

 * Unigit (for 1D arbitrary multilayer gratings