## Preprint 2016-22

## Akhlesh Lakhtakia, Peter Monk, Cinthya Rivas, Rodolfo Rodríguez, Manuel Solano:

### Asymptotic model for finite-element calculations of diffraction by shallow metallic surface-relief gratings

### Abstract:

We have formulated an asymptotic model for implementation in the finite element method to calculate diffraction from a planar multilayered structure having a shallow surface-relief grating. The thin grating layer containing the shallow grating is replaced by a planar interface with transmission conditions that differ from the standard continuity conditions. The parameters defning the shallow surface-relief grating are thereby removed from the geometry to the transmission conditions, thereby speeding up finite-element calculations as a very fine mesh is not needed for the thin grating layer. This will considerably reduce the computational cost of optimizing the grating shape, since there is no need to re-mesh at every optimization step.

This preprint gave rise to the following definitive publication(s):

**Akhlesh LAKHTAKIA, Peter MONK, Cinthya RIVAS, Rodolfo RODRíGUEZ, Manuel SOLANO: ***Asymptotic model for finite-element calculations of diffraction by shallow metallic surface-relief gratings*. Journal of the Optical Society of America A, vol. 34, 1, pp. 68-79, (2017).