### Abstract

Numerical calculation of electromagnetic scattering properties and structural parameters of periodic structures is disclosed. A reflection coefficient has a representation as a bilinear or sesquilinear form. Computations of reflection coefficients and their derivatives for a single outgoing direction can benefit from an adjoint-state variable. Because the linear operator is identical for all angles of incidence that contribute to the same outgoing wave direction, there exists a single adjoint-state variable that generates all reflection coefficients from all incident waves that contribute to the outgoing wave. This adjoint-state variable can be obtained by numerically solving a single linear system, whereas one otherwise would need to solve a number of linear systems equal to the number of angles of incidence.

Original language | English |
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Patent number | US8645109 (B2) |

Priority date | 29/11/10 |

Publication status | Published - 4 Feb 2014 |

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## Cite this

Dirks, R., Setija, I. D., Kraaij, van, M. G. M. M., & Beurden, van, M. C. (2014). Methods and apparatus for determining electromagnetic scattering properties and structural parameters of periodic structures. (Patent No.

*US8645109 (B2)*).