Computing shape parameter sensitivity of the field of one-dimensional surface-relief gratings by using an analytical approach based on RCWA

The rigorous coupled-wave analysis (RCWA) is a method to compute diffraction of a field by a given grating structure. Within various applications, such as metrology, it is important to know how the field reacts to small perturbations in the grating. This behavior can be expressed by the field derivatives with respect to a certain parameter. Approximations of these derivatives can be found by using finite differences where the field is computed for a neighboring value of the parameter, and the difference gives the derivative. Unfortunately, RCWA involves solving eigenvalue systems that are computationally expensive. Therefore, a faster alternative is given that computes the derivatives by straightforward differentiation of the relations within RCWA. Solving additional eigensystems is replaced by finding derivatives of eigenvalues and eigenvectors, which is less computationally expensive