Integral equation method with parametrization of grating profile theory and experiments

Integral equation methods from grating theory to photonics: an overview and new approaches for conical diffraction

“…Moreover, an efficient summation method for the integral kernels and special treatment of the integrals V ± having logarithmic singularities (30,31) ensured O(N −3 )-accuracy of the IESMP for smooth profiles. The summation method consists in a power series representation of the kernel functions by a polynomial approximation of the coefficients to the fifth order (31, Appendix A).…”

“…3.2 and hence, is a modification of the 'single equation integral method' IEM. Furthermore, it uses an adapted Nyström collocation method with piecewise constant basis functions for solving the integral equations over the profile, which is a robust and universal technique and can be given parametrised as shown in (30). Hence, overhanging profiles are allowed and a uniform discretisation along the arc length of the profile is possible.…”

“…The algorithm and method (29)(30)(31)54), implemented from 1984 to 1986, is the first boundary integral method using a parametrisation of the grating profile from the beginning, whereas the IEM described in Sect. 3.2 started with a discretisation along the x-axis and a parametrisation was implemented later (47).…”

Space applications: monolithic diffraction grating elements from EUV to NIR spectral range

“…The method used Rigorous Coupled Wave Analysis (RCWA) [1] that is acknowledged as well suited technique to simulate spectra or diffraction responses. The approximation of simulated efficiencies and polarization properties will be aligned with already manufactured grating profiles to achieve high conformity between theoretical simulation and manufactured profiles while analyzing their efficiency and polarization sensitivity (See Fig.…”

Using advanced simulation to aid microlithography development

“…Lastly, the integral equation method was used by Kleemann to simulate light scattering from 2-D wafer topography [70]. Yeung used a periodic fast multipole method to model scattering from 3-D wafer topography [71].…”