Comparison of modal and differential methods for multilayer gratings

Modal theory is applied in calculating the lamellar multilayer grating performances. Comparison of numerical results obtained with the differential and modal methods is performed. Both methods give the same values of diffraction order efficiency and are in good agreement with experimental data. Tungsten-carbon multilayer gratings having a 4 μm lamellar period and a 3 nm bilayer spacing for a 0.154 nm wavelength were used as the test object. The diffraction properties of multilayer gratings are discussed using reciprocal space and dispersive surfaces representation. A strong dependence of the multilayer grating properties on the lamellar period and the optical characteristics of multilayer grating materials are shown.