Cover -- Half Title -- Title -- Copyrights -- Contents -- Introduction -- Chapter 1. The Fourier modal method and its use in plasmonics and the theory of resonant diffraction gratings -- 1.1. The Fourier modal method of solving the diffraction problems -- 1.1.1. The equation of a plane wave -- 1.1.2. The Fourier modal method for two-dimensional periodic structures -- 1.1.2.1. The geometry of the structure and formulation of the problem -- 1.1.2.2. Description of the field above and below the structure -- 1.1.2.3. The system of differential equations for the description of the field in the layer -- 1.1.2.4. Representation of the field inside the layer -- 1.1.2.5. 'Stitching' of the electromagnetic field at the boundaries of layers -- 1.1.2.6. The scattering matrix algorithm -- 1.1.2.7. Calculation of the field distribution -- 1.1.2.8. Intensities of the diffraction orders -- 1.1.2.9. Numerical example -- 1.1.3. The Fourier modal method for three-dimensional periodic structures -- 1.1.4. The Fourier modal method for two-dimensional nonperiodic structures -- 1.1.4.1. The geometry of the structure and formulation of the problem -- 1.1.4.2. Perfectly matched absorbing layers -- 1.1.4.3. Solution of the diffraction problem -- 1.1.4.4 The energy characteristics of the reflected and transmitted light -- 1.1.4.5. Numerical example -- 1.2. Methods for calculating eigenmodes of periodic diffractive structures -- 1.2.1. Calculation of modes based on the calculation of the poles of the scattering matrix -- 1.2.1.1. Resonant representation of the scattering matrix -- 1.2.1.2. Calculation of the poles of the scattering matrix -- 1.2.1.3. Numerical examples -- 1.2.2. Calculation of events based on calculating eigenvalues of the transfer matrix -- 1.2.2.1. Calculation of modes