A Tutorial Introduction

This chapter is especially devoted to beginners, that is to say to those who are perhaps experienced in optics but who are not specialists in microwave theory. We first derive the well-known grating formula from Maxwell equations and the associated boundary conditions. Then we give an idea of the different methods which can be used to predict theoretically the efficiencies of a grating, when the groove shape and the index of the material are known.

[1]  Lord Rayleigh,et al.  On the Dynamical Theory of Gratings , 1907 .

[2]  U. Fano,et al.  The Theory of Anomalous Diffraction Gratings and of Quasi-Stationary Waves on Metallic Surfaces (Sommerfeld’s Waves) , 1941 .

[3]  B. A. Lippmann,et al.  Note on the Theory of Gratings , 1953 .

[4]  William C. Meecham,et al.  Variational Method for the Calculation of the Distribution of Energy Reflected from a Periodic Surface. I. , 1956 .

[5]  A. Hadni,et al.  Polarisation de la lumire par les rseaux chelettes dans l'infrarouge lointain , 1963 .

[6]  W. F. Trench.  An Algorithm for the Inversion of Finite Toeplitz Matrices , 1964 .

[7]  R. Petit,et al.  Quelques Propriétés des Réseaux Métalliques , 1967 .

[8]  Armand Wirgin,et al.  Theoretical and Experimental Investigation of a New Type of Blazed Grating , 1969 .

[9]  R. F. Millar.  On the Rayleigh assumption in scattering by a periodic surface. II , 1969, Mathematical Proceedings of the Cambridge Philosophical Society.

[10]  J.-F. Bousquet,et al.  Diffraction par un Rseau Conducteur Nouvelle Mthode de Rsolution , 1970 .

[11]  M. Nevière,et al.  Sur la validite du developpement de Rayleigh , 1970 .

[12]  R. F. Millar.  Singularities of two-dimensional exterior solutions of the Helmholtz equation , 1971, Mathematical Proceedings of the Cambridge Philosophical Society.

[13]  R. Petit,et al.  Diffraction par un reseau lamellaire infiniment conducteur , 1972 .

[14]  S. Šesnić,et al.  Diffraction of a Parallel- and Perpendicular-Polarized Wave from an Echelette Grating* , 1972 .

[15]  R. Petit,et al.  Applications of conformal mappings to the diffraction of electromagnetic waves by a grating , 1973 .

[16]  G. Jiracek.  Numerical comparisons of a modified rayleigh approach with other rough surface EM scattering solutions , 1973 .

[17]  R. Petit,et al.  Diffraction par un reseau lamellaire infinement conducteur en presence de dioptres paralleles aux lamelles , 1973 .

[18]  H. Ikuno,et al.  Improved point-matching method with application to scattering from a periodic surface , 1973 .

[19]  R. F. Millar.  The Rayleigh hypothesis and a related least‐squares solution to scattering problems for periodic surfaces and other scatterers , 1973 .

[20]  H. Akaike.  Block Toeplitz Matrix Inversion , 1973 .

[21]  Scattering from a sinusoid: derivation of linear equations for the field amplitudes , 1974 .

[22]  M. Nevière,et al.  Sur Une Propriété de Symétrie des Réseaux Diélectriques , 1976 .

[23]  H. Kalhor,et al.  Numerical evaluation of Rayleigh hypothesis for analyzing scattering from corrugated gratings--TE polarization , 1976 .

[24]  D. Marcuse,et al.  Exact theory of te-wave scattering from blazed dielectric gratings , 1976, The Bell System Technical Journal.

[25]  R. Petit,et al.  A numerical study of the problem of diffraction at a non-periodic obstacle , 1977 .

[26]  Reciprocity identity for periodic surface scattering , 1979 .

[27]  A Basu,et al.  Random fluctuations in first-order waveguide grating filters. , 1979, Applied optics.

[28]  Power losses in lamellar gratings. , 1979, Applied optics.

[29]  T. Harada,et al.  Diffraction Gratings in Japan , 1979 .

[30]  Arthur K. Jordan,et al.  Electromagnetic scattering patterns from sinusoidal surfaces , 1979 .

[31]  D. Maystre,et al.  A new theoretical method for diffraction gratings and its numerical application , 1980 .

[32]  Thomas K. Gaylord,et al.  Bragg diffraction of finite beams by thick gratings , 1980 .

[33]  J. Kong,et al.  Diffraction of optical beams with arbitrary profiles by a periodically modulated layer , 1980 .

[34]  Katsunori Shimohara,et al.  Numerical analysis of a thin-film waveguide by mode-matching method , 1980 .

[35]  H. Kalhor.  EM scattering by an array of perfectly conducting strips by a physical optics approximation , 1980 .

[36]  General Modal Theory of Scalar Wave Scattering by Periodic Surfaces , 1980 .

[37]  D. Maystre,et al.  A phenomenological theory for gratings: Perfect blazing for polarized light in nonzero deviation mounting , 1981 .

[38]  R. Petit,et al.  Plane-wave expansions used to describe the field diffracted by a grating , 1981 .