Introduction to Matrix Methods in Optics

PREFACE CHAPTER I Introduction to matrix calculations I.1 Introductory discussion I.2 Matrix multiplication I.3 Null matrices I.4 Unit matrices I.5 Diagonal matrices I.6 Multiple products I.7 Matrix addition and subtraction I.8 Transpose matrices I.9 Determinants I.10 Division of matrices and matrix inversion I.11 Matrix diagonlaization I.12 Eigenvalues and eignevectors of a 2 × 2 unimodular matrix CHAPTER II Matrix methods in paraxial optics II.1 Introductory discussion II.2 Ray-transfer matrices II.3 The translation matrix T II.4 The refraction matrix R II.5 The ray-transfer matrix for a system II.6 Derivation of properties of a system from its matrix II.7 Illustrative problems II.8 Experimental determination of the matrix elements of an optical system II.9 Locating the cardinal points of a system II.10 Further problems II.11 Extension of ray-transfer method to reflecting systems CHAPTER III Optical resonators and laser beam propagation III.1 Review of results obtained for paraxial imaging systems III.2 Description of wave propagation in terms of geometrical optics III.3 "Resolving power, étendue and the space-bandwidth product" III.4 Marix representation of an optical resonator III.5 The distinction between stable and unstable resonators III.6 Propagation of a Gaussian beam and its complex cruvature parameter III.7 Predicting the output of a laser oscillator III.8 Application of the ABCD rule to mode-matching problems III.9 Ray-transfer matrices for distributed lens-like media III.10 Illustrative problems CHAPTER IV Matrices in polarization optics IV.1 Polarized light - its production and analysis IV.2 The Stokes parameters for specifying polarization IV.3 Use of the Mueller calulus for transforming a Stokes column IV.4 Experimental determination of the elements of a Mueller matrix or a Stokes column IV.5 Use of the Jones calculus for transforming a Maxwell column IV.6 Experimental determination of the elements of a Jones matrix or a Maxwell column IV.7 Illustrative problems soled by Mueller calculus and by Jones calculus CHAPTER V Propagation of light through crystals V.1 Introductory discussion V.2 Expression of vector operations in matrx form V.3 Dielectric properties of an anisotropic medium V.4 Propagation of plane waves in a uniaxial crystal V.5 Huygens wavelets in a uniaxial crystal APPENDIXES A Aperature properties of centred lens systems B Matrix representation of centring and squaring errors C Statistical derivation of the Stokes parameters D Derivation of Mueller matrices E Derivation of Jones matrices F Connection between Jones and Mueller calculi BIBLIOGRAPHY AND CONCLUSION INDEX