Mathematical Optics

4	Basis Expansions for Monochromatic Field Propagation in Free Space
Miguel A. Alonso and Nicole J. Moore

CONTENTS

4.1      Introduction

4.2      Bases for Finite-Dimensional Vector Spaces

4.2.1    Orthonormal Bases

4.2.2    Nonorthogonal Bases: Biorthogonal Basis Pairs

4.2.3    Truncation Error

4.2.4    Nonorthogonal Bases: Minimization of the Truncation Error

4.3      Bases for Functions

4.3.1    Continuous Bases

4.3.1.1    Dirac Delta Basis

4.3.1.2    Fourier Transformation

4.3.2    Discrete Orthonormal Bases

4.3.2.1    Hermite–Gaussian Basis

4.3.2.2    Laguerre–Gaussian Bases

4.3.3    Discrete Nonorthonormal Bases

4.3.3.1    Nonorthogonal Combination of Hermite Polynomials and Gaussians

4.3.3.2    Nonorthogonal Combination of Laguerre ...