Laser Beam Shaping, 2nd Edition

2	Mathematical and Physical Theory of Lossless Beam Shaping
Louis A. Romero and Fred M. Dickey

CONTENTS

2.1    Introduction

2.2    Mathematical Preliminaries

2.2.1    Basic Fourier Analysis

2.2.2    The Uncertainty Principle and the Space Bandwidth Product

2.2.3    Separation of Variables in Cylindrical Coordinates

2.2.4    Hankel Transforms

2.3    Method of Stationary Phase

2.3.1    Basic Idea of Stationary Phase

2.3.2    Rate of Convergence of the Method of Stationary Phase

2.3.3    A Preliminary Transformation

2.3.4    Generalized Functions

2.3.5    Higher Order Terms in the Method of Stationary Phase

2.3.6    Lower Order Discontinuities in the Phase Functions

2.3.7    Method of Stationary Phase in Higher Dimensions

2.4    Maxwell’s ...