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Mathematical Optics by Vasudevan Lakshminarayanan, María L. Calvo, Tatiana Alieva

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10

Paraxial Wave Equation

Lie-Algebra-Based Approach

Amalia Torre

CONTENTS

10.1    Introduction

10.2    KMB Method: From the Schrödinger to the Paraxial Wave Equation

10.3    2D “linear” Paraxial Wave Equation

10.3.1  Solving the 2D Linear PWE: The KMB Method

10.3.2  Solving the 2D Linear PWE: Symmetries and Solutions

10.3.2.1  Symmetry Algebra and Classes of Wavefunctions

10.3.2.2  Symmetry Algebra/Group and Classes of Symmetry Transformations

10.4    Optical Appell Transformation

10.4.1  Fractional Appell Transformation

10.5    2D “Radial” Paraxial Wave Equation

10.5.1  Solving the 2D Radial PWE: Symmetries and Solutions

10.5.1.1  Symmetry Algebra and Classes of Radial Wavefunctions

10.5.1.2  Symmetry Algebra/Group and Classes of Symmetry ...

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