Introduction to Holography, 2nd Edition

1 Light Waves and Rays

DOI: 10.1201/9781003155416-2

1.1 Introduction

We need a clear and thorough understanding of the nature of light in order to control and use it in holography and its applications.

1.2 Description of Light Waves

James Clerk Maxwell discovered that light consists of electromagnetic waves by manipulating the four equations which bear his name and describe the behaviour of the electric field, E, and the magnetic field, H.

The four equations are

(1.1)$$\nabla \times \mathit{E}\left(={\displaystyle \frac{\partial E_z}{\partial y}}-{\displaystyle \frac{\partial E_y}{\partial z}},{\displaystyle \frac{\partial E_x}{\partial z}}-{\displaystyle \frac{\partial E_z}{\partial x}},{\displaystyle \frac{\partial E_y}{\partial x}}-{\displaystyle \frac{\partial E_x}{\partial y}}\right)=-{\mu }_0{\mu }_r{\displaystyle \frac{\partial \mathit{H}}{\partial t}}$$

(1.2)$$\nabla \times \mathit{H}={\epsilon }_0{\epsilon }_r{\displaystyle \frac{\partial E}{\partial t}}+\sigma \mathit{E}$$

(1.3)$$\begin{array}{l}\nabla ·\mathit{D}={\displaystyle \frac{\partial E_x}{\partial x}}+{\displaystyle \frac{\partial E_y}{\partial y}}+{\displaystyle \frac{\partial E_z}{\partial z}}=0\\ \left(\mathrm{assuming}\mathrm{no}\mathrm{volume}\mathrm{electrical}\mathrm{charges}\right)\end{array}$$

(1.4)$$\nabla \cdot \mathit{H}=0$$

where μ_r is the relative permeability with a value of 1 in a non-magnetic medium, μ₀ is the permeability of a vacuum, ε₀ its permittivity, ...