Page 1

Introduction: Generation of Wavefields using Diffractive Optical Elements (DOEs)

I.1 Phase DOEs

A brief explanation is given here of the major concepts that are employed and detailed in the subsequent chapters.

Phase DOEs are the diffractive elements designed for implementing the required transformations of the light field without the loss of light energy, which means that the action of the phase DOE is limited to the modulation of the phase of incident light. Throughout this book, light is considered in terms of the scalar theory of diffraction, is perceived as being monochromatic and absolutely coherent, and is described by the complex function of one or two spatial variables. The module of this complex function is said to be the amplitude of the light field, and the argument is called the phase.

The propagation of light in free space can be described using the Kirchhoff diffraction approximation, and a mathematical aspect of light propagation through optical elements (lenses and DOEs) reduces to the multiplication of the complex function of incident light by the complex transmittance of an optical element.

Phase DOEs represent either a flat surface with microrelief (see Fig. I.1a) or a plane-parallel plate transparent for the light used and having a surface relief (see Fig. I.1b).

The term ‘calculation of a DOE’ is used to mean ‘calculation of the phase function of a DOE’. Strictly speaking, the methods for iteratively calculating the phase function are the main subject of discussion in this book. The result of calculation is the function of two variables φ(u, v) that have the meaning of DOE phase. An analytical formula for φ(u, v) determines an optical surface that would theoretically be fabricated by conventional optical