25.1 INTRODUCTION

Being able to produce and to analyze a general polarization of an electromagnetic wave has long benefited scientists and researchers in the field of visible light optics, as well as those engaged in studying the optical properties of condensed matter.1 3 In the X-ray regime, however, such abilities have been very limited because of the weak interaction of X rays with materials, especially for production and analysis of circularly polarized X-ray beams. The situation has changed significantly in recent years. The growing interest in studying magnetic and anisotropic electronic materials by X-ray scattering and spectroscopic techniques has initiated many new developments in both the production and the analysis of specially polarized X rays. Routinely available, high-brightness synchrotron radiation sources can now provide naturally collimated X rays that can be easily manipulated by special X-ray optics to generate energytunable as well as polarization-tunable X-ray beams. The recent developments in X-ray phase retarders and multiple-Bragg-beam interference have allowed complete analyses of general elliptical polarization of X rays from special optics and special insertion devices. In this article, we will review these recent advances, especially in the area of the production and detection of circular polarization.

As for any electromagnetic wave,1 3 a general X-ray beam defined by

can be linearly polarized if ?=0 or 180 , circularly polarized if ?= 90 and E _?= E _?, and...