ABSTRACT

In this chapter, we present an overview of the diffraction of visible light and x-rays in opal-like structures. Special attention will be paid to the transformation of diffraction patterns on building up the opal structure from a two-dimensional (2D) single layer of silica  particles a-SiO2 toward a bulk three-dimensional (3D) opal structure as well as to the  effects  of disorder such as stacking faults. The consideration here will be limited

CONTENTS

3.6.1 Introduction ....................................................................................................................... 275 3.6.2 Two-Dimensional Optical Diffraction from Thin Opal Films ...................................280 3.6.3 Two-Dimensional to Three-Dimensional Transition in Optical Diffraction ............284 3.6.4 Three-Dimensional Optical Diffraction and Selective Switching of Diffraction Reƒections .................................................................................................285 3.6.5 Sample Thickness Dependence in Small-Angle X-Ray Diffraction ........................... 289 3.6.6 Order and Disorder from Microradian X-Ray Diffraction .......................................... 291 3.6.7 How X-Ray Diffraction Can Serve the Technology of Opal Growth ........................ 294 3.6.8 Three-Dimensional Reciprocal Space Reconstruction ................................................ 296 3.6.9 Conclusions ........................................................................................................................ 297 Acknowledgments ...................................................................................................................... 298 References ..................................................................................................................................... 298

to structures with low permittivity contrast Δε. For small-angle x-ray diffraction, this condition is automatically fullled for all materials: Δε ~ 10−5−10−6. For optical studies, such a situation can be realized for different opal-based structures by lling the voids of the structure with a medium having nearly matching ε. An enhancement of Δε can lead to broadening of the Bragg reƒections and a modication of the relative intensity of different Bragg reƒections as well as to signicant extinction of the incident wave (see Chapter 3.7), which are not considered here. A different approach considering the full set of Maxwell equations to calculate the electromagnetic eigenmodes and photonic band structure is unavoidable for high Δε, especially if one moves toward the full band-gap materials. This approach is considered in Chapter 3.7 in detail, whereas in this chapter the case of high dielectric contrast is left out.