**1. Introduction**

Impressive diffraction phenomena can be found in animate and inanimate nature: in the form of iridescence in birds, insects, shells, plants or muscle cells as well as in clouds and minerals. The fascination emanating from phenomena where light interacts with micro‐ and nano‐ structures may be traced back to the principle *from structure to function*, which is not limited to optical phenomena, but can be found in nature as a fundamental quality. In case of holog‐ raphy, light itself is capable to create the structures with which it subsequently interacts. The (optical) functionality of a holographic structure consists in its diffractive properties.

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In turn, the principle *from structure to function* also comprises the possibility to under‐ stand function through structure. Taking advantage of this relation between structure and function culminates in the attempt of mimicking nature. Notable examples are functional surfaces with hierarchical structures based on the lotus effect to induce superhydropho‐ bicity, the gecko effect for controlled adhesion or the moth's eye effect for anti‐reflection coatings.

While the examples mentioned above remain limited to surface phenomena, the third dimen‐ sion opens up entirely new possibilities with major relevance for many applications. Structures with a periodic modulation of the refractive index are of interest wherever light must be manipulated. Volume holographic gratings can be considered as such three‐dimensional (3D) optical structures with diffractive properties.

Volume gratings made by nature can be found in the form of crystals wherever atoms are regularly arranged [1]. The dimensions of atomic and molecular structures usually result in interaction rather with a non‐visible range of the electromagnetic spectrum, enabling access by means of X‐ray crystallography. However, light‐based photonic crystals (PCs), with func‐ tionality in the visible range, can be created artificially [2].

While holography allows three‐dimensional imaging, the holographic structure itself extends not necessarily in three dimensions. Depending on the hologram formation tech‐ nique as well as on the recording medium, the hologram itself takes shape as a surface pat‐ tern or rather emerges as a three‐dimensional structure. A volume hologram or photonic crystal may only be formed if recording technique and recording medium allow modifica‐ tion of the optical properties in all three dimensions. The performance of such a grating with thickness in the range of 100 μm differ significantly from thin gratings or surface gratings: Volume Bragg gratings stand out due to their high diffraction efficiency, rigorous wavelength selectivity and the ability that multiple holograms may be superimposed by means of multiplexing.

There are many ways to create optical surface patterns by photolithography, self‐assem‐ bly or other nano‐ and microfabrication methods with both, bottom‐up and top‐down approaches. However, entering the third dimension in optical structuring is accompanied with considerable challenges. Among existing techniques for three‐dimensional optical structuring, such as direct laser writing [3] or self‐assembly [4], volume holography pro‐ vides the unique possibilities to create optical structures through the entire volume beyond a point‐by‐point, line‐by‐line or plane‐by‐plane fabrication, with high resolution and accu‐ racy in a single step.

At the same time, the analysis of volume holographic structures emerges as a challenging task. Optical structures inside a volume may not readily be mapped by means of common microscopic methods [5]. This is where the mutuality of function and structure opens up new possibilities. In fact, the diffraction efficiency represents the only accessible parameter to entirely characterize a volume grating. Based on the optical functionality, conclusions may be drawn on grating parameters as well as on material parameters such as material response and energetic sensitivity.

Within this chapter, the interrelation between material compositions, analytical methods and advanced applications for volume holographic systems is investigated with particular emphasis on analytical methods. According to the leading idea of a correlation between function and structure, the deeper understanding of volume holographic grating formation appears prerequisite to design novel material systems for advanced applications.
