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Several decades ago, one of the authors of this chapter was grading junior high school exams from a geographic science class taught by his wife, when he was rewarded with a wonderful answer to this seemingly straightforward question: "What is a rock?" The student's answer was 100% correct but not especially informative: "A rock is not a mineral." It is quite difficult to define something by the set of all things it is not. Yet it seems important to state at the beginning that this tutorial is not about holography as most people know it: a means to record and reproduce 3D images. In fact, we explicitly exclude image-forming holograms from the discussion.
This tutorial deals with holograms used as parts of more complex systems as ways of controlling or manipulating properties of that light - its direction, spectrum, polarization, speed of pulse propagation, etc. As there are other light manipulation means available, it will be important to understand when holograms offer advantages and what those advantages may be.
Like all of the materials discussed in this book, holograms are complex structures. Like most of the other complex media discussed, holograms are metamaterials. In electromagnetism (covering areas such as optics and photonics), a metamaterial is a structure that gains its (electromagnetic) material properties from the details of structure itself (and the properties of its components), rather than merely inheriting those properties directly from the materials of which it is composed. This term metamaterial is particularly used when the resulting material has properties not found in naturally formed substances. That is, metamaterials are "designer materials" created to have specific properties that the system or component designer needs.
Holographic metamaterials share one critical property with most other metamaterials: their behavior with respect to electromagnetic waves is related directly to the 3D periodic structure produced. Thus, we are forced to make an embarrassing confession (or boastful claim, depending on how you choose to look at it): most metamaterials are holograms.
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