This paper gives an overview of recent work on three-dimensional (3D)
photonic crystals with a "full and complete" 3D photonic band gap. We review
five main aspects: 1) spontaneous emission inhibition, 2) spatial localization
of light within a tiny nanoscale volume (aka "a nanobox for light"), 3) the
introduction of a gain medium leading to thresholdless lasers, 4) breaking of
the weak-coupling approximation of cavity QED, both in the frequency and in the
time-domain, 5) decoherence, in particular the shielding of vacuum fluctuations
by a 3D photonic bandgap. In addition, we list and evaluate all known photonic
crystal structures with a demonstrated 3D band gap.Comment: 21 pages, 6 figures, 2 tables, Chapter 8 in "Light Localisation and
Lasing: Random and Pseudorandom Photonic Structures", Eds. M. Ghulinyan and
L. Pavesi (Cambridge University Press, Cambridge, 2015, ISBN
978-1-107-03877-6
