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Eli Yablonovitch proposed using a three-dimensional periodic dielectric to inhibit spontaneous emission. If an electronic transition lies inside a complete photonic band gap, the surrounding material supplies no propagating electromagnetic modes at that frequency. The proposal therefore treats spontaneous emission as a process controlled by both the emitter and its electromagnetic environment. It motivated engineering photonic crystals to control light and to reduce unwanted radiative processes; a complete gap is a stronger condition than blocking propagation in only one direction.^[ref]

Photonic structures control light through the spatial arrangement of dielectric material. Waveguides confine transverse modes; periodic photonic crystals combine interference and scattering to produce a photonic band structure ${\omega }_n(\mathbf{k})$. A photonic band gap excludes propagating modes in specified directions and polarizations. A one-dimensional stop band is not automatically a complete three-dimensional gap.

A simple example is a distributed Bragg reflector with alternating high- and low-index layers. At normal incidence, the quarter-wave choicelets successive interface reflections reinforce near the design wavelength. A departure from periodicity can create a localized defect mode inside the stop band. An isolated defect forms a cavity; a line defect can guide light through otherwise forbidden bulk propagation. Finite structures leak and real materials absorb, so ideal band arguments do not ensure infinite confinement.

Changing the photonic density of states can suppress or enhance spontaneous emission and control how emitters couple to selected modes. This is distinct from electronic band-gap engineering: it is the electromagnetic modes that are being structured. A complete electromagnetic gap overlapping an emitter's transition is the ideal mechanism proposed for suppressing otherwise allowed spontaneous emission.^[ref]

A photonic crystal has a spatially periodic dielectric response on the scale of the optical wavelength. For a nonmagnetic, lossless, nondispersive dielectric, the source-free Maxwell equations can be written as the eigenproblemThe Bloch theorem gives ${\mathbf{H}}_{n\mathbf{k}}=e^{i\mathbf{k}\cdot \mathbf{r}}{\mathbf{u}}_{n\mathbf{k}}(\mathbf{r})$ with periodic $\mathbf{u}$. The allowed frequencies form photonic band structures. Coupling of counterpropagating waves near a Brillouin zone boundary opens a stop band. A one-dimensional dielectric multilayer is a simple example; two-dimensional hole arrays and three-dimensional dielectric networks allow more extensive control.

A complete photonic band gap excludes bulk propagating modes for every direction and polarization in a frequency interval. Periodicity alone does not guarantee such a gap: dimensionality, symmetry and refractive-index contrast matter. A missing or altered element can support a localized defect state in the gap, making a cavity; a line defect can guide light. Finite crystals have leakage and wavelength-dependent transmission rather than an infinitely sharp exclusion. Applications include selective mirrors, optical filters, small resonators and integrated waveguides.^[ref]

A designed spatial arrangement of dielectric or other electromagnetic material controls optical propagation, confinement or emission. Examples include waveguides, distributed Bragg reflectors, photonic crystals and defect cavities. Spatial interference and mode boundary conditions act on electromagnetic states; they are distinct from the electronic band structure of the material itself.

A researcher and teacher whose work connects electromagnetic waves with mathematical and computational methods. His MIT course treats optical structures whose dimensions are comparable to a wavelength, using eigenvalue problems and Bloch's theorem to explain photonic crystals. Periodic changes in a material can exclude a range of optical frequencies, while a defect can localize light; this gives a physical reason to study both periodic structures and their imperfections.^[ref]