  An overview is provided over the physics of dielectric microcavities with
non-paraxial mode structure; examples are microdroplets and edge-emitting
semiconductor microlasers. Particular attention is given to cavities in which
two spatial degrees of freedom are coupled via the boundary geometry. This
generally necessitates numerical computations to obtain the electromagnetic
cavity fields, and hence intuitive understanding becomes difficult. However, as
in paraxial optics, the ray picture shows explanatory and predictive strength
that can guide the design of microcavities. To understand the ray-wave
connection in such asymmetric resonant cavities, methods from chaotic dynamics
are required.
