  Coupled states of semiconductor quantum well (QW) excitons and photons in a
two dimensional (2D) periodic lattice of microcavities are analyzed
theoretically, revealing allowed bands and forbidden gaps in the energy
spectrum of exciton polaritons. Photonic crystal exciton polaritons have
spatially uniform excitonic constituent set by flat QWs, but exhibit periodic
Bloch oscillations in the plane of QWs due to their photonic component. The
envelope functions of photonic crystal exciton polaritons can be tailored via
effective potential of a photonic crystal heterostructure, by using
quasi-periodic lattices of microcavities. Confined envelope function states of
lower and upper polaritons and the Bose-Einstein condensation of lower
polaritons are analyzed here in a photonic crystal heterostructure trap with
harmonic oscillator potential. This concept is numerically illustrated on
example of CdTe/CdMgTe microcavities.
