Towards r-space Bose-Einstein condensation of photonic crystal exciton   polaritons
  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. 
D. L. Boiko