Cholesteric blue phases: effect of strong confinement

After an overview of cholesteric blue phases, we review our recent numerical studies on possible defect structures when blue phase I (BP I) is confined in a thin cell composed of two parallel surfaces imposing homeotropic anchoring. The cell thickness is of the order of the unit cell dimension of the bulk cubic BP I. We find several structures of disclination lines which, to our knowledge, have never been discussed in the field of liquid crystals as equilibrium structures. Those structures include a parallel array of double helix disclination lines, and two parallel arrays of undulating disclination lines almost (but not exactly) perpendicular to each other. A first-order transition between those two structures is possible, and the similarity between them is discussed.