Many highly chiral liquid crystals exhibit intricate orientationally ordered structures referred to as cholesteric blue phases (BPs) . They are made up of arrays of disclination lines and double-twist cylinders. They have intrigued scientists as an interesting class of frustration-induced order, and are attracting growing attention because of their potential for next-generation fast-switching displays.
Fukuda was interested in what kind of structures would be formed when a highly chiral liquid crystal exhibiting BPs was confined in a very thin cell whose thickness is of the order of or smaller than the unit cell dimension of bulk BPs. With the aid of numerical calculations based on a Landau-de Gennes theory that describes the orientational order by a second-rank tensor, he found various exotic structures not found in bulk BPs, or any other liquid crystalline systems ever studied [3,4,5]. The stability of these structures depends on temperature, cell thickness, and anchoring condition at the confining surfaces. In the case of strong normal anchoring, the structures he found include a parallel array of winding disclination lines of double-helix form , parallel arrays of undulating disclination lines , inchworm-like fragmented disclination lines at the confining surfaces , and a hexagonal lattice of Skyrmion excitations . When the confining surfaces impose strong planar anchoring and the cell thickness is incommensurate with the intrinsic pitch of the twist in the liquid crystal, he showed that a regular array of ring disclinations with centered-rectangular symmetry forms . Recently, He is also investigating the optical properties of these exotic structures by solving the Maxwell equations directly using plane-wave expansions , envisaging stimulation of experimental studies towards the demonstration of these exotic structures, together with design of novel photonic materials based on blue phases. His work is a clear demonstration of novel frustration-induced order in soft materials having analogy with those in different condensed matter systems, and these exotic structures are a manifestation that liquid crystals can exhibit much more interesting ordered structures than one already knows or can imagine.
He also showed with Miha Ravnik that the trapping potential of spherical colloidal particles in such structures sensitively depends on the particle radius. In the cases where the cell thickness is of the order of or larger than the unit cell dimension of bulk BPs, he demonstrated that the force between confining surfaces mediated by the liquid crystal is oscillatory, indicating the discreteness of the orientational structures the liquid crystal adopts .
He also discussed the thermodynamic stability of cholesteric blue phases with a polymer network . A simple argument based on the numerical order parameter profiles of cholesteric blue phases revealed  that the replacement of defect cores by the polymer network well accounts for the stabilization of blue phases, and that the temperature range of stable blue phases can be 60K or even more, in agreement with experimental demonstrations . Furthermore, by extending a simple analytical argument of Meiboom et al., he discussed the effect of the variation of Frank elastic constants on the stability of cholesteric blue phases. He showed that smaller K33 drastically widens the stability range of blue phases , again in agreement with recent experiments .
The present work concerning the structures of cholesteric blue phases under confinement was carried out with Slobodan Žumer who financially supported his stay in Univ. of Ljubljana, Slovenia. The present work was supported also by Grants-in-Aid for Scientific Research (KAKENHI) from the Ministry of Education, Culture, Sports, Science and Technology of Japan and the Japan Society for Promotion of Science (JSPS). Fukuda is also seeking the possibility of collaborations with Hirotsugu Kikuchi (Kyushu University), and Liang-Chy Chien (Liquid Crystal Institute, Kent State University).