Bragg reflection blue phase

Another way to identify the dominant contributions of the order parameter for a particular line, is to experimentally determine the reflecting Mueller matrix of the Bragg-reflecting blue phase. The polarizations of light incident and scattered from a surface can be described by four-component Stokes vectors. The matrix which transforms one to the other (and describes the blue phase) is a 4 x 4 Mueller matrix. By analyzing the reflected Stokes vectors for a range of incident Stokes vectors, the complete Mueller matrix can be determined. The result of such measurements [61], [62] was that the e 2 coefficient completely dominates the other coefficients, which rules out certain space groups. 

Note 2 The name blue phase derives historically from the optical Bragg reflection of blue light but, because of larger lattice constants, BPs can reflect visible light of longer wavelengths. 

The reflection from cholesteric and blue phases is Bragg-type scattering, similar to the diffraction of X-rays by crystals. The wave vector of the incident light Ko, the wave vector of the scattered light Kg, and the wave vector of the dielectric constant component q must satisfy the Bragg condition ... 

As discussed in the above section, blue phases allow Bragg reflection of visible Ught Therefore the transmittance is less than 100%. The precise treatments of the optics of blue phases are complex and are given by Belyakov, Dmitrienko, Homreich, et al. [32-35]. Here we only give some qualitative discussions, mainly for the purpose of understanding blue phase display based on electric field induced birefringence. 

J. Yan, Z. Luo, S.T. Wu, et al.. Low voltage and high contrast blue phase liquid crystal with red-shifted Bragg reflection, Appl. Phys. Lett. 102, 011113 (2013). 

The blue phases of types BPI and BPn are modeled as regular networks of disclination lines with periodicity of order p. Indeed, the three-dimensional periodic structure of these phases is revealed in their nonzero shear moduli, their ability to grow well-faceted monocrystals and Bragg reflection in the visible part of the spectrum (which is natural since p is of the order of a few tenths of a micron). The third identified phase, BPIH, that normally occurs between the isotropic melt and BPII, is less understood. It might be a melted array of disclinations. Note that although most blue phases have been observed in thermotropic systems, double-twist geometries are relatively frequently met in textures of biological polymers, like DNA. 

Like BPI and BPII, BPIII selectively reflects circularly polarized light [52], [53]. Unlike the cubic blue phases, however, the spectrum is quite broad ( 100 nm) [132]. Also, while BPI and BPII exhibit several Bragg peaks (corresponding to various crystal planes), BPIII exhibits only one peak. 

An external electric field interacts with the local dielectric anisotropy of a blue phase and contributes e E /An to the energy of the liquid crystal [45]. The field distorts the cubic lattice and results in a change in the angular (or spectral) positions of Bragg s reflections. Moreover, field-induced phase transitions to novel phases have been observed [42, 46, 47]. The field can also induce birefringence parallel to the field direction, due to the optical biaxiality of the distorted cubic lattice [48]. 

Due to the giant periodic stmcture discussed above, the blue phase exhibits Bragg diffraction in the ultraviolet-to-visible range. Blue phase I mainly exhibits diffraction from the (110), (200), to (211) planes, and blue phase 2 shows diffraction from the (100) to (110) planes. Hence, there are several reflection peaks, which is not the case with the chiral nematic phase. Typically, the diffractions from the (110) and (200) planes in blue phase 1 and from the (100) plane in blue phase II are in the blue region, which is the origin of the name blue phase. ... 

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