PHYSICAL REVIEW E 90, 042504 (2014) Optics of short-pitch deformed-helix ferroelectric liquid crystals: Symmetries, exceptional points, and polarization-resolved angular patterns Alexei D. Kiselev 1, 2, * and Vladimir G. Chigrinov 1 , † 1 Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong 2 Institute of Physics of National Academy of Sciences of Ukraine, prospekt Nauki 46, 03680 Kiev, Ukraine (Received 13 July 2014; published 24 October 2014) In order to explore electric-field-induced transformations of polarization singularities in the polarization- resolved angular (conoscopic) patterns emerging after deformed-helix ferroelectric liquid crystal (DHFLC) cells with subwavelength helix pitch, we combine the transfer matrix formalism with the results for the effective dielectric tensor of biaxial FLCs evaluated using an improved technique of averaging over distorted helical structures. Within the framework of the transfer matrix method, we deduce a number of symmetry relations and show that the symmetry axis of L lines (curves of linear polarization) is directed along the major in-plane optical axis which rotates under the action of the electric field. When the angle between this axis and the polarization plane of incident linearly polarized light is above its critical value, the C points (points of circular polarization) appear in the form of symmetrically arranged chains of densely packed star-monstar pairs. We also emphasize the role of phase singularities of a different kind and discuss the enhanced electro-optic response of DHFLCs near the exceptional point where the condition of zero-field isotropy is fulfilled. DOI: 10.1103/PhysRevE.90.042504 PACS number(s): 61.30.Gd, 78.20.Jq, 77.84.Nh, 42.70.Df I. INTRODUCTION Over the last more than three decades, ferroelectric liq- uid crystals (FLCs) have attracted considerable attention as promising chiral liquid crystal materials for applications in fast switching display devices (a detailed description of FLCs can be found, e.g., in monographs [1,2]). Equilibrium orientational structures in FLCs are represented by helical twisting patterns where FLC molecules align on average along a local unit director ˆ d = cos θ ˆ h + sin θ ˆ c, (1) where θ is the smectic tilt angle, ˆ h is the twisting axis normal to the smectic layers, and ˆ c ⊥ ˆ h is the c director. The FLC director (1) lies on the smectic cone depicted in Fig. 1(a) with the smectic tilt angle θ and rotates in a helical fashion about a uniform twisting axis ˆ h forming the FLC helix with the helix pitch P . This rotation is described by the azimuthal angle around the cone  that specifies orientation of the c director in the plane perpendicular to ˆ h and depends on the dimensionless coordinate along the twisting axis φ = 2π ( ˆ h · r)/P = qx, (2) where q = 2π/P is the helix twist wave number. The important case of a uniform lying FLC helix in the slab geometry with the smectic layers normal to the substrates and ˆ h = ˆ x, ˆ c = cos  ˆ y + sin  ˆ z, E = E ˆ z, (3) where E is the electric field applied across the cell, is illustrated in Fig. 1. This is the geometry of surface stabilized FLCs (SSFLCs) pioneered by Clark and Lagerwall in Ref. [3]. They studied electro-optic response of FLC cells confined between two parallel plates subject to homogeneous boundary * kiselev@iop.kiev.ua † eechigr@ust.hk conditions and made thin enough to suppress the bulk FLC helix. It was found that such cells exhibit high-speed, bistable electro-optical switching between orientational states stabi- lized by surface interactions. The response of FLCs to an applied electric field E is characterized by fast switching times due to linear coupling between the field and the spontaneous ferroelectric polarization P s = P s ˆ p, ˆ p = ˆ h × ˆ c = cos  ˆ z − sin  ˆ y, (4) where ˆ p is the polarization unit vector. There is also a threshold voltage necessary for switching to occur and the process of bistable switching is typically accompanied by a hysteresis. Figure 1(b) also describes the geometry of deformed-helix FLCs (DHFLCs) as it was introduced in Ref. [4]. This case will be of our primary concern. In DHFLC cells, the FLC helix is characterized by a short submicron helix pitch P< 1 μm, and a relatively large tilt angle θ> 30 ◦ . By contrast to SSFLC cells, where the surface induced unwinding of the bulk helix requires the helix pitch of a FLC mixture to be greater than the cell thickness, a DHFLC helix pitch is 5–10 times smaller than the thickness. This allows the helix to be retained within the cell boundaries. Electro-optical response of DHFLC cells exhibits a number of peculiarities that make them useful for LC devices such as high-speed spatial light modulators [5–9], color-sequential liquid crystal display cells [10], and optic fiber sensors [11]. The effects caused by electric-field-induced distortions of the helical structure underline the mode of operation of such cells. In a typical experimental setup, these effects are probed by performing measurements of the transmittance of normally incident linearly polarized light through a cell placed between crossed polarizers. A more general case of oblique incidence has not received a fair amount of attention. Theoretically, a powerful tool to deal with this case is the transfer matrix method which has been widely used in studies of both quantum mechanical and 1539-3755/2014/90(4)/042504(19) 042504-1 ©2014 American Physical Society