Twist Defect in Chiral Photonic Structures

Abstract

We demonstrate that twisting one part of a chiral photonic structure about its helical axis produces a single circularly polarized localized mode that gives rise to an anomalous crossover in propagation. Up to a crossover thickness, this defect results in a peak in transmission and exponential scaling of the linewidth for a circularly polarized wave with the same handedness as structure. Above the crossover, however, the linewidth saturates and the defect mode can be excited only by the oppositely polarized wave, resulting in a peak in reflection instead of transmission.PACS numbers: 42.70. Qs, 42.70.Df Localized modes produced by regular defects in periodic structures can serve as low threshold lasers [1], low loss waveguides, and narrow band filters in an expanding array of photonic devices [2,3]. When defects are randomly positioned, localized states are produced within the photonic band gap (PBG) by multiple scattering [4,5]. The photon dwell time at resonance with a defect state generally increases exponentially with the structure thickness L. This suppresses the lasing threshold in an active structure without the use of external feedback. In 3D PBGs, thresholdless lasing has been predicted when the band gap exceeds the emission bandwidth since emission can then couple only to the single defect mode [1]. Exceptionally low lasing thresholds have been achieved in vertical cavity surface emitting lasers (VCSELs), in which an amplifying defect layer is sandwiched between stacks of layers with periodically alternating refractive index [6]. A rich variety of physical effects have been observed when point, line and planar defects are introduced into periodic dielectric structures by the modifying refractive index or thickness of isotropic material. We consider here the unusual photonic properties of a defect created by twisting one part of an anisotropic structure relative to the rest of the sample. This "chiral twist" provides an additional degree of freedom for the design of photonic structures.Periodic chiral media appear in nature and can be synthesized as self-organized cholesteric liquid crystals (CLCs) [7] or fabricated by a variety of techniques, for example, by glancing-angle deposition on a rotating substrate [8]. In CLCs, the director, which is the average orientation of molecules in a plane, rotates with pitch P as shown in Fig. 1a. A reflection band forms for circularly polarized light with the same handedness as the structure itself. Light with opposite circular polarization is transmitted through the structure without attenuation. The edges of the band are defined by two sharp optical modes peaked at a wavelength inside the medium equal to P. These correspond to circularly polarized standing waves, in which the electric field in the bulk of the sample is aligned along either the ordinary or the extraordinary molecular axes [9]. It was in dyedoped CLCs that suppression of the density of states in a stop band and lasing in long-lived modes at the band edge were first demonstrated [10]. In analogy w...

Polarization characteristics of phase retardation defect mode lasing in polymeric cholesteric liquid crystals

“…This is why lasing occurs at the edge of PBG and the lasing emission is circularly polarized with the same handedness as CLC. As for CLC films containing a 908 phase jump inside the helix, Kopp et al [15] suggested theoretically that the polarization of light is affected by the film thickness. CP emission with the same handedness as the CLC helix is dominant below the crossover thickness, where equal contributions exist for L-and R-CP, and CP emission with opposite handedness as the CLC helix becomes dominant above the crossover thickness.…”

Quasi-optical Systems Based on Periodic Structures

“…Such samples can be obtained as follows : 1) we consider first an cholesteric elastomer without defects between planes orthogonal to the helix axis; 2) then we cut the sample in such a way to obtain two or more layers between parallel planes; and 3) we finally rotate any layer with respect to the preceding one around their common helix axis by a given angle  (twist angle) (Lakhtakia, 2000;Ozaki et al, 2003;Song et al, 2004). Some interesting numerical results have already been found recently for helical photonic crystals with only one twist defect (Becchi et al, 2004;Hodgkinson et al, 2000;Kopp & Genack, 2002;Schimdtke & Stille, 2003;Wang & Lakhtakia, 2003;Oldano, 2003;Kopp & Genack, 2003). Here we present a theoretical and analytical approach for samples with any number of twist defects under the action of axial strain.…”

Numerical Simulation of Lasing Dynamics in Choresteric Liquid Crystal Based on ADE-FDTD Method

“…Kopp and Genack have numerically demonstrated that twist-defect, discontinuous phase shift of the helical twist of CLC molecules (Fig. 3 (b)), could indeed function as a defect (Kopp & Genack, 2002). This type of defect is unique in CLC with optical anisotropy.…”