Umbilics : static properties and shear-induced displacements

Rapini, Alessandro

doi:10.1051/jphys:01973003407062900

Cited by 71 publications

(81 citation statements)

References 3 publications

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“…It can be inferred from energy calculations, or through numerical simulations, that for positive (negative) anisotropy the stable solutions are ϕ 0 = {π/2, 3π/2} (ϕ 0 = {0, π }). It is worth noting that it is known, from the variational approach to the Frank free energy, that the elastic anisotropy allows a discrete number of four possible phase jumps for umbilical defects [30,31]. These conditions are recovered by the above solutions.…”

Section: (B) Effects Of Elastic Anisotropymentioning

confidence: 89%

Light–matter interaction induces a single positive vortex with swirling arms

Barboza

Bortolozzo

Clerc

et al. 2014

Phil. Trans. R. Soc. A.

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Homeotropic nematic liquid crystal cells with a photosensitive wall and negative dielectric anisotropy exhibit, under the influence of local illumination, stable vortexes with swirling arms that are trapped at the illuminated area. Close to the Fréedericksz transition an amplitude equation is derived, which allows us to understand the origin of the induced vortex and the competition between the illuminating profile and the elastic anisotropy generating the swirling of the arms.

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Section: (B) Effects Of Elastic Anisotropymentioning

confidence: 89%

Light–matter interaction induces a single positive vortex with swirling arms

Barboza

Bortolozzo

Clerc

et al. 2014

Phil. Trans. R. Soc. A.

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“…where ∆(r) is the r-dependent birefringent phase retardation modeled following the work of Rapini [23]. Within such a description, one has ∆(r) = δ(r/r c )∆ ∞ , where…”

mentioning

confidence: 99%

“…Optical vortex masks realized without the need for a machining technique have also been obtained from other mesophases such as cholesteric [21] and smectic [22] liquid crystals, but at the expense of efficiency. Here, we propose exploring the potential of self-engineered liquid crystal vortex phase masks for high-contrast imaging applications, in particular, in the case of optical vortex coronagraphy.We choose the so-called umbilical defects that appear in homeotropic nematic liquid crystal films with negative dielectric anisotropy under a quasi-static electric field and above a threshold voltage U = U * of a few volts [23]. These defects are associated with optical axis orientation angle of the form ψ(φ) = mφ + ψ 0 with m = ±1 and ψ 0 a constant; see Figs.…”

mentioning

confidence: 99%

“…We choose the so-called umbilical defects that appear in homeotropic nematic liquid crystal films with negative dielectric anisotropy under a quasi-static electric field and above a threshold voltage U = U * of a few volts [23]. These defects are associated with optical axis orientation angle of the form ψ(φ) = mφ + ψ 0 with m = ±1 and ψ 0 a constant; see Figs.…”

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confidence: 99%

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Vortex coronagraphy from self-engineered liquid crystal spin-orbit masks

Aleksanyan

Brasselet

2016

Opt. Lett.

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We report on a soft route toward optical vortex coronagraphy based on self-engineered electrically tunable vortex masks made of liquid crystal topological defects. These results suggest that a natureassisted technological approach to the fabrication of complex phase masks could be useful in optical imaging whenever optical phase singularities are at play.The observation of faint objects near a bright source of light is a basic challenge of high-contrast imaging techniques such as the quest for extrasolar planets in astronomical imaging. This has led to the development of instruments called coronagraphs, which combine the high extinction of stellar light and the high transmission of a low-level signal at small angular separation. Stellar coronagraphy was initiated more than 80 years ago when Lyot studied solar corona without an eclipse by selective occultation of sunlight, placing an opaque disk in the focal plane of a telescope [1]. On the other hand, phase mask coronagraphs offer good performance for the observation of point-like sources. An early version consisted of using a disk π-phase mask [2] whose chromatic drawback arising from discrete radial phase step was solved a few years later by incorporating discrete radial [3] or azimuthal [4] phase modulation to the original design. Later on, continuous azimuthal phase ramps improved the approach [5,6] and led to the advent of optical vortex coronagraphy.Vortex coronagraphs rely on the selective peripheral redistribution of on-axis light outside an area of null intensity at the exit pupil plane of the instrument, which is done by placing a spiraling phase mask in the Fourier plane characterized by a complex transmittance of the form exp(i φ), where the charge is an even integer and φ is the usual azimuthal angle in the transverse plane. This enables optimal on-axis rejection of light by placing an iris (called Lyot stop) at the exit pupil plane, while the off-axis weak signal is almost unaffected for an angular separation larger than the diffraction limit [7]. There are two families of optical vortex phase masks that rely on the scalar (phase) and vectorial (polarization degree of freedom) properties of light. The former case refers to the helical shaping of the wavefront from a refractive phase mask, whereas the latter one exploits the polarization properties of space-variant birefringent optical elements. Indeed, inhomogeneous anisotropic phase masks endowed with azimuthal optical axis orientation of the form ψ(φ) = mφ with m half-integer and associated with half-wave birefringent phase retardation lead to a vortex mask of charge = 2σm for incident on-axis circularly polarized light beam with helicity σ = ±1, as originally shown in [8] using form birefringence (subwavelength grating of dielectric materials) and, in [9], using true birefringence.The achromatic features of the vectorial option versus its scalar counterpart [10,11] have eventually led to equip state-of-the-art large instruments such as Keck, Subaru, Hale, Large Binocular Telescope, and Very Larg...

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“…Further confirmation for the defect annihilation scaling was achieved using electric field induced defects generated in a nematic liquid crystal. [9] These so called umbilical defects [26][27][28] do not end in a singular point, but are otherwise very similar to the Schlieren defects. They only differ in so far as the director continuously tilts into the direction of the substrate normal, being parallel to it at the defect core, which is small, but of finite size.…”

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confidence: 99%

Kibble–Zurek Scaling during Defect Formation in a Nematic Liquid Crystal

Fowler

Dierking

2017

ChemPhysChem

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Symmetry breaking phase transitions are often accompanied by the formation of topological defects, like in cosmological theories of the early universe, superfluids, liquid crystals or solid state systems. This scenario is described by the Kibble-Zurek mechanism, which predicts respective scaling laws for the defect density ρ. One such scaling law suggests a relation ~ Q -1/2 with  Q the change of rate of a control parameter. In contrast to the scaling of the defect density during annihilation with ρ~t -1 , which is governed by the attraction of defects of the same strength but opposite sign, the defect formation process, which depends on the rate of change of a physical quantity initiating the transition, is only very scarcely investigated. We here use nematic liquid crystals as a different system to demonstrate the validity of the predicted scaling relation for defect formation. It is found that the scaling exponent is independent of temperature and material employed, thus universal, as predicted.Topological defects[1] are often generated following symmetry breaking phase transitions in many aspects of physics including cosmology, superfluids and liquid crystals. Kibble proposed a universal mechanism by which cosmological defects were formed in the early universe as it expanded and cooled shortly after the Big Bang[2.3]. During a cosmological symmetry breaking phase transition, uncorrelated domains with randomly determined order are produced which subsequently coalesce. Defects are formed that exist between two domains with non-compatible order. The initial density of defects is dependent on the rate at which domains grow which is limited by the finite speed of information transmission (causality). It became known as the "Kibble-Zurek mechanism" after Zurek suggested that

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Umbilics : static properties and shear-induced displacements

Abstract: We study the structure of umbilical « defects » which should appear under certain conditions in a nematic slab in an electric field. We show that a shear flow can induce a displacement of these defects

Cited by 71 publications

References 3 publications

Light–matter interaction induces a single positive vortex with swirling arms

Light–matter interaction induces a single positive vortex with swirling arms

Vortex coronagraphy from self-engineered liquid crystal spin-orbit masks

Kibble–Zurek Scaling during Defect Formation in a Nematic Liquid Crystal

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