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Laser-directed hierarchical assembly of liquid crystal defects and control of optical phase singularities.

Ackerman PJ, Qi Z, Lin Y, Twombly CW, Laviada MJ, Lansac Y, Smalyukh II - Sci Rep (2012)

Bottom Line: However, they are typically hard to control in a reliable manner.Here we describe facile erasable "optical drawing" of self-assembled defect clusters in liquid crystals.Our findings bridge the studies of defects in condensed matter physics and optics and may enable applications in data storage, singular optics, displays, electro-optic devices, diffraction gratings, as well as in both optically- and electrically-addressed pixel-free spatial light modulators.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics and Liquid Crystal Materials Research Center, University of Colorado, Boulder, Colorado 80309, USA.

ABSTRACT
Topological defect lines are ubiquitous and important in a wide variety of fascinating phenomena and theories in many fields ranging from materials science to early-universe cosmology, and to engineering of laser beams. However, they are typically hard to control in a reliable manner. Here we describe facile erasable "optical drawing" of self-assembled defect clusters in liquid crystals. These quadrupolar defect clusters, stabilized by the medium's chirality and the tendency to form twisted configurations, are shaped into arbitrary two-dimensional patterns, including reconfigurable phase gratings capable of generating and controlling optical phase singularities in laser beams. Our findings bridge the studies of defects in condensed matter physics and optics and may enable applications in data storage, singular optics, displays, electro-optic devices, diffraction gratings, as well as in both optically- and electrically-addressed pixel-free spatial light modulators.

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Voltage control of fingers gratings and the corresponding diffraction patterns.(a)–(d) POM images of a grating with an elementary dislocation at applied voltages of (a) 0 V, (b) 1.8 V, (c) 3.6 V, and (d) 5.6 V. The corresponding diffraction patterns are shown in the bottom of figure parts of (a)–(d). (e) intensity of light in different diffraction orders vs. applied voltage. The 1st and 2nd diffraction orders are labeled “1L”, “2L”, “1R”, and “2R” in (e) with “L” and “R” standing for “left” and “right,” respectively.
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f5: Voltage control of fingers gratings and the corresponding diffraction patterns.(a)–(d) POM images of a grating with an elementary dislocation at applied voltages of (a) 0 V, (b) 1.8 V, (c) 3.6 V, and (d) 5.6 V. The corresponding diffraction patterns are shown in the bottom of figure parts of (a)–(d). (e) intensity of light in different diffraction orders vs. applied voltage. The 1st and 2nd diffraction orders are labeled “1L”, “2L”, “1R”, and “2R” in (e) with “L” and “R” standing for “left” and “right,” respectively.

Mentions: Because of the LC's fluid nature and its facile response to electric field, the optically drawn phase gratings can be tuned and fully erased by AC voltages of about 1 V at 1 kHz. As voltage U applied to the transparent indium tin oxide electrodes of the cell continuously increases, the fingers first shrink in width for U ≤ 0.5 V (Fig. 5a,b) and then shrink in length starting from the edge dislocation core and grating ends (Fig. 5c) until the phase grating is fully erased at U ≈ 5.6 V (Fig. 5d). The structural changes in fingers and their eventual erasing are due to coupling of n(r) in the used LC of positive dielectric anisotropy with the low-frequency electric field E that tends to minimize the electric field term of the free energy by enforcing n(r)∥E. LC elasticity, on the other hand, resists this realignment as it drives the system away from the global or local minima of the elastic free energy. At each applied voltage, the observed equilibrated static director structures correspond to the minima of the total free energy (the sum of electric and elastic free energy terms) evaluated for the given vertical surface boundary conditions for n(r). The field induces structural transformations and ensuing changes in the effective refractive index distribution within the grating. By varying the applied voltage, one can tune the width of fingers and the effective index distribution within them at low voltages (Fig.5a,b) and then fully “erase” them at higher voltages (Fig. 5c,d). This control of the phase gratings enables the corresponding control of the diffraction patterns, as shown in the bottom parts of Fig. 5a–d and in Fig. 5e. Importantly, the left-right asymmetry of the diffraction patterns, which is due to the synclinic tilting of the fingers' structures in the grating, becomes even more pronounced at high voltages and persists until the grating disappears at voltages of 5.6 V and higher (Fig. 5e). Interestingly, as the voltage gradually increases from 0 to 1.4 V, the diffracted beam of first order on the left side first increases and then decrease in intensity while the beam of first order on the right side constantly increases in intensity (Fig. 5e). Both left-side and right-side second-order diffracted beams continuously decrease in intensity and the 0-th order beam continuously increases in intensity. In our experiments, similar voltage tunability was achieved for diffraction patterns with and without dislocation defects as well as for different polarizations of the incident light (e.g. circular and linear parallel, perpendicular and at 45 degrees to the fingers direction). The observed dependence of laser intensity in the diffraction patterns on the polarization of the incident laser beam is due to the fact that the spatially-varying effective refractive index of the uniaxial LC medium within the periodic grating is strongly dependent on the polarization of this beam. The ability to control intensities of different diffraction orders by varying relatively low applied voltages (0.5–2 V) and also “erasing” these gratings at somewhat higher (∼5 V) is of great interest for a number of important applications of phase diffraction gratings2930313233.


Laser-directed hierarchical assembly of liquid crystal defects and control of optical phase singularities.

Ackerman PJ, Qi Z, Lin Y, Twombly CW, Laviada MJ, Lansac Y, Smalyukh II - Sci Rep (2012)

Voltage control of fingers gratings and the corresponding diffraction patterns.(a)–(d) POM images of a grating with an elementary dislocation at applied voltages of (a) 0 V, (b) 1.8 V, (c) 3.6 V, and (d) 5.6 V. The corresponding diffraction patterns are shown in the bottom of figure parts of (a)–(d). (e) intensity of light in different diffraction orders vs. applied voltage. The 1st and 2nd diffraction orders are labeled “1L”, “2L”, “1R”, and “2R” in (e) with “L” and “R” standing for “left” and “right,” respectively.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3369196&req=5

f5: Voltage control of fingers gratings and the corresponding diffraction patterns.(a)–(d) POM images of a grating with an elementary dislocation at applied voltages of (a) 0 V, (b) 1.8 V, (c) 3.6 V, and (d) 5.6 V. The corresponding diffraction patterns are shown in the bottom of figure parts of (a)–(d). (e) intensity of light in different diffraction orders vs. applied voltage. The 1st and 2nd diffraction orders are labeled “1L”, “2L”, “1R”, and “2R” in (e) with “L” and “R” standing for “left” and “right,” respectively.
Mentions: Because of the LC's fluid nature and its facile response to electric field, the optically drawn phase gratings can be tuned and fully erased by AC voltages of about 1 V at 1 kHz. As voltage U applied to the transparent indium tin oxide electrodes of the cell continuously increases, the fingers first shrink in width for U ≤ 0.5 V (Fig. 5a,b) and then shrink in length starting from the edge dislocation core and grating ends (Fig. 5c) until the phase grating is fully erased at U ≈ 5.6 V (Fig. 5d). The structural changes in fingers and their eventual erasing are due to coupling of n(r) in the used LC of positive dielectric anisotropy with the low-frequency electric field E that tends to minimize the electric field term of the free energy by enforcing n(r)∥E. LC elasticity, on the other hand, resists this realignment as it drives the system away from the global or local minima of the elastic free energy. At each applied voltage, the observed equilibrated static director structures correspond to the minima of the total free energy (the sum of electric and elastic free energy terms) evaluated for the given vertical surface boundary conditions for n(r). The field induces structural transformations and ensuing changes in the effective refractive index distribution within the grating. By varying the applied voltage, one can tune the width of fingers and the effective index distribution within them at low voltages (Fig.5a,b) and then fully “erase” them at higher voltages (Fig. 5c,d). This control of the phase gratings enables the corresponding control of the diffraction patterns, as shown in the bottom parts of Fig. 5a–d and in Fig. 5e. Importantly, the left-right asymmetry of the diffraction patterns, which is due to the synclinic tilting of the fingers' structures in the grating, becomes even more pronounced at high voltages and persists until the grating disappears at voltages of 5.6 V and higher (Fig. 5e). Interestingly, as the voltage gradually increases from 0 to 1.4 V, the diffracted beam of first order on the left side first increases and then decrease in intensity while the beam of first order on the right side constantly increases in intensity (Fig. 5e). Both left-side and right-side second-order diffracted beams continuously decrease in intensity and the 0-th order beam continuously increases in intensity. In our experiments, similar voltage tunability was achieved for diffraction patterns with and without dislocation defects as well as for different polarizations of the incident light (e.g. circular and linear parallel, perpendicular and at 45 degrees to the fingers direction). The observed dependence of laser intensity in the diffraction patterns on the polarization of the incident laser beam is due to the fact that the spatially-varying effective refractive index of the uniaxial LC medium within the periodic grating is strongly dependent on the polarization of this beam. The ability to control intensities of different diffraction orders by varying relatively low applied voltages (0.5–2 V) and also “erasing” these gratings at somewhat higher (∼5 V) is of great interest for a number of important applications of phase diffraction gratings2930313233.

Bottom Line: However, they are typically hard to control in a reliable manner.Here we describe facile erasable "optical drawing" of self-assembled defect clusters in liquid crystals.Our findings bridge the studies of defects in condensed matter physics and optics and may enable applications in data storage, singular optics, displays, electro-optic devices, diffraction gratings, as well as in both optically- and electrically-addressed pixel-free spatial light modulators.

View Article: PubMed Central - PubMed

Affiliation: Department of Physics and Liquid Crystal Materials Research Center, University of Colorado, Boulder, Colorado 80309, USA.

ABSTRACT
Topological defect lines are ubiquitous and important in a wide variety of fascinating phenomena and theories in many fields ranging from materials science to early-universe cosmology, and to engineering of laser beams. However, they are typically hard to control in a reliable manner. Here we describe facile erasable "optical drawing" of self-assembled defect clusters in liquid crystals. These quadrupolar defect clusters, stabilized by the medium's chirality and the tendency to form twisted configurations, are shaped into arbitrary two-dimensional patterns, including reconfigurable phase gratings capable of generating and controlling optical phase singularities in laser beams. Our findings bridge the studies of defects in condensed matter physics and optics and may enable applications in data storage, singular optics, displays, electro-optic devices, diffraction gratings, as well as in both optically- and electrically-addressed pixel-free spatial light modulators.

Show MeSH
Related in: MedlinePlus