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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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Diffraction gratings with various dislocations and their use for generation of phase singularities.(a) POM image of a finger grating with an elementary dislocation. (b) (c) POM images of gratings with edge dislocations of larger Burgers vector. (d) Far field diffraction pattern from the grating shown in (a). (e) Far field diffraction pattern from grating shown in (c). (f) Enlarged image of the first-order diffracted beam shown in (d) (top) and its phase profile (bottom) with the phase varying from -π (black) to π (white). (g) 3D plot of the phase profile of the beam shown in (d). (h) Enlarged image of the first-order diffracted beam shown in (e) (top) and its phase surface (bottom). (i) 3D plot of the phase profile of the beam shown in (e). The vertical green lines mark the phase singularities.
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f3: Diffraction gratings with various dislocations and their use for generation of phase singularities.(a) POM image of a finger grating with an elementary dislocation. (b) (c) POM images of gratings with edge dislocations of larger Burgers vector. (d) Far field diffraction pattern from the grating shown in (a). (e) Far field diffraction pattern from grating shown in (c). (f) Enlarged image of the first-order diffracted beam shown in (d) (top) and its phase profile (bottom) with the phase varying from -π (black) to π (white). (g) 3D plot of the phase profile of the beam shown in (d). (h) Enlarged image of the first-order diffracted beam shown in (e) (top) and its phase surface (bottom). (i) 3D plot of the phase profile of the beam shown in (e). The vertical green lines mark the phase singularities.

Mentions: Since the effective refractive index of the LC depends on the orientation of n(r) with respect to the polarization and propagation direction of light, optically generated structures of fingers can be used as tunable and reconfigurable phase diffraction gratings (Fig. 1b). A typical diffraction pattern obtained by means of such a grating is shown in the inset of Fig. 1b. Computer programmed laser beam scanning provides the capability of unprecedented optical control over the structure of such gratings. Shown in Fig. 3a–c are POM images of optically generated diffraction gratings with edge dislocations (insertions) of different magnitude b = /b/ = ma of Burgers vector, where a is the periodicity of the optically drawn grating and m is the integer number of insertions. The diffraction patterns obtained by use of these phase gratings have one or more dark spots within the beams of 1st and higher diffraction orders (Fig. 3d,e). Characterization of phase profiles of laser beams in different diffraction orders ndo using the Stokes Polarimetry method25 and a setup shown in the supplementary Fig. S5 reveals optical phase singularities and the relation between their topological charge N and b (Fig. 3): , in agreement with theoretical predictions262728, where N is an integer number of 2π phase change on any closed circuit around the singularity center. The details of phase distributions are visualized by means of grayscale representations shown in the bottom parts of Fig. 3f,h and the 3D representations (Fig.3g,i). The phase varies continuously everywhere within the beams except for the locations of the screw dislocations ( = phase singularities), where phase is undefined. Remarkably, similar to the case of high-charge defects in LCs known to split into defects of lower charge17, the phase singularities of large N tend to split into multiple phase singularities of elementary charge N = ±1 (Fig. 3e,h,i). However, the physical origin of this splitting is very different from that of splitting of high-strength disclinations in LCs (driven by minimization of the elastic free energy) and is usually attributed to the presence of a weak coherent background in a screw-dislocated wave262728.


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)

Diffraction gratings with various dislocations and their use for generation of phase singularities.(a) POM image of a finger grating with an elementary dislocation. (b) (c) POM images of gratings with edge dislocations of larger Burgers vector. (d) Far field diffraction pattern from the grating shown in (a). (e) Far field diffraction pattern from grating shown in (c). (f) Enlarged image of the first-order diffracted beam shown in (d) (top) and its phase profile (bottom) with the phase varying from -π (black) to π (white). (g) 3D plot of the phase profile of the beam shown in (d). (h) Enlarged image of the first-order diffracted beam shown in (e) (top) and its phase surface (bottom). (i) 3D plot of the phase profile of the beam shown in (e). The vertical green lines mark the phase singularities.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f3: Diffraction gratings with various dislocations and their use for generation of phase singularities.(a) POM image of a finger grating with an elementary dislocation. (b) (c) POM images of gratings with edge dislocations of larger Burgers vector. (d) Far field diffraction pattern from the grating shown in (a). (e) Far field diffraction pattern from grating shown in (c). (f) Enlarged image of the first-order diffracted beam shown in (d) (top) and its phase profile (bottom) with the phase varying from -π (black) to π (white). (g) 3D plot of the phase profile of the beam shown in (d). (h) Enlarged image of the first-order diffracted beam shown in (e) (top) and its phase surface (bottom). (i) 3D plot of the phase profile of the beam shown in (e). The vertical green lines mark the phase singularities.
Mentions: Since the effective refractive index of the LC depends on the orientation of n(r) with respect to the polarization and propagation direction of light, optically generated structures of fingers can be used as tunable and reconfigurable phase diffraction gratings (Fig. 1b). A typical diffraction pattern obtained by means of such a grating is shown in the inset of Fig. 1b. Computer programmed laser beam scanning provides the capability of unprecedented optical control over the structure of such gratings. Shown in Fig. 3a–c are POM images of optically generated diffraction gratings with edge dislocations (insertions) of different magnitude b = /b/ = ma of Burgers vector, where a is the periodicity of the optically drawn grating and m is the integer number of insertions. The diffraction patterns obtained by use of these phase gratings have one or more dark spots within the beams of 1st and higher diffraction orders (Fig. 3d,e). Characterization of phase profiles of laser beams in different diffraction orders ndo using the Stokes Polarimetry method25 and a setup shown in the supplementary Fig. S5 reveals optical phase singularities and the relation between their topological charge N and b (Fig. 3): , in agreement with theoretical predictions262728, where N is an integer number of 2π phase change on any closed circuit around the singularity center. The details of phase distributions are visualized by means of grayscale representations shown in the bottom parts of Fig. 3f,h and the 3D representations (Fig.3g,i). The phase varies continuously everywhere within the beams except for the locations of the screw dislocations ( = phase singularities), where phase is undefined. Remarkably, similar to the case of high-charge defects in LCs known to split into defects of lower charge17, the phase singularities of large N tend to split into multiple phase singularities of elementary charge N = ±1 (Fig. 3e,h,i). However, the physical origin of this splitting is very different from that of splitting of high-strength disclinations in LCs (driven by minimization of the elastic free energy) and is usually attributed to the presence of a weak coherent background in a screw-dislocated wave262728.

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