Author Correction: Multifunctional light beam control device by stimuli-responsive liquid crystal micro-grating structures

Correction to: Scientific Reports https://doi.org/10.1038/s41598-020-70783-8, published online 14 August 2020 This Article contains a typographical error in the Acknowledgements section. “the Ministerio de Economía y Competitividad of Spain (TEC2013-47342-C2-2-R)” should read: "the Ministerio de Economía y Competitividad of Spain (TEC2016-77242-C3-1-R)"This work was supported by the Comunidad de Madrid and FEDER Program (S2018/NMT-4326), the Ministerio de Economía y Competitividad of Spain (TEC2013-47342-C2-2-R and TEC2016-76021-C2-2-R), the FEDER/Ministerio de Ciencia, Innovación y Universidades and Agencia Estatal de Investigación (RTC2017-6321-1, PID2019-109072RB-C31 and PID2019-107270RB-C21). The authors also acknowledge the support by the Ministry of National Defense of Poland (GBMON/13-995/2018/WAT), Military University of Technology (Grant no. 23-895)

Electrical switching of a chiral lasing from polariton condensate in a Rashba-Dresselhaus regime

Efficient optical classical and quantum information processing imposes on light novel requirements: chirality with low threshold non-linearities. In this work we demonstrate a chiral lasing from an optical modes due to emerging photonic Rashba-Dresselhaus spin-orbit coupling (SOC). For this purpose we developed a new electrically tunable device based on an optical cavity filled with birefringent liquid crystal (LC) and perovskite crystals. Our novel method for the growth of single crystals of CsPbBr$_3$ inorganic perovskite in polymer templates allows us to reach a strong light-matter coupling regime between perovskite excitons and cavity modes, and induce polariton condensation. The sensitivity of the LC to external electric fields lets us to tune the condensate energy in situ and induce synthetic SOC. This shapes the condensate between a single linearly polarized or two circularly polarized separated in momentum, emitting coherent light. The difference in the condensation thresholds between the two SOC regimes can be used to switch on and off the chiral condensate emission with a voltage.Comment: 8 pages, 5 figure

Positive-negative tunable liquid crystal lenses based on a microstructured transmission line

In this work, a novel technique to create positive-negative tunable liquid crystal lenses is proposed and experimentally demonstrated. This structure is based on two main elements, a transmission line acting as a voltage divider and concentric electrodes that distribute the voltage homogeneously across the active area. This proposal avoids all disadvantages of previous techniques, involving much simpler fabrication process (a single lithographic step) and voltage control (one or two sources). In addition, low voltage signals are required. Lenses with switchable positive and negative focal lengths and a simple, low voltage control are demonstrated. Moreover, by using this technique other optical devices could be engineered, e.g. axicons, Powell lenses, cylindrical lenses, Fresnel lenses, beam steerers, optical vortex generators, etc. For this reason, the proposed technique could open new venues of research in optical phase modulation based on liquid crystal materials.This work was supported by Comunidad de Madrid and FEDER Program (S2018/NMT-4326), the Ministerio de Economía y Competitividad of Spain (TEC2016-77242-C3-1-R and TEC2016-76021-C2-2-R), the FEDER/ Ministerio de Ciencia, Innovación y Universidades and Agencia Estatal de Investigación (RTC2017-6321-1). Also, the Ministry of National Defense of Poland (GBMON/13-995/2018/WAT)

The Influence of Microstructure and Lattice Strain on Tetragonality Factor and Dielectric Properties of Ferroelectric Ceramics BaTiO3BaTiO_3

This work is devoted to direct process of molten salt synthesis and studies on barium titanate ($BaTiO_3$, BT), belonging to ferroelectric crystal group type perovskite $BO_3$. This material thanks to its noncentrosymmetric, fully tetragonal structure possesses at room temperature (up to $T_{c}$ = 135°C) the spontaneous polarization. Due to this fact BT can be applied as piezoelectric material in electromechanical transducers, so as an excellent dielectric in multilayer capacitors and many other devices. With grain size reduction of BT ceramics to nanometric level it leads to permanent transformation into paraelectric state with minimized energy and to lose its specific features as a consequence, even at room temperature. In case of structural agent, means as tetragonality factor, it has a crucial influence on investigated material properties and it is referred in current paper. It is a row of complementary researching methods allows to confirm the presence of desired tetragonal BT phase in nano or micropowders obtained by means of molten salt synthesis route. For different temperature variants of synthesis X-ray diffraction analysis were undertaken and precise unit cells parameters both with tetragonality factor were determined using the Cohen method. Based on structural studies the lattice strains and crystallite sizes were estimated through the Williamson-Hall method. Using scanning electron microscopy the powders morphology and grain size distribution were done. Dielectric measurements of sintered BT ceramics were carried out to determine the Curie temperatures, dielectric permittivities and loss factors in prepared capacitors

The Influence of Microstructure and Lattice Strain on Tetragonality Factor and Dielectric Properties of Ferroelectric Ceramics BaTiO_3

This work is devoted to direct process of molten salt synthesis and studies on barium titanate ($BaTiO_3$, BT), belonging to ferroelectric crystal group type perovskite $BO_3$. This material thanks to its noncentrosymmetric, fully tetragonal structure possesses at room temperature (up to $T_{c}$ = 135°C) the spontaneous polarization. Due to this fact BT can be applied as piezoelectric material in electromechanical transducers, so as an excellent dielectric in multilayer capacitors and many other devices. With grain size reduction of BT ceramics to nanometric level it leads to permanent transformation into paraelectric state with minimized energy and to lose its specific features as a consequence, even at room temperature. In case of structural agent, means as tetragonality factor, it has a crucial influence on investigated material properties and it is referred in current paper. It is a row of complementary researching methods allows to confirm the presence of desired tetragonal BT phase in nano or micropowders obtained by means of molten salt synthesis route. For different temperature variants of synthesis X-ray diffraction analysis were undertaken and precise unit cells parameters both with tetragonality factor were determined using the Cohen method. Based on structural studies the lattice strains and crystallite sizes were estimated through the Williamson-Hall method. Using scanning electron microscopy the powders morphology and grain size distribution were done. Dielectric measurements of sintered BT ceramics were carried out to determine the Curie temperatures, dielectric permittivities and loss factors in prepared capacitors

Aspherical liquid crystal lenses based on a variable transmission electrode

In this work, a technique to generate aspherical liquid crystal lenses with positive and negative optical power is experimentally demonstrated. The main enabling element is a micro-metric electrode with variable spatial size. This produces a decreasing resistance towards the lens centre that generates the desired voltage/phase profiles. Then, the voltage is homogeneously distributed across the active area of the lens by micro-metric concentric electrodes. As it is demonstrated, the phase shift can be controlled with voltages from 0 to 4.5 VRMS. As a result, parabolic profiles are obtained both for negative and positive optical powers. Furthermore, this approach avoids some disadvantages of previous techniques; parabolic profiles can be obtained with only one lithographic step and one or two voltage sources. Other complex aspherical profiles could be fabricated using the same technique, such as elliptical or hyperbolic ones.Funding: European Social Fund (NAWA PROM projekt nr POWR.03.03.00-00-PN13/18); Comunidad de Madrid and FEDER Program (S2018/NMT-4326); MCIN/ AEI/10.13039/501100011033 and European Union "Next generation EU"/PTR (PDC2021-121172-C21); MCIN/ AEI/10.13039/501100011033 and FEDER "A way to make Europe" (PID2019-107270RB-C21, PID2019-109072RB-C31, RTC-2017-6321-1)

Annihilation of exceptional points from different Dirac valleys in a 2D photonic system

Topological physics relies on the existence of Hamiltonian's eigenstate singularities carrying a topological charge, such as quantum vortices, Dirac points, Weyl points and -- in non-Hermitian systems -- exceptional points (EPs), lines or surfaces. They appear only in pairs connected by a Fermi arc and are related to a Hermitian singularity, such as a Dirac point. The annihilation of 2D Dirac points carrying opposite charges has been experimentally reported. It remained elusive for Weyl points and second order EPs terminating different Fermi arcs. Here, we observe the annihilation of second order EPs issued from different Dirac points forming distinct valleys. We study a liquid crystal microcavity with voltage-controlled birefringence and TE-TM photonic spin-orbit-coupling. Two neighboring modes can be described by a two-band Hermitian Hamiltonian showing two topological phases with either two same-sign or four opposite-sign Dirac points (valleys). Non-Hermiticity is provided by polarization-dependent losses, which split Dirac points into pairs of EPs, connected by Fermi arcs. We measure their topological charges and control their displacement in reciprocal space by increasing the non-Hermiticity degree. EPs of opposite charges from different valleys meet and annihilate, connecting in a closed line the different Fermi arcs. This non-Hermitian topological transition occurs only when the Hermitian part of the Hamiltonian is topologically trivial (with four valleys), but is distinct from the Hermitian transition. Our results offer new perspectives of versatile manipulation of EPs, opening the new field of non-Hermitian valley-physics

Annihilation of exceptional points from different Dirac valleys in a 2D photonic system

Topological physics relies on the existence of Hamiltonian's eigenstate singularities carrying a topological charge, such as quantum vortices, Dirac points, Weyl points and -- in non-Hermitian systems -- exceptional points (EPs), lines or surfaces. They appear only in pairs connected by a Fermi arc and are related to a Hermitian singularity, such as a Dirac point. The annihilation of 2D Dirac points carrying opposite charges has been experimentally reported. It remained elusive for Weyl points and second order EPs terminating different Fermi arcs. Here, we observe the annihilation of second order EPs issued from different Dirac points forming distinct valleys. We study a liquid crystal microcavity with voltage-controlled birefringence and TE-TM photonic spin-orbit-coupling. Two neighboring modes can be described by a two-band Hermitian Hamiltonian showing two topological phases with either two same-sign or four opposite-sign Dirac points (valleys). Non-Hermiticity is provided by polarization-dependent losses, which split Dirac points into pairs of EPs, connected by Fermi arcs. We measure their topological charges and control their displacement in reciprocal space by increasing the non-Hermiticity degree. EPs of opposite charges from different valleys meet and annihilate, connecting in a closed line the different Fermi arcs. This non-Hermitian topological transition occurs only when the Hermitian part of the Hamiltonian is topologically trivial (with four valleys), but is distinct from the Hermitian transition. Our results offer new perspectives of versatile manipulation of EPs, opening the new field of non-Hermitian valley-physics