Abstract

We demonstrate that birefringent profiles of double-twist cylinders, found in some chiral nematic systems such as blue phases, can perform as polarization-selective microlenses and waveguides in the regime of negative birefringence. Specifically, we solve Maxwell’s equation using the finite-difference time-domain (FDTD) method, to simulate light propagation through double-twist cylinder birefringent structures. We show that, in case of negative material birefringence, azimuthally polarized beams experience lensing which can further be extended to waveguiding in double-twist cylinders. Lensing and waveguiding efficiency are shown to be strongly dependent on the ratio between the width of the double-twist cylinder profile and the beam width. We further characterize waveguiding in terms of losses, which are investigated in case of straight as well as curved double-twist cylinders. More generally, this work is a contribution to the design and development of (soft) birefringent profiles for optical and photonic applications.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Many photonic elements in use today are optically birefringent, especially, those for altering or probing the polarization [1]. Non-linear crystals possess birefringence that is used to phase match and increase the efficiency of non-linear processes, such as second-harmonic generation or spontaneous parametric down-conversion [1,2]. Birefringence is the prominent property of liquid crystals (LCs), widely used today in optical and display applications, as it can be manipulated by external fields on diverse length scales, from tens of nano- to tens of micrometers as well as diverse time scales, from seconds to nanoseconds and even picoseconds [3–5]. This broad spatial and temporal tuneability makes LCs important building blocks of (micro)photonic circuits. As a consequence, a diverse range of micro-photonic applications using LCs have already been reported, such as LC lasers [6, 7], tunable microresonators [8], tunable lenses [9–11], tunable fiber-couplers [12], tunable fibers [13], tunable waveplates [14], optical sensors [15], curved optical solitons [16], modulators and switches [17,18]. A liquid crystal waveguide was realized using a silicon channel filled with LC in which the number of possible guided modes can be controlled using an electric field [19].

Nematic LCs or nematics are liquids in which the constituent parts, molecules of elongated shape, have a long-range orientational order but no long-range positional order. Nematic order is typically characterized by the average local orientation vector n called the director and a scalar nematic degree of order S. Alternatively, the two can be combined to form a single tensorial order parameter Qij, that is further related to generally anisotropic quantities such as electric or magnetic susceptibility [4]. Birefringence of nematics stems from orientationally dependent response of single molecules to external electric field at optical frequencies. In bulk, uniaxial nematic materials are thus distinguished by two different indices of refraction. The direction of n with respect to the light wavevector k of light, where |k| = 2π/λ, and its polarization E determine the two distinctive modes of light determined by the two refractive indices [4].

In chiral nematics, nematic molecules are chiral in nature or a chiral dopant is added to a non-chiral nematic [4]. They can exhibit a cholesteric phase, which is characterized by the director describing a helix with a finite pitch along the z-direction [4, 20]. For materials or regimes of high chirality i.e. pitch in the order of a few hundred nanometers, blue phases (BPs), can occur in a distinct temperature range and are characterized by effective twisting of the director in multiple directions, especially along the so-called double-twist cylinders (DTCs) (see Fig. 1). Indeed, these double-twist cylinders stack into structures with face-centered cubic or simple cubic lattice symmetry forming blue phase I and blue phase II, respectively. [4,21]. A variety of other chiral vortex and solitonic structures can form as well [22, 23]. In principle arbitrary birefringent profiles can also be created by in-situ laser polymerization [24]. In this work, we are interested in the photonic properties of a single double-twist cylinder, inside which the director is parallel to the cylinder axis at its center and then rotate uniformly for angle ϕ in the radial direction away from the axis.

 figure: Fig. 1

Fig. 1 Double-twist cylinder as a photonic element. Azimuthally polarized light (electric field Eopt direction is illustrated with red arrows) propagating along the of double-twist birefringent profile (optical axis is represented by colored ellipsoids) observes radially dependent refractive index which can result in lensing and waveguiding.

Download Full Size | PPT Slide | PDF

Vectorial beams of light have a cross-sectionally varying local electric (and magnetic) field direction i.e. polarization. In case of cylindrical symmetry, they can be formally obtained as solutions of the paraxial vector wave equation where two opposite cases arise. The first is the radially polarized, with electric field oriented in the radial direction and the second is the azimuthally polarized beam, with electric field pointed in in the perpendicular, azimuthal, direction at every point of the beam cross section [25]. An inherent property of radially polarized beams on focussing are the radially symmetric longitudinal electric field components that allow for beam waists below the standard Gaussian limit [26]. This property is used in atom and particle trapping [26], laser cutting [27], optical microscopy [28] and even for charged particle acceleration [29]. Vectorial beams can be generated from linearly polarized beams using conic Brewster prisms [30], few-mode optical fibers [31] or by special LC phase modulators [32]. With relation to liquid crystals, recent simulations show that vectorial beams could be generated using nematic defect lines [33]. It was reported that due to the symmetry matching of the radially polarized beam and radially escaped nematic profile, such beams experience a spatially variant refractive index that can lead to lensing and waveguiding [34]. Specifically radially escaped and radial birefringent profiles, were shown to perform as photonic waveguides, considering these inhomogeneous profiles surrounded by isotropic claddings of lower index of refraction [35–38] or by enclosing them inside the fiber cladding [39].

In this work, we report that birefringent double-twist cylinder profiles, the common birefringent structures in chiral or blue phase nematics, can perform as waveguiding or lensing photonic elements for azimuthally polarized beams. Effective refractive index for an azimuthally polarized beam inside such profile is always extraordinary, but the angle between the optical axis and local direction of polarization, changes continuously and symmetrically in the azimuthal direction, causing the light to effectively experience ordinary refractive index at the double-twist cylinder axis and extraordinary index at the profile edge. If material birefringence is assumed negative (positive), refractive index is greater (lower) at cylinder axis and lower (greater) at outer parts of the cylinder causing lensing effects on the incident beam. Specifically, we describe the lensing effects of double-twist profile in case of negative birefringence and show the role of input Laguerre-Gaussian beam width and especially polarization. We then extend the lensing effects to waveguiding and report on the main mechanism for losses occuring on waveguiding in double twist cylinders: change of polarization at the start of the nematic profile and outward pointing in-plane components of the Poynting vector.

2. Numerical method and implementation

Custom-developed finite-difference time-domain (FDTD) method was used for modelling flow of light through the birefringent double-twist nematic structure. This explicit method computes time evolution of electric and magnetic fields E and H using the Maxwell’s equations [40]

ε̳ε0Et=×H,μμ0Ht=×E,
where ε0 and μ0 are vacuum permitivity and permeability, respectively, and μ is magnetic permeability set to unity, since nematics usually response much more readily to electric than magnetic fields. ε̳ is the dielectric tensor. Standard approach to discretization of Maxwell’s equations is by using the Yee lattice [41,42] where each field component is stored at a different lattice site. This ensures that all space derivatives are in a form of central-differences, giving the method second-order accuracy and stability. Such discretization is not possible in nonuniform birefringent materials such as liquid crystal nematics, where the light fields components may be coupled. Propagation of light in such cases can be modeled using a full 3D FDTD method, where all six components of E and H are considered [34]. Fields are updated with a half-step delay with respect to each other as well as stored in the customised Yee lattice in which all the components of E and H are stored at the usual Yee lattice points. Because FDTD is based on solving the Maxwell’s equations directly [40, 42], it allows for simulations of light flow in materials, where refractive index changes on length scales comparable to the wavelength. Additionally, our implementation of the method sacrifices some computational power in order to ensure stability [43] and allow for modeling light propagation through complex anisotropic materials of general coordinate dependence [34].

The components of the dielectric tensor εij at a certain coordinate is connected to the local order parameter tensor Qij through the following relation

εij=ε¯δij+23εamolQij,
where ε̄ = (ε + 2ε)/3 is the average refractive index (ε and ε are permittivities along and perpendicular to the molecular axis) and εa = εε is the molecular dielectric anisotropy. In our case, Qij = S(3ninjδij)/2 is that of a uniform chiral nematic, ordered into a double-twist cylinder in which the director n is described in cylindrical coordinates as
n(r,ϕ,z)=e^zcos(k0r)e^ϕsin(k0r),
where r is the radial distance from the z-oriented cylindrical axis and k0 a parameter determining the rate at which molecules twist with the radius, and is set at k0 = π/2R so that molecules twist for π/2 as we reach the outer cylinder radius R. Note that optically, the effective phase retardation in the radial direction of the double-twist cylinder does not follow the parabolic retardation profile of the ideal lens which can lead to a less clearly defined focusing and focal spot. External fields and self-coupling of the birefringent profile could be explored to futrher control or adapt this profile [34]. Experimentally, such or a simillar director fields occur locally in chiral nematics, with high enough chirality which favour twisting in two instead of only in one direction, such as in blue phases or chiral nematic skyrmions [44,45]. Recently, doubly twisted structure has been also reported to emerge when lyotropic chromonic liquid crystal are confined to cylindrical capillaries with planar anchoring [46].

FDTD method is highly parallelizable and was implemented for calculations on graphics processing units (GPUs), which significantly reduces the computational time when dealing with large systems. A typical run involving 50 million data points takes around 8 hours on a machine with four Nvidia Titan GPUs. The simulation box is taken to be three-dimensional with typical size equal to x × y × z = 3.6 μm × 3.6 μm × 30 μm for lensing and a few times longer for waveguiding with the beam propagating mainly along the z direction. Resolution is chosen to be 30 nm/voxel. Simulation box sizes and resolution were optimized and chosen in a way that waveguides could be elongated as much as is possible with GPU memory restrictions. Two additional layers around the simulation box, with thicknesses of couple voxels each, are used to introduce external light sources (the incoming beam) and at other regions that any light reaching the boundary can radiate out of the simulation box, as implemented by the perfectly-matched layer (PML) [47]. We should though emphasize, that essentially all mode intensity (except at the beam source) is far from the boundaries as it is sustained by the birefringent profile and not the simulation box boundary conditions. Light and material parameters used in our simulations were chosen to optimize lensing and waveguiding regimes. The wavelength λ = 390 nm of input light, was chosen as it provides suitably low divergence inside the waveguides and lenses that are of ∼ μm size. Input beam was azimuthally polarized with Laguerre-Gaussian shape but without phase dependence in the cross-section. Such a beam was chosen as it is the most basic realizable beam with azimuthal polarization. Beam half-width was typically ∼ 1 μm, while the half-width of the double-twist profile was ∼ 2 μm for lenses and ∼ 1 μm for waveguides. Values of refractive indices ne and no were taken to be 1.45 and 1.50, respectively. Nematic birefringence parameter, the difference between molecular extraordinary and ordinary refractive indices, was Δn = neno = −0.05, where we note, that although possible [48], it is not a common value of birefringence at optical frequencies for nematics, as it is usually positive. No light absorption mechanism was introduced into the simulations. Also no dynamic effect, such as thermal fluctuations of the director field were considered. In real systems, further light losses would originate from liquid crystal light absorption, which is usually small in the visible range, as well as from light scattering from the director fluctuations. Out of the visible range, absorption properties are frequently strongly material dependent.

3. Results

3.1. Lensing

Spatially varying optical axis in a cross-section of a double-twist cylinder (see Fig. 1) provides a refractive index profile that can lead to polarization dependent lensing and partial waveguiding. It is particularly interesting when we consider azimuthally polarized beams and negative nematic birefringence, which we show leads to convergent lensing and long-range waveguiding. Azimuthally polarized beam is sent along a birefringent double-twist profile segment of thickness d and lensing emerges.

For lensing on birefringent profiles the profile thickness d and the profile of the birefringence Δn(r) = ne(r) − no determine the phase retardation variation with radial distance. In a double-twist birefringent profile azimuthally polarized light observes ordinary refractive index no at the axis of the profile and ne near its edges. Therefore Δn < 0 gives a focussing lens with f < 0. In Figs. 2(A)–2(D) light intensity profiles are shown. The beam incoming from the left side and travelling toward the right, reaches a beam waist of w0 as it enters the birefringent profile. Lensing starts after the azimuthally polarized beam enters the double-twist profile. The focal spot size and the longitudinal position of the focus is determined by the ratio between the entry beam width and the profile width w0/R. In Figs. 2(A)–2(D) the profile width 2R was kept constant and the input beam half-width w0 was varied: w0/R values are shown in Fig. 2(E) where longitudinal half-width profiles for cases A–D are plotted.

 figure: Fig. 2

Fig. 2 Lensing on short segments of a double-twist nematic profile for different input beam widths. (A–D) Plots of light intensity at the central plane of the beam. Lensing of azimuthally polarized input beams with different input beam waists on identical double-twist profiles results in lensing with different numerical apertures. (E) Beam width profiles along the beam path for different input beam widths.

Download Full Size | PPT Slide | PDF

Double-twist cylinders perform as polarization dependent lenses. Orthogonal to the azimuthal is the radial polarization for which polarization is radially directed at every point of the cross-section. Through superposition of polarization states, any other axially symmetric polarization states can be devised [25]. Figure 3 shows propagation of three beams with distinct vectorial polarizations-radial, azimuthal and their combination-beams through double-twist profiles. Clearly, the simulated light profiles show that lensing is optimal when beam is azimuthally polarized and non-existent when the input polarization is radial, with obvious differences in the width of the beam profiles.

 figure: Fig. 3

Fig. 3 Lensing in birefringent double-twist cylinders for differently polarized input beams. In case of azimuthally polarized beam (A) lensing occurs, since the light experiences radially dependent refractive index. In case of radially polarized beam (B) the refractive index is uniform and no lensing occurs. In the intermediate case of radially-azimuthally polarized beam (C) only only partial lensing occurs. Double-twist profiles of the optical axis variation are shown in red, with green dashed line indicating the end of the profile region.

Download Full Size | PPT Slide | PDF

A known property of radially polarized beams is the onset of a strong longitudinal E component when focussing the beam close to the width determined by the resolution limit [25]. In a symmetric case of azimuthal polarization, it is the magnetic field H that is radially oriented; therefore the magnetic field obtains a stronger longitudinal component Hz. This is shown in Fig. 4(A), where the beam entered the profile at the coordinate z1, reached focus at z2 and then expanded towards z3 as marked in the subfigure below. In three smaller subfigures above, the longitudinal magnetic field component |Hz|2 is shown in the cross-section of the beam at the three respective coordinates. We see that the longitudinal magnetic field component |Hz|2 is strongest at the focal point and at the centre of the beam cross-section (r = 0). A smaller rise for the longitudinal amplitude of the electric field |Ez|2(r = 0, z) can be observed upon lensing as shown in Fig. 4(B) which occurs as a result of a change in the beam polarization state and decreases lensing efficiency and causes waveguiding losses. We will return to this point in more detail below.

 figure: Fig. 4

Fig. 4 Longitudinal component of the magnetic field of azimuthally polarized beam. Lensing of azimuthally polarized beams results in occurence of strong longitudinal magnetic field component in the center of the beam. (A) Color plots of magnetic field component Hz in the cross section of the beam in three different positions along the beam path, z1, z2, z3 (marked with white dashed lines on the lower plot) are shown, indicating that Hz is greatest at the centre of the beam cross-section at the beam waist. (B) Square of absolute amplitudes of longitudinal components Hz and Ez in the beam centre, marked with yellow line on the beam yz cross-section plot.

Download Full Size | PPT Slide | PDF

3.2. Waveguiding

Lensing can be extended to light guiding inside a double-twist cylinder for an incoming azimuthally polarized beam. To test, whether such system can support propagating light eigenmodes, we performed simulations of beam propagation inside a double-twist nematic profiles with lengths of several hundred wavelengths. Laguerre-Gaussian beams with azimuthal polarization is used as a sensible initial guess of a possible eigenmode in such a waveguide and also were chosen as they are well experimentally realizable [25].

Waveguding of double-twist cylinders is presented in Fig. 5. Figure 5(A) shows longitudinal light intensity profiles for input azimuthally polarized Laguerre-Gaussian beams with different input beam widths. Simillarly as before, the coupling efficiency (i.e. how much light remains inside the profile) depends centrally on the ratio between the input beam waist 2w0 and width of the double-twist cylinder 2R. In this case, the profile width was 6λ as shown in Fig. 5(A) and the optimal coupling regime occurs when w0/R is slightly below one-half (w0/R ∼ 0.4). When r is lower (w0/R ≲ 0.25) or larger (w0/R ≳ 0.7) initial losses become greater and light that is coupled into the fiber experiences large intensity fluctuations, that result from longitudinal focussing and defocussing of the beam inside the profile – see especially the first and last example in Fig. 5(A). Graph of relative beam power as a function of the travelled length in Fig. 5(C) shows that the azimuthally polarized Laguerre-Gaussian beams first experience losses as a consequence of a mismatch between their widths and the profile width. But additionally losses are observed even as the beam is further propagated inside the profile.

 figure: Fig. 5

Fig. 5 Waveguiding in a double-twist cylinder birefringent profile. (A) Azimuthally polarized beams propagating inside the double twist cylinders for different input beam widths 2w0. (B) Transversal components of the electric field E of the guided beam at three different representative positions along the beam path, denoted by green arrows. They indicate partial transformation of the initial azimuthal polarization to a polarization that is partially radial. (C) Beam power in units of initial beam power P0 along the double twist cylinder for different input beam widths 2w0. (D, E) Components of the Poynting vector averaged along the beam. Note the emergence of the radially twisted component of S in the transversal plane.

Download Full Size | PPT Slide | PDF

For in-depth investigation of these losses, polarization of the beam along its path was observed. What we found is that initial azimuthal polarization acquires some degree of the radial polarization immediately after the beam enters the double-twist profile. We assumed in simulations, that azimuthally polarized beam entered the double-twist profile from an isotropic medium of refractive index niso = 1.475 – value chosen to reduce reflections at entry. At this boundary between two dielectric materials, boundary conditions for electric displacement field D and magnetic field B (not that different to H) need to be considered. As the longitudinal component of electric field density Dz needs to be preserved at the boundary Dziso=DzDTC. We take that in the initial isotropic layer the light polarization field E = E(r)eϕ is purely azimuthal but, using D = ε0ε̳(r)E, it follows from the boundary condition that the longitudinal component of electric field intensity is non-zero in the double-twist profile

EzDTC=(ε̳DTC1(r)ε̳isoEiso)ez0,
where ε̳iso and ε̳DTC are dielectric tensors in the isotropic (diagonal and single valued) and birefringent double-twist cylinder material, respectively. This shows us there is a non-zero component Ez of light polarization immediately after it enters the double-twist profile. Indeed, this emergence of the non-zero longitudinal component of the electric field is seen already upon lensing shown in Fig. 4(B), where a small but non-zero component of Ez occurred after the beam entered the nematic profile. This emergence of Ez causes the light magnetic field H to also acquire azimuthal components and this in turn causes changes in the in-plane profile of E. Figure 5(B) shows snapshots of transversal components of the beam electric field E at three different representative positions along the beam path. Initially purely azimuthal polarization clearly acquires a degree of radial polarization. Radial polarization component in a double-twist profile experiences strictly ordinary refractive index which is a cause for the observed losses. We note, that these losses could in principle be avoided if purely azimuthal beams were made to originate from inside the double-twist cylinders. Observing the longitudinal electric field component Ez in the center of the beam it is lowest in the case of optimal widths ratio w0/R. In a non-optimal case, we observe not only intensity oscillations (see last panel in Fig. 5(A)), but also oscillations of the longitudinal component Ez at the beam center, reaching a few times larger values than in the optimal case. In turn such non-optimal width ratio causes a more significant change of the polarization state and losses.

Losses can be alternatively described by the direction of energy flow inside a double-twist cylinder. Directional energy flux is represented with a Poynting vector defined as S=12E×H. Figures 5(D) and 5(E) show the profile of the transversal and longitudinal components of the Poynting vector averaged along the waveguide at a given moment. Clearly, the Poynting vector points mainly along the z direction; however, it has also a non-zero, outward pointing and twisted component in the x y plane. This is a direct consequence of the beam polarization changes described above.

To generalise, we have shown that, effectively, double-twist cylinders can perform as waveguides based on their birefringent profile for azimuthally polarized beams over lengths of several tens of micrometres with leakage losses of roughly 0.2% = −0.0087dB per one wavelength of travelled distance. The calculated values of the Poynting vectors can be used to estimate the magnitude of the radiated energy from such a waveguide. The radial component of the Poynting vector averaged along the waveguide (Fig. (5E)) is of the order of magnitude 3 × 10−3W/μm2, giving effective radiated power per unit length of the waveguide ∼ 5 × 10−3W/μm ∼ 1 × 10−3W/λ. Note that these values agree within the order of magnitude with the energy losses shown in Fig. (5C).

3.3. Waveguiding along the curved double-twist cylinders

We explore light propagation along curved double-twist profiles as a part of a circle with curvature radius Rc, where nematic director at the centre of the curved profile follows its curvature. To characterise the losses due to curvature of the double twist cylinder, we calculate the ratio between power at a fixed travelled length of l = 60λ inside a curved profile and the input power P0 for different curvature radii Rc. The ratio between the input beam waist at the entry and the diameter of the double-twist profile is set to 0.6, being within the optimal coupling regime (optimal beam width to profile width ratio). Note that setting non-optimal w0/R will lead to larger initial losses and possible intensity and Ez oscillations.

In Fig. 6(B) dependence of the ratio between the output and input power on the curvature radius Rc is shown. We find that, losses increase notably after the curvature radius is smaller than a certain value, of the critical bend radius, which for the considered double-twist cylinder waveguides is of the order of ∼ 300λ. In standard (isotropic) waveguides critical radius is usually dependent on the numerical aperture, and thus on the difference of the refractive indices, of the fiber and cladding and, in case of multimode fibers, also on the propagating mode [49]. The field distribution inside curved waveguides also usually changes its shape due to curvature – it is forced toward the outer wall and some light leaves the waveguide. This effect can be also seen in Fig. 6(A) , where representative light intensity plots of an initially azimuthally polarized Laguerre-Gaussian beams inside a curved double-twist profile are shown.

 figure: Fig. 6

Fig. 6 Waveguiding in curved birefringent double-twist profiles. (A) Light intensity of the azimuthally polarized beam inside a double-twist cylinder nematic structure curved with a radius of curvature Rc. For smaller radii of curvature substantial bending losses occur. (B) Ratio between the input and output beam power after travelling a fixed length of 60λ inside a curved nematic profile as a function of the radius of curvature Rc.

Download Full Size | PPT Slide | PDF

4. Conclusion

In conclusion, we have shown that the birefringent profile of double-twist cylinders can perform as polarization dependent microlenses and as single-mode waveguides. Double-twist profile is transversed with an azimuthally polarized beam, for which the effective refractive index profile causes radially variable phase retardation. We have shown that in case of negative (positive) birefringence the double-twist cylinder profile of constant thickness can act as a converging (diverging) lens. Influence of input beam width and polarization on lensing performance were also demonstrated, showing that width of the input beam relative to the profile width, determines the beam width in focus and that lensing is most efficient in case of purely azimuthal input polarization.

Lensing was generalized into waveguiding of light inside the double-twist cylinders. Coupling efficiency was shown to be strongly dependent of the ratio r between the light-beam width (2w0) and double-twist profile width (2R), showing effectively optimal coupling when r ∼ 0.9. The efficiency of such waveguides was considered by investigating losses along the waveguide, and the waveguide was found to be lossy with intensity losses of ∼ −0.0087dB per travelled wavelength. Losses were atributed to the emergence of the longitudinal component of the beam electric field, which appears upon entry of the azimuthally polarized beam into the birefringent profile of the double twist-cylinder. Potential losses from curvature of the double-twist cylinder profile are also determined, showing that losses increase significantly as curvature radius Rc drops below the critical value of waveguide curvature Rc ∼ 300λ.

Finally, the photonic system of a double-twist cylinder described here is an example of micro-scale polarization selective optical element. Due to liquid nature and good tunability with external fields –including external or self-light fields– such birefringent elements are interesting candidates for new generations of photonic circuits.

5. Funding

Slovenian Research Agency grants (P1-0099, J1-7300, L1-8135); USAF AFRL EOARD research project Nematic Colloidal Tilings as Tunable Soft Metamaterials (grant no. FA9550-15-1-0418).

References

1. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 2007).

2. P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zelienger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 24 (1995). [CrossRef]  

3. L. Cattaneo, M. Savoini, I. Muševič, A. Kimel, and T. Rasing, “Ultrafast all-optical response of a nematic liquid crystal,” Opt. Express 23, 14010 (2015). [CrossRef]   [PubMed]  

4. P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, (Clarendon Press, Oxford, 1998).

5. N. Kamanina, S. Putilin, and D. Staselko, “Nano-, pico- and femtosecond study of fullerene-doped polymer-dispersed liquid crystals: holographic recording and optical limiting effect,” Synthetic Met. 127, 129–133 (2002). [CrossRef]  

6. H. Coles and S. Morris, “Liquid-crystal lasers,” Nat. Photonics 4, 676–685 (2010). [CrossRef]  

7. J. Xiang, A. Varanytsia, F. Minkowski, D. A. Paterson, J. M. D. Storey, C. T. Imrie, O. D. Lavrentovich, and P. P. Muhoray, “Electrically tunable laser based on oblique heliconical cholesteric liquid crystal,” Proc. Nat. Ac. Sci. USA , 113, 12925 (2016). [CrossRef]  

8. M. Humar, M. Ravnik, S. Pajk, and I. Muševič, “Electrically tunable liquid crystal optical microresonators,” Nat. Photonics 3, 595–600 (2009). [CrossRef]  

9. H. Ren and S. T. Wu, Introduction to adaptive lenses, (Wiley, 2012). [CrossRef]  

10. F. Fan, A. K. Srivastava, T. Du, M. C. Tseng, V. Chigrinov, and H. S. Kwok, “Low voltage tunable liquid crystal lens,” Opt. Lett. 38, 4116 (2013). [CrossRef]   [PubMed]  

11. Y. H. Lin, Y. J. Wang, and V. Reshetnyak, “Liquid crystal lenses with tunable focal length,” Liq. Crys. Rev. , 5, 111–143 (2017). [CrossRef]  

12. M. Chen, C. C. Chen, Y. C. Lai, and Y. H. Lin, “An electrically tunable liquid crystal lens for fiber coupling and variable optical attenuation,” J. Electr. Electron. Syst. 3, 124–129 (2014).

13. S. Ertman, T. R. Wolinski, J. Beeckman, K. Neyts, P. J. M. Vanbrabant, R. James, and F. A. Fernandez, “Numerical simulations of electrically induced birefringence in photonic liquid crystal fibers,” Act. Phys. Pol. A 118, 1113 (2010). [CrossRef]  

14. E. Perivolari, J. Gill, E. Ronald, V. Apostolopoulos, T.J. Sluckin, G. D’Alessandro, and M. Kaczmarek, “Optically controlled bistable waveplates,” J. Mol. Liq. 12, 119 (2017).

15. S. Residori, U. Bortolozzo, A. Peigne, S. Molin, P. Nouchi, D. Dolfi, and J. P. Huignard, “Liquid crystals for optical modulation and sensing applications,” Proc. SPIE 9940, 99400N (2016).

16. U. A. Laudyn, M. Kwasny, F. A. Sala, M. A. Karpierz, N. F Smyth, and G. Assanto, “Curved optical solitons subject to transverse acceleration in reorientational soft matter,” Sci. Rep. 7, 12385 (2017). [CrossRef]   [PubMed]  

17. J. Beeckman, K. Neyts, and P. J. M. Vanbrabant, “Liquid crystal photonic applications,” Opt. Eng. 8, 081202 (2011). [CrossRef]  

18. A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71, 1929 (2000). [CrossRef]  

19. D. C. Zografopoulos, R. Asquini, E. E. Kriezis, A. dAlessandro, and R. Beccherel, “Guided-wave liquid-crystal photonics,” Lab. Chip. 12, 3598–3610 (2012). [CrossRef]   [PubMed]  

20. H. S. Kitzerow and C. Bahr, Chirality In Liquid Crystals (Springer Verlag, 2001). [CrossRef]  

21. D. C. Wright and N. D. Mermin, „ ”Crystalline liquids: the blue phases,” Rev. Mod. Phys. 61, 385–432 (1989). [CrossRef]  

22. P. J. Ackerman and I. I. Smalyukh, “Static three-dimensional topological solitons in fluid chiral ferromagnets and colloids,” Nat. Mater. 16, 426 (2017). [CrossRef]  

23. J. Kobashi, H. Yoshida, and M. Ozaki, “Polychromatic optical vortex generation from patterned cholesteric liquid crystals,” Phys. Rev. Lett. 116253903 (2016). [CrossRef]   [PubMed]  

24. C. C. Tartan, P. S. Salter, T. D. Wilkinson, M. J. Booth, S. M. Morris, and S. J. Elston, “Generation of 3-dimensional polymer structures in liquid crystaliline devices using direct laser writing,” RSC Adv. 7, 507 (2017). [CrossRef]  

25. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1, 1–57 (2009). [CrossRef]  

26. R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phy. Rev. Lett. 91, 23 (2003). [CrossRef]  

27. V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D 32, 13 (1999). [CrossRef]  

28. K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7, 77–87 (2000). [CrossRef]   [PubMed]  

29. C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P. L. Fortin, N. Thiré, T. Brabec, F. Légaré, J. C. Kieffer, and M. Piché, “Direct Electron Acceleration with Radially Polarized Laser Beams,” Appl. Sci. 3, 70–93 (2013). [CrossRef]  

30. Y. Kozawa and S. Sato, “Generation of radially polarized laser beam by use of a conical Brewster prism,” Opt. Lett. 30, 3063–3065 (2005). [CrossRef]   [PubMed]  

31. G. Volpe and D. Petrov, “Generation of cylindrical vector beams with few-mode fibers excited by Laguerre–Gaussian beams,” Opt. Commun. 237, 89–95 (2004). [CrossRef]  

32. S. Ko, C. Ting, A. Fuh, and T. Lin, “Polarization converters based on axially symmetric twisted nematic liquid crystal,” Opt. Express 18, 3601–3607 (2010). [CrossRef]   [PubMed]  

33. M. Čančula, M. Ravnik, and S. Žumer, “Generation of vector beams with liquid crystal disclinations lines,” Phy. Rev. E 90, 022503 (2014). [CrossRef]  

34. M. Čančula, M. Ravnik, I. Muševič, and S. Žumer, “Liquid microlenses and waveguides from bulk nematic birefringent profiles,” Opt. Exp. 24, 22177 (2016). [CrossRef]  

35. H. Lin, P. Palffy-Muhoray, and M. A. Lee, “Liquid crystalline cores for optical fibers,” Mol. Cryst. Liq. Cryst. 204, 189 (1991). [CrossRef]  

36. H. Lin and P. Palffy-Muhoray, “TE and TM modes in a cylindrical liquid-crystal waveguide,” Opt. Lett. 17, 722 (1992). [CrossRef]   [PubMed]  

37. H. Lin and P. Palffy-Muhoray, “Propagation of TM modes in a nonlinear liquid-crystal waveguide,” Opt. Lett. 19, 436 (1994). [CrossRef]   [PubMed]  

38. C. G. Avendaño and J. A. Reyes, “Nonlinear TM modes in cylindrical liquid crystal waveguide,” Opt. Commun. 283, 5016 (2010). [CrossRef]  

39. S. H. Chen and T. J. Chen, “Observation of mode selection in a radially anisotropic cylindrical waveguide with liquid-crystal cladding,” Appl. Phys. Lett. 64, 1893 (1991). [CrossRef]  

40. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-difference Time-domain Method, 3rd ed. (Artech House, London2005).

41. K.S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenna Propag. 14, 302 (1966). [CrossRef]  

42. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J.D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Commun. 181, 687–702 (2010). [CrossRef]  

43. G. R. Werner and J. R. Cary, “A stable FDTD algorithm for non-diagonal, anisotropic dielectrics,” J. Comp. Phys. 10, 1085 (2007). [CrossRef]  

44. J. Fukuda and S. Žumer, ”Quasi-two-dimensional skyrmion lattices in a chiral nematic liquid crystal,” Nat. Commun. 2, 246 (2011). [CrossRef]   [PubMed]  

45. A. Nych, J. Fukuda, U. Ognysta, S. Žumer, and I. Muševič, ”Spontaneous formation and dynamics of half-skyrmions in a chiral liquid-crystal film,” Nat. Phys. 13, 1215 (2017). [CrossRef]  

46. K. Nayani, R. Chang, J. Fu, P. W. Ellis, A. Fernandez-Nievers, J. Ok Park, and M. Srinivasarao, “Spontaneous emergence of chirality in achiral lyotropic chromonic liquid crystals confined to cylinders,” Nat. Commun. 6, 8067 (2015). [CrossRef]   [PubMed]  

47. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comp. Phys. , 114, 185–200 (1994). [CrossRef]  

48. D. Bhattacharjee, P. R. Alapati, and A. Bhattacharjee, “Negative optical anisotropic behaviour of two higher homologues of 5O. m series of liquid crystals,” J. Mol. Liq. 222, 55–60 (2016). [CrossRef]  

49. D. Marcuse, “Curvature loss formula for optical fibers,” J. Opt. Soc. Am. 66, 216–220 (1976). [CrossRef]  

References

  • View by:
  • |
  • |
  • |

  1. B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 2007).
  2. P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zelienger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 24 (1995).
    [Crossref]
  3. L. Cattaneo, M. Savoini, I. Muševič, A. Kimel, and T. Rasing, “Ultrafast all-optical response of a nematic liquid crystal,” Opt. Express 23, 14010 (2015).
    [Crossref] [PubMed]
  4. P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, (Clarendon Press, Oxford, 1998).
  5. N. Kamanina, S. Putilin, and D. Staselko, “Nano-, pico- and femtosecond study of fullerene-doped polymer-dispersed liquid crystals: holographic recording and optical limiting effect,” Synthetic Met. 127, 129–133 (2002).
    [Crossref]
  6. H. Coles and S. Morris, “Liquid-crystal lasers,” Nat. Photonics 4, 676–685 (2010).
    [Crossref]
  7. J. Xiang, A. Varanytsia, F. Minkowski, D. A. Paterson, J. M. D. Storey, C. T. Imrie, O. D. Lavrentovich, and P. P. Muhoray, “Electrically tunable laser based on oblique heliconical cholesteric liquid crystal,” Proc. Nat. Ac. Sci. USA,  113, 12925 (2016).
    [Crossref]
  8. M. Humar, M. Ravnik, S. Pajk, and I. Muševič, “Electrically tunable liquid crystal optical microresonators,” Nat. Photonics 3, 595–600 (2009).
    [Crossref]
  9. H. Ren and S. T. Wu, Introduction to adaptive lenses, (Wiley, 2012).
    [Crossref]
  10. F. Fan, A. K. Srivastava, T. Du, M. C. Tseng, V. Chigrinov, and H. S. Kwok, “Low voltage tunable liquid crystal lens,” Opt. Lett. 38, 4116 (2013).
    [Crossref] [PubMed]
  11. Y. H. Lin, Y. J. Wang, and V. Reshetnyak, “Liquid crystal lenses with tunable focal length,” Liq. Crys. Rev.,  5, 111–143 (2017).
    [Crossref]
  12. M. Chen, C. C. Chen, Y. C. Lai, and Y. H. Lin, “An electrically tunable liquid crystal lens for fiber coupling and variable optical attenuation,” J. Electr. Electron. Syst. 3, 124–129 (2014).
  13. S. Ertman, T. R. Wolinski, J. Beeckman, K. Neyts, P. J. M. Vanbrabant, R. James, and F. A. Fernandez, “Numerical simulations of electrically induced birefringence in photonic liquid crystal fibers,” Act. Phys. Pol. A 118, 1113 (2010).
    [Crossref]
  14. E. Perivolari, J. Gill, E. Ronald, V. Apostolopoulos, T.J. Sluckin, G. D’Alessandro, and M. Kaczmarek, “Optically controlled bistable waveplates,” J. Mol. Liq. 12, 119 (2017).
  15. S. Residori, U. Bortolozzo, A. Peigne, S. Molin, P. Nouchi, D. Dolfi, and J. P. Huignard, “Liquid crystals for optical modulation and sensing applications,” Proc. SPIE 9940, 99400N (2016).
  16. U. A. Laudyn, M. Kwasny, F. A. Sala, M. A. Karpierz, N. F Smyth, and G. Assanto, “Curved optical solitons subject to transverse acceleration in reorientational soft matter,” Sci. Rep. 7, 12385 (2017).
    [Crossref] [PubMed]
  17. J. Beeckman, K. Neyts, and P. J. M. Vanbrabant, “Liquid crystal photonic applications,” Opt. Eng. 8, 081202 (2011).
    [Crossref]
  18. A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71, 1929 (2000).
    [Crossref]
  19. D. C. Zografopoulos, R. Asquini, E. E. Kriezis, A. dAlessandro, and R. Beccherel, “Guided-wave liquid-crystal photonics,” Lab. Chip. 12, 3598–3610 (2012).
    [Crossref] [PubMed]
  20. H. S. Kitzerow and C. Bahr, Chirality In Liquid Crystals (Springer Verlag, 2001).
    [Crossref]
  21. D. C. Wright and N. D. Mermin, „ ”Crystalline liquids: the blue phases,” Rev. Mod. Phys. 61, 385–432 (1989).
    [Crossref]
  22. P. J. Ackerman and I. I. Smalyukh, “Static three-dimensional topological solitons in fluid chiral ferromagnets and colloids,” Nat. Mater. 16, 426 (2017).
    [Crossref]
  23. J. Kobashi, H. Yoshida, and M. Ozaki, “Polychromatic optical vortex generation from patterned cholesteric liquid crystals,” Phys. Rev. Lett. 116253903 (2016).
    [Crossref] [PubMed]
  24. C. C. Tartan, P. S. Salter, T. D. Wilkinson, M. J. Booth, S. M. Morris, and S. J. Elston, “Generation of 3-dimensional polymer structures in liquid crystaliline devices using direct laser writing,” RSC Adv. 7, 507 (2017).
    [Crossref]
  25. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1, 1–57 (2009).
    [Crossref]
  26. R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phy. Rev. Lett. 91, 23 (2003).
    [Crossref]
  27. V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D 32, 13 (1999).
    [Crossref]
  28. K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7, 77–87 (2000).
    [Crossref] [PubMed]
  29. C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P. L. Fortin, N. Thiré, T. Brabec, F. Légaré, J. C. Kieffer, and M. Piché, “Direct Electron Acceleration with Radially Polarized Laser Beams,” Appl. Sci. 3, 70–93 (2013).
    [Crossref]
  30. Y. Kozawa and S. Sato, “Generation of radially polarized laser beam by use of a conical Brewster prism,” Opt. Lett. 30, 3063–3065 (2005).
    [Crossref] [PubMed]
  31. G. Volpe and D. Petrov, “Generation of cylindrical vector beams with few-mode fibers excited by Laguerre–Gaussian beams,” Opt. Commun. 237, 89–95 (2004).
    [Crossref]
  32. S. Ko, C. Ting, A. Fuh, and T. Lin, “Polarization converters based on axially symmetric twisted nematic liquid crystal,” Opt. Express 18, 3601–3607 (2010).
    [Crossref] [PubMed]
  33. M. Čančula, M. Ravnik, and S. Žumer, “Generation of vector beams with liquid crystal disclinations lines,” Phy. Rev. E 90, 022503 (2014).
    [Crossref]
  34. M. Čančula, M. Ravnik, I. Muševič, and S. Žumer, “Liquid microlenses and waveguides from bulk nematic birefringent profiles,” Opt. Exp. 24, 22177 (2016).
    [Crossref]
  35. H. Lin, P. Palffy-Muhoray, and M. A. Lee, “Liquid crystalline cores for optical fibers,” Mol. Cryst. Liq. Cryst. 204, 189 (1991).
    [Crossref]
  36. H. Lin and P. Palffy-Muhoray, “TE and TM modes in a cylindrical liquid-crystal waveguide,” Opt. Lett. 17, 722 (1992).
    [Crossref] [PubMed]
  37. H. Lin and P. Palffy-Muhoray, “Propagation of TM modes in a nonlinear liquid-crystal waveguide,” Opt. Lett. 19, 436 (1994).
    [Crossref] [PubMed]
  38. C. G. Avendaño and J. A. Reyes, “Nonlinear TM modes in cylindrical liquid crystal waveguide,” Opt. Commun. 283, 5016 (2010).
    [Crossref]
  39. S. H. Chen and T. J. Chen, “Observation of mode selection in a radially anisotropic cylindrical waveguide with liquid-crystal cladding,” Appl. Phys. Lett. 64, 1893 (1991).
    [Crossref]
  40. A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-difference Time-domain Method, 3rd ed. (Artech House, London2005).
  41. K.S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenna Propag. 14, 302 (1966).
    [Crossref]
  42. A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J.D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Commun. 181, 687–702 (2010).
    [Crossref]
  43. G. R. Werner and J. R. Cary, “A stable FDTD algorithm for non-diagonal, anisotropic dielectrics,” J. Comp. Phys. 10, 1085 (2007).
    [Crossref]
  44. J. Fukuda and S. Žumer, ”Quasi-two-dimensional skyrmion lattices in a chiral nematic liquid crystal,” Nat. Commun. 2, 246 (2011).
    [Crossref] [PubMed]
  45. A. Nych, J. Fukuda, U. Ognysta, S. Žumer, and I. Muševič, ”Spontaneous formation and dynamics of half-skyrmions in a chiral liquid-crystal film,” Nat. Phys. 13, 1215 (2017).
    [Crossref]
  46. K. Nayani, R. Chang, J. Fu, P. W. Ellis, A. Fernandez-Nievers, J. Ok Park, and M. Srinivasarao, “Spontaneous emergence of chirality in achiral lyotropic chromonic liquid crystals confined to cylinders,” Nat. Commun. 6, 8067 (2015).
    [Crossref] [PubMed]
  47. J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comp. Phys.,  114, 185–200 (1994).
    [Crossref]
  48. D. Bhattacharjee, P. R. Alapati, and A. Bhattacharjee, “Negative optical anisotropic behaviour of two higher homologues of 5O. m series of liquid crystals,” J. Mol. Liq. 222, 55–60 (2016).
    [Crossref]
  49. D. Marcuse, “Curvature loss formula for optical fibers,” J. Opt. Soc. Am. 66, 216–220 (1976).
    [Crossref]

2017 (6)

Y. H. Lin, Y. J. Wang, and V. Reshetnyak, “Liquid crystal lenses with tunable focal length,” Liq. Crys. Rev.,  5, 111–143 (2017).
[Crossref]

E. Perivolari, J. Gill, E. Ronald, V. Apostolopoulos, T.J. Sluckin, G. D’Alessandro, and M. Kaczmarek, “Optically controlled bistable waveplates,” J. Mol. Liq. 12, 119 (2017).

U. A. Laudyn, M. Kwasny, F. A. Sala, M. A. Karpierz, N. F Smyth, and G. Assanto, “Curved optical solitons subject to transverse acceleration in reorientational soft matter,” Sci. Rep. 7, 12385 (2017).
[Crossref] [PubMed]

P. J. Ackerman and I. I. Smalyukh, “Static three-dimensional topological solitons in fluid chiral ferromagnets and colloids,” Nat. Mater. 16, 426 (2017).
[Crossref]

C. C. Tartan, P. S. Salter, T. D. Wilkinson, M. J. Booth, S. M. Morris, and S. J. Elston, “Generation of 3-dimensional polymer structures in liquid crystaliline devices using direct laser writing,” RSC Adv. 7, 507 (2017).
[Crossref]

A. Nych, J. Fukuda, U. Ognysta, S. Žumer, and I. Muševič, ”Spontaneous formation and dynamics of half-skyrmions in a chiral liquid-crystal film,” Nat. Phys. 13, 1215 (2017).
[Crossref]

2016 (5)

D. Bhattacharjee, P. R. Alapati, and A. Bhattacharjee, “Negative optical anisotropic behaviour of two higher homologues of 5O. m series of liquid crystals,” J. Mol. Liq. 222, 55–60 (2016).
[Crossref]

M. Čančula, M. Ravnik, I. Muševič, and S. Žumer, “Liquid microlenses and waveguides from bulk nematic birefringent profiles,” Opt. Exp. 24, 22177 (2016).
[Crossref]

J. Kobashi, H. Yoshida, and M. Ozaki, “Polychromatic optical vortex generation from patterned cholesteric liquid crystals,” Phys. Rev. Lett. 116253903 (2016).
[Crossref] [PubMed]

S. Residori, U. Bortolozzo, A. Peigne, S. Molin, P. Nouchi, D. Dolfi, and J. P. Huignard, “Liquid crystals for optical modulation and sensing applications,” Proc. SPIE 9940, 99400N (2016).

J. Xiang, A. Varanytsia, F. Minkowski, D. A. Paterson, J. M. D. Storey, C. T. Imrie, O. D. Lavrentovich, and P. P. Muhoray, “Electrically tunable laser based on oblique heliconical cholesteric liquid crystal,” Proc. Nat. Ac. Sci. USA,  113, 12925 (2016).
[Crossref]

2015 (2)

L. Cattaneo, M. Savoini, I. Muševič, A. Kimel, and T. Rasing, “Ultrafast all-optical response of a nematic liquid crystal,” Opt. Express 23, 14010 (2015).
[Crossref] [PubMed]

K. Nayani, R. Chang, J. Fu, P. W. Ellis, A. Fernandez-Nievers, J. Ok Park, and M. Srinivasarao, “Spontaneous emergence of chirality in achiral lyotropic chromonic liquid crystals confined to cylinders,” Nat. Commun. 6, 8067 (2015).
[Crossref] [PubMed]

2014 (2)

M. Chen, C. C. Chen, Y. C. Lai, and Y. H. Lin, “An electrically tunable liquid crystal lens for fiber coupling and variable optical attenuation,” J. Electr. Electron. Syst. 3, 124–129 (2014).

M. Čančula, M. Ravnik, and S. Žumer, “Generation of vector beams with liquid crystal disclinations lines,” Phy. Rev. E 90, 022503 (2014).
[Crossref]

2013 (2)

F. Fan, A. K. Srivastava, T. Du, M. C. Tseng, V. Chigrinov, and H. S. Kwok, “Low voltage tunable liquid crystal lens,” Opt. Lett. 38, 4116 (2013).
[Crossref] [PubMed]

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P. L. Fortin, N. Thiré, T. Brabec, F. Légaré, J. C. Kieffer, and M. Piché, “Direct Electron Acceleration with Radially Polarized Laser Beams,” Appl. Sci. 3, 70–93 (2013).
[Crossref]

2012 (1)

D. C. Zografopoulos, R. Asquini, E. E. Kriezis, A. dAlessandro, and R. Beccherel, “Guided-wave liquid-crystal photonics,” Lab. Chip. 12, 3598–3610 (2012).
[Crossref] [PubMed]

2011 (2)

J. Beeckman, K. Neyts, and P. J. M. Vanbrabant, “Liquid crystal photonic applications,” Opt. Eng. 8, 081202 (2011).
[Crossref]

J. Fukuda and S. Žumer, ”Quasi-two-dimensional skyrmion lattices in a chiral nematic liquid crystal,” Nat. Commun. 2, 246 (2011).
[Crossref] [PubMed]

2010 (5)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J.D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Commun. 181, 687–702 (2010).
[Crossref]

S. Ertman, T. R. Wolinski, J. Beeckman, K. Neyts, P. J. M. Vanbrabant, R. James, and F. A. Fernandez, “Numerical simulations of electrically induced birefringence in photonic liquid crystal fibers,” Act. Phys. Pol. A 118, 1113 (2010).
[Crossref]

H. Coles and S. Morris, “Liquid-crystal lasers,” Nat. Photonics 4, 676–685 (2010).
[Crossref]

S. Ko, C. Ting, A. Fuh, and T. Lin, “Polarization converters based on axially symmetric twisted nematic liquid crystal,” Opt. Express 18, 3601–3607 (2010).
[Crossref] [PubMed]

C. G. Avendaño and J. A. Reyes, “Nonlinear TM modes in cylindrical liquid crystal waveguide,” Opt. Commun. 283, 5016 (2010).
[Crossref]

2009 (2)

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1, 1–57 (2009).
[Crossref]

M. Humar, M. Ravnik, S. Pajk, and I. Muševič, “Electrically tunable liquid crystal optical microresonators,” Nat. Photonics 3, 595–600 (2009).
[Crossref]

2007 (1)

G. R. Werner and J. R. Cary, “A stable FDTD algorithm for non-diagonal, anisotropic dielectrics,” J. Comp. Phys. 10, 1085 (2007).
[Crossref]

2005 (1)

2004 (1)

G. Volpe and D. Petrov, “Generation of cylindrical vector beams with few-mode fibers excited by Laguerre–Gaussian beams,” Opt. Commun. 237, 89–95 (2004).
[Crossref]

2003 (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phy. Rev. Lett. 91, 23 (2003).
[Crossref]

2002 (1)

N. Kamanina, S. Putilin, and D. Staselko, “Nano-, pico- and femtosecond study of fullerene-doped polymer-dispersed liquid crystals: holographic recording and optical limiting effect,” Synthetic Met. 127, 129–133 (2002).
[Crossref]

2000 (2)

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71, 1929 (2000).
[Crossref]

K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7, 77–87 (2000).
[Crossref] [PubMed]

1999 (1)

V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D 32, 13 (1999).
[Crossref]

1995 (1)

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zelienger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 24 (1995).
[Crossref]

1994 (2)

H. Lin and P. Palffy-Muhoray, “Propagation of TM modes in a nonlinear liquid-crystal waveguide,” Opt. Lett. 19, 436 (1994).
[Crossref] [PubMed]

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comp. Phys.,  114, 185–200 (1994).
[Crossref]

1992 (1)

1991 (2)

S. H. Chen and T. J. Chen, “Observation of mode selection in a radially anisotropic cylindrical waveguide with liquid-crystal cladding,” Appl. Phys. Lett. 64, 1893 (1991).
[Crossref]

H. Lin, P. Palffy-Muhoray, and M. A. Lee, “Liquid crystalline cores for optical fibers,” Mol. Cryst. Liq. Cryst. 204, 189 (1991).
[Crossref]

1989 (1)

D. C. Wright and N. D. Mermin, „ ”Crystalline liquids: the blue phases,” Rev. Mod. Phys. 61, 385–432 (1989).
[Crossref]

1976 (1)

1966 (1)

K.S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenna Propag. 14, 302 (1966).
[Crossref]

Ackerman, P. J.

P. J. Ackerman and I. I. Smalyukh, “Static three-dimensional topological solitons in fluid chiral ferromagnets and colloids,” Nat. Mater. 16, 426 (2017).
[Crossref]

Alapati, P. R.

D. Bhattacharjee, P. R. Alapati, and A. Bhattacharjee, “Negative optical anisotropic behaviour of two higher homologues of 5O. m series of liquid crystals,” J. Mol. Liq. 222, 55–60 (2016).
[Crossref]

Apostolopoulos, V.

E. Perivolari, J. Gill, E. Ronald, V. Apostolopoulos, T.J. Sluckin, G. D’Alessandro, and M. Kaczmarek, “Optically controlled bistable waveplates,” J. Mol. Liq. 12, 119 (2017).

April, A.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P. L. Fortin, N. Thiré, T. Brabec, F. Légaré, J. C. Kieffer, and M. Piché, “Direct Electron Acceleration with Radially Polarized Laser Beams,” Appl. Sci. 3, 70–93 (2013).
[Crossref]

Asquini, R.

D. C. Zografopoulos, R. Asquini, E. E. Kriezis, A. dAlessandro, and R. Beccherel, “Guided-wave liquid-crystal photonics,” Lab. Chip. 12, 3598–3610 (2012).
[Crossref] [PubMed]

Assanto, G.

U. A. Laudyn, M. Kwasny, F. A. Sala, M. A. Karpierz, N. F Smyth, and G. Assanto, “Curved optical solitons subject to transverse acceleration in reorientational soft matter,” Sci. Rep. 7, 12385 (2017).
[Crossref] [PubMed]

Avendaño, C. G.

C. G. Avendaño and J. A. Reyes, “Nonlinear TM modes in cylindrical liquid crystal waveguide,” Opt. Commun. 283, 5016 (2010).
[Crossref]

Bahr, C.

H. S. Kitzerow and C. Bahr, Chirality In Liquid Crystals (Springer Verlag, 2001).
[Crossref]

Beccherel, R.

D. C. Zografopoulos, R. Asquini, E. E. Kriezis, A. dAlessandro, and R. Beccherel, “Guided-wave liquid-crystal photonics,” Lab. Chip. 12, 3598–3610 (2012).
[Crossref] [PubMed]

Beeckman, J.

J. Beeckman, K. Neyts, and P. J. M. Vanbrabant, “Liquid crystal photonic applications,” Opt. Eng. 8, 081202 (2011).
[Crossref]

S. Ertman, T. R. Wolinski, J. Beeckman, K. Neyts, P. J. M. Vanbrabant, R. James, and F. A. Fernandez, “Numerical simulations of electrically induced birefringence in photonic liquid crystal fibers,” Act. Phys. Pol. A 118, 1113 (2010).
[Crossref]

Berenger, J. P.

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comp. Phys.,  114, 185–200 (1994).
[Crossref]

Bermel, P.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J.D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Commun. 181, 687–702 (2010).
[Crossref]

Bhattacharjee, A.

D. Bhattacharjee, P. R. Alapati, and A. Bhattacharjee, “Negative optical anisotropic behaviour of two higher homologues of 5O. m series of liquid crystals,” J. Mol. Liq. 222, 55–60 (2016).
[Crossref]

Bhattacharjee, D.

D. Bhattacharjee, P. R. Alapati, and A. Bhattacharjee, “Negative optical anisotropic behaviour of two higher homologues of 5O. m series of liquid crystals,” J. Mol. Liq. 222, 55–60 (2016).
[Crossref]

Booth, M. J.

C. C. Tartan, P. S. Salter, T. D. Wilkinson, M. J. Booth, S. M. Morris, and S. J. Elston, “Generation of 3-dimensional polymer structures in liquid crystaliline devices using direct laser writing,” RSC Adv. 7, 507 (2017).
[Crossref]

Bortolozzo, U.

S. Residori, U. Bortolozzo, A. Peigne, S. Molin, P. Nouchi, D. Dolfi, and J. P. Huignard, “Liquid crystals for optical modulation and sensing applications,” Proc. SPIE 9940, 99400N (2016).

Brabec, T.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P. L. Fortin, N. Thiré, T. Brabec, F. Légaré, J. C. Kieffer, and M. Piché, “Direct Electron Acceleration with Radially Polarized Laser Beams,” Appl. Sci. 3, 70–93 (2013).
[Crossref]

Brown, T. G.

Cancula, M.

M. Čančula, M. Ravnik, I. Muševič, and S. Žumer, “Liquid microlenses and waveguides from bulk nematic birefringent profiles,” Opt. Exp. 24, 22177 (2016).
[Crossref]

M. Čančula, M. Ravnik, and S. Žumer, “Generation of vector beams with liquid crystal disclinations lines,” Phy. Rev. E 90, 022503 (2014).
[Crossref]

Cary, J. R.

G. R. Werner and J. R. Cary, “A stable FDTD algorithm for non-diagonal, anisotropic dielectrics,” J. Comp. Phys. 10, 1085 (2007).
[Crossref]

Cattaneo, L.

Chang, R.

K. Nayani, R. Chang, J. Fu, P. W. Ellis, A. Fernandez-Nievers, J. Ok Park, and M. Srinivasarao, “Spontaneous emergence of chirality in achiral lyotropic chromonic liquid crystals confined to cylinders,” Nat. Commun. 6, 8067 (2015).
[Crossref] [PubMed]

Chen, C. C.

M. Chen, C. C. Chen, Y. C. Lai, and Y. H. Lin, “An electrically tunable liquid crystal lens for fiber coupling and variable optical attenuation,” J. Electr. Electron. Syst. 3, 124–129 (2014).

Chen, M.

M. Chen, C. C. Chen, Y. C. Lai, and Y. H. Lin, “An electrically tunable liquid crystal lens for fiber coupling and variable optical attenuation,” J. Electr. Electron. Syst. 3, 124–129 (2014).

Chen, S. H.

S. H. Chen and T. J. Chen, “Observation of mode selection in a radially anisotropic cylindrical waveguide with liquid-crystal cladding,” Appl. Phys. Lett. 64, 1893 (1991).
[Crossref]

Chen, T. J.

S. H. Chen and T. J. Chen, “Observation of mode selection in a radially anisotropic cylindrical waveguide with liquid-crystal cladding,” Appl. Phys. Lett. 64, 1893 (1991).
[Crossref]

Chigrinov, V.

Coles, H.

H. Coles and S. Morris, “Liquid-crystal lasers,” Nat. Photonics 4, 676–685 (2010).
[Crossref]

D’Alessandro, G.

E. Perivolari, J. Gill, E. Ronald, V. Apostolopoulos, T.J. Sluckin, G. D’Alessandro, and M. Kaczmarek, “Optically controlled bistable waveplates,” J. Mol. Liq. 12, 119 (2017).

dAlessandro, A.

D. C. Zografopoulos, R. Asquini, E. E. Kriezis, A. dAlessandro, and R. Beccherel, “Guided-wave liquid-crystal photonics,” Lab. Chip. 12, 3598–3610 (2012).
[Crossref] [PubMed]

de Gennes, P. G.

P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, (Clarendon Press, Oxford, 1998).

Dolfi, D.

S. Residori, U. Bortolozzo, A. Peigne, S. Molin, P. Nouchi, D. Dolfi, and J. P. Huignard, “Liquid crystals for optical modulation and sensing applications,” Proc. SPIE 9940, 99400N (2016).

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phy. Rev. Lett. 91, 23 (2003).
[Crossref]

Du, T.

Ellis, P. W.

K. Nayani, R. Chang, J. Fu, P. W. Ellis, A. Fernandez-Nievers, J. Ok Park, and M. Srinivasarao, “Spontaneous emergence of chirality in achiral lyotropic chromonic liquid crystals confined to cylinders,” Nat. Commun. 6, 8067 (2015).
[Crossref] [PubMed]

Elston, S. J.

C. C. Tartan, P. S. Salter, T. D. Wilkinson, M. J. Booth, S. M. Morris, and S. J. Elston, “Generation of 3-dimensional polymer structures in liquid crystaliline devices using direct laser writing,” RSC Adv. 7, 507 (2017).
[Crossref]

Ertman, S.

S. Ertman, T. R. Wolinski, J. Beeckman, K. Neyts, P. J. M. Vanbrabant, R. James, and F. A. Fernandez, “Numerical simulations of electrically induced birefringence in photonic liquid crystal fibers,” Act. Phys. Pol. A 118, 1113 (2010).
[Crossref]

Fan, F.

Fernandez, F. A.

S. Ertman, T. R. Wolinski, J. Beeckman, K. Neyts, P. J. M. Vanbrabant, R. James, and F. A. Fernandez, “Numerical simulations of electrically induced birefringence in photonic liquid crystal fibers,” Act. Phys. Pol. A 118, 1113 (2010).
[Crossref]

Fernandez-Nievers, A.

K. Nayani, R. Chang, J. Fu, P. W. Ellis, A. Fernandez-Nievers, J. Ok Park, and M. Srinivasarao, “Spontaneous emergence of chirality in achiral lyotropic chromonic liquid crystals confined to cylinders,” Nat. Commun. 6, 8067 (2015).
[Crossref] [PubMed]

Fortin, P. L.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P. L. Fortin, N. Thiré, T. Brabec, F. Légaré, J. C. Kieffer, and M. Piché, “Direct Electron Acceleration with Radially Polarized Laser Beams,” Appl. Sci. 3, 70–93 (2013).
[Crossref]

Fourmaux, S.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P. L. Fortin, N. Thiré, T. Brabec, F. Légaré, J. C. Kieffer, and M. Piché, “Direct Electron Acceleration with Radially Polarized Laser Beams,” Appl. Sci. 3, 70–93 (2013).
[Crossref]

Fu, J.

K. Nayani, R. Chang, J. Fu, P. W. Ellis, A. Fernandez-Nievers, J. Ok Park, and M. Srinivasarao, “Spontaneous emergence of chirality in achiral lyotropic chromonic liquid crystals confined to cylinders,” Nat. Commun. 6, 8067 (2015).
[Crossref] [PubMed]

Fuh, A.

Fukuda, J.

A. Nych, J. Fukuda, U. Ognysta, S. Žumer, and I. Muševič, ”Spontaneous formation and dynamics of half-skyrmions in a chiral liquid-crystal film,” Nat. Phys. 13, 1215 (2017).
[Crossref]

J. Fukuda and S. Žumer, ”Quasi-two-dimensional skyrmion lattices in a chiral nematic liquid crystal,” Nat. Commun. 2, 246 (2011).
[Crossref] [PubMed]

Gill, J.

E. Perivolari, J. Gill, E. Ronald, V. Apostolopoulos, T.J. Sluckin, G. D’Alessandro, and M. Kaczmarek, “Optically controlled bistable waveplates,” J. Mol. Liq. 12, 119 (2017).

Hagness, S. C.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-difference Time-domain Method, 3rd ed. (Artech House, London2005).

Huignard, J. P.

S. Residori, U. Bortolozzo, A. Peigne, S. Molin, P. Nouchi, D. Dolfi, and J. P. Huignard, “Liquid crystals for optical modulation and sensing applications,” Proc. SPIE 9940, 99400N (2016).

Humar, M.

M. Humar, M. Ravnik, S. Pajk, and I. Muševič, “Electrically tunable liquid crystal optical microresonators,” Nat. Photonics 3, 595–600 (2009).
[Crossref]

Ibanescu, M.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J.D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Commun. 181, 687–702 (2010).
[Crossref]

Imrie, C. T.

J. Xiang, A. Varanytsia, F. Minkowski, D. A. Paterson, J. M. D. Storey, C. T. Imrie, O. D. Lavrentovich, and P. P. Muhoray, “Electrically tunable laser based on oblique heliconical cholesteric liquid crystal,” Proc. Nat. Ac. Sci. USA,  113, 12925 (2016).
[Crossref]

James, R.

S. Ertman, T. R. Wolinski, J. Beeckman, K. Neyts, P. J. M. Vanbrabant, R. James, and F. A. Fernandez, “Numerical simulations of electrically induced birefringence in photonic liquid crystal fibers,” Act. Phys. Pol. A 118, 1113 (2010).
[Crossref]

Joannopoulos, J.D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J.D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Commun. 181, 687–702 (2010).
[Crossref]

Johnson, S. G.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J.D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Commun. 181, 687–702 (2010).
[Crossref]

Kaczmarek, M.

E. Perivolari, J. Gill, E. Ronald, V. Apostolopoulos, T.J. Sluckin, G. D’Alessandro, and M. Kaczmarek, “Optically controlled bistable waveplates,” J. Mol. Liq. 12, 119 (2017).

Kamanina, N.

N. Kamanina, S. Putilin, and D. Staselko, “Nano-, pico- and femtosecond study of fullerene-doped polymer-dispersed liquid crystals: holographic recording and optical limiting effect,” Synthetic Met. 127, 129–133 (2002).
[Crossref]

Karpierz, M. A.

U. A. Laudyn, M. Kwasny, F. A. Sala, M. A. Karpierz, N. F Smyth, and G. Assanto, “Curved optical solitons subject to transverse acceleration in reorientational soft matter,” Sci. Rep. 7, 12385 (2017).
[Crossref] [PubMed]

Kieffer, J. C.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P. L. Fortin, N. Thiré, T. Brabec, F. Légaré, J. C. Kieffer, and M. Piché, “Direct Electron Acceleration with Radially Polarized Laser Beams,” Appl. Sci. 3, 70–93 (2013).
[Crossref]

Kimel, A.

Kitzerow, H. S.

H. S. Kitzerow and C. Bahr, Chirality In Liquid Crystals (Springer Verlag, 2001).
[Crossref]

Ko, S.

Kobashi, J.

J. Kobashi, H. Yoshida, and M. Ozaki, “Polychromatic optical vortex generation from patterned cholesteric liquid crystals,” Phys. Rev. Lett. 116253903 (2016).
[Crossref] [PubMed]

Kozawa, Y.

Kriezis, E. E.

D. C. Zografopoulos, R. Asquini, E. E. Kriezis, A. dAlessandro, and R. Beccherel, “Guided-wave liquid-crystal photonics,” Lab. Chip. 12, 3598–3610 (2012).
[Crossref] [PubMed]

Kwasny, M.

U. A. Laudyn, M. Kwasny, F. A. Sala, M. A. Karpierz, N. F Smyth, and G. Assanto, “Curved optical solitons subject to transverse acceleration in reorientational soft matter,” Sci. Rep. 7, 12385 (2017).
[Crossref] [PubMed]

Kwiat, P. G.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zelienger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 24 (1995).
[Crossref]

Kwok, H. S.

Lai, Y. C.

M. Chen, C. C. Chen, Y. C. Lai, and Y. H. Lin, “An electrically tunable liquid crystal lens for fiber coupling and variable optical attenuation,” J. Electr. Electron. Syst. 3, 124–129 (2014).

Laudyn, U. A.

U. A. Laudyn, M. Kwasny, F. A. Sala, M. A. Karpierz, N. F Smyth, and G. Assanto, “Curved optical solitons subject to transverse acceleration in reorientational soft matter,” Sci. Rep. 7, 12385 (2017).
[Crossref] [PubMed]

Lavrentovich, O. D.

J. Xiang, A. Varanytsia, F. Minkowski, D. A. Paterson, J. M. D. Storey, C. T. Imrie, O. D. Lavrentovich, and P. P. Muhoray, “Electrically tunable laser based on oblique heliconical cholesteric liquid crystal,” Proc. Nat. Ac. Sci. USA,  113, 12925 (2016).
[Crossref]

Lee, M. A.

H. Lin, P. Palffy-Muhoray, and M. A. Lee, “Liquid crystalline cores for optical fibers,” Mol. Cryst. Liq. Cryst. 204, 189 (1991).
[Crossref]

Légaré, F.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P. L. Fortin, N. Thiré, T. Brabec, F. Légaré, J. C. Kieffer, and M. Piché, “Direct Electron Acceleration with Radially Polarized Laser Beams,” Appl. Sci. 3, 70–93 (2013).
[Crossref]

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phy. Rev. Lett. 91, 23 (2003).
[Crossref]

Lin, H.

Lin, T.

Lin, Y. H.

Y. H. Lin, Y. J. Wang, and V. Reshetnyak, “Liquid crystal lenses with tunable focal length,” Liq. Crys. Rev.,  5, 111–143 (2017).
[Crossref]

M. Chen, C. C. Chen, Y. C. Lai, and Y. H. Lin, “An electrically tunable liquid crystal lens for fiber coupling and variable optical attenuation,” J. Electr. Electron. Syst. 3, 124–129 (2014).

Marceau, V.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P. L. Fortin, N. Thiré, T. Brabec, F. Légaré, J. C. Kieffer, and M. Piché, “Direct Electron Acceleration with Radially Polarized Laser Beams,” Appl. Sci. 3, 70–93 (2013).
[Crossref]

Marcuse, D.

Mattle, K.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zelienger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 24 (1995).
[Crossref]

Mermin, N. D.

D. C. Wright and N. D. Mermin, „ ”Crystalline liquids: the blue phases,” Rev. Mod. Phys. 61, 385–432 (1989).
[Crossref]

Minkowski, F.

J. Xiang, A. Varanytsia, F. Minkowski, D. A. Paterson, J. M. D. Storey, C. T. Imrie, O. D. Lavrentovich, and P. P. Muhoray, “Electrically tunable laser based on oblique heliconical cholesteric liquid crystal,” Proc. Nat. Ac. Sci. USA,  113, 12925 (2016).
[Crossref]

Molin, S.

S. Residori, U. Bortolozzo, A. Peigne, S. Molin, P. Nouchi, D. Dolfi, and J. P. Huignard, “Liquid crystals for optical modulation and sensing applications,” Proc. SPIE 9940, 99400N (2016).

Morris, S.

H. Coles and S. Morris, “Liquid-crystal lasers,” Nat. Photonics 4, 676–685 (2010).
[Crossref]

Morris, S. M.

C. C. Tartan, P. S. Salter, T. D. Wilkinson, M. J. Booth, S. M. Morris, and S. J. Elston, “Generation of 3-dimensional polymer structures in liquid crystaliline devices using direct laser writing,” RSC Adv. 7, 507 (2017).
[Crossref]

Muhoray, P. P.

J. Xiang, A. Varanytsia, F. Minkowski, D. A. Paterson, J. M. D. Storey, C. T. Imrie, O. D. Lavrentovich, and P. P. Muhoray, “Electrically tunable laser based on oblique heliconical cholesteric liquid crystal,” Proc. Nat. Ac. Sci. USA,  113, 12925 (2016).
[Crossref]

Muševic, I.

A. Nych, J. Fukuda, U. Ognysta, S. Žumer, and I. Muševič, ”Spontaneous formation and dynamics of half-skyrmions in a chiral liquid-crystal film,” Nat. Phys. 13, 1215 (2017).
[Crossref]

M. Čančula, M. Ravnik, I. Muševič, and S. Žumer, “Liquid microlenses and waveguides from bulk nematic birefringent profiles,” Opt. Exp. 24, 22177 (2016).
[Crossref]

L. Cattaneo, M. Savoini, I. Muševič, A. Kimel, and T. Rasing, “Ultrafast all-optical response of a nematic liquid crystal,” Opt. Express 23, 14010 (2015).
[Crossref] [PubMed]

M. Humar, M. Ravnik, S. Pajk, and I. Muševič, “Electrically tunable liquid crystal optical microresonators,” Nat. Photonics 3, 595–600 (2009).
[Crossref]

Nayani, K.

K. Nayani, R. Chang, J. Fu, P. W. Ellis, A. Fernandez-Nievers, J. Ok Park, and M. Srinivasarao, “Spontaneous emergence of chirality in achiral lyotropic chromonic liquid crystals confined to cylinders,” Nat. Commun. 6, 8067 (2015).
[Crossref] [PubMed]

Nesterov, A. V.

V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D 32, 13 (1999).
[Crossref]

Neyts, K.

J. Beeckman, K. Neyts, and P. J. M. Vanbrabant, “Liquid crystal photonic applications,” Opt. Eng. 8, 081202 (2011).
[Crossref]

S. Ertman, T. R. Wolinski, J. Beeckman, K. Neyts, P. J. M. Vanbrabant, R. James, and F. A. Fernandez, “Numerical simulations of electrically induced birefringence in photonic liquid crystal fibers,” Act. Phys. Pol. A 118, 1113 (2010).
[Crossref]

Niziev, V. G.

V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D 32, 13 (1999).
[Crossref]

Nouchi, P.

S. Residori, U. Bortolozzo, A. Peigne, S. Molin, P. Nouchi, D. Dolfi, and J. P. Huignard, “Liquid crystals for optical modulation and sensing applications,” Proc. SPIE 9940, 99400N (2016).

Nych, A.

A. Nych, J. Fukuda, U. Ognysta, S. Žumer, and I. Muševič, ”Spontaneous formation and dynamics of half-skyrmions in a chiral liquid-crystal film,” Nat. Phys. 13, 1215 (2017).
[Crossref]

Ognysta, U.

A. Nych, J. Fukuda, U. Ognysta, S. Žumer, and I. Muševič, ”Spontaneous formation and dynamics of half-skyrmions in a chiral liquid-crystal film,” Nat. Phys. 13, 1215 (2017).
[Crossref]

Ok Park, J.

K. Nayani, R. Chang, J. Fu, P. W. Ellis, A. Fernandez-Nievers, J. Ok Park, and M. Srinivasarao, “Spontaneous emergence of chirality in achiral lyotropic chromonic liquid crystals confined to cylinders,” Nat. Commun. 6, 8067 (2015).
[Crossref] [PubMed]

Oskooi, A. F.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J.D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Commun. 181, 687–702 (2010).
[Crossref]

Ozaki, M.

J. Kobashi, H. Yoshida, and M. Ozaki, “Polychromatic optical vortex generation from patterned cholesteric liquid crystals,” Phys. Rev. Lett. 116253903 (2016).
[Crossref] [PubMed]

Pajk, S.

M. Humar, M. Ravnik, S. Pajk, and I. Muševič, “Electrically tunable liquid crystal optical microresonators,” Nat. Photonics 3, 595–600 (2009).
[Crossref]

Palffy-Muhoray, P.

Paterson, D. A.

J. Xiang, A. Varanytsia, F. Minkowski, D. A. Paterson, J. M. D. Storey, C. T. Imrie, O. D. Lavrentovich, and P. P. Muhoray, “Electrically tunable laser based on oblique heliconical cholesteric liquid crystal,” Proc. Nat. Ac. Sci. USA,  113, 12925 (2016).
[Crossref]

Payeur, S.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P. L. Fortin, N. Thiré, T. Brabec, F. Légaré, J. C. Kieffer, and M. Piché, “Direct Electron Acceleration with Radially Polarized Laser Beams,” Appl. Sci. 3, 70–93 (2013).
[Crossref]

Peigne, A.

S. Residori, U. Bortolozzo, A. Peigne, S. Molin, P. Nouchi, D. Dolfi, and J. P. Huignard, “Liquid crystals for optical modulation and sensing applications,” Proc. SPIE 9940, 99400N (2016).

Perivolari, E.

E. Perivolari, J. Gill, E. Ronald, V. Apostolopoulos, T.J. Sluckin, G. D’Alessandro, and M. Kaczmarek, “Optically controlled bistable waveplates,” J. Mol. Liq. 12, 119 (2017).

Petrov, D.

G. Volpe and D. Petrov, “Generation of cylindrical vector beams with few-mode fibers excited by Laguerre–Gaussian beams,” Opt. Commun. 237, 89–95 (2004).
[Crossref]

Piché, M.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P. L. Fortin, N. Thiré, T. Brabec, F. Légaré, J. C. Kieffer, and M. Piché, “Direct Electron Acceleration with Radially Polarized Laser Beams,” Appl. Sci. 3, 70–93 (2013).
[Crossref]

Prost, J.

P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, (Clarendon Press, Oxford, 1998).

Putilin, S.

N. Kamanina, S. Putilin, and D. Staselko, “Nano-, pico- and femtosecond study of fullerene-doped polymer-dispersed liquid crystals: holographic recording and optical limiting effect,” Synthetic Met. 127, 129–133 (2002).
[Crossref]

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phy. Rev. Lett. 91, 23 (2003).
[Crossref]

Rasing, T.

Ravnik, M.

M. Čančula, M. Ravnik, I. Muševič, and S. Žumer, “Liquid microlenses and waveguides from bulk nematic birefringent profiles,” Opt. Exp. 24, 22177 (2016).
[Crossref]

M. Čančula, M. Ravnik, and S. Žumer, “Generation of vector beams with liquid crystal disclinations lines,” Phy. Rev. E 90, 022503 (2014).
[Crossref]

M. Humar, M. Ravnik, S. Pajk, and I. Muševič, “Electrically tunable liquid crystal optical microresonators,” Nat. Photonics 3, 595–600 (2009).
[Crossref]

Ren, H.

H. Ren and S. T. Wu, Introduction to adaptive lenses, (Wiley, 2012).
[Crossref]

Reshetnyak, V.

Y. H. Lin, Y. J. Wang, and V. Reshetnyak, “Liquid crystal lenses with tunable focal length,” Liq. Crys. Rev.,  5, 111–143 (2017).
[Crossref]

Residori, S.

S. Residori, U. Bortolozzo, A. Peigne, S. Molin, P. Nouchi, D. Dolfi, and J. P. Huignard, “Liquid crystals for optical modulation and sensing applications,” Proc. SPIE 9940, 99400N (2016).

Reyes, J. A.

C. G. Avendaño and J. A. Reyes, “Nonlinear TM modes in cylindrical liquid crystal waveguide,” Opt. Commun. 283, 5016 (2010).
[Crossref]

Ronald, E.

E. Perivolari, J. Gill, E. Ronald, V. Apostolopoulos, T.J. Sluckin, G. D’Alessandro, and M. Kaczmarek, “Optically controlled bistable waveplates,” J. Mol. Liq. 12, 119 (2017).

Roundy, D.

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J.D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Commun. 181, 687–702 (2010).
[Crossref]

Sala, F. A.

U. A. Laudyn, M. Kwasny, F. A. Sala, M. A. Karpierz, N. F Smyth, and G. Assanto, “Curved optical solitons subject to transverse acceleration in reorientational soft matter,” Sci. Rep. 7, 12385 (2017).
[Crossref] [PubMed]

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 2007).

Salter, P. S.

C. C. Tartan, P. S. Salter, T. D. Wilkinson, M. J. Booth, S. M. Morris, and S. J. Elston, “Generation of 3-dimensional polymer structures in liquid crystaliline devices using direct laser writing,” RSC Adv. 7, 507 (2017).
[Crossref]

Sato, S.

Savoini, M.

Schmidt, B.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P. L. Fortin, N. Thiré, T. Brabec, F. Légaré, J. C. Kieffer, and M. Piché, “Direct Electron Acceleration with Radially Polarized Laser Beams,” Appl. Sci. 3, 70–93 (2013).
[Crossref]

Sergienko, A. V.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zelienger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 24 (1995).
[Crossref]

Shih, Y.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zelienger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 24 (1995).
[Crossref]

Sluckin, T.J.

E. Perivolari, J. Gill, E. Ronald, V. Apostolopoulos, T.J. Sluckin, G. D’Alessandro, and M. Kaczmarek, “Optically controlled bistable waveplates,” J. Mol. Liq. 12, 119 (2017).

Smalyukh, I. I.

P. J. Ackerman and I. I. Smalyukh, “Static three-dimensional topological solitons in fluid chiral ferromagnets and colloids,” Nat. Mater. 16, 426 (2017).
[Crossref]

Smyth, N. F

U. A. Laudyn, M. Kwasny, F. A. Sala, M. A. Karpierz, N. F Smyth, and G. Assanto, “Curved optical solitons subject to transverse acceleration in reorientational soft matter,” Sci. Rep. 7, 12385 (2017).
[Crossref] [PubMed]

Srinivasarao, M.

K. Nayani, R. Chang, J. Fu, P. W. Ellis, A. Fernandez-Nievers, J. Ok Park, and M. Srinivasarao, “Spontaneous emergence of chirality in achiral lyotropic chromonic liquid crystals confined to cylinders,” Nat. Commun. 6, 8067 (2015).
[Crossref] [PubMed]

Srivastava, A. K.

Staselko, D.

N. Kamanina, S. Putilin, and D. Staselko, “Nano-, pico- and femtosecond study of fullerene-doped polymer-dispersed liquid crystals: holographic recording and optical limiting effect,” Synthetic Met. 127, 129–133 (2002).
[Crossref]

Storey, J. M. D.

J. Xiang, A. Varanytsia, F. Minkowski, D. A. Paterson, J. M. D. Storey, C. T. Imrie, O. D. Lavrentovich, and P. P. Muhoray, “Electrically tunable laser based on oblique heliconical cholesteric liquid crystal,” Proc. Nat. Ac. Sci. USA,  113, 12925 (2016).
[Crossref]

Taflove, A.

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-difference Time-domain Method, 3rd ed. (Artech House, London2005).

Tartan, C. C.

C. C. Tartan, P. S. Salter, T. D. Wilkinson, M. J. Booth, S. M. Morris, and S. J. Elston, “Generation of 3-dimensional polymer structures in liquid crystaliline devices using direct laser writing,” RSC Adv. 7, 507 (2017).
[Crossref]

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 2007).

Thiré, N.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P. L. Fortin, N. Thiré, T. Brabec, F. Légaré, J. C. Kieffer, and M. Piché, “Direct Electron Acceleration with Radially Polarized Laser Beams,” Appl. Sci. 3, 70–93 (2013).
[Crossref]

Ting, C.

Tseng, M. C.

Vanbrabant, P. J. M.

J. Beeckman, K. Neyts, and P. J. M. Vanbrabant, “Liquid crystal photonic applications,” Opt. Eng. 8, 081202 (2011).
[Crossref]

S. Ertman, T. R. Wolinski, J. Beeckman, K. Neyts, P. J. M. Vanbrabant, R. James, and F. A. Fernandez, “Numerical simulations of electrically induced birefringence in photonic liquid crystal fibers,” Act. Phys. Pol. A 118, 1113 (2010).
[Crossref]

Varanytsia, A.

J. Xiang, A. Varanytsia, F. Minkowski, D. A. Paterson, J. M. D. Storey, C. T. Imrie, O. D. Lavrentovich, and P. P. Muhoray, “Electrically tunable laser based on oblique heliconical cholesteric liquid crystal,” Proc. Nat. Ac. Sci. USA,  113, 12925 (2016).
[Crossref]

Varin, C.

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P. L. Fortin, N. Thiré, T. Brabec, F. Légaré, J. C. Kieffer, and M. Piché, “Direct Electron Acceleration with Radially Polarized Laser Beams,” Appl. Sci. 3, 70–93 (2013).
[Crossref]

Volpe, G.

G. Volpe and D. Petrov, “Generation of cylindrical vector beams with few-mode fibers excited by Laguerre–Gaussian beams,” Opt. Commun. 237, 89–95 (2004).
[Crossref]

Wang, Y. J.

Y. H. Lin, Y. J. Wang, and V. Reshetnyak, “Liquid crystal lenses with tunable focal length,” Liq. Crys. Rev.,  5, 111–143 (2017).
[Crossref]

Weiner, A. M.

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71, 1929 (2000).
[Crossref]

Weinfurter, H.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zelienger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 24 (1995).
[Crossref]

Werner, G. R.

G. R. Werner and J. R. Cary, “A stable FDTD algorithm for non-diagonal, anisotropic dielectrics,” J. Comp. Phys. 10, 1085 (2007).
[Crossref]

Wilkinson, T. D.

C. C. Tartan, P. S. Salter, T. D. Wilkinson, M. J. Booth, S. M. Morris, and S. J. Elston, “Generation of 3-dimensional polymer structures in liquid crystaliline devices using direct laser writing,” RSC Adv. 7, 507 (2017).
[Crossref]

Wolinski, T. R.

S. Ertman, T. R. Wolinski, J. Beeckman, K. Neyts, P. J. M. Vanbrabant, R. James, and F. A. Fernandez, “Numerical simulations of electrically induced birefringence in photonic liquid crystal fibers,” Act. Phys. Pol. A 118, 1113 (2010).
[Crossref]

Wright, D. C.

D. C. Wright and N. D. Mermin, „ ”Crystalline liquids: the blue phases,” Rev. Mod. Phys. 61, 385–432 (1989).
[Crossref]

Wu, S. T.

H. Ren and S. T. Wu, Introduction to adaptive lenses, (Wiley, 2012).
[Crossref]

Xiang, J.

J. Xiang, A. Varanytsia, F. Minkowski, D. A. Paterson, J. M. D. Storey, C. T. Imrie, O. D. Lavrentovich, and P. P. Muhoray, “Electrically tunable laser based on oblique heliconical cholesteric liquid crystal,” Proc. Nat. Ac. Sci. USA,  113, 12925 (2016).
[Crossref]

Yee, K.S.

K.S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenna Propag. 14, 302 (1966).
[Crossref]

Yoshida, H.

J. Kobashi, H. Yoshida, and M. Ozaki, “Polychromatic optical vortex generation from patterned cholesteric liquid crystals,” Phys. Rev. Lett. 116253903 (2016).
[Crossref] [PubMed]

Youngworth, K. S.

Zelienger, A.

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zelienger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 24 (1995).
[Crossref]

Zhan, Q.

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1, 1–57 (2009).
[Crossref]

Zografopoulos, D. C.

D. C. Zografopoulos, R. Asquini, E. E. Kriezis, A. dAlessandro, and R. Beccherel, “Guided-wave liquid-crystal photonics,” Lab. Chip. 12, 3598–3610 (2012).
[Crossref] [PubMed]

Žumer, S.

A. Nych, J. Fukuda, U. Ognysta, S. Žumer, and I. Muševič, ”Spontaneous formation and dynamics of half-skyrmions in a chiral liquid-crystal film,” Nat. Phys. 13, 1215 (2017).
[Crossref]

M. Čančula, M. Ravnik, I. Muševič, and S. Žumer, “Liquid microlenses and waveguides from bulk nematic birefringent profiles,” Opt. Exp. 24, 22177 (2016).
[Crossref]

M. Čančula, M. Ravnik, and S. Žumer, “Generation of vector beams with liquid crystal disclinations lines,” Phy. Rev. E 90, 022503 (2014).
[Crossref]

J. Fukuda and S. Žumer, ”Quasi-two-dimensional skyrmion lattices in a chiral nematic liquid crystal,” Nat. Commun. 2, 246 (2011).
[Crossref] [PubMed]

Act. Phys. Pol. A (1)

S. Ertman, T. R. Wolinski, J. Beeckman, K. Neyts, P. J. M. Vanbrabant, R. James, and F. A. Fernandez, “Numerical simulations of electrically induced birefringence in photonic liquid crystal fibers,” Act. Phys. Pol. A 118, 1113 (2010).
[Crossref]

Adv. Opt. Photonics (1)

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photonics 1, 1–57 (2009).
[Crossref]

Appl. Phys. Lett. (1)

S. H. Chen and T. J. Chen, “Observation of mode selection in a radially anisotropic cylindrical waveguide with liquid-crystal cladding,” Appl. Phys. Lett. 64, 1893 (1991).
[Crossref]

Appl. Sci. (1)

C. Varin, S. Payeur, V. Marceau, S. Fourmaux, A. April, B. Schmidt, P. L. Fortin, N. Thiré, T. Brabec, F. Légaré, J. C. Kieffer, and M. Piché, “Direct Electron Acceleration with Radially Polarized Laser Beams,” Appl. Sci. 3, 70–93 (2013).
[Crossref]

Comp. Phys. Commun. (1)

A. F. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J.D. Joannopoulos, and S. G. Johnson, “Meep: A flexible free-software package for electromagnetic simulations by the FDTD method,” Comp. Phys. Commun. 181, 687–702 (2010).
[Crossref]

IEEE Trans. Antenna Propag. (1)

K.S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antenna Propag. 14, 302 (1966).
[Crossref]

J. Comp. Phys. (2)

J. P. Berenger, “A perfectly matched layer for the absorption of electromagnetic waves,” J. Comp. Phys.,  114, 185–200 (1994).
[Crossref]

G. R. Werner and J. R. Cary, “A stable FDTD algorithm for non-diagonal, anisotropic dielectrics,” J. Comp. Phys. 10, 1085 (2007).
[Crossref]

J. Electr. Electron. Syst. (1)

M. Chen, C. C. Chen, Y. C. Lai, and Y. H. Lin, “An electrically tunable liquid crystal lens for fiber coupling and variable optical attenuation,” J. Electr. Electron. Syst. 3, 124–129 (2014).

J. Mol. Liq. (2)

E. Perivolari, J. Gill, E. Ronald, V. Apostolopoulos, T.J. Sluckin, G. D’Alessandro, and M. Kaczmarek, “Optically controlled bistable waveplates,” J. Mol. Liq. 12, 119 (2017).

D. Bhattacharjee, P. R. Alapati, and A. Bhattacharjee, “Negative optical anisotropic behaviour of two higher homologues of 5O. m series of liquid crystals,” J. Mol. Liq. 222, 55–60 (2016).
[Crossref]

J. Opt. Soc. Am. (1)

J. Phys. D (1)

V. G. Niziev and A. V. Nesterov, “Influence of beam polarization on laser cutting efficiency,” J. Phys. D 32, 13 (1999).
[Crossref]

Lab. Chip. (1)

D. C. Zografopoulos, R. Asquini, E. E. Kriezis, A. dAlessandro, and R. Beccherel, “Guided-wave liquid-crystal photonics,” Lab. Chip. 12, 3598–3610 (2012).
[Crossref] [PubMed]

Liq. Crys. Rev. (1)

Y. H. Lin, Y. J. Wang, and V. Reshetnyak, “Liquid crystal lenses with tunable focal length,” Liq. Crys. Rev.,  5, 111–143 (2017).
[Crossref]

Mol. Cryst. Liq. Cryst. (1)

H. Lin, P. Palffy-Muhoray, and M. A. Lee, “Liquid crystalline cores for optical fibers,” Mol. Cryst. Liq. Cryst. 204, 189 (1991).
[Crossref]

Nat. Commun. (2)

J. Fukuda and S. Žumer, ”Quasi-two-dimensional skyrmion lattices in a chiral nematic liquid crystal,” Nat. Commun. 2, 246 (2011).
[Crossref] [PubMed]

K. Nayani, R. Chang, J. Fu, P. W. Ellis, A. Fernandez-Nievers, J. Ok Park, and M. Srinivasarao, “Spontaneous emergence of chirality in achiral lyotropic chromonic liquid crystals confined to cylinders,” Nat. Commun. 6, 8067 (2015).
[Crossref] [PubMed]

Nat. Mater. (1)

P. J. Ackerman and I. I. Smalyukh, “Static three-dimensional topological solitons in fluid chiral ferromagnets and colloids,” Nat. Mater. 16, 426 (2017).
[Crossref]

Nat. Photonics (2)

H. Coles and S. Morris, “Liquid-crystal lasers,” Nat. Photonics 4, 676–685 (2010).
[Crossref]

M. Humar, M. Ravnik, S. Pajk, and I. Muševič, “Electrically tunable liquid crystal optical microresonators,” Nat. Photonics 3, 595–600 (2009).
[Crossref]

Nat. Phys. (1)

A. Nych, J. Fukuda, U. Ognysta, S. Žumer, and I. Muševič, ”Spontaneous formation and dynamics of half-skyrmions in a chiral liquid-crystal film,” Nat. Phys. 13, 1215 (2017).
[Crossref]

Opt. Commun. (2)

C. G. Avendaño and J. A. Reyes, “Nonlinear TM modes in cylindrical liquid crystal waveguide,” Opt. Commun. 283, 5016 (2010).
[Crossref]

G. Volpe and D. Petrov, “Generation of cylindrical vector beams with few-mode fibers excited by Laguerre–Gaussian beams,” Opt. Commun. 237, 89–95 (2004).
[Crossref]

Opt. Eng. (1)

J. Beeckman, K. Neyts, and P. J. M. Vanbrabant, “Liquid crystal photonic applications,” Opt. Eng. 8, 081202 (2011).
[Crossref]

Opt. Exp. (1)

M. Čančula, M. Ravnik, I. Muševič, and S. Žumer, “Liquid microlenses and waveguides from bulk nematic birefringent profiles,” Opt. Exp. 24, 22177 (2016).
[Crossref]

Opt. Express (3)

Opt. Lett. (4)

Phy. Rev. E (1)

M. Čančula, M. Ravnik, and S. Žumer, “Generation of vector beams with liquid crystal disclinations lines,” Phy. Rev. E 90, 022503 (2014).
[Crossref]

Phy. Rev. Lett. (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phy. Rev. Lett. 91, 23 (2003).
[Crossref]

Phys. Rev. Lett. (2)

J. Kobashi, H. Yoshida, and M. Ozaki, “Polychromatic optical vortex generation from patterned cholesteric liquid crystals,” Phys. Rev. Lett. 116253903 (2016).
[Crossref] [PubMed]

P. G. Kwiat, K. Mattle, H. Weinfurter, A. Zelienger, A. V. Sergienko, and Y. Shih, “New high-intensity source of polarization-entangled photon pairs,” Phys. Rev. Lett. 75, 24 (1995).
[Crossref]

Proc. Nat. Ac. Sci. USA (1)

J. Xiang, A. Varanytsia, F. Minkowski, D. A. Paterson, J. M. D. Storey, C. T. Imrie, O. D. Lavrentovich, and P. P. Muhoray, “Electrically tunable laser based on oblique heliconical cholesteric liquid crystal,” Proc. Nat. Ac. Sci. USA,  113, 12925 (2016).
[Crossref]

Proc. SPIE (1)

S. Residori, U. Bortolozzo, A. Peigne, S. Molin, P. Nouchi, D. Dolfi, and J. P. Huignard, “Liquid crystals for optical modulation and sensing applications,” Proc. SPIE 9940, 99400N (2016).

Rev. Mod. Phys. (1)

D. C. Wright and N. D. Mermin, „ ”Crystalline liquids: the blue phases,” Rev. Mod. Phys. 61, 385–432 (1989).
[Crossref]

Rev. Sci. Instrum. (1)

A. M. Weiner, “Femtosecond pulse shaping using spatial light modulators,” Rev. Sci. Instrum. 71, 1929 (2000).
[Crossref]

RSC Adv. (1)

C. C. Tartan, P. S. Salter, T. D. Wilkinson, M. J. Booth, S. M. Morris, and S. J. Elston, “Generation of 3-dimensional polymer structures in liquid crystaliline devices using direct laser writing,” RSC Adv. 7, 507 (2017).
[Crossref]

Sci. Rep. (1)

U. A. Laudyn, M. Kwasny, F. A. Sala, M. A. Karpierz, N. F Smyth, and G. Assanto, “Curved optical solitons subject to transverse acceleration in reorientational soft matter,” Sci. Rep. 7, 12385 (2017).
[Crossref] [PubMed]

Synthetic Met. (1)

N. Kamanina, S. Putilin, and D. Staselko, “Nano-, pico- and femtosecond study of fullerene-doped polymer-dispersed liquid crystals: holographic recording and optical limiting effect,” Synthetic Met. 127, 129–133 (2002).
[Crossref]

Other (5)

H. Ren and S. T. Wu, Introduction to adaptive lenses, (Wiley, 2012).
[Crossref]

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 2007).

P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, (Clarendon Press, Oxford, 1998).

H. S. Kitzerow and C. Bahr, Chirality In Liquid Crystals (Springer Verlag, 2001).
[Crossref]

A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-difference Time-domain Method, 3rd ed. (Artech House, London2005).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1 Double-twist cylinder as a photonic element. Azimuthally polarized light (electric field Eopt direction is illustrated with red arrows) propagating along the of double-twist birefringent profile (optical axis is represented by colored ellipsoids) observes radially dependent refractive index which can result in lensing and waveguiding.
Fig. 2
Fig. 2 Lensing on short segments of a double-twist nematic profile for different input beam widths. (A–D) Plots of light intensity at the central plane of the beam. Lensing of azimuthally polarized input beams with different input beam waists on identical double-twist profiles results in lensing with different numerical apertures. (E) Beam width profiles along the beam path for different input beam widths.
Fig. 3
Fig. 3 Lensing in birefringent double-twist cylinders for differently polarized input beams. In case of azimuthally polarized beam (A) lensing occurs, since the light experiences radially dependent refractive index. In case of radially polarized beam (B) the refractive index is uniform and no lensing occurs. In the intermediate case of radially-azimuthally polarized beam (C) only only partial lensing occurs. Double-twist profiles of the optical axis variation are shown in red, with green dashed line indicating the end of the profile region.
Fig. 4
Fig. 4 Longitudinal component of the magnetic field of azimuthally polarized beam. Lensing of azimuthally polarized beams results in occurence of strong longitudinal magnetic field component in the center of the beam. (A) Color plots of magnetic field component Hz in the cross section of the beam in three different positions along the beam path, z1, z2, z3 (marked with white dashed lines on the lower plot) are shown, indicating that Hz is greatest at the centre of the beam cross-section at the beam waist. (B) Square of absolute amplitudes of longitudinal components Hz and Ez in the beam centre, marked with yellow line on the beam yz cross-section plot.
Fig. 5
Fig. 5 Waveguiding in a double-twist cylinder birefringent profile. (A) Azimuthally polarized beams propagating inside the double twist cylinders for different input beam widths 2w0. (B) Transversal components of the electric field E of the guided beam at three different representative positions along the beam path, denoted by green arrows. They indicate partial transformation of the initial azimuthal polarization to a polarization that is partially radial. (C) Beam power in units of initial beam power P0 along the double twist cylinder for different input beam widths 2w0. (D, E) Components of the Poynting vector averaged along the beam. Note the emergence of the radially twisted component of S in the transversal plane.
Fig. 6
Fig. 6 Waveguiding in curved birefringent double-twist profiles. (A) Light intensity of the azimuthally polarized beam inside a double-twist cylinder nematic structure curved with a radius of curvature Rc. For smaller radii of curvature substantial bending losses occur. (B) Ratio between the input and output beam power after travelling a fixed length of 60λ inside a curved nematic profile as a function of the radius of curvature Rc.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

ε̳ ε 0 E t = × H , μ μ 0 H t = × E ,
ε i j = ε ¯ δ i j + 2 3 ε a mol Q i j ,
n ( r , ϕ , z ) = e ^ z cos ( k 0 r ) e ^ ϕ sin ( k 0 r ) ,
E z DTC = ( ε̳ DTC 1 ( r ) ε̳ iso E iso ) e z 0 ,

Metrics