Photonic defect modes of cholesteric liquid crystals

Photonic bound states in the continuum governed by heating

A photonic crystal microcavity with the liquid crystal resonant layer tunable by heating has been implemented. The multiple vanishing resonant lines corresponding to optical bound states in the continuum are observed. The abrupt change in the resonant linewidth near the vanishing point can be used for temperature sensing.

Defects and defect engineering in Soft Matter

Soft matter covers a wide range of materials based on linear or branched polymers, gels and rubbers, amphiphilic (macro)molecules, colloids, and self-assembled structures. These materials have applications in various industries, all highly important for our daily life, and they control all biological functions; therefore, controlling and tailoring their properties is crucial. One way to approach this target is defect engineering, which aims to control defects in the material's structure, and/or to purposely add defects into it to trigger specific functions. While this approach has been a striking success story in crystalline inorganic hard matter, both for mechanical and electronic properties, and has also been applied to organic hard materials, defect engineering is rarely used in soft matter design. In this review, we present a survey on investigations on defects and/or defect engineering in nine classes of soft matter composed of liquid crystals, colloids, linear polymers with moderate degree of branching, hyperbranched polymers and dendrimers, conjugated polymers, polymeric networks, self-assembled amphiphiles and proteins, block copolymers and supramolecular polymers. This overview proposes a promising role of this approach for tuning the properties of soft matter.

Localized Conical Edge Modes in Optics of Spiral Media (First Diffraction Order)

In cholesteric liquid crystals (CLC) problems related to the localized optical modes for a non-collinear geometry are studied here in the two wave dynamic diffraction theory approximation. This approximation, which insures the results accuracy order of δ (where δ is the CLC dielectric anisotropy), is applied because for a non-collinear geometry there is no exact analytic solution of the Maxwell equations and a theoretical description of the experimental data becomes more complicated. The dispersion equation for non-collinear localized edge modes (called conical modes (CEM)) is found and analytically solved for the case of thick layers and for this case the lasing threshold and the conditions of the anomalously strong absorption effect are found. It is shown that qualitatively CEMs are very similar to the localized edge modes (EM) in CLCs related to a collinear geometry, i.e., for the case of light propagation along the spiral axis however the CEMs differ by their polarization properties (the CEM eigen polarizations are elliptical ones depending on the degree of CEM deviation from the collinear geometry in contrast to the circular eigen polarizations in the EM case). What is concerned of the CEM quantitative values of the parameters they are “worth” (the photonic effects are not so pronounced) than for the corresponding ones for EM. The CEM lasing threshold is higher than the one for EM, etc. Performed theoretical studies of possible conversion of EMs into CEMs showed that it can be due to the EM reflection at dielectric boundaries at the conditions of a high pumping wave focusing. Known experimental results on the CEM are discussed and optimal conditions for CEM observations are formulated.

Chiral Optical Tamm States at the Interface between an All-Dielectric Polarization-Preserving Anisotropic Mirror and a Cholesteric Liquid Crystal

As a new localized state of light, the chiral optical Tamm state exists at the interface between a polarization-retaining anisotropic mirror and a substance with optical activity. Considering a hybrid structure comprising a metal-free polarization-preserving mirror and a cholesteric liquid crystal, we highlight the high Q factor arising from the all-dielectric framework. The intensity of localized light decreases exponentially with increasing distance from the interface. The penetration of the field into the cholesteric liquid crystal is essentially prohibited for wavelengths lying in the photonic bandgap and close to the cholesteric pitch length. The dielectric mirror has its own photonic bandgap. The energy transfer along the interface can be effectively switched off by setting the tangential wave vector to zero. The spectral behavior of the chiral optical Tamm state is observed both as reflection and transmission resonance. This Fano resonance is analogous to the Kopp–Genack effect. Our analytics are well in line with precise calculations, which may pave a new route for the future development of intelligent design for laser and sensing applications.

Coupling of Defect Modes in Cholesteric Liquid Crystals Separated by Isotropic Polymeric Layers

Cholesteric liquid crystal structures with multiple isotropic defect layers exhibit localized optical modes (defect modes). Coupling effects between these modes were simulated using the finite difference time domain method. Analogous to the well-known result of the tight-binding approximation in solid state physics, splitting of the defect modes takes place, as soon as the structure contains more than one defect layer. The dispersion relation of the mini-bands forming within the photonic band gap of the structure is calculated numerically. The structures might have promising applications for multiwavelength filters and low-threshold lasers.

Tunable hybrid optical modes in a bounded cholesteric liquid crystal with a twist defect

Coupling between the defect mode of a cholesteric liquid crystal and the localized mode of a cholesteric liquid crystal-phase plate-metal structure is theoretically demonstrated. It is shown that the transmittance spectrum can be tuned by changing the twist-defect angle and helix pitch, which are governed by external factors. The spectra for different circular polarizations of the incident light are different; specifically, at the nondiffracting polarization, there is no defect-mode transmittance peak.

Electrically Reconfigurable Liquid Crystalline Mirrors

Reconfigurable optical materials are critical to realizing light control in eyewear or architectural windows. Here, we report on the electrical reconfiguration of the selective reflection of cholesteric liquid crystals (LCs). The distinctive responses detailed here are enabled by the preparation of a structurally chiral polymer stabilizing network that enforces anchoring of a low-molar-mass liquid crystalline media with positive dielectric anisotropy. The pitch of the reflective optical elements is directly regulated by a dc field, resulting in red or blue reflection wavelength tuning or broadening. The use of the positive dielectric LC host in concert with optimization of the material preparation conditions allows for reorientation of the LC molecules to achieve an optically clear state (homeotropic orientation) by the application of an ac field. In this way, the selective reflection of the optical elements can be moved, widened, and turned on and off. The electro-optic characteristics of these materials are another step forward to enabling the use of these materials in optics and photonics.

Lasing in imperfectly aligned cholesterics

Optically pumped light emissions in imperfectly aligned dye-doped cholesteric cells with glance and frosted glass substrates of three different cell gap thicknesses are experimentally studied. Alignment imperfections show up in emission spectra by a broadening of the photonic bandgap (PhBG) lasing (allowed) lines at short- and long-wavelength PhBG edges and by an additional (forbidden) emission line inside the PhBG. Forbidden and allowed lines differ distinctively by their stability in the course of pumping. The origin of the forbidden line is discussed.

Photonic defect modes in a cholesteric liquid crystal with a resonant nanocomposite layer and a twist defect

We have studied spectral properties of a cholesteric liquid crystal with a combined defect consisting of a nanocomposite layer and a twist. The nanocomposite layer is made of metallic nanoballs dispersed in a transparent matrix and featuring effective resonant permittivity. A solution has been found for the transmission spectrum of circularly polarized waves in the structure. We have analyzed spectral splitting of the defect mode in the band gap of the cholesteric when its frequency coincides with the nanocomposite resonant frequency. Defect modes have characteristics strongly dependent on the magnitude and the sign of the phase difference of the cholesteric helix on both sides of the defect layer. It has been found that the band gap width and the position and localization degree of defect modes can be effectively controlled by external fields applied to the cholesteric.

Ultralow-threshold single-mode lasing based on a one-dimensional asymmetric photonic bandgap structure with liquid crystal as a defect layer

In this Letter, we propose defect-mode lasing from a one-dimensional asymmetric photonic structure with dye-doped nematic liquid crystal as a central defect layer. The local field intensity of the distinguished single defect mode at the overlapped photonic band edges is drastically enhanced by the asymmetric structure consisting of two distinct multilayer photonic crystals. With high density of states of photons, effective output lasing emission and maximum input excitation are ensured. As a result, the single-mode lasing with a low excitation threshold of 0.2  μJ/pulse is achieved due to the combination of the defect layer and the photonic band edge effect.

Tunable reflectance of a two-defect-layer cholesteric liquid crystal

In the present paper we consider reflection spectra peculiarities of a cholesteric liquid crystal (CLC) cell with two defect layers. We consider both the isotropic and anisotropic defect cases. The problem is solved by Ambartsumian's modified layer addition and Muller's matrix methods. We investigated the influence of the defect layer thicknesses and location changes in the CLC cell on the defect modes and the photonic band gap. In particular, we considered (in detail) the cases when the defect layers are half-wave or quarter-wave plates. We also investigated the influence of dielectric borders on the reflection spectra. We showed that the subject system possesses the property of structural nonreciprocity, and that the system can work as a tunable filter, a mirror, and a low threshold laser. We also showed that the system can work as a light modulator, or as an optical diode, or as a system for getting linearly polarized light with electrically tunable polarization plane rotation, as well as a device for getting linearly polarized light from nonpolarized light, again with electrically tunable polarization plane rotation.

Resonant modes in cholesteric liquid crystals with a gaussian pitch profile

In this paper, we investigate the spectral properties of a cholesteric film presenting a pitch profile with a gaussian deformation. Using the Berreman 4 × 4 matrix formalism, we numerically obtain the transmission spectrum at normal and oblique light incidence as a function of width and the position of the deformation. Our results reveal that a pair of resonant modes emerges inside the main stop band of the transmission spectrum as the width of the deformation becomes comparable to the helical pitch length. The mechanism behind the emergence of the resonant modes is discussed. The case of a pitch profile with multiple gaussian deformations is also analyzed. At this configuration, a crossover from single to multiple band-gap pattern can be observed in the transmission spectrum, depending on the deformation parameters.

Tunable reflectance spectra of multilayered cholesteric photonic structures with anisotropic defect layers

In this paper, we investigate the spectral characteristics of normal incident light reflected by a multilayered structure composed of an alternated sequence of single-pitch cholesteric liquid-crystal (ChLC) and anisotropic layers. Using the Berreman 4x4 matrix formalism, we numerically obtain the reflection spectrum and the chromaticity diagram as a function of the anisotropic layers thickness d. For d-->0 , the structure behaves like a single ChLC layer, showing a single reflection band. As the anisotropic layer thickness increases, the reflection band shifts toward high-wavelength spectral regions, while new reflection bands appear. As a consequence, the reflection chromaticity continuously changes with d . It is observed that a suitable choice of the anisotropic layer thickness can produce a threefold reflection band with a red-green-blue associated color for both polarized and unpolarized incident lights.

Wide band gap materials as a new tuning strategy for dye doped cholesteric liquid crystals laser

A new tuning strategy for mirror-less liquid crystals laser is presented. A three layer cell is prepared with two cholesteric layers sandwiching a layer containing an isotropic mixture of a photoluminescent dye. One of the chiral layers contains a wide band gap material while the second layer consists of a series of small band gap materials. Through the combination of these two layers, a set of mirrors that can selectively reflect different wavelengths is obtained. A different laser wavelength is emitted from different regions of the cell under the pumping beam irradiation.

Fabrication of a simultaneous red-green-blue reflector using single-pitched cholesteric liquid crystals

A cholesteric liquid crystal (CLC) is a self-assembled photonic crystal formed by rodlike molecules, including chiral molecules, that arrange themselves in a helical fashion. The CLC has a single photonic bandgap and an associated one-colour reflection band for circularly polarized light with the same handedness as the CLC helix (selective reflection). These optical characteristics, particularly the circular polarization of the reflected light, are attractive for applications in reflective colour displays without using a backlight, for use as polarizers or colour filters and for mirrorless lasing. Recently, we showed by numerical simulation that simultaneous multicolour reflection is possible by introducing fibonaccian phase defects. Here, we design and fabricate a CLC system consisting of thin isotropic films and of polymeric CLC films, and demonstrate experimentally simultaneous red, green and blue reflections (multiple photonic bandgaps) using the single-pitched polymeric CLC films. The experimental reflection spectra are well simulated by calculations. The presented system can extend applications of CLCs to a wide-band region and could give rise to new photonic devices, in which white or multicolour light is manipulated.

Chiral photonic crystals with an anisotropic defect layer

In the present paper we consider some properties of defect modes in chiral photonic crystals with an anisotropic defect layer. We solved the problem by Ambartsumian's layer addition method. We investigated the influence of the defect layer thickness variation and its location in the chiral photonic crystal (CPC) and also its optical axes orientation, as well as of CPC thickness variation on defect mode properties. Variations of the optical thickness of the defect layer have its impact on the defect mode linewidth and the light accumulation in the defect. We obtain that CPCs lose their base property at certain defect layer thicknesses; namely, they lose their diffraction reflection dependence on light polarization. We also show that the circular polarization handedness changes from right-handed to left-handed if the defect layer location is changed, and therefore, such systems can be used to create sources of elliptically polarized light with tunable ellipticity. Some nonreciprocity properties of such systems are investigated, too. In particular, it is also shown that such a system can work as a practically ideal wide band optical diode for circularly polarized incident light provided the defect layer thickness is properly chosen, and it can work as a narrow band diode at small defect layer thicknesses.

Enhanced photonic band edge laser emission in a cholesteric liquid crystal resonator

A highly efficient photonic band edge dye-doped cholesteric liquid crystal (CLC) laser is demonstrated. By sandwiching an active CLC cell within a resonator consisting of two passive CLC reflectors, the lasing efficiency is dramatically enhanced. Theoretical analysis using the improved 4x4 transfer matrix and scattering matrix shows that the band edge laser mode can be supported by the external CLC resonator and its optimal output can be achieved by a relatively thin active CLC layer and thin passive CLC reflectors. Theoretical analysis agrees well with the experimental results.

Theoretical and experimental optical studies of cholesteric liquid crystal films with thermally induced pitch gradients

The reflection properties of cholesteric films with thermally induced pitch gradients are theoretically and experimentally studied. It is shown that the optical behavior of such films corresponds to the averaged contribution of a number of stochastic pitch variation profiles, due to the transversal and longitudinal nonuniformities that develop in the helical structure of such samples. Depending on the annealing time, both narrow-band and broadband behavior can be selectively achieved. The influence of the pitch profile gradient on the broadband reflection performance of cholesteric samples is theoretically analyzed, and a multi-slab structure for achieving optimum efficiency is proposed.

Optical crossover phenomenon due to a central 90°-twist defect in a chiral sculptured thin film or chiral liquid crystal

We present a theoretical analysis of a remarkable phenomenon evinced by a periodic structurally chiral material—for example, a chiral sculptured thin film (STF) or a chiral liquid crystal—with a central 90°-twist defect illuminated with normally incident, circularly polarized light. Based on the coupled-wave theory (CWT), an approximate but closed-form solution of the relevant boundary-value problem is obtained in terms of a 4 × 4 CWT transmission matrix. The CWT transmission matrix is decomposed into two terms. The first term favours total transmission in the central part of the Bragg regime of the axially excited, structurally chiral material, while the second term favours total reflection in the whole Bragg regime. When the thickness of the structurally chiral material is relatively small, the second term is dominated by the first, which gives rise to a co-handed transmittance peak in the centre of the Bragg regime. As the thickness increases, the second term becomes significant and interferes with the first term such that the transmission matrix is isomorphic to that of a defect-free structurally chiral material—except in a tiny wavelength-regime wherein the L ∞ -norms of the two terms become identical to engender the total-reflection feature. Hence, the co-handed transmittance peak diminishes (and eventually vanishes) as the thickness increases and is replaced by a cross-handed reflectance peak. The bandwidths of the two peaks depend, in different ways, on the local birefringence of the structurally chiral material.

Defect modes in a stacked structure of chiral photonic crystals

An optical propagation simulation is carried out for the study of photonic defect modes in a stacked structure of cholesteric liquid crystal films with spatially varying pitch. The defects are introduced by a pitch jump and a phase jump in the cholesteric helix. The effect of a finite sample thickness on transmission of the defect mode and on the required polarization of incident light to create the defect mode is discussed. For normal and near-normal incidence of circularly polarized light with the same handedness as structure, the defect caused by a pitch jump results in discrete peaks within a forbidden band in the transmission. The particular spectrum is similar to the feature of a Fabry-Pérot interferometer. By introducing an additional phase jump, linear blueshifts of the defect modes in transmission spectra are correlated with an increase in the twist angle.

Tunable photonic defect modes in a cholesteric liquid crystal induced by optical deformation of helix

We have demonstrated, based on numerical analyses, that the introduction and tuning of photonic defect modes in a cholesteric liquid crystal (CLC) can be realized by the local deformation of its one-dimensional periodic helical structure. The defect modes appear in transmission spectra only when incident circularly polarized light has the same handedness as CLC's. The tuning of defect modes position can be performed upon both local elongation and shortening of the helix; however, the direction of the shift of the defect mode wavelength is opposite. By controlling the degree of the deformation of helix, a continuous shift of the defect modes can be realized. Our results will open the way for the optical introduction and tuning of defect modes in CLC's.

Photonic defect modes in cholesteric liquid crystal films

We discuss the properties of photonic defect modes in cholesteric liquid crystals. Twist defects, isotropic defect layers, and combinations of both are considered. After deriving the reflection and transmission properties of the defects, we study the effect of a finite sample thickness on the defect mode's amplitude and on the required polarization of incident light to excite the defect mode.

Supermodes of chiral photonic filters with combined twist and layer defects

We consider the circularly polarized localized modes of chiral photonic structures with combined central twist and isotropic layer defects. The general filter is shown to suffer from anomalous remittance and saturation of linewidth as the thickness of the structure is increased. However, by choosing parameters that phase match the elements of the round-trip matrix of the isotropic layer defect, we demonstrate the existence of supermodes that maintain exceptional purity of polarization state and exponential decrease in linewidth as the thickness is increased.

Double-helix chiral fibers

A polarization-selective photonic stop band is demonstrated in a new chiral fiber structure with double-helix symmetry. The stop band exists for only circularly polarized radiation with the same handedness as the structure and is centered at a wavelength in the fiber equal to the fiber pitch. When one part of the chiral fiber is twisted about its axis, a localized mode is produced, which can be tuned across the gap by changing the twist angle. Observations in single-mode fibers are in good agreement with one-dimensional simulations of a dispersive cholesteric material. At higher frequencies, however, we find a sharp onset of a broad polarization-selective scattering band, which is not present in one-dimensional simulations.

Optical second-harmonic generation enhanced by a twist defect in ferroelectric liquid crystals

Second-harmonic generation (SHG) spectra were numerically calculated in ferroelectric liquid crystals with a twist defect. It is shown that SHG is enhanced when the SHG wavelength is close to the defect mode. The spectral width of the enhanced peak becomes sharper with increasing the sample thickness at the same rate for the width of the defect mode peak. The SHG peak intensity increases with about seventh power of the sample thickness.

Twist defects in helical sonic structures

We analyze theoretically both the acoustic wave propagation in periodic media made of anisotropic materials whose stiffness tensor is uniformly rotating along a given axis x(3) and the defect mode produced by twisting about x(3) one part of the helical structure with respect to the other. Within the Bragg band of the periodic structure, the twist defect gives rise to a resonant mode that is a superposition of two standing waves: one localized with exp(-gamma|x(3)|) dependence centered at the defect and the other extended over the whole sample. The ratio between the amplitudes of the localized and nonlocalized waves depends sharply on both the twist angle and the elastic anisotropy, and can assume huge values. The defect mode and the resonance frequency omega(0) are defined by fully analytical and very simple expressions. Finally, we discuss how around omega(0), a finite sample acts as a frequency filter for circularly polarized shear waves, whose bandwidth can be changed by many orders of magnitude by varying the sample thickness, the twist angle, or the elastic anisotropy.

Transmission through chiral twist defects in anisotropic periodic structures

A long-lived photonic state is observed in measurements of microwave transmission through a helical stack of anisotropic overhead transparencies with various twist defects in the center of the structure. Once account is taken of absorption and of the angular spread of the source, computer simulations of transmission through a polarized localized state are in agreement with measurements. Unlike for isotropic one-dimensional bandgaps, the intensity of the localized mode is not modulated in space on a wavelength scale.

Defect mode emission of a dye doped cholesteric polymer network

We have observed enhanced fluorescence and laser emission due to a photonic defect mode in a dye doped cholesteric polymer network. The defect is caused by a phase jump of the cholesteric helix at the interface of two stacked layers of a cholesteric polymer film. Fluorescence spectra show an additional resonant mode inside the photonic stop band. Pulsed excitation gives rise to laser emission of the defect mode, with an exceptionally low lasing threshold. The defect mode emission has a circular polarization whose sense of rotation is opposite to that of the cholesteric helix.

Twist defect in chiral photonic structures

We demonstrate that twisting one part of a chiral photonic structure about its helical axis produces a single circularly polarized localized mode that gives rise to an anomalous crossover in propagation. Up to a crossover thickness, this defect results in a peak in transmission and exponential scaling of the linewidth for a circularly polarized wave with the same handedness as structure. Above the crossover, however, the linewidth saturates and the defect mode can be excited only by the oppositely polarized wave, resulting in a peak in reflection instead of transmission.

Blue phases of cholesteric liquid crystals as thermotropic photonic crystals

The study of dye-doped low pitch cholesteric liquid crystals in their blue phases as an example of tunable "weak" photonic crystals is proposed and demonstrated. The presence of the blue phases in cholesterics can be tuned with temperature, and this allows for an easy in situ comparison of the emission and/or absorption of the dyes with or without an enwrapping lattice of disclination lines. The fluorescence emission of the dyes is shown to be affected by the presence of the blue phases. Although unlikely to be suitable for real applications (due to the natural low refractive index contrast), these systems may represent unique examples of tunable photonic crystals. It is proposed that single crystals of dye-doped blue phases should provide a very interesting testing ground for the study of optical emission anisotropies which can, on the other hand, be controlled by an external parameter.