Second harmonic generation in anisotropic stratified media: a generalization of the Berreman method and its application to photonic materials

We have developed a numerical method for calculating the second-harmonic generation (SHG) generated by an anisotropic material whose optical properties present an arbitrary modulation in one dimension. The method is based on the Berreman 4 × 4 matrix formalism, which is generalized to include nonlinear optical phenomena. It can be used under oblique incidences of the input beam, and is valid even when the SHG frequency is close to photonic bands, where the usual slowly-varying-amplitude approximation breaks down. As an example of application, we have studied the SHG performance of ferroelectric and helielectric fluids. The obtained results indicate that the present procedure may contribute to improving the structural design and enlarging the variety of nonlinear optical materials for application in optical devices.

Kinetic behavior of light emission in cholesteric liquid crystal lasers: An experimental study

Some dynamical aspects of fluorescence and lasing have been studied in a dye-doped cholesteric liquid crystal by measuring the response of the material to nanosecond optical pumping. It has been found that as the pumping energy is increased the fluorescence pulse duration decreases, reaching a minimum at the lasing threshold. Above the threshold the temporal profiles are irregular and consist of a set of narrow pulses whose measured duration is limited by the detector risetime (1 ns). The results are interpreted in terms of a recently proposed model [JETP, 118, 822 (2014)] that makes use of rate equations to account for the laser generation in cholesteric liquid crystals. The prediction of such equations for an experimental configuration appropriate for fluorescence lifetime measurements is analyzed.

Thermally induced light-scattering effects as responsible for the degradation of cholesteric liquid crystal lasers

We have studied the degradation process of the laser emission in a cholesteric liquid crystal laser. We have found that there exists a negative correlation between the laser efficiency and the amount of light scattered by the liquid-crystal sample in the illuminated area. The growth of scattering is attributed to the appearance of small imperfections generated in the sample as a result of certain thermal processes that involve the dye molecules. The scattering implies an increase of the coefficient of distributed losses, which is the main response of the rise of the laser threshold.

Spontaneous and field-induced mesomorphism of a silyl-terminated bent-core liquid crystal as determined from second-harmonic generation and resonant X-ray scattering

The polarity and structure of the phases of a liquid crystal constituted by thiophene-based bent-core molecules is investigated by means of optical second-harmonic generation (SHG), and resonant and conventional X-ray diffraction. The material studied is representative of a wide family of mesogens that contain silyl groups at the ends of the chains. These bulky terminal groups have been reported to give rise to smectic phases showing ferroelectric switching. However, the analysis of the SHG signal before and after application of electric fields has allowed us to establish unambiguously that the reported ferroelectricity is not intrinsic to the material but stabilized by the cell substrates once an electric field has been applied. In addition, the results obtained from resonant X-ray diffraction indicate that virgin samples have antiferroelectric undulated synclinic smectic structures.

Second-harmonic generation in a laterally azo-bridged trimer ferroelectric liquid crystal: phase matching in the presence of a helicoidal structure

Optical second-harmonic generation (SHG) has been studied in a trimer smectic C* liquid crystal especially designed for nonlinear optical applications. The molecule has a long conjugated donor-acceptor unit that transversally links three parallel rod-shaped moieties. A strong SHG signal has been observed at a fundamental wavelength of 1369 nm even in the presence of the spontaneous helicoidal structure of the smectic C* phase. This unusual behavior has been interpreted as due to the existence of phase matching, in which the wave vector mismatch is compensated by the wave vector of the helix. This point has been confirmed by the study of the SHG intensity versus sample thickness and light polarization characteristics. The main coefficient of the second-order susceptibility tensor of the material has been estimated to be d(22) = 28 pm/V.

Electric-field-induced phase transitions in bent-core mesogens determined by x-ray diffraction

The changes in the x-ray diffraction diagram induced by an electric field have been studied in four bent-core liquid crystals. Two of the compounds present columnar B1 phases and the other two show dark conglomerate (DC) structures. In the B1 materials the electric field gives rise to switchable phases whose diffraction pattern is that of the smectic C polar (SmCP) phase. In the DC structures the positions of the Bragg reflections remain essentially unaltered, but in one of the compounds the peaks become narrower under field, indicating that the correlation length of the smectic order increases. A slight enhancement of the smectic spacing is found in the DC phases upon field application.

Polarization periodicity in the B(1) columnar phase determined by resonant x-ray scattering

We report structural results that evidence the polarization distribution of the blocks in the columnar phase of an achiral bent-core liquid crystal. The study was performed using resonant x-ray diffraction at the sulfur K edge on oriented samples aligned on substrates. The extra periodicity is revealed through the violation of the systematic extinction rule of the structural symmetry group along the experimentally accessible diffraction direction. Further data obtained from the polarization analysis of a resonant reflection give information concerning the transition mechanism between B(1) and B(2) phases.

Pseudolayered structure of the columnar B1 phase of bent-core liquid crystals

Three bent-core liquid-crystal compounds presenting the unusual columnar B1 to tilted polar smectic (Sm-CP or B2) phase transition are studied through small-angle x-ray diffraction on aligned samples. The well-established character of the smectic phase helps to characterize the structural changes during the transition. A mechanism for this transition is proposed, which accounts for the low enthalpy usually observed in this process. The B1 phase is found to possess a great degree of lamellarization, with pseudosmectic ferroelectric layers along the crystallographic (11) planes. As a consequence of these observations a distribution of the block polarizations in the columnar structure is proposed.

Polar structures of bent-core liquid crystals with tetrathiafulvalene units

We report on a series of three bent-core liquid crystals containing tetrathiafulvalene units. Their characterization consisted of electro-optical observations, second-harmonic generation (SHG) analysis, and x-ray diffraction measurements. Compound I exhibits a lamellar optically isotropic phase on cooling from the isotropic liquid and undergoes a nonreversible field-induced transition to a birefringent state. The two others present two-dimensional structural periodicities, being only compound II switchable. Additionally, the electron density maps of compounds II and III have been obtained based on the analysis of the x-ray diffraction intensities. According to SHG measurements the ground state is antiferroelectric in the three compounds. A quite good SHG performance is found in compounds I and II.

Bent-core liquid-crystalline derivative of tetrathiafulvalene: photoresponsivity and deracemization

A bent-core mesogen containing a tetrathiafulvalene group is studied. The mesophase is an optically isotropic spongelike smectic phase without optical activity. The material responds to uv light in a peculiar way, showing photoconductivity and, in some circumstances, changing its mesomorphic properties. Under an electric field, large chiral domains are segregated from an initial racemic phase within a few minutes.

Relationship between structure and optical properties of lithium triborate

Measurements of the optical rotation of LiB3O5have been carried out using a high-accuracy universal polarimeter in the temperature range 298–503 K. The results have been analyzed within the framework of a point-dipole model for the optical rotation. Though the magnitude of the rotation is very small, its sign has been clearly determined and linked to the crystallographic structure. A slight modification of the point-dipole model also permits an explanation of the values of the second-order susceptibility coefficients for second-harmonic generation.

Quantitative analysis of the x-ray diffraction intensities of undulated smectic phases in bent-core liquid crystals

X-ray diffraction diagrams of undulated smectic phases in bent-core liquid crystals have been theoretically studied. The intensities of the reflections have been obtained for different layer modulations, and a general expression has been deduced for orthogonal cells in terms of the different harmonics of the distortion. The case of sinusoidal modulation is especially simple and has been studied also in oblique cells. High-quality x-ray measurements of three compounds reported in the literature have been analyzed as examples. In all cases it has been deduced that the modulation is sinusoidal and its amplitude has been easily obtained by fitting the experimental intensities. Equatorial (h0) reflections have been also considered to obtain information about the structure of defects at the maxima and minima of the undulation.

Some aspects about the structure of the optically isotropic phase in a bent-core liquid crystal: chiral, polar, or steric origin

We have studied a bent-core liquid crystal where two different optically isotropic phases can be induced by a strong electric field. Depending on the field treatment the phases can present optical rotation or be optically inactive. The switching dynamics of the phases is studied by means of electrooptic and optical second-harmonic generation measurements. It is found that the ground state of the phases is locally antiferroelectric. The structure of the phases is consistent with a disordered version of the kind of structures recently proposed for the smectic blue phase: layered systems with high Gaussian curvature. The origin of the smectic layer distortion is discussed. It is concluded that the direct reason for the curvature of planes is of steric nature.

Structure of mesogens possessing B7 textures: the case of the bent-core mesogen 8-OPIMB-NO2

A structural investigation of the compound 8-OPIMB-NO2 is carried out. This material is a mesogen formed by bent-core molecules where the so-called B7 phase was originally proposed. X-ray data are successfully indexed in terms of a oblique two-dimensional lattice. Using additional information from optical second harmonic generation several possible structural models are proposed. The models are based on molecular packing considerations. All these structures are clearly different from those of other materials previously classified as B7. The necessity of a revised nomenclature for classifying the structures of these compounds is pointed out.

Electric-field-induced B1-B2 transition in bent-core mesogens

We report experimental results on two bent-shaped mesogens showing the B1 phase. Contrary to the conventional B1 structures, we have found that our compounds display a clear electro-optic effect in this phase. Under the influence of a 100-Hz square-wave electric field of moderate amplitude, an increase of the birefringence is observed. However, no switching current is detected, indicating that the materials remain antiferroelectric. For high enough fields, a drastic change in the texture occurs. This change is a phase transition to a B2 phase, and shows the typical antiferroelectric switching of this phase. The induced B2 phase has been identified to be homochiral. Upon removal of the field, the B1 structure is recovered. Our study is based on differential scanning calorimetry, x-ray, electro-optics, polarization reversal, and dielectric measurements.

Interpretation of unusual textures in the B2 phase of a liquid crystal composed of bent-core molecules

A liquid crystal material of bent-core molecules is investigated by means of optical texture observations, x-ray measurements, and miscibility studies. While the x-ray and miscibility data point towards a B2 phase, the texture is however unusual, showing optical isotropy and segregation in two domains with opposite gyrations. It is shown that the texture can be interpreted successfully in terms of a smectic-C(A)P(A) structure in small domains with random orientations. The optical activity data are also explained semiquantitatively.

Induction of ferroelectricity in the B2 phase of a liquid crystal composed of achiral bent-core molecules

We report the observation of a transition from the antiferroelectric B2 phase to a ferroelectric phase in a liquid crystal composed of achiral bent-core (banana-shaped) molecules. The transition is induced by an electric field of magnitude larger than the switching threshold and is not reversible, i.e., the original B2 phase does not reappear upon field removal. The transformation is accompanied by a dramatic texture change, resulting in an almost optically isotropic structure in the absence of field. The ferroelectric character assigned to the structure is based on the electro-optic behavior of the material and on previously reported dielectric measurements. A short-pitch smectic-C*-type structure is proposed for the ferroelectric phase.

Structural study of the low-temperature phase of TlH2PO4 at 180 K

The low-temperature phase of TlH(2)PO(4) has been studied by X-ray diffraction. A structural model is proposed with space group P1. This model is compared with the structure of the antiferroelectric phase of TlD(2)PO(4) at room temperature to analyze the expected isomorphism at low temperature. Given the structural distortion of TlH(2)PO(4), such isomorphism present in the common high-temperature phase is not recovered in this phase. Through the analysis of the displacements of the PO(4) groups there is some evidence that the ordering of the H atoms responsible for the appearance of antiferroelectricity seems to be incomplete. An exhaustive study of the detected ferroelastic domains is also performed.

Gyrotropy problem in nonhomogeneous media: The case of short-pitch chiral-smectic-C liquid crystals and incommensurate structures

The question about the existence of macroscopic models for gyrotropy in inhomogeneous materials is examined. We have carried out a detailed polarimetric study on a short-pitch chiral-smectic-C liquid crystal, which has been taken as an example of an inhomogeneous optical medium. In accordance to the theoretical predictions, we have found that, as a first approximation, the inhomogeneous liquid crystal can be modeled as a homogeneous uniaxial medium with huge optical activity in a direction perpendicular to the optic axis. However, some deviations have been determined in the precise values of the optical activity predicted by the theory. These discrepancies have been attributed to higher-order gyration-like effects, which are usually negligible and have not been considered in previous theoretical approaches. The agreement improves when these higher-order effects are incorporated. In the light of the above results, the theory is applied to the case of incommensurate structures. The origin of gyrotropy in these materials is clarified, and it is shown that this quantity can be described by a usual macroscopic tensor. If the incommensurate structure has an inversion center we deduce that all gyration effects rigorously vanish, contrary to the opinion maintained by several authors.

Characterization of the room-temperature phase of Tl2MoO4: crystal structure, symmetry mode analysis and second-harmonic generation measurements

The crystal structure of the glaserite-related compound dithallium(I)-molybdate(VI), which at 293 K crystallizes monoclinic, space group C121 with lattice parameters a = 10.565 (3), b = 6.418 (1), c = 8.039 (2) A, beta = 91.05 (4) degrees, has been determined. The structure was refined as an inversion twin to a final R(F(all)) value of 0.0611 for 1006 unique reflections [R(F(obs)) = 0.0285 for 644 observed reflections]. Second-harmonic generation measurements led to a value of d(eff) = 5.5 +/- 0.5 pm V(-1) as an estimation of the second-harmonic conversion efficiency at phase matching. Symmetry mode analysis shows that, in general, primary modes have the highest amplitudes, yet surprisingly some of the secondary modes assume amplitudes of comparable magnitude. A comparison of the phase at 293 K with that at 350 K (space group P3m1) shows that the main change can be described as a rotation of the molybdate tetrahedra around the trigonal a(b) axis. The molybdate tetrahedra as well as the octahedra around one of the symmetry-independent Tl atoms are more strongly distorted in the monoclinic phase. The coordination number for the other two Tl atoms is decreased from 12 and 10 in the high-symmetry phase to 10 and 9 in the monoclinic phase. Furthermore, the number of common edges between the Tl and Mo coordination polyhedra is reduced and the common face which is observed between them in the high-temperature phase is changed to a common edge in the low-temperature phase. The contribution of the primary symmetry modes leads exactly to this change in the coordination spheres of the atoms.

Second-harmonic generation studies in the B2 and B4 phases of a banana-shaped liquid crystal

Second-harmonic generation (SHG) measurements have been performed in the B2 phase of the achiral banana-shaped molecule with n=12 alkoxy end chains (P-12-O-PIMB). A quantitative value of the nonlinear efficiency has been obtained from SHG curves at oblique incidences, taking into account that the signal is generated by a random orientation of different domains. In the B4 phase, circular dichroism, optical absorption and SHG studies have been carried out. It has been found that there are no simple helical arrangements giving rise to selective reflection in the visible region of the spectrum. In addition, some unusual features of the SHG behavior are pointed out. It is concluded that the phase is intrinsically inactive for the SHG process. The detected signal is due to the presence of some birefringent inclusions that are created at the B2 to B4 transition and slowly disappear while the sample is maintained within the B4 phase. A structural model for these inclusions is presented.

Comparison between the switching dynamics of homeotropic and planar cells of chiral smectic-C liquid crystals

The molecular dynamics during the switching of homeotropic and planar cells of chiral smectic-C liquid crystals has been investigated using electrooptic measurements and second-harmonic-generation interferometry. Two ferroelectric liquid crystals with great differences in their molecular structures have been studied. It has been found that the molecular motion is rather different depending on the type of cell used. For planar cells, the azimuthal rotation of the molecules is limited within half the smectic cone and the molecules rotate in opposite directions in the two halves of the chevron structure. In contrast, for homeotropic cells there is no chevron structure and a uniform macroscopic optical indicatrix can be defined all over the sample during the whole switching process. However, the molecular reorientation takes place within numerous microdomains of size smaller than the optical wavelength. There are two types of microdomains that occur with different probabilities depending on the material. Within each domain the molecules rotate in opposite directions, and the molecules describe a complete cone during a whole switching period.

Origin of the optical activity of silver thiogallate

Using a high-accuracy universal polarimeter, the birefringence and optical activity of AgGaS2have been determined between 300 and 500 K. The optical rotation has been found to be 94° mm−1at room temperature for a wavelength of 632.8 nm. This value is unexpectedly small if compared with values close to 1000° mm−1at 485 nm reported previously. The present optical data are well explained using a point-dipole model for the calculation of the refractive indices and optical activity. The main contributors to the optical rotation are the S atoms. However, these atoms are not at positions especially suitable to promote extremely large gyrations. Consequently, the size of the optical rotation reported before in the blue part of the spectrum is presumably due to the existence of a circular dichroism band close to that region. Using an optical system based on a photoelastic modulator, a strong linear dichroism peak has been measured in the range 450–500 nm. This fact has prevented reliable measurement of the circular dichroism.