V. A. Belyakov

Low Threshold DFB Lasing in Chiral LC at Diffraction of Pumping Wave

The possibilities of reduction of the lasing threshold due to the anomalously strong absorption effect are theoretically investigated for a distributed feedback (DFB) lasing in chiral smectics. It is shown that a minimum of the pumping wave intensity may be reached for the pumping wave propagating at an angle to the helical axes under diffraction of the pumping wave. The lowest threshold pumping wave intensity occurs for the lasing at the first band-edge lasing mode and the pumping wave propagating at an angle to the spiral axes corresponding to the first absorption maximum of the anomalously strong absorption effect at the edge of stop band. The corresponding analytical expressions are given for the case of the average dielectric constant of LC coinciding with the dielectric constant of the material limiting LC. If the pumping wave frequency is close to the lasing frequency the pumping wave propagation direction minimizing the threshold is not far from the helical axes and the pumping wave polarization minimizing the threshold is close to the circular one with the sense of chirality the same as one of the LC helix. Numerical calculations of the DFB lasing threshold at diffraction of pumping wave are performed for the typical values of the related parameters.

Comparison of calculated and observed CD spectra of liquid crystalline dispersions formed from double-stranded DNA and from DNA complexes with coloured compounds

Abstract The CD spectra of dispersions of DNA, in the form of cholesteric liquid crystalline droplets, in an aqueous continuum have been studied. Calculated curves have been fitted to experimental spectra. The amplitude and the sign of the intense absorption band of the purine and pyrimidine bases vary with the droplet size, the pitch and the twist sense of the cholesteric phase. The CD spectra of dispersions of the complex formed by DNA and a coloured intercalating antibiotic have been similarly studied. A general satisfactory level of fitting between observed and calculated CD spectra was found.

Optics of Chiral Liquid Crystals

In Chap.3 we considered the interaction between Mossbauer (short wave) radiation and crytals within the framework of diffraction theory. Here we demonstrate that the same approach describes the interaction between optical (long wave) radiation and periodic media of complex structure, specifically, chiral liquid crystals.

Optical defect modes in chiral liquid crystals

An analytic approach to the theory of optical defect modes in chiral liquid crystals (CLCs) is developed. The analytic study is facilitated by the choice of the problem parameters. Specifically, an isotropic layer (with the dielectric susceptibility equal to the average CLC dielectric susceptibility) sandwiched between two CLC layers is studied. The chosen model allows eliminating the polarization mixing and reducing the corresponding equations to the equations for light of diffracting polarization only. The dispersion equation relating the defect mode (DM) frequency to the isotropic layer thickness and an analytic expression for the field distribution in the DM structure are obtained and the corresponding dependences are plotted for some values of the DM structure parameters. Analytic expressions for the transmission and reflection coefficients of the DM structure (CLC-defect layer-CLC) are presented and analyzed for nonabsorbing, absorbing, and amplifying CLCs. The anomalously strong light absorption effect at the DM frequency is revealed. The limit case of infinitely thick CLC layers is considered in detail. It is shown that for distributed feedback lasing in a defect structure, adjusting the lasing frequency to the DM frequency results in a significant decrease in the lasing threshold. The DM dispersion equations are solved numerically for typical values of the relevant parameters. Our approach helps clarify the physics of the optical DMs in CLCs and completely agrees with the corresponding results of the previous numerical investigations.

On the enhancement of the nonlinear frequency transformation in periodic media

Abstract It is theoretically shown that an enhancement of the nonlinear frequency transformation in a periodic medium occurs under definite conditions if it is accompanied by light diffraction in this medium. The enhancement of the phase-matched frequency transformation occurs if the harmonic frequency ω approaches the stop band frequency ω e . In the nondepleted pump approximation the corresponding increase of the harmonic intensity is proportional to ω e (ω−ω e ) −1 and is restricted by a quantity proportional to the fourth power of the sample thickness. The formulas for the enhancement of second harmonic generation are presented.

Untwisting of the helical structure in a plane layer of chiral liquid crystal

The untwisting of the helical structure of a chiral liquid crystal (CLC) in a thin plane layer exposed to an external action (temperature or field) and its dependence on the molecular adhesive forces at the layer boundaries are studied theoretically. It is shown that the critical electric (magnetic) field for complete untwisting in a thin layer may be appreciably lower than in the corresponding bulk CLC sample, and, contrary to the latter, the untwisting proceeds jumpwise. The expressions relating the jump temperature (field), i.e., the magnitude of untwisting action, to the CLC material parameters, layer thickness, and surface adhesive potential are given. The jump temperature (field) hysteresis is studied. In particular, it is shown that, for certain parameters, the untwisted helix remains untwisted after the removal of external action. The revealed qualitative regularities of untwisting are illustrated by numerical computations with the use of particular parameters of a CLC layer.

Optical edge modes in photonic liquid crystals

An analytic theory of localized edge modes in chiral liquid crystals (CLCs) is developed. Equations determining the edge-mode frequencies are found and analytically solved in the case of low decaying modes and are solved numerically for the problem parameter values typical for the experiment. The discrete edge-mode frequencies specified by the integer numbers n are located close to the stop-band edge frequencies outside the band. The expressions for the spatial distribution of the n’s mode field in a CLC layer and for its temporal decay are presented. The possibilities of a reduction of the lasing threshold due to the anomalously strong absorption effect are theoretically investigated for a distributed feedback lasing in CLCs. It is shown that a minimum of the threshold pumping wave intensity may be reached, generally, for the pumping wave propagating at an angle to the helical axis. However, for lucky values of the related parameters, it may be reached for the pumping wave propagating along the helical axis. The lowest threshold pumping wave intensity occurs for the lasing at the first low-frequency band-edge lasing mode and the pumping wave propagating at an angle to the spiral axis corresponding to the first angular absorption maximum of the anomalously strong absorption effect at the high-frequency edge of the stop band. The study is performed in the case of the average dielectric constant of the liquid crystal coinciding with the dielectric constant of the ambient material. Numerical calculations of the distributed feedback lasing threshold at the edge-mode frequencies are performed for typical values of the relevant parameters.

Surface anchoring and temperature variations of the pitch in thin cholesteric layers

The temperature variations of the cholesteric pitch in thin planar layers of cholesterics and their dependence on the surface anchoring force are investigated theoretically. It is shown that the temperature variations of the pitch in a layer are of a universal character. This is manifested in the fact that they depend not separately on the parameters of the sample but only on one dimensionless parameter Sd=K22/dW, where K22 is the torsional modulus in the Frank elastic energy, W is the height of the surface-anchoring potential, and d is the thickness of the layer. The investigation is performed the parameter Sd in a range where the change per unit number of cholesteric half-turns within the thickness of the layer accompanying a change in the temperature is due to the slipping of the director on the surface of the layer through the potential barrier for surface anchoring. The critical values of the parameter Sd (which are most easily attained experimentally by varying the thickness of the layer), determining the region of applicability of the approach employed, are presented. The temperature variations of the free energy of the layer and the pitch of the cholesteric helix in the layer as well as the temperature hysteresis in the variations of the pitch with increasing and decreasing temperature are investigated for the corresponding values of Sd. Numerical calculations of the quantities mentioned above are performed using the Rapini anchoring potential.

Temperature hysteresis of the change in the cholesteric pitch and surface anchoring in thin planar layers

Hysteresis of the temperature of jumps in the cholesteric pitch in planar layers of cholesteric liquid crystals (CLCs) has been observed in the temperature dependence of the optical transmission spectra measured in a 4.8 ¼m thick specimen of a 60% chiral racemic mixture of CE6. The temperature difference for the pitch jumps during heating and cooling was equal to about 0.1°C near 40.3°C. No difference in the temperature of the pitch jumps during heating and cooling was observed for an 18 µm thick specimen. A theoretical description of this hysteresis is presented on the basis of a continuum theory of elasticity of CLCs that also takes account of the surface anchoring of the CLC. Different possible mechanisms leading to a change in the director configuration in the layer during a pitch jump and their correspondence to the jump mechanism and hysteresis which occur in the experimental specimens are discussed.

Dynamics of jumpwise temperature pitch variations in planar cholesteric layers for a finite strength of surface anchoring

The dynamics of pitch jumps in cholesteric layers with a finite surface anchoring strength under variations in temperature is investigated theoretically. General expressions are presented that connect the dynamics of pitch jumps with the parameters that determine the process, such as the viscosity, the specific form of the anchoring potential, and the dimensionless parameter Sd = K22/Wd, where W is the depth of the anchoring potential, K22 is the twist elastic modulus, and d is the layer thickness. It is found that the shape of the anchoring potential significantly influences the temporal behavior of the cholesteric helix in the process of a pitch jump. To illustrate this revealed dependence of the pitch jump dynamics on the shape and strength of the anchoring potential, the problem was investigated for two different models of the surface anchoring potential for a jump mechanism in connection with the director at the surface slipping over the barrier of the anchoring potential. Calculations for the unwinding (winding) of the helix in the process of the jump were performed to investigate the case of infinitely strong anchoring on one surface and finite anchoring on the other, which is important in applications. The results show that an experimental investigation of the dynamics of the pitch jumps will make it possible to distinguish different shapes of the finite strength anchoring potential and, in particular, it will provide a means for determining whether the well-known Rapini-Papoular anchoring potential is the best suited potential relevant to the dynamics of pitch jumps in cholesteric layers with a finite surface anchoring strength. The optimal conditions for experimental observation of these phenomena are briefly considered.