Kerr Relaxation Research Articles

Optical Kerr effect for underlying the orientational and translational fluctuations of molecular interactions in non-polar CS2 vapor and liquid states

A femtosecond optical Kerr gate is used for first time to experimentally study the temporal behavior of the molecular interactions of carbon disulfide (CS2) vapor in comparison to its liquid state. This Kerr effect is observed due to the optical birefringence induced in a CS2 sample. Results show that the Kerr relaxation time in the vapor state is faster than in the liquid state, with an overall exponential fit of 0.8 ps molecular relaxation time versus 1.7 ps, respectively. A faster relaxation decay time is observed for the first time in free CS2 molecules, this is attributed to fewer neighboring intermolecular interactions, which results in a lower local viscosity in the vapor compared to the liquid state. Fitting the temporal response of the Kerr vapor signal to individual components of n2 arising from the ultrafast and fast components yields two main decay times: τultrfast = 126 fs and τfast = 530 fs molecular relaxation times, one which agrees with the Debye equation for the air viscosity (associated to the free rotation in air) giving 126 fs and the other is approximately close to the translational diffusion equation producing 530 fs, respectively. In the liquid state, fitting yields three main components: τultrfast = 50 as, τfast = 500 fs, and τslow = 1.5 ps, overall, the tail fits the 1.7 ps molecular relaxation time.

Liquid crystal blue phases: stability, field effects and alignment

The blue phases are fascinating structures in liquid crystals, fluids that exhibit cubic structures that have true crystalline order. The blue phases were discovered in the 1970s and were the subject of extensive research in the 1980s, when a deep understanding of many of their properties was established. The discovery that the blue phases could be stabilised to exist over wide temperature ranges meant that they became more than scientific curiosities and led to a recent resurgence in research into them as they offer some promise in applications. This paper considers some important aspects of the blue phases that are recurrent topics in their research. It describes factors affecting blue phase stability, demonstrating on the role of the bend elastic constant; field effects, including the Kerr effect, electrostriction and relaxation phenomena; and alignment, in particular production and control of blue phase monodomains. The dependence of these phenomena on the physical properties of the liquid crystalline system, including the twist and bend elastic constants and the dielectric anisotropy, is emphasised wherever possible. The paper links work carried out in the 1980s with contemporary research, using a few key examples to show how there is still much to understand in this beautiful topic.

Ultrafast all-optical switching in one-dimensional semiconductor–polymer hybrid nonlinear photonic crystals with relaxing Kerr nonlinearity

The achievement of ultrafast all-optical switching on chip is a fundamental issue of all-optical integration. A feasible and promising method for this is to combine semiconductor photonic crystals with highly nonlinear polymer materials to form the hybrid nonlinear photonic crystal. In this paper we numerically investigate the femtosecond dynamic response of all-optical switching based on the effect of band gap edge shift in one-dimensional (1D) semiconductor–polymer hybrid nonlinear photonic crystal (NPC) structures. Taking into account the Kerr relaxation time of the polymer and semiconductor materials simultaneously, the introduction of highly nonlinear polymer materials with femtosecond relaxation time can realize all-optical switching in the femtosecond range in spite of the low response speed of the semiconductor materials. The physical origin is the large and ultrafast response Kerr nonlinearity of the polymer materials and this is proved by examining the dependence of switching time on the relaxation speed of the polymer materials. The results can be extended to 2D and 3D NPC structures.

Optically induced magnetization dynamics and variation of damping parameter in epitaxialCo2MnSiHeusler alloy films

All-optical pump-probe measurements of magnetization dynamics have been performed upon epitaxial ${\text{Co}}_{2}\text{MnSi}(001)$ Heusler alloy thin films annealed at temperatures of 300, 400, and $450\text{ }\ifmmode^\circ\else\textdegree\fi{}\text{C}$. An ultrafast laser-induced modification of the magnetocrystalline anisotropy triggers precession which is detected by time-resolved magneto-optical Kerr effect measurements. From the damped oscillatory Kerr rotation, the frequency and relaxation rate of the precession is determined. Using a macrospin solution of the Landau-Lifshitz-Gilbert equation the effective fields acting upon the sample magnetization are deduced. This reveals that the magnetization is virtually independent of the annealing temperature while the fourfold magnetocrystalline anisotropy decreases dramatically with increasing annealing temperature as the film structure changes between the B2 and $\text{L}{2}_{1}$ phases. From the measured relaxation rates, the value of the apparent Gilbert damping parameter is found to depend strongly upon the static field strength and in-plane static field orientation. The variation of the apparent damping parameter is generally well reproduced by an inhomogeneous broadening model in which the presence of B2 and $\text{L}{2}_{1}$ phases leads to a large dispersion of the magnetocrystalline anisotropy. However, for the sample annealed at a temperature of $300\text{ }\ifmmode^\circ\else\textdegree\fi{}\text{C}$, the lack of a detailed fit to the data suggests that the apparent anisotropy of the apparent damping parameter might alternatively arise due to a network of dislocations with fourfold symmetry.

In search of temporal power laws in the orientational relaxation near isotropic-nematic phase transition in model nematogens.

Recent Kerr relaxation experiments by Gottke et al. have revealed the existence of a pronounced temporal power law decay in the orientational relaxation near the isotropic-nematic phase transition (INPT) of nematogens of rather small aspect ratio, kappa (kappa approximately 3-4). We have carried out very long (50 ns) molecular dynamics simulations of model (Gay-Berne) prolate ellipsoids with aspect ratio 3 in order to investigate the origin of this power law. The model chosen is known to undergo an isotropic to nematic phase transition for a range of density and temperature. The distance dependence of the calculated angular pair correlation function correctly shows the emergence of a long range correlation as the INPT is approached along the density axis. In the vicinity of INPT, the single particle second rank orientational time correlation function exhibits power law decay, (t(-alpha)) with exponent alpha approximately 2/3. More importantly, we find the sudden appearance of a pronounced power-law decay in the collective part of the second rank orientational time correlation function at short times when the density is very close to the transition density. The power law has an exponent close to unity, that is, the correlation function decays almost linearly with time. At long times, the decay is exponential-like, as predicted by Landau-de Gennes mean field theory. Since Kerr relaxation experiments measure the time derivative of the collective second rank orientational pair correlation function, the simulations recover the near independence of the signal on time observed in experiments. In order to capture the microscopic essence of the dynamics of pseudonematic domains inside the isotropic phase, we introduce and calculate a dynamic orientational pair correlation function (DOPCF) obtained from the coefficients in the expansion of the distinct part of orientational van Hove time correlation function in terms of spherical harmonics. The DOPCF exhibits power law relaxation when the pair separation length is below certain critical length. The orientational relaxation of a local director, defined in terms of the sum of unit vectors of all the ellipsoidal molecules, is also found to show slow power law relaxation over a long time scale. These results have been interpreted in terms of a newly developed mode coupling theory of orientational dynamics near the INPT. In the present case, the difference between the single particle and the collective orientational relaxation is huge which can be explained by the frequency dependence of the memory kernel, calculated from the mode coupling theory. The relationship of this power law with the one observed in a supercooled liquid near its glass transition temperature is explored.

Kerr relaxation of anisotropic dielectric particles and Néel relaxation of anisotropic magnetic particles after a sudden change of field

Kerr relaxation of anisotropic dielectric particles and Néel relaxation of anisotropic magnetic particles after a sudden change of electric or magnetic field are studied on the basis of the Smoluchowski equation for the orientation distribution function. The equilibrium average of a Legendre moment of any order is evaluated. The time dependence of the relaxation of polarization (first-order Legendre moment) and order parameter (second-order Legendre moment) after a sudden change of field is determined by a fast and accurate numerical method.

Electro-Optic Kerr Effect Investigations in a New Homologous Series of Liquid Crystal

Measurements are reported for the first time for the D.C. Kerr response and the pretransitional behaviour of a new homologous series of liquid crystal 4′-(trans-4′-alkylcyclohexyl)-benzonitrile(for n=5 to 9) at and above the nematic-isotropic phase transition temperatures. The real part of the third order nonlinear susceptibilities(χ(3)) have been determined for this homologous series of liquid crystals from the Electro-optic Kerr effect (EOKE) experiments at and above the nematic-isotropic phase transition temperatures. The variation of the Kerr constant with temperature has been discussed on the basis of the Landau-de Gennes model of nematic-isotropic phase transition. The Kerr relaxation time and other statistical parameters concerned with a nematic-isotropic phase transition like the latent heat of transition have also been determined using the Landau-de Gennes' theory of phase transition. The variation of the Kerr constant, the values of the third order nonlinear susceptibilities, the Kerr relaxation time and the latent heat of transition with the number of carbon atoms in the alkyl chain within the series have been discussed on the basis of an interesting effect called the “ODD-EVEN” effect. The results and discussions are presented.

Solvation Dynamics in Nonassociated Polar Solvents

Ultrafast solvation dynamics in three nonassociated polar solvents, namely, acetonitrile, dimethyl sulfoxide, and acetone, have been studied by using the molecular hydrodynamic theory. For solvation in acetonitrile, the solvent memory function required for this study has been obtained from recent dielectric relaxation measurements of Venabales and Schuttenmaer; earlier theoretical studies used only the Kerr relaxation data. As the latter provides only an indirect information regarding the polar dynamical response of the dipolar liquid, it fails to provide a fully quantitative description of the solvation time correlation function, S(t). The present study with full dielectric data, on the other hand, gives excellent agreement with the experimental results. The theory shows that the ultrafast part of the solvation dynamics originates almost entirely from the high-frequency component of dielectric relaxation (with time constant 0.177 ps), although the latter represents only a small part of the latter. For DMSO and acetone, however, the present theory predicts a decay slower than the experimental observation. It is proposed that for these two solvents specific chromophore−solvent interactions might be responsible for the large discrepancy. On the basis of the theory, two experimental studies have also been proposed.

A quantum statistical model of a three-dimensional linear rigid rotator in a bath of oscillators: II. The electrical birefringence in relaxation regime

The Kerr effect relaxation resulting from the sudden removal of a DC field previously applied to a system of dilute rigid linear polar rotators in a sea of non-interacting bath harmonic oscillators is presented. In the quantum mechanical model proposed, we take account of permanent and induced dipole effects while the inertial effect of the bath is described by a collision operator. Hyperpolarizabilities are neglected. We use a generalized master equation governing the evolution of the rotator probability density operator to calculate the Kerr relaxation function . In the search for this function, we define matrix elements and whose knowledge at all times t, completely gives . We recover the classical limits of the quantum expressions. A quantum result valid for the rotating wave approximation limit is given. This paper is a logical continuation of our recent work.

Optical parametric oscillator incoherent spectroscopy

A new incoherent Kerr shutter is demonstrated. It utilizes nanosecond optical pulses from an optical parametric oscillator (OPO) that has a broad bandwidth. Through the use of abeta-BaB(2)O(4) crystal, the OPO has a coherence time of 60-800 fs and shows wide wavelength tunability from 410 to 2600 nm. Kerr relaxation time constants for CS(2) and nitrobenzene are the same as those cited in previous works. We also show, for the first time to our knowledge, a 100-fs response for a nitrobenzene solution of 4-(N,N-diethylamino)-beta-nitrostyrene at a 740-nm idler wavelength.

Induced electric birefringence and viscosity studies in microemulsions

Abstract The Kerr constant was determined for the AOT-water-dodecane water-in-oil microemulsion. The goal of these experiments has been to test the validity of the theoretical approach of van der Linden, S. Geiger and D. Bedaux, Phys. A., 156 (1989) 130, which explains the electro-optical process through an elastic deformation of the droplets. The bending modulus of the curved surfactant monolayer along different paths of the phase diagram was measured. It was concluded that for concentrations relatively far from phase transition regions the theory can account for the experimental results. However, we have measured the Kerr constant, relaxation times and viscosity in microemulsion-based (gelatin) gels. These magnitudes have been measured as a function of gelatin concentration. For low biopolymer concentrations, Kerr constants do not vary too much, whereas in a certain concentration range (about 3–4%), they increase abruptly. This behaviour is similar to those of electric conductivity and viscosity. We have estimated the characteristic size of anisotropic microstructures. The possibility of the presence of a branched structure has been analysed by using a stretched-exponents approach proposed by M. Daoud and J. Klafter, J. Phys. A: Math. Nucl. Gen., 23 (1990) L981.

Electro-Optic Kerr Relaxation Studiesin a Nematic Liquid Crystal 4-(Trans-4'-n-Pentylcyclohexyl)Benzonitrile (PCH-5)

In this paper we report the variation of the Electro-optic Kerr relaxation time (τ) with temperature at and above the nematic to isotropic phase transition ( T NI ) in a polar nematic Liquid crystal 4-(trans-4'-n Pentylcyclohexyl) Benzonitrile (PCH-5). The measurements of τ and the Electro-optic Kerr constant ( B ) have been made using an indigeneously built square pulse generator with a fall time of 45 nanoseconds. The variations of B and τ with temperature have been found to follow the predictions of the Landau-de Gennes theory for pretransitional behaviour in Liquid crystals.

Fabrication of high voltage square pulse generators for electro-optic Kerr relaxation studies

High voltage square pulse generators, with fall times of 1 μs and 45 ns have been fabricated for the measurement of electro-optic Kerr relaxation studies in macromolecules. These have been fabricated with a pulse forming network in the Blumlein line configuration with discrete components. The switching is brought about by high voltage spark gaps, instead of the thyratrons and silicon controlled rectifiers (SCRs), which have voltage limitations. The performance of these pulse generators are found to be consistent and stable, without any change in the pulse shape even at very high voltages and repetition rates. The Kerr constants and relaxation times measured with these pulse generators for the liquid crystal p-(methoxybenzelidene)-p-butylaniline (MBBA) at its nematic to isotropic phase transition temperature (43.5 °C) are found to be in very good agreement with the reported values obtained from the optical Kerr effect investigations using high power Q-switched solid state lasers.

Molecular theory of ultrafast solvation in liquid acetonitrile

A microscopic calculation of solvation dynamics of an immobile solute ion in liquid acetonitrile is presented. The dynamical information necessary for this calculation is obtained from the Kerr and dielectric relaxation of the neat liquid. The calculated solvation time correlation function is in excellent agreement with both the experimental and the simulated results.

Supermolecular self organization via molecular aggregation. Non-discotic three chain diols displaying a hexagonal columnar phase

Abstract A new class of mesogen formed by three chain diols is described. These compounds consist of a central part to which three aliphatic chains of various length (n = 4–14) are attached at one end and two hydroxy groups at the other. X-ray scattering, dilatometric measurements, dielectric and Kerr relaxation studies were carried out. Both X-ray investigations, dielectric and electro-optic studies revealed that the molecules are aggregated in the isotropic fluid state and that hydrogen bonding and dipole correlation contribute to this aggregation. Columnar assemblies of up to several hundred molecules are orientationally correlated in the isotropic fluid phase. Correlated reorientations occur in the presence of external electric fields. The X-ray data show that the aggregates pack in a hexagonal way at lower temperatures giving a structure which strongly resembles that of the hexagonal disordered columnar phase. This anisotropic phase can be quenched to a glassy liquid-crystalline state. It is evident ...

Electrooptical properties of liquid crystalline side chain polymers with laterally attached mesogenic units

AbstractThe electrooptical properties of side‐chain liquid crystalline polymers were investigated for the case that the mesogenic units were attached laterally rather than longitudinally to a flexible chain backbone via flexible spacer units. The experimental finding is that these polymers display unusual electrooptical properties within the isotropic phase in the neighborhood of the transition into the nematic phase.The polymers are characterized by the occurrence of a fast and a slow electrooptical response both of which show a critical divergence of the Kerr constant and the Kerr relaxation time. In addition, they show deviations between the rise and the decay values of the Kerr constants and in certain cases also of the Kerr relaxation times. Finally an overshoot of the induced birefringence following a sudden stepwise increase of the applied electric field has been found for one of these polymers. All these features can be accounted for on the basis of a newly developed theoretical approach that considers the particular dipolar and optical polarization configurations of these polymers.

Kerr relaxation theory of liquids in a cosine field. The case of small intertial effects

The modified Smoluchowski equation of rotational diffusion of molecules in a liquid is solved by the method of statistical perturbation calculus and applied to the description of the time evolution of the Kerr effect induced by a cosine reorienting field. The deviations from the classical theory of Kerr relaxation based on Smoluchowski's equation of rotational Brownian motion are analyzed.

Ultrashort pulse reshaping with a nonlinear Fabry–Perot cavity matched to a train of short pulses

Reshaping of ultrashort pulses is predicted to occur when a pulse train from a mode-locked laser is incident upon a nonlinear Fabry–Perot cavity whose length is matched to the period of the pulse train. The temporal shape of the transmitted pulses depends on the relaxation time of the nonlinearity of the Kerr medium inserted into the Fabry– Perot cavity. When the pulse duration is shorter than the Kerr relaxation time, considerable pulse narrowing (by factors of 101–103) is predicted. If the Kerr relaxation time is longer than the period of the pulse train, the analysis shows the existence of two temporal shapes of the output pulse, leading to the possibility of bistability between these two states. A Kerr nonlinearity with an instantaneous response can be used to generate square output pulses. Both the transient and the permanent regimes are investigated, and analytical expressions for the narrowing factors are found.

Molecular Kerr relaxation theory for liquids in reorienting pulse fields The case of small inertial effects

Our previous results concerning molecular Kerr relaxation theory in dipolar anisotropically polarizable liquids in a rectangular field are extended to the case of small inertial effects. Sack's modification of the Smoluchowski equation of rotational diffusion is applied and solved by statistical perturbation calculus.

Molecular kerr relaxation theory for nondipolar liquids in reorienting pulse fields

The time variations of the difference in refractive index in optical birefringence are calculated for a liquid composed of nondipolar anisotropically polarizable molecules acted on by reorienting pulse fields. The molecular dynamics is based on Sack's equation, taking into account small inertial effects (a modification of the Smoluchowski rotational diffusion equation). The time variations in birefringence are analyzed for rectangular and cosine pulse shapes on the basis of Sack's equation and are plotted for a gaussian pulse on the basis of Smoluchowski's equation. Measurements are proposed of the birefringence component with frequency 4ω related to the square of the electric anisotropy reorientation parameter of the molecules.