Anisotropic Optical Media Research Articles

Exact closed forms for the transfer matrix of free oscillations in finite periodic Timoshenko–Ehrenfest beams

In this work, we obtain closed-form expressions for the transfer matrix of free oscillations in finite periodic Timoshenko–Ehrenfest beams with an arbitrary number of cells. By invoking the Cayley–Hamilton theorem on the transfer matrix for free oscillations of a beam composed of N cells, we obtain a fourth-order recursive relation for the matrix coefficients, which defines the so-called Tetranacci Polynomials. Such recursive relation provides an algorithm to compute the Nth power of the transfer matrix, avoiding the matrix product of the N matrices. Furthermore, in the symmetric case of free oscillations in finite periodic Timoshenko-Ehrenfest beams, closed-form expressions for the solutions to the recursive relation have recently been derived, which we use to write the transfer matrix of a finite beam composed of N cells in a closed form. We find a good agreement between the natural frequencies calculated with the obtained expressions and finite element simulations. These expressions are very useful for studying the interaction of evanescent oscillations and find application, for instance, in the development of phononic topological insulators. Our formalism can be applied to waves propagating in finite periodic layers described by a 4 × 4-transfer matrix, such as electromagnetic waves in anisotropic optical media.

Extremely Short Pulses in Anisotropic Optical Media with Carbon Nanotubes Taking into Account Multiphoton Absorption

Extremely Short Pulses in Anisotropic Optical Media with Carbon Nanotubes Taking into Account Multiphoton Absorption

Influence of nonlinear absorption on the propagation of ultrashort optical pulses in an anisotropic optical medium with carbon nanotubes

We study the features of the evolution of a pulse in a dielectric medium (crystal) with optical anisotropic properties taking into account pumping. The medium contains semiconductor carbon nanotubes of a fixed orientation directed at an angle to one of the principal axes of the crystal. We analyze the influence of pumping and resistance to disturbances. Our study shows that the effects of pumping and nonlinear absorption suppress the dispersive pulse spreading caused by the optically anisotropic properties of the medium.

Extremely short pulses in an anisotropic optical medium containing carbon nanotubes with metal conduction

In this work, we study the interaction of extremely short pulses with a nonlinear anisotropic optical medium with carbon nanotubes (armchair and zigzag type) with metallic conductivity. The dependence of the pulse shape, width, and intensity on the nanotube chirality indices is analyzed. The most appropriate type of carbon nanotubes is substantiated for providing localized propagation of an electromagnetic field in a medium with anisotropic properties. Keywords: optical anisotropy, extremely short pulse, carbon nanotubes, metallic conduc.

Extremely short pulses in anisotropic optical media with carbon nanotubes taking into account multiphoton absorption

In this paper, we study the influence of multiphoton absorption on the propagation of electromagnetic waves in a nonlinear optical anisotropic medium with carbon nanotubes. The effective equation for the vector potential of the electromagnetic field of the pulse is obtained, taking into account the second component of the polarization of the field, as well as two- and three-photon absorption processes. The dependence of the components of the pulse field on the parameters of the problem is revealed. Keywords: optical anisotropy, extremely short pulse, multiphoton absorption.

Предельно короткие импульсы в оптически анизотропной среде, содержащей углеродные нанотрубки с металлической проводимостью

In this work, we study the interaction of extremely short pulses with a nonlinear anisotropic optical medium with carbon nanotubes (armchair and zigzag type) with metallic conductivity. The dependence of the pulse shape, width, and intensity on the nanotube chirality indices is analyzed. The most appropriate type of carbon nanotubes is substantiated for providing localized propagation of an electromagnetic field in a medium with anisotropic properties.

Propagation of Ultrashort Optical Pulses in Anisotropic Optical Media with Impurity-Containing Carbon Nanotubes

Propagation of Ultrashort Optical Pulses in Anisotropic Optical Media with Impurity-Containing Carbon Nanotubes

Influence of a magnetic field on the propagation of ultrashort optical pulses in anisotropic optical media with carbon nanotubes

Influence of a magnetic field on the propagation of ultrashort optical pulses in anisotropic optical media with carbon nanotubes

Propagation of ultrashort optical pulses in anisotropic optical media with carbon nanotubes

In this paper, we investigate the evolution of electromagnetic waves in a nonlinear anisotropic optical medium with carbon nanotubes (CNTs). Based on Maxwell’s equation, an effective equation is obtained for the vector potential of the electromagnetic field, which takes into account different values of the velocity and polarization with two directions. The dependence of the pulse shape on the crystal type, as well as the angle between the electric field and the CNTs axis is revealed.

Thermal and optical manipulation of morphology in cholesteric liquid crystal microdroplets constrained on microfibers

Liquid crystals (LCs) are distinctive materials that are applicable to a wide range of disciplines, such as continuum mechanics, optics of anisotropic media, statistical physics, and crystallography. The diverse structures and eye-catching topological defects of LCs in confined geometries are affected by nematic elasticity, chirality, and surface anchoring. Herein, we report the formation and detailed configuration of cholesteric LC (CLC) microdroplets with different pitches pierced by electrospun poly(methyl methacrylate) microfibers. Two kinds of surface anchoring, namely, homeotropic anchoring at the air–CLC droplet interface and planar anchoring at the fiber–CLC droplet interface, coexist in this system. By controlling temperature and light irradiation, the system exhibits thermal- and photo-dependent LC morphological and topological evolutions. The observed structures are complemented by numerical simulations of possible director fields decorated by defects. The externally controllable CLC necklaces constitute extraordinary systems for exploring the morphology and topological defects and open a route for applications in topological remote control, nanoscience, biomedical research, and the development of devices based on topologically structured soft media.

Spin-selective scattering modes in a disordered anisotropic optical medium

Geometrical and dynamical phase have competing effects as far a scattering of light form inhomogeneous anisotropic optical medium is concerned. If fine-tuned appropriately, these effects can completely cancel each other for a chosen spin component while having an additive effect on the orthogonal components. Here, we show a manifestation of extraordinary spin selective modes in Fourier spectrum of Gaussian beam transmitted through anisotropic disordered medium. We realize the concept using a twisted nematic liquid crystal-based spatial light modulator (SLM) with random gray level distribution for incident Gaussian beam.

Flat polarization-controlled cylindrical lens based on the Pancharatnam–Berry geometric phase

The working principle of ordinary refractive lenses can be explained in terms of the space-variant optical phase retardations they introduce, which reshape the optical wavefront curvature and hence affect the subsequent light propagation. These phases, in turn, are due to the varying optical path length followed by light at different transverse positions relative to the lens center. A similar lensing behavior can, however, be obtained when the optical phases are introduced by an entirely different mechanism. Here, we consider the ‘geometric phases’ that arise from the polarization transformations occurring in anisotropic optical media, named after Pancharatnam and Berry. The medium anisotropy axis is taken to be space-variant in the transverse plane and the resulting varying geometric phases give rise to the wavefront reshaping and lensing effect, which however also depends on the input polarization. We describe the realization and characterization of a cylindrical geometric-phase lens that is converging for a given input circular-polarization state and diverging for the orthogonal one, which provides one of the simplest possible examples of optical elements based on geometric phases. The demonstrated lens is flat and only a few microns thick (not including the supporting substrates); moreover, its working wavelength can be tuned and the lensing can be switched on and off by the action of an external control electric field. Other kinds of lenses or more general phase elements inducing different wavefront distortions can be obtained by a similar approach. Besides their potential for optoelectronic technology, these devices offer good opportunities for introducing college-level students to an advanced topic of modern physics, such as the Berry phase, with the help of interesting optical demonstrations.

Soliton enhancement of spontaneous symmetry breaking

Spontaneous symmetry breaking (SSB) occurs when noise triggers an initially symmetric system to evolve toward one of its nonsymmetric states. Topological and optical SSB involve material reconfiguration/transition and light propagation/distribution in time or space, respectively. In anisotropic optical media, light beam propagation and distribution of the optic axis can be linked, thereby connecting topological and optical SSB. Using nonlinear soft matter, namely uniaxial liquid crystals, we report on simultaneous topological and optical SSB, showing that spatial solitons enhance the noise-driven transition of the medium from a symmetric to an asymmetric configuration, while acquiring a power-dependent transverse velocity in either of two specular directions with respect to the initial wavevector. Solitons enhance SSB by further distorting the optic axis distribution through nonlinear reorientation, resulting in power-tunable walk-off as well as hysteresis in beam refraction versus angle of incidence.

Extended magneto optic method to explore the longitude magneto optic Kerr effect of the magnetic ultrathin film grown on optically anisotropic substrate

The traditional magneto optic Kerr effect (MOKE) method is extended and the new method can be applied to investigate the magnetic properties of magnetic ultrathin film even multilayer containing anisotropic optical medium as long as we choose a proper coordinate system. Based on this method, any interface structure—magnetic ultrathin film grown on optically anisotropic substrate—can be explored by MOKE. The computer simulation shows relation between longitude Kerr rotation and incident angle. A further analysis indicates that the three elements of dielectric tensor of the anisotropic substrate play different roles in determining the relation between Kerr rotation and incident angle. Besides, the influence of the three dielectric constants of the substrate on the Kerr rotation is also found and parameters of special crystals have been taken into simulation to find the error ratio that the traditional method results for multilayer containing anisotropic optical substrate. These results show that the extended method can enhance the accuracy of measurement and help us to choose proper substrate for the ultrathin magnetic films when using MOKE to explore them.

Selective modulation of infrared radiation by an Al2O3 particles — liquid crystal system

Introduction. Liquid crystals (LC) are anisotropic optical media which have found broad application, in particular in LC displays and other photonic devices in the visible range. Little attention has been focused on studying LCs for conversion of radiation in the IR region of the spectrum, even though CO2 and other IR lasers are used in industry and medicine. Well-oriented nematic LC samples are strongly birefringent media, and are characterized by ordinary and extraordinary refractive indices no and ne. An electric field can change the orientation of LC molecules (the Frederiks effect), leading to a change in the effective refractive index along the direction of propagation of the light. In this case, the long axes of molecules of an LC with positive dielectric anisotropy are aligned parallel to the field direction, while in an LC with negative dielectric anisotropy they are aligned perpendicular to the field. This is a fundamental property of liquid crystals, and the basis for the operating principle of most photonic devices. Earlier in [1] a method was proposed for controllable filtration of IR radiation, based on a combination of the Frederiks effect and the Christiansen effect. The latter effect arises if particles are dispersed in a sufficiently transparent medium and the particle sizes are comparable with the wavelength of the incident light. In this case, the system transmits light in a narrow range of wavelengths, where the refractive indices are close for the particle material and the medium in which the particles are dispersed. Using LCs made it possible to control the position of the transmission maximum of the system when an electric field is applied. Application of this effect is also possible for a fixed value of the applied voltage (by varying its frequency). In this case, we propose using a dual-frequency LC as the medium in which the particles are dispersed, where the LC has positive anisotropy of the dielectric constant at low frequencies of the applied electric field and negative dielectric anisotropy at high frequencies. Aluminum oxide is used as the particle material; the refractive index of aluminum oxide varies considerably in the IR region of the spectrum [2]. In this paper, we present the results of a study of the Christiansen effect in an aluminum oxide particles — dual-frequency LC system.

Wave surfaces and wave velocities in optics of non-absorbing optically active media

General relations between phase normal vectors, refraction vectors and ray refraction vectors as well as between phase and ray velocities of plane waves are obtained for linear non-absorbing optically active (bianisotropic) media. For such media the geometric constraint on the wave surfaces is discussed. Equality of the group and ray velocities of the monochromatic plane waves in dispersive bianisotropic media is proven. It is shown that the degree of the ray surface equation generally exceeds the degree of the refraction surface and phase velocity surface equations but it cannot be greater than 108. In particular, for gyrotropic dielectric media of symmetry classes 3, , 4, , 4/m, 6, and 6/m it equals 12. The domain of applicability of the duality principle known in optics of anisotropic media is determined.

Anisotropy without tensors: a novel approach using geometric algebra

The most widespread approach to anisotropic media is dyadic analysis. However, to get a geometrical picture of a dielectric tensor, one has to resort to a coordinate system for a matrix form in order to obtain, for example, the index-ellipsoid, thereby obnubilating the deeper coordinate-free meaning of anisotropy itself. To overcome these shortcomings we present a novel approach to anisotropy: using geometric algebra we introduce a direct geometrical interpretation without the intervention of any coordinate system. By applying this new approach to biaxial crystals we show the effectiveness and insight that geometric algebra can bring to the optics of anisotropic media.

Geometric phase from a dielectric matrix

The dielectric property $(2\times2)$ of the anisotropic optical medium is found out considering the polarized photon as two component spinor of spherical harmonics.The Geometric Phase of single polarized photon has been evaluated in two ways. The phase two-form of the dielectric matrix through a twist and the Pancharatnam phase (GP) through the change of angular momentum of the incident polarized photon over a closed triangular path on the extended Poincare sphere. The helicity in connection with the spin angular momentum of the chiral photon plays the key role in developing these phase holonomies.

Three-Wave Resonant Interactions in Self-Defocusing OpticalMedia

A three-wave resonant interaction for nonlinear excitationscreated from a continuous-wave background is shown to be possible in anisotropic optical medium with a self-defocusing cubicnonlinearity. Under suitable phase-matching conditions thenonlinear envelope equations for the resonant interaction arederived by using a method of multiple-scales. Some explicitthree-wave solitary wave and lump solutions are discussed.

Parametric vector solitons in tetragonal crystals.

We introduce novel types of spatial vector soliton that can be generated in anisotropic optical media, such as tetragonal crystals with third-order nonlinear susceptibility. We demonstrate that these vector solitons provide a nontrivial generalization to both conventional vector solitons of birefringent cubic media and parametric solitons supported by third-order cascaded nonlinearities.