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We theoretically investigate the electro-optic (EO) effect in a yz-cut potassium niobate (KNbO3, KN) single crystal when a direct-current (DC) electric field is applied in the direction of [101]. We derived an analytical expression describing the change in the index ellipsoid under the applied DC electric field and solved its characteristic equation to obtain the refractive-index change induced by the EO effect. In order to show the practicality of our approach, we consider a classic application of the technique — an integrated Mach-Zehnder (MZ) modulator used for optical communication systems. The phase- and the intensity-modulation properties of the KN MZ modulator are discussed in detail, and all simulation results are compared with those for the lithium niobate (LN) counterpart that are widely used in current optical infrastructures. The results show that smaller-size or lower power-consuming EO modulators are feasible based on the proposed KN scheme due to its higher modulation efficiency.

A metal-insulator-metal plasmonic structure that contains a circular cavity with anisotropic material (AM) is designed and numerically simulated. Attributed to filling the cavity with AM, the standing wave patterns in the cavity rotate clockwise as the wavelength increases, resulting in a new valley on the transmission spectrum, which will not appear in the isotropic-material case. In order to understand the underlying physical mechanism of the phenomena, the influences of the parameters of AM, such as optical axis angle and refractive indexes, on transmission spectrum were investigated. All results can be explained well by the index ellipsoid method and the coupled mode theory. This work shows the unique role of AM in the plasmonics nanostructure and these phenomena may have potential applications in the nanoscale integrated photonic circuits.

Measurement of birefringence is crucial for the investigation of polarization optical components, including frequency-doubling crystal, electro-optic crystal, liquid crystal modulator. The commonly used measurement methods are based on determining the phase difference after transmission, and scarcely any method based on reflection is utilized. We propose an improved method of measuring the refractive index curve mode of anisotropy crystals during rotation, based on which we are able to determine the refractive indices and optical axis directions of the crystal according to a retrieval method. The measurement method involves precisely rotating and scanning the index ellipsoid and extracts two refractive indices from images captured at every rotation angle. The retrieval method processes two sets of data in a group and gives the fitted parameters, including the refractive indices and the optical axis direction in space. Simulation results are given, and two types of crystal, quartz and selenite, exemplifying uniaxial crystal and biaxial crystal, are experimented. The experiment results show that the fitted parameters are in good agreement with the theory. Compared with existing methods, our method has two main advantages. The sample does not need to be cut into a specific shape or prior information of the sample obtained, meanwhile the complete optical axis direction in space, including the intersection angle to the surface plane and the azimuth angle in the plan, can be determined, which benefits the evaluation and improvement of the material.

We present a geometric method for computing an ellipse that subtends the same solid-angle domain as an arbitrarily positioned ellipsoid. With this method we can extend existing analytical solid-angle calculations of ellipses to ellipsoids. Our idea consists of applying a linear transformation on the ellipsoid such that it is transformed into a sphere from which a disk that covers the same solid-angle domain can be computed. We demonstrate that by applying the inverse linear transformation on this disk we obtain an ellipse that subtends the same solid-angle domain as the ellipsoid. We provide a MATLAB implementation of our algorithm and we validate it numerically.

The complex symmetric dielectric tensor of a monoclinic crystal cannot be diagonalized by a space rotation operation in general, which poses a serious difficulty in analyzing the propagation of electromagnetic fields in monoclinic crystals so far. This propagation issue is discussed in a general case without using the index ellipsoid scheme. It is found that, when incident waves travel along the mirror plane normal or 2-fold rotation axis of monoclinic crystals, two eigenmodes following specific dispersion relations are elliptically polarized with the same ellipticity and chirality but have spatially orthogonal elliptical principal axes. The frequency independent features are the unique manifestation of the crystal symmetry. Using polarization sensitive terahertz time-domain spectroscopy and our developed data analyzing and processing methods, three complex permittivity tensor elements for a monoclinic crystal BaGa4Se7 are straightforwardly extracted and the properties of the two eigenmodes are characterized in full. It is also interesting that the spectral components beyond 1.7 THz show a very high refraction index (>10) and low dissipation during propagation, which suggests that the bulk phonon-polariton waves may be excited and effectively propagate in the crystal, resulting from the coherent phonon excitations by the incident terahertz waves. Our results may promote to develop novel terahertz devices based on polariton excitation and propagation in monoclinic crystals.

This paper introduces integration of silicon nitride onto electro-optic (EO) materials to realize novel RF-photonic modulators. The introduction of silicon nitride to EO material enables novel modulator relying on modifying its index ellipsoid. Design, fabrication, and experimental demonstration of such a modulator is presented.

Several nonlinear crystals that are used in laser and optical signal processing technologies belong to the {\overline 4}2m point group. This group exhibits as primary effects natural birefringence, optical activity, linear and quadratic electro-optic effects, and linear and quadratic electro-gyration effects, and, as secondary effects, photo-elasticity and piezo-gyrationviathe inverse piezo-electric phenomenon. The combination of these effects makes the study of light propagation a complicated task. In this work, the influence of each of these effects on light propagation is analytically reviewed, and suitable configurations for the light propagation and applied electric field directions are identified, which decouple the contribution of the individual effects. It is found that the complete decoupling of the linear electro-gyration from the linear electro-optic effect is not possible for this symmetry, while the inverse is feasible, and that the separation of the quadratic from the linear electro-optic effect can be achieved. For the linear phenomena, index ellipsoid geometries and eingenpolarizations are calculated, and analytic expressions are derived for the intensity of a light beam propagating through a crystal followed by a polarizer, thus providing valuable information for the design of devices and/or measurements of corresponding coefficients.

We introduce the stochastic geometry of a Gaussian random ellipsoid (GE) and, with the discrete-dipole approximation, carry out preliminary computations for light scattering by wavelength-scale GE particles. In the GE geometry, we describe the base ellipsoid by the three semiaxes a ⩾ b ⩾ c . The axial ratios b:a and c:a appear as two shape parameters additional to those of the Gaussian random sphere geometry (GS). We compare the scattering characteristics of GE particles to those of ellipsoids. Introducing irregularities on ellipsoids smoothens the angular scattering characteristics, in a way analogous to the smoothening of spherical particle characteristics in the case of GS particles.

Based on the photo-elastic effect and index ellipsoid,the relationship between transverse force and dielectric constant variation of polarization maintaining fiber(PMF) was obtained under the consideration of the difference between isotropic and anisotropic optical fiber under transverse force.Polarization coupling characteristic of PMF under transversal force was analyzed based on coupled-mode theory.The relationships between the coupling intensity and the amplitude,direction and the acting length of the transversal force were clarified by numerical simulation.When the direction of force was 45°,the coupling intensity of PMF was the best sensitive to the transversal force.The output extinction ratio changed periodically with acting length of the force,and different amplitude of the force corresponded to different period.The linear relation between the output extinction ratio and the amplitude of transverse force in the part region was found.These characteristics are consistent with previous experimental results.

Amongst the most common thin film characterization tools, spectroscopic ellipsometry (SE) is increasingly used to determine the layer optical properties. Such characterization is still a challenge when optical anisotropy is present either in the film or in the substrate. The study of thin films deposited on polymeric substrates is an example because polymers often show optical anisotropy. In this contribution the optical characterization of poly(ethylene 2,6-naphtalate) (PEN) in its transparent region is carried out by means of Transmission Generalized Ellipsometry (TGE) and reflection multi- angle SE measurements. TGE measurements allow the determination of the in-plane and out-of-plane anisotropy and orientation of the material index ellipsoid, with respect to the laboratory frame. Reflection multi-angle SE measurements are performed to determine the absolute refractive index values along the x, y and z directions (i.e. the laboratory frame). The full optical characterization of PEN substrates has been carried out first by identifying its in plane anisotropy (i.e. ?nxy = ny – nx) and in-plane orientation of the material index ellipsoid with respect to the x axis, by means of TGE measurements at 0° angle of incidence. A second step consisting of TGE measurements at different angles of incidence has allowed the determination of the out-of-plane anisotropy (i.e. ?nxz = nx – nz) and the material index ellipsoid out-of-plane orientation with respect to the z axis. Finally, reflection multi angle measurements have allowed the determination of the optical dispersions along the three axes (x, y, z). The values of the refractive index calculated at 633 nm are nx = 1. 74, ny = 1.75 and nz = 1.52. This characterization is functional to the determination of the refractive index of plasma-deposited SiO2-like layers deposited on PEN substrates. The SiO2-like samples have been deposited in Atmospheric Pressure Glow discharges [1,2] from Ar/O2/hexamethyldisiloxane mixtures at different duty cycles. SE measurements have been performed in ambient air and in vacuum: an increase of the refractive index values with the duty cycle has been observed, attributed, on the basis of complementary diagnostics, to an increase in film density with the duty cycle.

Expressions for the polarizability of a conducting ellipsoid and for the capacitance of an isolated conducting ellipsoid are suggested.

The dependence of the eigenvalues of the TM1n and TE1n electromagnetic triplet modes on the shape of a triaxial ellipsoid cavity resonator is investigated. For an ellipsoid with semi-axes proportional to 1 : (1 + 1) : (1 + 2) the fractional perturbations of the triplet components are found to second order in 1 and 2. The formulae are derived from the results of Kokkorakis and Roumeliotis (1997 J. Electromagn. Waves Appl. 11 279–92) for prolate and oblate spheroids. Finite-element calculations were carried out to confirm the accuracy of the formulae and to determine the next correction terms.

The molecular orientation of plastic optical films was examined in this study. The target is to develop a method of predicting retardation and optic axes. In this study, we propose a mechanism for the molecular orientation, and a calculation method for these parameters. The method has two assumptions. One is that the retardation is proportional to the input energy going into the film, the other is that the retardation decreases owing to the successive relaxation effect. The increment vectors of an index ellipsoid and the total index were introduced to describe the molecular orientation behavior. These definitions enable us to relate finite element analysis (FEA) results of film stretching to the assumptions. The uniaxial stretching process is focused to examine the method of predicting the retardation. Although the method can also be used to predict optic axes, this issue will be discussed in a succeeding report. The results had good agreement with the experimental results. The method is potentially useful in predicting the optical properties of films in commercialized stretching processes, for example, the tenter stretching process.

The temperature dependence of three principal refractive indices of the biaxial KGd(WO4)2 and KY(WO4)2 crystals in the temperature range of 288–673 K was measured at wavelengths of 438.5 and 632.8 nm. Their thermo-optical coefficients (TOC) of the first and second orders were determined on the basis of the experimental data obtained. TOC were found to be negative for the ng and np refractive indices of the KY(WO4)2 crystal and for the ng refractive index of the KGd(WO4)2 crystal. It was established that in a fairly wide temperature range contributions of the positive and negative TOC to the refractive index of a light wave propagating in these crystals in certain directions compensate each other. Such athermal directions were determined for the index ellipsoid principal planes of these crystals on the basis of experimental data.

The expressions of the refractive indices corresponding wave vector k(θ,ϕ)k(θ,ϕ) are given by using coordinate transformations for the refractive indices ellipsoid equation of biaxial crystals. The refractive index expression of the wave, whose velocity is slower, is given by 1n1‴2=[(cos2ϕn12+sin2ϕn22)cos2θ+sin2θn32]cos2δ+(sin2ϕn12+cos2ϕn22)sin2δ-12(1n12-1n22)sin(2ϕ)cosθsin(2δ), and that of the wave, whose velocity is faster, is given by 1n2‴2=[(cos2ϕn12+sin2ϕn22)cos2θ+sin2θn32]sin2δ+(sin2ϕn12+cos2ϕn22)cos2δ+12(1n12-1n22)sin(2ϕ)cosθsin(2δ). tg(2δ)=-(1n12-1n22)sin(2ϕ)cosθ(cos2ϕn12+sin2ϕn22)+[(sin2ϕn12+cos2ϕn22)cos2θ+sin2θn32].

Distributions of ellipsoids are often used to simulate the optical properties of non-ellipsoidal atmospheric particles, such as dust. In this work, the applicability of ellipsoids for retrieving the refractive index of dust-like target model particles from scattering data is investigated. This is a pure modeling study, in which stereogrammetrically retrieved model dust shapes are used as targets. The primary objective is to study whether the refractive index of these target particles can be inverted from their scattering matrices using ellipsoidal model particles. To achieve this, first scattering matrices for the target model particles with known refractive indices are computed. First, a non-negative least squares fitting is performed, individually for each scattering matrix element, for 46 differently shaped ellipsoids by using different assumed refractive indices. Then, the fitting error is evaluated to establish whether the ellipsoid ensemble best matches the target scattering matrix elements when the correct refractive index is assumed. Second, we test whether the ellipsoids best match the target data with the correct refractive index, when a predefined (uniform) shape distribution for ellipsoids is assumed, instead of optimizing the shape distribution separately for each tested refractive index. The results show not only that for both of these approaches using ellipsoids with the true refractive index produces good results but also that for each scattering matrix element even better results are acquired by using wrong refractive indices. In addition, the best agreement is obtained for different scattering matrix elements using different refractive indices. The findings imply that retrieval of refractive index of non-ellipsoidal particles whose single-scattering properties have been modeled with ellipsoids may not be reliable. Furthermore, it is demonstrated that the differences in single-scattering albedo and asymmetry parameter between the best-match ellipsoid ensemble and the target particles may give rise to major differences in simulated aerosol radiative effects.

The three-dimensional optical technique has been applied to analysis of the experimental results related to magnetic wave scattering phenomena. Recently, we have developed an ideal equation for analyzing the three-dimensional transmittance character of light scattered due to many index ellipsoids. The index ellipsoids are arranged directly along the light axis in series. In this case, the index ellipsoid size and the gap distance between each index ellipsoid and neighbor one are considered as a calculation condition. By using an analysis equation devised by us, we have sought to determine the condition under which the light can be passed through many transparent mediums with high efficiency. From the numerical calculations, the condition for maximum transmittance of light 100% is obtained when a spherical and elliptic index ellipsoids are alternately arranged with respect to each other. © 2006 Wiley Periodicals, Inc. Electr Eng Jpn, 158(3): 12–18, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20311

We undertake a theoretical study of the polarization behavior and mode structure of Vertical-Cavity Surface-Emitting Lasers (VCSELS) with an elliptical surface relief. The aim of the relief is twofold, first to enhance the single mode operation by introducing spatially distributed losses, and second, to enhance polarization stability by making these losses anisotropic. First, we use an analytical variational approach, for the two fundamental VCSEL modes within a Gaussian and weak guidance approximation. As a second approach we use a more refined numerical technique based on vectorial plane wave decomposition with periodic boundary conditions, which we formulate to include material anisotropy. Our studies show that whereas the polarization direction is governed by the orientation of the index ellipsoid, the selection of the lasing LP mode is mainly determined by the anisotropy in the mirror losses introduced by the elliptical surface relief.

The three dimensional optical technique has been applied to analyze the experimental results relating to the magnetic wave scattering phenomena. Recently, we have developed an ideal equation for analyzing the three dimensional transmittance character of light scattered due to many index-ellipsoids. The index-ellipsoids are arranged directly along the light axis in series. In this case, the size of index-ellipsoid and the gap distance between each index-ellipsoid and neighbor one are considered as a calculation condition. By using an analyzing equation devised by us, we have tried to find out the condition under which the light can be passed trough many transparent mediums with high efficiency. From the numerical calculations, we succeeded to look for the condition the maximum transmittance of light 100% is obtained when a spherical and elliptic index-ellipsoids are alternately arranged each other.

The three dimensional optical technique has been applied to investigate the electromagnetic wave scattering phenomena. Recently, we have developed an ideal equation for analyzing the three dimensional transport character of light scattered due to many index-ellipsoids arranged directly along the light axis in series. The size of index-ellipsoid, the distance between two adjacent index-ellipsoids, the ellipsoid rate and others are considered. By using an analyzing equation devised by us, we succeeded to derive the condition the light can pass trough many spherical and transparent mediums connected in series with high efficiency.

The accurate solution of scattering field by an ellipsoid in arbitrary shape is presented utilizing transformation of coordinates. The cross polarization discriminations and differential scattering section for electromagnetic waves induced by the ellipsoid are derived and simulated. Results show that XPD and DSS changes versus the sizes of an ellipsoid in three direction and its pose in free space, the back scattering field is larger than the forward scattering. The small the size for an ellipsoid in the propagation direction effects small cross component in the scattering waves.

External electro-optic sampling utilizing a poled polymer asymmetry Fabry–Perot cavity as electro-optic probe tip has been demonstrated. Electro-optical polymer spin coated on the high-reflectivity mirror (HRM) was corona poled. Thus, an asymmetric F–P cavity was formed based on the different reflectivity of the polymer and HRM and it converted the phase modulation that originates from electro-optic effect of the poled polymer to amplitude modulation, so only one laser beam is needed in this system. The principle of the sampling was analyzed by multiple reflection and index ellipsoid methods. A 1.2 GHz microwave signal propagating on coplanar waveguide transmission line was sampled, and the voltage sensitivity about 0.5 mV / Hz was obtained.

This study treats the quasistatic internal field of a hollow dielectric ellipsoid. The cavity is assumed to be a confocal ellipsoid relative to the dielectric ellipsoid. Special attention is paid to the amplification effect (the internal field amplitude is larger than the external uniform field) in hollow spheroids. The amplification effect is not very large: not more than 0.245 dB for a prolate spheroid and 9.5 dB for an oblate spheroid. The analysis is valid also for time-varying fields as long as the size of the ellipsoid is considerably smaller than the wavelength of the field.

The sampling of high-frequency signals using poled electro-optic polymer films as electro-optic probe tips has been demonstrated for the first time. The electro-optic polymer, which was spin coated onto a high-reflectivity glass substrate, was corona poled; thus an asymmetric Fabry–Perot microcavity was formed, based on the difference between the polymer reflectivity and that of high-reflectivity glass. This converts phase modulation to amplitude modulation, so only one laser beam is needed in this system. The sampling technique has been analyzed by multiple reflection and index ellipsoid methods. A 1.2 GHz microwave signal propagating on a coplanar waveguide transmission line has been sampled, and a voltage sensitivity of about 0.5 mV/\(\sqrt\Box Hz\Box \) was obtained.

The applied field can cause the inversion symmetry of the silicon single crystal is destroyed and disappears. So the silicon produce a second-order nonlinear optical effect. We exhibition electro-optic effect with index ellipsoid method for analyzing along different direction applied electric field. The result can be used to designing silicon electro-optic modulation.

In this chapter, we learn about the influence of the spatial symmetry of material media on the nature optical nonlinearity exhibited by them. We have seen that nth-order nonlinearity is governed by a tensor of rank \((n+1)\) with \(3^{(n+1)}\) tensor components in general. It would indeed be very inconvenient if we have to consider such a large number of quantities to describe nonlinearity. For example, it appears we need to specify 81 tensor components to characterize the third-order susceptibility of a medium.

Introduction In this chapter we discuss wave propagation in anisotropic media. We shall see that in such media the electric vector of a propagating wave is not in general parallel to its polarization direction, which is defined by the direction of its electric displacement vector. Further, for propagation of plane waves in a particular direction through an anisotropic medium two distinct possible polarization directions exist, and waves having these polarization directions propagate with different velocities. We shall discuss an ellipsoidal surface called the indicatrix and show how with its aid the allowed polarization directions and their corresponding refractive indices can be determined for wave propagation in a given direction. Other three-dimensional surfaces related to the indicatrix and their use in describing different optical properties of anisotropic media are also discussed. We shall concentrate our attention primarily on uniaxial crystals, which have optical properties that can be referred to an indicatrix with two equal axes, and will discuss how such crystals can be used to control the polarization characteristics of light. Important anisotropic optical media are generally crystalline, and their optical properties are closely related to various symmetry properties possessed by crystals. To assist the reader who is not familiar with basic ideas of crystal symmetry, Appendix 8 summarizes a number of aspects of this subject that should be helpful in reading this chapter and some of those succeeding it.

A geometric calculation method is developed to study the pulsed photoacoustic wave forming of an arbitrarily shaped droplet. It is found that for an ellipsoid droplet, either a prolate ellipsoid or an oblate ellipsoid, strict analytical formulas for describing the wave profile developed along the rotation axis can be derived. The results show intriguing differences compared to those of a sphere droplet in terms of the multiple geometric parameters being in effect, the pulse wave profile variant, and the existing of unlimited points of infinite tensile pressure.

The theory governing the propagation of light in the region near a plane strain crack tip is extended to optically anisotropic media. As for the case of isotropic media, an incident wavefront of light is split into two independent wavefronts. The planes of polarization of the two wavefronts lie in planes parallel and perpendicular to the crack front only for specific crystal orientations relative to the crack front. The general functional forms for the index of refraction of both the parallel and perpendicular wavefronts are given in terms of the principal indices of refraction, orientation of the index ellipsoid, and the direction of propagation of the wavefront. It is demonstrated how the principal indices of refraction and the orientation of the index ellipsoid can be calculated from the results of a finite element analysis and the coefficients of the elasto-optic tensor for a specific case. The characteristic equations which govern the propagation of light in anisotropic media are solved for a specific case to calculate the path of light relative to a crack tip in a bicrystal specimen. We also report the path of light rays approaching a mixed Mode I and Mode II crack tip in a material that is optically isotropic in its unstrained state.

An easy way to determine linear electro-optic effect of poled polymer materials was demonstrated by polymer-based asymmetric Fabry–Perot multiple reflection cavity. The standing-free technique of the cavity and reflective light path configuration was adopted in the measurement. This method can convert probe beam from phase modulation to intensity modulation without the reference beam for electro-optic application of poled polymer. The polymer used was a disperse red 1 doped guest/host material. The principle of the system was analyzed by multiple reflection and index ellipsoid methods, and the voltage sensitivity about 6 mV/√Hz of the system was obtained at 1 kHz input signal.

A photo-crosslinked side-chain second-order nonlinear optical polymer was synthesized with bis-phenol-A as the polymer backbone, p-nitroaniline as the chromophore and cinnamyl group as the photo-sensitizer. The characterization of the polymer was made by nuclear magnetic resonance, infrared, ultraviolet-vis, and dynamic mechanical analysis methods. An electro-optic film was obtained by spin coating of the polymer and corona poling then photo-crosslinking reaction. An external electro-optic measurement system was established based on the film and reflective light path configuration, and successfully applied to measure the electrical signals propagating on the under-test circuits. The poled and crosslinked film showed high glass transition temperature (160°C) and improved chromophore orientation stability. The measuring principle was analyzed by electro-optic tensor matrix and index ellipsoid methods. The results showed that the designed polymer film had the linear electro-optic effect, the voltage sensitivity of the system was measured to be 5 mv/ at the condition of 1 kHz input signal. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 77: 1506–1512, 2000

An external linear electro-optic measuring system based on a poled polymer asymmetric Fabry–Perot multiple reflection film has been built, and the electric signals propagating on an indium tin oxide coplanar strip transmission line have been successfully measured. The nonlinear polymer spin coated on the high-reflectivity glass substrate was corona poled, thus an asymmetric Fabry–Perot film was fabricated based on polymer reflectivity and high reflectivity glass. The film standing-free technique and reflective configuration were adopted in this system. The principle of the system was analyzed by multiple reflection and index ellipsoid methods. The voltage sensitivity about 5 mv/Hz was obtained as 1 kHz sine input electric signals propagating on coplanar electrodes.

The linear birefringence induced in a crystal by the first power of an applied electric field E - the Pockels effect - is traditionally described by the index ellipsoid model and the impermeability tensor. An alternative approach is presented which, unlike the ellipsoid model, allows ready extension to explain other effects, such as optical activity. This approach shows that for certain crystal symmetries and field and light path directions, a second linear birefringence may be induced in addition to the Pockels birefringence, of comparable magnitude and having different fast-slow axes. Where it exists this Jones birefringence, as it is termed, would therefore be an undesirable accompaniment to the Pockels effect in an electro-optic device. Also undesirable would be any coexisting natural circular birefringence and the magnitude of this is compared with a Pockels birefringence in potassium dihydrogen phosphate (KDP).

The Kelvin-inverted ellipsoid, with the center of inversion at the center of the ellipsoid, is a nonconvex biquadratic surface that is the image of a triaxial ellipsoid under the Kelvin mapping. It is the most general nonconvex 3-D body for which the Kelvin inversion method can be used to obtain analytic solutions for low-frequency scattering problems. We consider Rayleigh scattering by such a fourth-degree surface and provide all relevant analytical calculations possible within the theory of ellipsoidal harmonics. It is shown that only ellipsoidal harmonics of even degree are needed to express the capacity of the inverted ellipsoid. Special cases of prolate or oblate spheroids and that of the sphere are recovered through appropriate limiting processes. The crucial calculations of the norm integrals, which are expressible in terms of known ellipsoidal harmonics, are outlined in Appendix B.

A simple three-dimensional model is proposed which is based on characteristic surface the second rank tensor - three-axial ellipsoid. It is shown that due to symmetry of molecular oscillations in a liquid crystal (LC) it is possible to calculate its basic anisotropic characteristics by using oscillation magnitudes in isotropic state as a reference. It has been found that in ellipsoid sections there are directions, corresponding to an angle Θ0 = arccos√1/3 relative to major semiaxes of ellipsoid sections, with respect to which thermal properties of anisotropic physical quantities remain invariant. It is shown that ordinary wave refractive index n0 has different values for light beams propagating along and normal to the oriented nematic director.

We demonstrate experimental results on the angular dependence of the optical axis in biaxial materials from 430 nm to 1580 nm. Using pure KGd(WO 4 ) 2 (KGW) and Neodymium doped KGW crystals of around 1 cm in length. The variation of the angle is about 2.4° over the above wavelength range. Within the investigated spectral domain, a rotation of the index ellipsoid along the crystallographic b-axis is not observed, the variation occurs only in one plane. Moreover, no significant influence of doping of the crystal was observed. Comparison with literature refractive index data results in a difference of up to 0.5° with our data based on an arbitrary reference chosen at 560 nm, showing the importance of this measurement for conical refraction applications.

Guided acoustic waves propagating in transparent and isotropic solids are studied by optical interferometry via the photoelastic effect. Unlike the photoelastic technique, the interferometric method permits the measurement of the phase shift rather than the polarization change of the light passing through an acoustic field. By analyzing the acoustically induced change in the index ellipsoid of refraction, it is demonstrated that the optical phase shift is proportional to the dilatation or the relative change in volume of the material. The dilatation fields of the symmetric and antisymmetric Lamb modes S0 and A0, as well as that of the Rayleigh wave, were calculated. Experiments performed in fused quartz by the interferometric method are in good agreement with theoretical predictions. Compared to the conventional photoelastic technique, the interferometric measurement of acoustic wave is phase sensitive and quantitative.

There often appears unwanted elasto-optical birefringence in optical devices such as electro-optical, magneto-optical modulators and sensors when they are manufactured and used. This kind of elasto-optical birefringence causes unwanted effect for optical device and needs to be removed. Based on the method of index ellipsoid analysis, we theoretically analyze elasto-optical effects in various point groups of optical crystals and glasses, and accordingly propose some methods to eliminate unwanted elasto-optical birefringences in optical crystals and glasses. Main conclusions show that for orthorhombic biaxial crystal and the light wave propagating along any one crystalline axis of the crystal, if there is no shearing stress and the two external normal stresses applied to the other two crystalline axes can keep a constant ratio related to crystal parameters including refractive index and photoelastic constants, then unwanted elasto-optical birefringence can be eliminated from relevant optical devices, typical crystals include potassium titanium oxide phosphate (KTiOPO4, KTP) crystal and rubidium titanium oxide phosphate (RbTiOPO4, RTP) crystal, which are usually used as electrooptic Q-switchers in laser systems. For all the uniaxial crystyals such as potassium dihydron phosphate (KH2PO4, KDP), beta-barium borate ( -BaB2O4, BBO) and lithiun niobate (LiNbO3, LN) crystals, cubic crystals of 43 m, 432, m3 m point groups such as bismuth germanate (Bi4Ge3O12, BGO) crystal, and optical glasses, if the two normal stresses applied to the x1- and x2- crystalline axes of the crystal are equal to each other and there is no shearing stress, or there exists only one normal stress applied to the x3- crystalline axis of the crystal, then for the light wave propagating along the x3- crystalline axis, unwanted elasto-optical birefringence in relevant optical devices can also be eliminated. The above-proposed method to remove unwanted elasto-optical birefringence is benificial to design, manufacture, and usage of related optical devices.

For a triaxial ellipsoid in an optical trap with spherical aberration, the optical forces, torque and stress are analyzed using vectorial ray tracing. The torque will automatically regulate ellipsoid's long axis parallel to optic axis. For a trapped ellipsoid with principal axes in the ratio 1:2:3, the high stress distribution appears in x-z plane. And the optical force at x-axis is weaker than at y-axis due to the shape size. While the ellipsoid departs laterally from trap center, the measurable maximum transverse forces will be weakened due to axial equilibrium and affected by inclined orientation. For an appropriate ring beam, the maximum optical forces are strong in three dimensions, thus, this optical trap is appropriate to trap cells for avoiding damage from laser.

SUMMARY The free oscillations of elastically anisotropic spheres are computed here using a Rayleigh-Ritz method developed by Mochizuki (1988). The computation of eigenfrequencies was made for elastic spheres with orthorhombic, tetragonal, cubic and isotropic crystal symmetries, and how the degenerate eigenfrequencies split due to the elastic anisotropy has been shown. A perturbation theory combined with the Rayleigh-Ritz method was presented to compute shifts in and splits of eigenfrequencies due to deformation of an elastic sphere into an ellipsoid. The frequency shifts are expressed by δω=φxEx+φyEy+φzEz, where Ej and φj (j = x, y, z) are, respectively, asphericities and aspherical coefficients of the ellipsoid. This equation was used not only to compute the free-oscillation frequencies of an elastically anisotropic ellipsoid, but also to determine the asphericities of an olivine ellipsoid from observed resonant frequencies.

In this work we consider the problem of scattering of a plane acoustic wave by a multi-layered ellipsoid with a hard core, in the low-frequency region. Explicit closed-form solutions for the zeroth, first and second order approximations are obtained in terms of the physical and geometrical characteristics of the scatterer. The leading low-frequency term for the normalized scattering amplitude and the scattering cross-section are also given explicitly. Degenerate multilayered ellipsoids corresponding to the multi-layered prolate and oblate spheroids and the multilayered sphere are considered as special cases.