138 results on '"Index ellipsoid"'
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2. Phase-matching effect on the second harmonic and terahertz generations in [formula omitted]-barium borate.
- Author
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Xu, Ziwen, Mou, Sen, Tomarchio, Luca, D'Arco, Annalisa, Guo, Kangxian, Petrarca, Massimo, and Lupi, Stefano
- Subjects
- *
SECOND harmonic generation , *OPTICAL frequency conversion , *NONLINEAR optics , *HARMONIC generation , *BORATES , *NONLINEAR optical spectroscopy - Abstract
Nonlinear optics is of fundamental importance for frequency conversion and nonlinear optical spectroscopy. For instance, the second harmonic (SH) and terahertz (THz) generations are commonly utilized as frequency-conversion methodologies, and they are also employed as spectroscopic approaches. SH is generated through frequency doubling and THz through optical rectification (OR) in β -barium borate (BBO). Although the frequency doubling and OR are second-order nonlinear optical processes resulting from the same second-order susceptibility tensor, these two processes generate waves in totally different wavelength ranges. It is also interesting to find out other differences between these two nonlinear optical processes. This paper theoretically and experimentally investigates how phase matching affects the SH and THz generations. The theoretical results successfully explain the experimental ones. • The polar plot of second harmonic power versus pump polarization has two lobes. • The polar plot of terahertz power versus pump polarization possesses two lobes. • Susceptibility d o o e contributes to second harmonic generation. • Susceptibilities d o o e and d e e e contribute to terahertz generation. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
3. Characterization of the Electro-Optic Modulation Properties of a yz-Cut Potassium Niobate Single Crystal
- Author
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Yung Kim and Kwang Jo Lee
- Subjects
010302 applied physics ,Materials science ,Potassium niobate ,Birefringence ,business.industry ,Lithium niobate ,General Physics and Astronomy ,02 engineering and technology ,Index ellipsoid ,021001 nanoscience & nanotechnology ,Polarization (waves) ,01 natural sciences ,chemistry.chemical_compound ,chemistry ,Modulation ,Electric field ,0103 physical sciences ,Optoelectronics ,0210 nano-technology ,business ,Single crystal - Abstract
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.
- Published
- 2019
4. Anisotropic-Material-Induced Rotation of Field Distribution in Circular Plasmonic Resonator
- Author
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Yinxing Ding, Li Yu, Gaoyan Duan, Shilei Li, Xiaokang Song, Lulu Wang, and Yuanyuan Chen
- Subjects
lcsh:Applied optics. Photonics ,Nanostructure ,interference ,Physics::Optics ,Surface plasmons ,02 engineering and technology ,Coupled mode theory ,01 natural sciences ,010309 optics ,Standing wave ,Resonator ,Optics ,0103 physical sciences ,lcsh:QC350-467 ,Electrical and Electronic Engineering ,Physics ,business.industry ,lcsh:TA1501-1820 ,Index ellipsoid ,021001 nanoscience & nanotechnology ,anisotropic ,Atomic and Molecular Physics, and Optics ,Wavelength ,integrated optics ,Photonics ,0210 nano-technology ,business ,Refractive index ,lcsh:Optics. Light - Abstract
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.
- Published
- 2019
5. Critical angle method applied in determining the refractive indices and axis direction of crystal
- Author
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Wenping Guo, Tanbin Shao, Min Xia, Guan Congyuan, and Kecheng Yang
- Subjects
Optical axis ,Crystal ,Total internal reflection ,Birefringence ,Optics ,Materials science ,Uniaxial crystal ,business.industry ,Physics::Optics ,Optical polarization ,Index ellipsoid ,business ,Refractive index - Abstract
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.
- Published
- 2021
6. index ellipsoid
- Author
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Herrmann, Helmut and Bucksch, Herbert
- Published
- 2014
- Full Text
- View/download PDF
7. index ellipsoid
- Author
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Manutchehr-Danai, Mohsen, editor
- Published
- 2009
- Full Text
- View/download PDF
8. Three-dimensional analysis of light transmittance characteristics in many index ellipsoids connected in series.
- Author
-
Yoshida, Taro, Makishima, Kazuhiro, Sone, Mototaka, and Murooka, Yoshihiro
- Subjects
- *
LIGHT transmission , *ELLIPSOIDS , *LIGHT scattering , *ELECTROMAGNETIC waves , *NUMERICAL analysis - Abstract
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 [ABSTRACT FROM AUTHOR]- Published
- 2007
- Full Text
- View/download PDF
9. Analytical calculation of the solid angle subtended by an arbitrarily positioned ellipsoid to a point source
- Author
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Eric Heitz
- Subjects
Physics ,Nuclear and High Energy Physics ,business.industry ,Mathematical analysis ,Solid angle ,Geodesics on an ellipsoid ,Index ellipsoid ,Ellipse ,Ellipsoid ,Flattening ,Domain (mathematical analysis) ,030218 nuclear medicine & medical imaging ,Linear map ,03 medical and health sciences ,0302 clinical medicine ,Optics ,030220 oncology & carcinogenesis ,business ,Instrumentation - Abstract
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.
- Published
- 2017
10. Propagation of terahertz waves in a monoclinic crystal BaGa4Se7
- Author
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Li Wang, Yiwen E, and Jiyong Yao
- Subjects
Physics ,Multidisciplinary ,Condensed matter physics ,Terahertz radiation ,Phonon ,lcsh:R ,lcsh:Medicine ,Physics::Optics ,02 engineering and technology ,Index ellipsoid ,Elliptical polarization ,021001 nanoscience & nanotechnology ,01 natural sciences ,Article ,010309 optics ,Crystal ,Dispersion relation ,0103 physical sciences ,Polariton ,lcsh:Q ,lcsh:Science ,0210 nano-technology ,Monoclinic crystal system - Abstract
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.
- Published
- 2018
11. ANALYSIS OF THE ELECTRO-OPTIC EFFECT IN ANISOTROPIC CRYSTALS WITH 2-mm AND 3-m POINT GROUP SYMMETRY USING A FIRST-ORDER PERTURBATION TECHNIQUE.
- Author
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Faria, J. A. Brandão
- Subjects
- *
LITHIUM , *NIOBATES , *PERTURBATION theory , *DOUBLE refraction , *OPTICS - Abstract
The results of a recently proposed perturbation approach are successfully applied to the analysis of the Pockels effect in some representative electro-optic crystals, namely, potassium niobate and lithium niobate crystals. [ABSTRACT FROM AUTHOR]
- Published
- 1993
- Full Text
- View/download PDF
12. A PERTURBATION APPROACH TO THE ANALYSIS OF INDEX ELLIPSOID DEFORMATIONS IN BIAXIAL AND UNIAXIAL MEDIA.
- Author
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Faria, J. A. Brandão
- Subjects
- *
ANISOTROPY , *PHOTOELASTICITY , *PIEZOELECTRIC devices , *ELECTROOPTICS , *ELLIPSOIDS , *PERTURBATION theory - Abstract
Under the disturbing influence of photoelastic, piezoelectric, or electrooptic effects, anisotropic media have their natural behavior modified, the modification being described by a change in both the dimensions and orientation of the index ellipsoid. A first-order perturbation method useful for determining the perturbed index ellipsoid based on the unperturbed one is developed. Results concerning the new principal axes and principal refractive indices of the perturbed optical medium are presented. [ABSTRACT FROM AUTHOR]
- Published
- 1993
- Full Text
- View/download PDF
13. Thin-Film Silicon Nitride on Electro-Optic Materials for a Novel Modulator Architecture
- Author
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Janusz Murakowski, Christopher J. Cullen, Shouyuan Shi, and Dennis W. Prather
- Subjects
chemistry.chemical_compound ,Fabrication ,Materials science ,Silicon nitride ,chemistry ,business.industry ,Optoelectronics ,Index ellipsoid ,Thin film ,business - Abstract
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.
- Published
- 2018
14. On-wafer electrooptic probing using rotational deformation modulation.
- Author
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Chen, W.H., Kuo, W.K., Huang, S.L., and Huang, Y.T.
- Abstract
On-wafer electrooptic probing of two-dimensional electric-field vector (E-vector) is demonstrated by using one laser beam and one electrooptic prober. This technique utilizes both compressed-stretched deformation and rotational deformation on the index ellipsoid of the electrooptic crystal. Both experiment and simulation were performed to map the E-vector on a circuit board, and the measurement error is within 2.2% [ABSTRACT FROM PUBLISHER]
- Published
- 2000
- Full Text
- View/download PDF
15. Electro-optic and electro-gyration effects on light propagation in \bf \overline 4 2mpoint-group crystals
- Author
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S. Ves, Anastasios T. Efremidis, Evaggelos D. Vanidhis, Nikolaos C. Deliolanis, Konstantinos Vyrsokinos, and Constantinos Manolikas
- Subjects
Physics ,Birefringence ,Electro-gyration ,business.industry ,Physics::Optics ,Inverse ,Index ellipsoid ,Polarizer ,General Biochemistry, Genetics and Molecular Biology ,Symmetry (physics) ,Computational physics ,law.invention ,Optics ,Quadratic equation ,law ,Light beam ,business - Abstract
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.
- Published
- 2011
16. Light scattering by Gaussian random ellipsoid particles: First results with discrete-dipole approximation
- Author
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T. Pieniluoma and Karri Muinonen
- Subjects
Physics ,Radiation ,010504 meteorology & atmospheric sciences ,Scattering ,Gaussian ,Index ellipsoid ,Discrete dipole approximation ,01 natural sciences ,Ellipsoid ,Atomic and Molecular Physics, and Optics ,Light scattering ,Gaussian random field ,Computational physics ,symbols.namesake ,Classical mechanics ,0103 physical sciences ,symbols ,Particle ,010303 astronomy & astrophysics ,Spectroscopy ,0105 earth and related environmental sciences - Abstract
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.
- Published
- 2011
17. Polarization Coupling Characteristic of Polarization Maintaining Fiber Under Transversal Force
- Author
-
韩彪 Han Biao, 刘继芳 Liu Ji-fang, 宋家争 Song Jia-zheng, 蒋治国 Jiang Zhi-guo, and 马琳 Ma Lin
- Subjects
Coupling ,Physics ,Optical fiber ,Extinction ratio ,Condensed matter physics ,business.industry ,Isotropy ,Polarization-maintaining optical fiber ,Index ellipsoid ,Atomic and Molecular Physics, and Optics ,law.invention ,Transverse plane ,Amplitude ,Optics ,law ,business - Abstract
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.
- Published
- 2011
18. Optical Characterization of Plasma-Deposited SiO2 -Like Layers on Anisotropic Polymeric Substrates
- Author
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Peter Antony Premkumar, H.W. de Vries, Gianfranco Aresta, Mariadriana Creatore, M.C.M. van de Sanden, and Serguei Starostine
- Subjects
Reflection (mathematics) ,Materials science ,Polymers and Plastics ,Angle of incidence (optics) ,Ellipsometry ,Analytical chemistry ,Index ellipsoid ,Substrate (electronics) ,Thin film ,Condensed Matter Physics ,Anisotropy ,Refractive index - Abstract
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.
- Published
- 2010
19. Polarizability and capacitance of a conducting ellipsoid
- Author
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M. A. Nechaev
- Subjects
Physics ,Classical mechanics ,Polarizability ,fungi ,General Physics and Astronomy ,sense organs ,Index ellipsoid ,Capacitance ,Ellipsoid ,Flattening - Abstract
Expressions for the polarizability of a conducting ellipsoid and for the capacitance of an isolated conducting ellipsoid are suggested.
- Published
- 2009
20. Second-order electromagnetic eigenfrequencies of a triaxial ellipsoid
- Author
-
James B. Mehl
- Subjects
Resonator ,Classical mechanics ,Triaxial ellipsoid ,Mathematical analysis ,General Engineering ,Spheroid ,Order (ring theory) ,Index ellipsoid ,Prolate spheroid ,Ellipsoid ,Eigenvalues and eigenvectors ,Mathematics - Abstract
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.
- Published
- 2009
21. Prediction of Molecular Orientation in Film Stretching Processes
- Author
-
Motohiro Itadani, Kohei Arakawa, Toshiro Yamada, and Takashi Sato
- Subjects
Liquid-crystal display ,Materials science ,Physics and Astronomy (miscellaneous) ,business.industry ,General Engineering ,Process (computing) ,General Physics and Astronomy ,Index ellipsoid ,Mechanics ,Finite element method ,law.invention ,Optical axis ,Optics ,law ,Orientation (geometry) ,Successive relaxation ,business - Abstract
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.
- Published
- 2007
22. Negative thermo-optical coefficients and athermal directions in monoclinic KGd(WO4)2 and KY(WO4)2 laser host crystals in the visible region
- Author
-
V. V. Filippov, N. V. Kuleshov, and I.T. Bodnar
- Subjects
Quantum optics ,Materials science ,Physics and Astronomy (miscellaneous) ,business.industry ,General Engineering ,Analytical chemistry ,General Physics and Astronomy ,Index ellipsoid ,Atmospheric temperature range ,Laser ,law.invention ,Crystal ,Wavelength ,Optics ,law ,business ,Refractive index ,Monoclinic crystal system - Abstract
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.
- Published
- 2007
23. Refractive indices of biaxial crystals evaluated from the refractive indices ellipsoid equation
- Author
-
Shaojun Zhang, Xin Yin, and Zhaobing Tian
- Subjects
Physics ,business.industry ,Index ellipsoid ,Ellipsoid ,Atomic and Molecular Physics, and Optics ,Electronic, Optical and Magnetic Materials ,Optics ,Optical materials ,Biaxial crystal ,Wave vector ,Electrical and Electronic Engineering ,Atomic physics ,business ,Refractive index - Abstract
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].
- Published
- 2007
24. Retrieving microphysical properties of dust-like particles using ellipsoids: the case of refractive index
- Author
-
Osku Kemppinen, Timo Nousiainen, Petri Räisänen, S. Merikallio, Department of Applied Physics, Aalto-yliopisto, and Aalto University
- Subjects
Physics ,Atmospheric Science ,business.industry ,Scattering ,media_common.quotation_subject ,education ,Index ellipsoid ,Asymmetry ,Ellipsoid ,lcsh:QC1-999 ,Computational physics ,lcsh:Chemistry ,Matrix (mathematics) ,Optics ,Distribution (mathematics) ,lcsh:QD1-999 ,Radiative transfer ,business ,Refractive index ,lcsh:Physics ,media_common - Abstract
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.
- Published
- 2015
25. Three-dimensional analysis of light transmittance characteristics in many index ellipsoids connected in series
- Author
-
Mototaka Sone, Kazuhiro Makishima, Taro Yoshida, and Yoshihiro Murooka
- Subjects
Three dimensional analysis ,Index (economics) ,Series (mathematics) ,Scattering ,business.industry ,Energy Engineering and Power Technology ,Index ellipsoid ,Ellipsoid ,Optics ,Transmittance ,Ideal (ring theory) ,Electrical and Electronic Engineering ,business ,Mathematics - Abstract
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
- Published
- 2006
26. Modeling of the polarization behavior of elliptical surface-relief VCSELs
- Author
-
Hugo Thienpont, Krassimir Panajotov, Miren Camarena, and Rafal Kotynski
- Subjects
Physics ,Birefringence ,business.industry ,Single-mode optical fiber ,Physics::Optics ,Index ellipsoid ,Polarization (waves) ,Atomic and Molecular Physics, and Optics ,Electronic, Optical and Magnetic Materials ,Semiconductor laser theory ,Optics ,Periodic boundary conditions ,Electrical and Electronic Engineering ,business ,Anisotropy ,Gaussian beam - Abstract
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.
- Published
- 2005
27. Three Dimensional Analysis of Light Transmittance Character in Many Index-ellipsoids Connected in Series
- Author
-
Mototaka Sone, Kazuhiro Makishima, Taro Yoshida, and Yoshihiro Murooka
- Subjects
Physics ,Character (mathematics) ,Optics ,Series (mathematics) ,Scattering ,business.industry ,Transmittance ,Multiangle light scattering ,Index ellipsoid ,Electrical and Electronic Engineering ,business ,Ellipsoid ,Light scattering - Abstract
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.
- Published
- 2005
28. Three-Dimensional Analysis of Light Scattering Phenomena in Index-ellipsoid
- Author
-
Yoshihiro Murooka, Mototaka Sone, Kazuhiro Makishima, Taro Yoshida, and Takeshi Yamada
- Subjects
Physics ,Three dimensional analysis ,Optics ,business.industry ,Multiangle light scattering ,Static light scattering ,Index ellipsoid ,Electromagnetic wave scattering ,Electrical and Electronic Engineering ,business ,Ellipsoid ,Light scattering - Abstract
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.
- Published
- 2004
29. THE ACCURATE SOLUTION OF SCATTERING FIELD FOR A DIELECTRIC ELLIPSOID
- Author
-
J. Huang and Y. Li
- Subjects
Physics ,Field (physics) ,business.industry ,Forward scatter ,Scattering ,General Physics and Astronomy ,Scattering length ,Dielectric ,Index ellipsoid ,Ellipsoid ,Electromagnetic radiation ,Electronic, Optical and Magnetic Materials ,Computational physics ,Optics ,Electrical and Electronic Engineering ,business - Abstract
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.
- Published
- 2003
30. External electro-optic sampling utilizing a poled polymer asymmetric Fabry–Perot cavity as an electro-optical probe tip
- Author
-
Darning Zhang, Kaixin Chen, Maobin Yi, Hongbo Zhang, and Han Yang
- Subjects
Materials science ,Electro-optic effect ,business.industry ,Coplanar waveguide ,Physics::Optics ,Index ellipsoid ,Signal ,Atomic and Molecular Physics, and Optics ,Electronic, Optical and Magnetic Materials ,Amplitude modulation ,Optics ,Electrical and Electronic Engineering ,business ,Phase modulation ,Microwave ,Fabry–Pérot interferometer - Abstract
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.
- Published
- 2002
31. Internal field of a hollow dielectric ellipsoid: the amplification effect
- Author
-
Ari Sihvola and Juha Avelin
- Subjects
Physics ,Field (physics) ,business.industry ,Spheroid ,Physics::Optics ,Index ellipsoid ,Dielectric ,Condensed Matter Physics ,Ellipsoid ,Surfaces, Coatings and Films ,Electronic, Optical and Magnetic Materials ,Wavelength ,Optics ,Amplitude ,Electrical and Electronic Engineering ,business ,Astrophysics::Galaxy Astrophysics ,Quasistatic process ,Biotechnology - Abstract
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.
- Published
- 2002
32. Sampling high-frequency signals using a poled-polymer asymmetric FabryPerot microcavity as an electro-optic probe tip
- Author
-
K.X. Chen, H.B. Zhang, M.B. Yi, Yufen Zhao, and Hongxin Yang
- Subjects
Materials science ,Physics and Astronomy (miscellaneous) ,business.industry ,Coplanar waveguide ,General Engineering ,Physics::Optics ,General Physics and Astronomy ,Index ellipsoid ,Optical microcavity ,Signal ,law.invention ,Amplitude modulation ,Optics ,law ,business ,Phase modulation ,Fabry–Pérot interferometer ,Microwave - Abstract
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.
- Published
- 2002
33. Research on theory of the silicon material electro-optic modulator
- Author
-
Yu-hong Zhang, Hang Liu, and Wan-min Li
- Subjects
Materials science ,Field (physics) ,Silicon ,business.industry ,Point reflection ,Physics::Optics ,chemistry.chemical_element ,Electro-optic modulator ,Index ellipsoid ,Optics ,chemistry ,Modulation ,Electric field ,Optoelectronics ,business ,Single crystal - Abstract
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.
- Published
- 2014
34. Symmetry and Susceptibility Tensors
- Author
-
Y. V. G. S. Murti and C. Vijayan
- Subjects
Physics ,Optical nonlinearity ,Nonlinear system ,Rank (linear algebra) ,Quantum mechanics ,Tensor ,Index ellipsoid ,Symmetry (geometry) ,Mathematical physics - Abstract
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.
- Published
- 2014
35. The optics of anisotropic media
- Author
-
Christopher C. Davis
- Subjects
Classical mechanics ,Optics ,Materials science ,Wave propagation ,business.industry ,Plane wave ,Index ellipsoid ,Polarization (waves) ,business ,Anisotropy ,Waveplate ,Circular polarization ,Jones calculus - Abstract
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.
- Published
- 2014
36. Photoacoustic pulse wave forming along the rotation axis of an ellipsoid droplet: a geometric calculation study
- Author
-
Yong Li and Hui Fang
- Subjects
Physics ,business.industry ,Photoacoustic imaging in biomedicine ,Index ellipsoid ,Rotation ,Pulse shaping ,Ellipsoid ,Atomic and Molecular Physics, and Optics ,Cardinal point ,Optics ,Attenuation coefficient ,Physics::Atomic and Molecular Clusters ,Pulse wave ,Electrical and Electronic Engineering ,business ,Engineering (miscellaneous) - Abstract
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.
- Published
- 2014
37. Path of light in near crack tip region in anisotropic medium and under mixed-mode loading
- Author
-
Jeffrey W. Kysar
- Subjects
Wavefront ,Physics ,business.industry ,Applied Mathematics ,Mechanical Engineering ,Isotropy ,Physics::Optics ,Index ellipsoid ,Condensed Matter Physics ,Polarization (waves) ,Ray ,Optics ,Mechanics of Materials ,Modeling and Simulation ,General Materials Science ,business ,Anisotropy ,Refractive index ,Plane stress - Abstract
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.
- Published
- 2001
38. [Untitled]
- Author
-
Alin Hou, Xiaojian Tian, Daming Zhang, Kaixin Chen, Wei Sun, and Maobin Yi
- Subjects
Materials science ,Electro-optic effect ,business.industry ,Index ellipsoid ,Atomic and Molecular Physics, and Optics ,Electronic, Optical and Magnetic Materials ,Optics ,Reference beam ,Reflection (physics) ,Optoelectronics ,Electrical and Electronic Engineering ,business ,Phase modulation ,Intensity modulation ,Beam (structure) ,Fabry–Pérot interferometer - Abstract
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.
- Published
- 2000
39. Synthesis of a photo-crosslinked stable nonlinear optical polymer and application to external electro-optic measurement
- Author
-
Jiacong Shen, Daming Zhang, Maobin Yi, and Jingzhi Sun
- Subjects
chemistry.chemical_classification ,Spin coating ,Materials science ,Polymers and Plastics ,business.industry ,General Chemistry ,Dynamic mechanical analysis ,Index ellipsoid ,Polymer ,Chromophore ,Corona poling ,Surfaces, Coatings and Films ,Optics ,chemistry ,Materials Chemistry ,Optoelectronics ,Thin film ,business ,Glass transition - Abstract
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
- Published
- 2000
40. External electro-optic measurement utilizing poled polymer-based asymmetric Fabry–Perot reflection film
- Author
-
Wenjing Tian, A. L. Hou, M. B. Yi, Y. G. Ma, J. C. Shen, Wei Sun, D. M. Zhang, X. J. Tian, and J. Z. Sun
- Subjects
Optics ,Materials science ,business.industry ,Transmission line ,Electrode ,Reflection (physics) ,General Physics and Astronomy ,Substrate (electronics) ,Index ellipsoid ,business ,Fabry–Pérot interferometer ,Voltage ,Indium tin oxide - Abstract
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.
- Published
- 1999
41. A new theory of Pockels birefringence in non-magnetic crystals
- Author
-
R E Raab and Ernesta M. Meintjes
- Subjects
Crystal ,Materials science ,Kerr effect ,Birefringence ,Optics ,Field (physics) ,business.industry ,Electric field ,Index ellipsoid ,Tensor ,business ,Atomic and Molecular Physics, and Optics ,Pockels effect - Abstract
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).
- Published
- 1999
42. Rayleigh scattering for the Kelvin-inverted ellipsoid
- Author
-
Touvia Miloh and George Dassios
- Subjects
Physics ,symbols.namesake ,Scattering ,Applied Mathematics ,symbols ,Index ellipsoid ,Rayleigh scattering ,Ellipsoid ,Computational physics - Abstract
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.
- Published
- 1999
43. Three-Dimensional Model of Anisotropic Properties of Liquid Crystals in Thermal Fields
- Author
-
G. L. Nekrasov
- Subjects
Condensed matter physics ,Chemistry ,Oscillation ,business.industry ,Isotropy ,Index ellipsoid ,Maxwell stress tensor ,Condensed Matter Physics ,Ellipsoid ,Symmetry (physics) ,Optics ,Liquid crystal ,Anisotropy ,business - Abstract
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.
- Published
- 1997
44. Wavelength dependence of the optical axis in double tungstate crystals
- Author
-
Inka Manek-Hönninger, Marc Tondusson, Romain Cattoor, Daniel Rytz, Marc Eichhorn, Todor K. Kalkandjiev, and Lionel Canioni
- Subjects
Materials science ,Uniaxial crystal ,business.industry ,chemistry.chemical_element ,Index ellipsoid ,Refraction ,Neodymium ,Crystal ,Optical axis ,Wavelength ,Optics ,chemistry ,business ,Refractive index - Abstract
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.
- Published
- 2013
45. Analysis of optical interferometric measurements of guided acoustic waves in transparent solid media
- Author
-
Xiaoping Jia, Gerard Quentin, and Christophe Mattei
- Subjects
Photoelasticity ,Materials science ,business.industry ,Acoustics ,Surface acoustic wave ,Acoustic interferometer ,Physics::Optics ,General Physics and Astronomy ,Index ellipsoid ,Acoustic wave ,Polarization (waves) ,symbols.namesake ,Interferometry ,Optics ,symbols ,Rayleigh wave ,business - Abstract
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.
- Published
- 1995
46. How to eliminate unwanted elasto-optical birefringence from optical devices
- Author
-
Li Chang-Sheng and Chen Jia
- Subjects
Optic axis of a crystal ,Birefringence ,Materials science ,business.industry ,010401 analytical chemistry ,General Physics and Astronomy ,Index ellipsoid ,Laser ,01 natural sciences ,Bismuth germanate ,0104 chemical sciences ,law.invention ,010309 optics ,Crystal ,chemistry.chemical_compound ,Optics ,chemistry ,law ,0103 physical sciences ,Optoelectronics ,Orthorhombic crystal system ,business ,Refractive index - Abstract
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.
- Published
- 2016
47. Calculation of optical forces on an ellipsoid using vectorial ray tracing method
- Author
-
Jinhua Zhou, Yinmei Li, Min-Cheng Zhong, and Ziqiang Wang
- Subjects
Physics ,business.industry ,Optical force ,Physics::Optics ,Index ellipsoid ,Ellipsoid ,Atomic and Molecular Physics, and Optics ,Optical axis ,Ray tracing (physics) ,Spherical aberration ,Optics ,Optical tweezers ,business ,Principal axis theorem - Abstract
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.
- Published
- 2012
48. Free oscillations of elastically anisotropic spheres and ellipsoids
- Author
-
W. M. Visscher, Hitoshi Oda, J. Hirao, Isao Suzuki, and O. L. Anderson
- Subjects
Physics ,Tetragonal crystal system ,Geophysics ,Classical mechanics ,Geochemistry and Petrology ,Degenerate energy levels ,Isotropy ,SPHERES ,Index ellipsoid ,Perturbation theory ,Anisotropy ,Ellipsoid - Abstract
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.
- Published
- 1994
49. The hard-core multi-layered ellipsoid in a low-frequency acoustic field
- Author
-
Christodoulos Athanasiadis
- Subjects
Physics ,Plane (geometry) ,Scattering ,Mechanical Engineering ,Degenerate energy levels ,General Engineering ,Acoustic wave ,Index ellipsoid ,Ellipsoid ,Scattering amplitude ,Classical mechanics ,Zeroth law of thermodynamics ,Mechanics of Materials ,General Materials Science - Abstract
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.
- Published
- 1994
50. Free Oscillation of an Elastically Anisotropic Ellipsoid with Arbitrary Crystal Orientation
- Author
-
Hitoshi Oda
- Subjects
Classical mechanics ,Free oscillation ,Amplitude ,Orientation (geometry) ,General Earth and Planetary Sciences ,Natural frequency ,Index ellipsoid ,Anisotropy ,Ellipsoid ,Mathematics ,Sphericity - Published
- 1994
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