scholarly journals The refractive indices of calcite and aragonite

1924 ◽  
Vol 105 (732) ◽  
pp. 370-386 ◽  
Keyword(s):  
Dielectric Constant ◽  
Electric Field ◽  
Wave Train ◽  
Relative Displacement ◽  
Effective Dielectric Constant ◽  
Refractive Indices ◽  
Double Refraction ◽  
Isotropic Media ◽  
Cubic System ◽  
The Moment

1. The two crystalline forms of calcium carbonate, calcite and aragonite, have been analyzed by X-ray methods, and they both display strong double refraction. It is therefore of interest to see whether the large difference in the refractive indices for light polarized in different planes can be explained by the atomic arrangements in the crystals. The electron theory of dielectric media supposes that the atoms of the medium become polarized under the influence of an external electric field. The positive and negative components of the atom suffer a relative displacement, which is equivalent to the development of an electric doublet placed at or near the centre of the atom. The moment of the doublet is proportional to the strength of the electric field in its immediate neighbourhood, the constant of proportionality being characteristic of the atom considered. The local field which causes the polarization of the atom may for convenience be divided into two parts, the first being the force arising from charges in the field, including the doublets of the polarized medium not in the immediate neighbourhood of the atom, the second being the force arising from the doublets in its immediate neighbourhood. In isotropic media, such as liquids or amorphous solids, the average effect of the neighbouring doublets will be same what-ever the direction of the electric field which causes polarization. In Crystals of lower symmetry than that of the cubic system, this will not be the case. The influence of the neighbouring doublets on an atom will depend on the orientation of the electric field with reference to the crystal axes; this will be the case both for the alternating fields of a wave train as well as for a steady field. The effective dielectric constant will therefore depend upon the direction of the electric vector of the waves, and since the velocity of light is inversely proportional to the square root of the dielectric constant, the crystal will display double refraction.

Crystal optics

2004 ◽  
Author(s):  
Robert E. Newnham
Keyword(s):  
Dielectric Constant ◽  
Refractive Index ◽  
Acoustic Waves ◽  
Electromagnetic Waves ◽  
Constitutive Relations ◽  
Dielectric Anisotropy ◽  
Refractive Indices ◽  
Double Refraction ◽  
Light Waves ◽  
Wave Normal

Calcite (CaCO3) is a beautiful transparent mineral that readily cleaves into rhombohedra. Images viewed through a thin slice of a cleaved calcite crystal are split into two images, an effect known as double refraction, or birefringence. Birefringence is the most obvious manifestation of optical anisotropy in crystals. For any given wave normal, there are two light waves, transversely polarized in mutually perpendicular directions, traveling with different velocities, and consequently different refractive indices. Double refraction is caused by dielectric anisotropy. For transparent crystals like calcite, the magnetic susceptibility is small and the permeability μ ≌ μ0, the permeability of free space. In this class of materials the refractive index n = c/v = where c is the speed of light in vacuum, v the velocity of light in the crystal, and K is the dielectric constant measured at optical frequencies. Refractive indices of transparent materials lie between 1 and 3. Electromagnetic waves differ from acoustic waves in that there are, for a given wave normal, two waves rather than three. In the acoustic case there are, in general, two quasitransverse waves and a quasilongitudinal wave. Starting with Maxwell’s Equations and the material constitutive relations, the propagation of electromagnetic waves through transparent crystals are described in terms of the refractive indices, wave normals, and polarization directions.

Enhancement of Electric Field inside Metallodielectric Metamaterial

2006 ◽  
Vol 11-12 ◽  
pp. 117-120
Author(s):  
Won Woo Cho ◽  
G. Zouganelis ◽  
Hitoshi Ohsato
Keyword(s):  
Dielectric Constant ◽  
Finite Difference ◽  
Electric Field ◽  
Time Domain ◽  
Finite Difference Time Domain ◽  
Near Field ◽  
Effective Dielectric Constant ◽  
Incident Electric Field ◽  
Metal Wires ◽  
Difference Time

A metallodielectric metamaterial have been investigated by using FDTD (Finite Difference Time Domain) method and fabricated with a resin based rapid prototyping machine. It was composed of 7 layers of parallel periodic copper wires embedded in resin. The metallodielectric metamaterial shows a different near field distribution with direction of incident electric field E that causes different electromagnetic (EM) properties. In particular, when incident electric field E is vertical to the wires inside resin, we observe enhacement of electric field in the vicinity of the embedded metal wires according to the incident direction of electirc field E as compared with dielectirc wihout metal wires. The enhanced electric field by the embedded metal wire is responsible for the enhancement of effective dielectric constant.

POLARON IN A QUANTUM DOT UNDER AN ELECTRIC FIELD

2007 ◽  
Vol 21 (24) ◽  
pp. 1635-1642
Author(s):  
MIAN LIU ◽  
WENDONG MA ◽  
ZIJUN LI
Keyword(s):  
Quantum Dot ◽  
Electric Field ◽  
Field Intensity ◽  
Ground State Energy ◽  
Ground State ◽  
Electric Field Intensity ◽  
State Energy ◽  
Theoretical Study ◽  
The Moment ◽  
Transformation Methods

We conducted a theoretical study on the properties of a polaron with electron-LO phonon strong-coupling in a cylindrical quantum dot under an electric field using linear combination operator and unitary transformation methods. The changing relations between the ground state energy of the polaron in the quantum dot and the electric field intensity, restricted intensity, and cylindrical height were derived. The numerical results show that the polar of the quantum dot is enlarged with increasing restricted intensity and decreasing cylindrical height, and with cylindrical height at 0 ~ 5 nm , the polar of the quantum dot is strongest. The ground state energy decreases with increasing electric field intensity, and at the moment of just adding electric field, quantum polarization is strongest.

Investigation of the Thermodynamic Properties of Anharmonic Crystals with Defects and Influence of Anharmonicity in Exafs by the Moment Method

1998 ◽  
Vol 12 (02) ◽  
pp. 191-205 ◽  
Author(s):  
Vu Van Hung ◽  
Nguyen Thanh Hai
Keyword(s):  
Thermal Expansion ◽  
Thermodynamic Properties ◽  
Phase Change ◽  
Specific Heat ◽  
Thermal Expansion Coefficient ◽  
Expansion Coefficient ◽  
Moment Method ◽  
Adiabatic Compressibility ◽  
Relative Displacement ◽  
The Moment

By the moment method established previously on the basis of the statistical mechanics, the thermodynamic properties of a strongly anharmonic face-centered and body-centered cubic crystal with point defect are considered. The thermal expansion coefficient, the specific heat Cv and Cp, the isothermal and adiabatic compressibility, etc. are calculated. Our calculated results of the thermal expansion coefficient, the specific heat Cv and Cp… of W, Nb, Au and Ag metals at various temperatures agrees well with the measured values. The anharmonic effects in extended X-ray absorption fine structure (EXAFS) in the single-shell model are considered. We have obtained a new formula for anharmonic contribution to the mean square relative displacement. The anharmonicity is proportional to the temperature and enters the phase change of EXAFS. Our calculated results of Debye–Waller factor and phase change in EXAFS of Cu at various temperatures agrees well with the measured values.

Measurement of effective dielectric constant : A comparison

2011 ◽  
Author(s):  
Aakashdeep ◽  
Saurav Kr. Basu ◽  
G. V. Ujjwal ◽  
Sakshi Kumari ◽  
V. R. Gupta
Keyword(s):  
Dielectric Constant ◽  
Effective Dielectric Constant

scholarly journals On the dispersion of artificial double refraction

1907 ◽  
Vol 79 (529) ◽  
pp. 200-202
Keyword(s):  
Wave Front ◽  
Optic Axis ◽  
Refractive Indices ◽  
Principal Stresses ◽  
Double Refraction ◽  
Optical Coefficient ◽  
Relative Retardation

1. It is well known that glass compressed unequally in different directions behaves like a crystal whose optic axis is along the line of stress. If T 1 , T 2 are the principal stresses in the wave front, μ 1 , μ 2 the refractive indices of the two rays for which the directions of vibration are along T 1 , T 2 respectively, then the relative retardation of the two oppositely polarised rays is R = ( μ 1 — μ 2 ) τ = C (T 1 — T 2 ) τ , where τ is the thickness of glass traversed. C may be called the “stress-optical coefficient ” of the glass. It differs for different glasses and in the same glass for different colours, but it is usually assumed independent of the value of the stress.

scholarly journals IV. On double refraction in a viscous fluid in motion

1874 ◽  
Vol 22 (148-155) ◽  
pp. 46-47 ◽  
Keyword(s):  
Internal Friction ◽  
Viscous Fluid ◽  
Polarized Light ◽  
Elastic Solid ◽  
The State ◽  
Solid Cylinder ◽  
Annular Space ◽  
Double Refraction ◽  
Fresh Start ◽  
The Moment

According to Poisson’s theory of the internal friction of fluids, a viscous fluid behaves as an elastic solid would do if it were periodically liquefied for an instant and solidified again, so that at each fresh start it becomes for the moment like an elastic solid free from strain. The state of strain of certain transparent bodies may be investigated by means of their action on polarized light. This action was observed by Brewster, and was shown by Fresnel to be an instance of double refraction. In 1866 I made some attempts to ascertain whether the state of strain in a viscous fluid in motion could be detected by its action on polarized light. I had a cylindrical box with a glass bottom. Within this box a solid cylinder could be made to rotate. The fluid to be examined was placed in the annular space between this cylinder and the sides of the box. Polarized light was thrown up through the fluid parallel to the axis, and the inner cylinder was then made to rotate. I was unable to obtain any result with solution of gum or sirup of sugar, though I observed an effect on polarized light when I compressed some Canada balsam which had become very thick and almost solid in a bottle.

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