Crystal optics

The most important application of crystal optics is the identification of crystals and single-crystal domains in polycrystalline aggregates. The polarizing micro- 

Maxwells equations allow us to explain birefringence if we take into account the crystal anisotropy  

IXq is the permeability of free space. The relation between the magnetic induction B and the magnetic field H is exactly analogous to that which relates the electric displacement D and the electric field E (Section 4.4.1). With the exception of ferromagnetic crystals (which are only rarely transparent), the eigenvalues of i are close to 1  

there is no risk in neglecting the tensor nature of i and supposing that B fiofiH In contrast, the eigenvalues of e are very different from 1 (between 4 and 5 for quartz, Section 4.4.1) and the tensor nature of e has important consequences. The terms of this tensor also vary with the frequency of light. Consider the existence of a plane wave in the interior of the crystal  

Using relation (4.47), for the electric energy density w, we obtain  

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Optical counters Optical crystals Optical data storage Optical device Optical devices... 

Spectral Gamma Ray Log. This log makes use of a very efficient tool that records the individual response to the different radioactive minerals. These minerals include potassium-40 and the elements in the uranium family as well as those in the thorium family. The GR spectrum emitted by each element is made up of easily identifiable lines. As the result of the Compton effect, the counter records a continuous spectrum. The presence of potassium, uranium and thorium can be quantitatively evaluated only with the help of a computer that calculates in real time the amounts present. The counter consists of a crystal optically coupled to a photomultiplier. The radiation level is measured in several energy windows. 

Kobayashi et al. [508] developed an effective method to control particle size and fluoride content in granular tantalum oxide and niobium oxide. The resultant powders are suitable for application in the manufacturing of ceramics, single crystals, optical glass, etc. 

Cao J, Berne BJ (1993) Theory of polarizable liquid crystals optical birefringence. J Chem Phys 99(3) 2213-2220... 

Enantioselective [2 + 2 cycloaddition.2 The chiral allylic ether (1), prepared from (lS,2R)-( + )-2-phenylcyclohexanol, undergoes enantioselective cycloaddition with dichloroketene to furnish, after one crystallization, optically pure (-)-2. This cyclobutanone after ring expansion and exposure to chromium(II) perchlorate gives... 

B. Agate, E.U. Rafailov, W. Sibbett, S.M. Saltiel, P. Battle, T. Fry, and E. Noonan, Highly efficient blue-ligbt generation from a compact diode-pumped femtosecond laser by use of a periodically poled KTP waveguide crystal. Optics Letters 28(20), 1963-1965 (2003). 

A. M. Weiner, A. M. Kan an, and D. E. Leaird, High-efficiency blue generation by fi equency doubling of femtosecond pulses in a thick nonlinear crystal. Optics Letters 23(18), 1441-1443 (1998). 

R. DeSalvo, M. Sheik-Bahae, A.A. Said, D.J. Hagan, and E.W. Van Stryland, Z-scan measurements of the anisotropy of nonlinear refiaction and absorption in crystals. Optics Letters 18(3), 194 (1993). 

D. Artigas and D.T. Reid, Efficient femtosecond optical parametric oscillators based on aperiodically poled nonlinear crystals. Optics Letters 27(10), 851-853 (2002). 

N.V. Sidorov, M.N. Palatnikov, V.T. Kalinnikov, Raman spectra and peculiarities of the structure of LiNbOs crystals, Optics and Spectroscopy 82, 38-45, (1997), in Russian. 

The molecules produced by living organisms, natural products, are employed in our lives as flavors, fragrances, pharmaceuticals, nontraditional medicines, dyes, and pesticides, among other uses. The products of chemistry are employed in our food as preservatives, artificial sweeteners, thickeners, dyes, taste enhancers, flavors, and textnring agents. Chemistry creates such key materials as plastics, ceramics, fabrics, alloys, semiconductors, liquid crystals, optical media, and biomaterials. Chemistry also does many kinds of analysis and these include measurements of air quahty, water quality, food safety, and the search for substances that compromise the enviromnent or workplace safety. 

In frequency regions where absorption is small the two indices of refraction , and n2 give rise to the phenomenon of double refraction. One of the most common uses for this property is in making wave retarders such as quarter-wave plates incident light linearly polarized with equal x and y field components is phase shifted upon transmission because of the two different phase velocities c/w, and c/n2. An entire field, usually referred to as crystal optics, arises out of this and further applications of crystal anisotropy. 

Crystal optics—the optics of anisotropic media—is treated at an elementary level by Wood (1977). More advanced treatises are those by Nye (1957) and by Ramachandran and Ramaseshan (1961). 

Part I (on identification) comprises four chapters. Chapter II is an introduction to the shapes of crystals and the relation between shape and structure, and Chapter III is an elementary account of crystal optics some knowledge of both subjects is essential, not only for the identification of crystals by microscopic methods, but also for the under-... 

Of the morphological phenomena mentioned in the last few paragraphs, that of twinning is likely to be of most frequent value in identification problems, but all the phenomena are significant from the point of view of crystal structure and the relation between internal structure and growth characteristics. The subject of crystal morphology in relation to internal structure will not, however, be pursued further at present it will be taken up again in Chapters VII and VIII. For the present, we shall continue our consideration of the problem of the identification of microscopic crystals we pass oij to discuss crystal optics, the relation between optical properties and crystal shape and symmetry, and the determination of refractive indices and other optical characteristics under the microscope. 

For polarized IR spectroscopy, one must consider crystal optics. If the crystal is birefringent, the optical disturbance is usually perturbed in some cases it is not even perpendicular to the direction of propagation. This could pose severe problems with some crystals, but our measurements of refractive index... 

The general dispersion formula obtained for the coupling of the vibrational equations with the Maxwell field can be brought into the form of Fresnel s wellknown equation for the wave normal from crystal optics. It is usually written in the form... 

Figure 1. Scheme of Hr31 levels and optical transitions in a magnetic crystal. Optical transitions that remain (disappear) at low temperature are shown hv thick tthinl lines. 

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