Caustic coordinates in Platzeck-Gaviola test of conic mirrors.
The centers of curvature of all zones of a spherical mirror coincide at the center of that sphere. In the case of all other conies of revolution, however, the radii of curvature of dif­ ferent zones have different magnitudes; hence their centers of curvature do not coincide but lie along the caustic curve, as shown by Wadsworth. Based on this property Platzeck and Gaviola devised a test to measure the shape of a para­ boloid being figured. What they do is to measure the posi­ tions of the centers of curvature of different regions in the optical surface, then the results are compared with the theo­ retical values. The theoretical positions of these centers of curvature for a paraboloid are computed with two simple formulas given by Schroader, but to our knowledge the ex­ pressions for any conic of revolution have not been given. To derive the expressions for the caustic coordinates (η,ξ) of the centers of curvature of the conic surface (see Fig. 1), we
Accurate numerical analysis of an elliptically cored optical fiber for polarization preservation, using mode-matching method
The Mode-Matching Method has been known as an accurate and reliable method for numerical analysis not only on the diffraction problem in the electromagnetic field, but also on the elastic waveguide and the optical thin-film waveguide. This method is applied for the rigorous analysis of an elliptically-cored optical fiber with large ellipticity whose accurate analysis in the wide range of frequency including the cutoff has so far been difficult. Moreover, a very high degree of accuracy of five figures is achieved for the normalized propagation constant. Both the dispersion relation and the field distribution in the hybrid modes are clarified and it is also confirmed that the hybrid mode analysis is not always necessary in the case of larger ellipticity. The properties of the higher-order mode cutoff and the polarization preservation whose rigorous discussion has not been always sufficient, are analyzed more accurately. The results are compared with the results obtained by other methods, and more exact design data for the single mode, polarization-preserved optical fiber with elliptical core are presented. Through these analyses, it is also confirmed that the Mode-Matching Method is still a useful and reliable method for rigorous analysis of the rod-type dielectric waveguide with arbitrarily shaped cross section.
Germination ecology of Central Asian Stipa spp: differences among species, seed provenances, and the importance of field studies
Stipa-species are wide-spread in Central Asia, but sexual reproduction in the dry steppes is rare. To facilitate conservation and restoration of these important rangelands, we studied germination characteristics of three common Mongolian Stipa-species under field- and lab conditions. Seeds of Stipa krylovii, Stipa gobica and Stipa glareosa were sown at the study site in Southern Mongolia over two consecutive years during which period tests were carried out to ascertain whether competition or herbivory are the main constraints of seedling establishment. In addition, we tested germination and seed viability in the laboratory under two different temperature regimes (20/10°C and 8/4°C), as well as the effect of cold-stratification. The lab experiments also included S. krylovii seeds originating from three climatically different provenances. None of the three Stipa-species seedlings emerged during the first 2 years of the field study. However, after an unusually intense rain event in the third year, 3% of S. krylovii, 0.6% of S. glareosa and 0.1% of S. gobica seeds germinated in the study plots. The factors ‘sowing-year’ and ‘vegetation’ significantly affected seedling emergence, whereas grazing had no effect at all. Under laboratory conditions a high percentage of viable seeds of S. gobica and S. glareosa germinated at both incubation temperatures, and cold-stratification had no effect on germination or viability. Germination of S. krylovii seeds required warmer temperatures and cold-stratification had a positive effect. Such evidence for dormancy was more pronounced in seeds from the moister, northern provenances. Germination of Stipa-species in the field is rare and only possible under exceptionally moist conditions. Conservation should thus concentrate on steppe conservation rather than on restoration. Where artificial reseeding is necessary, differences among species and also among different seed provenances should be taken into account.