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.
Modeling Coherent Backscattering Errors in Fiber Optic Gyroscopes for Sources of Arbitrary Line Width
We present a new model of the noise and drift induced by coherent backscattering in a fiber optic gyroscope (FOG) interrogated with a light source of arbitrary temporal coherence. This study is critical to understand whether a FOG driven with a laser instead of a broadband source can attain high sensitivity and stability, which would have the overwhelming benefit of improving the FOG scale factor stability by at least ten-fold and would enable the use of FOGs for inertial navigation of aircrafts. Analytical and numerical solutions bring to light two significant new predictions. First, coherent-backscattering noise can be made negligibly small by utilizing a laser with a very narrow linewidth (less than ~ 20 kHz), although in this regime the drift is high. Second, by using a laser with a broad linewidth (greater than ~ 10 MHz), both the noise and the drift are low enough for aircraft inertial navigation. The dependencies of the noise and drift on fiber loss, loop coupling coefficient, and backscattering coefficient are also presented to define the optimum mode of operation of this new class of FOGs.