REFRACTIVE-INDEXES FOR EXTRAORDINARY WAVES IN UNIAXIAL CRYSTALS

In order to support our earlier experimental investigation of extraordinary rays', behavior in uniaxial crystals [Zhongxing Shao and Chen Yi, Appl. Opt. 33, 1209 (1994)], as well as to determine the indices of refraction for the extraordinary waves at arbitrary incidence and in arbitrary orientation of the optical axis, and to compare with our experimental results, the ellipsoidal equation depicting double refraction propagation is solved with the expressions given in terms of the easily measured parameters: incident angle theta, rotational angle Phi of the crystal, and the inclined angle eta of the axes. Based on the solutions, the refractive angle r(p) of the ray (or the Poynting vector) and the angle beta(p) between the ray and the optical axis, as well as the refractive angle r(w) of the wave normal of the extraordinary wave and the angle beta(w) between the normal and the axis are given. The results of the indices of refraction for the extraordinary waves are practically presented by applying the derived angles combined with the equation [A. Yariv, Quantum Electronics, 2nd ed. (Wiley, New York, 1975)]: 1/n(e)(2)(beta(w))=cos(2)(beta(w))/n(0)(2) + sin(2)(beta(w))/n(e)(2). As an example of application, the indices of calcite and quartz are calculated using some angular parameters. To clarify the divergence [M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, New York, 1975); F. A. Jenkins and H. E. White, Fundamentals of Optics, 4th ed. (McGraw-Hill, New York, 1976), p. 508], regarding the index and by analogy with Snell's law, the ratio n(e)(r(w))=sin(theta)/sin(r(w)) is also discussed.