Radiation and propagation of light in crystals

Thesis (Ph.D.)--University of Rochester. College of Engineering and Applied Science. Institute of Optics. This thesis was digitized by the Institute of Optics in 2014 and was determined to have lapsed into the public domain. If you are the author and have questions about the digitization of your work, please contact Kari Brick, Graduate Program Coordinator for the Institute of Optics, at kbrick@ur.rochester.edu. Other contact information for the Institute is available at http://www.optics.rochester.eduA theory is developed that describes the radiation and propagation of nonplanar electromagnetic waves in linear, homogeneous, nondispersive, conducting and anisotropic media. The theory provides exact integral expressions for the fields radiated by known sources and by planar surfaces with known boundary values in uniaxial as well as biaxial media. Each of the solutions consists of a sum of two double integrals in the form of a superposition of plane waves, called the angular-spectrum representation. In the case of a uniaxial medium, one of these integrals is a superposition of ordinary plane waves, and the other is a superposition of extraordinary plane waves, whereas in the biaxial medium each of the two integrals is a superposition of extraordinary plane waves. The spectral amplitudes in these integrals are determined explicitly in terms of the source. The radiation by a localized source in a uniaxial medium is first treated by working in a Cartesian coordinate system that coincides with the principal axes of the medium. From the exact solutions, in the form of angular-spectrum representations, it follows that the electromagnetic field may be derived from two scalar potentials. Expressions for these potentials in terms of the source, are derived. These potentials are found very useful in applications. It is shown that the electromagnetic field radiated by a planar surface normal to the optic axis, may be determined easily from our solution. Next, a scaling procedure is developed for determining the field in a uniaxial medium by scaling the field radiated by an appropriate source in an isotropic medium. Finally, asymptotic approximations to the exact solutions that are valid at large distances from the sources or surfaces, are derived. The uniaxial radiation problem is then treated in a coordinate system that is oriented arbitrarily with respect to the principal axes. Again, an exact solution, in terms of angular-spectrum representations, is obtained; it is shown that the electromagnetic field may be derived from two scalar potentials, the electromagnetic field radiated by a planar surface oriented arbitrarily with respect to the principal axes, is determined, and asymptotic approximations to the exact solutions, are derived. This alternate form of the solution is useful in applications involving planar boundary surfaces, whose orientation is arbitrary with respect to the principal axes. The biaxial radiation problem is treated in the principal axes coordinate system only. An exact solution, expressed in terms of angular-spectrum representations, for the fields radiated by a localized source, is obtained. From this solution, the electromagnetic field radiated by a planar suface normal to one of the principal axes, is deduced. The latter solution is shown to be in agreement with previously-derived results. The theory is applied to solve the problem of reflection and refraction of an arbitrary wave at a planar interface separating two uniaxial media. First, the special case in which the optic axis in each medium is normal to the interface, is treated. The exact solution then appears in a rather simple form, and is very similar to the solution of the analogous problem involving two isotropic media. To obtain the asymptotic approximations for the reflected and transmitted fields, one must take into account that the reflection and transmission coefficients contain additional singularities that require special treatment. It is shown, that except for certain critical directions of observation, the first order contribution to the asymptotic approximations, is the same as if these additional singularities were not present. Next, the general case in which the optic axis in each medium is oriented arbitrarily with respect to the interface normal, is treated. The solutions are now very complicated due to the fact that mode coupling takes place, i.e. an ordinary or extraordinary incident plane wave gives rise to both types of reflected and transmitted plane waves. Secondly, the formulas for the reflection and transmission coefficients are lengthy. Conditions under which mode decoupling or mode conversion takes place are investigated, and simple formulas for the plane wave reflection and transmission coefficients are derived in those cases. It is shown that, except for certain critical angles of observation, the first order contributions to the asymptotic approximations of the reflected and transmitted fields, are the same as when the singularities of the reflection and transmission coefficients are disregarded