Biomedical subjects
Publications and source records attributed to Theodoros P Horikis.
The concept of fractal (self-similar) self-transform functions is examined. A general method to prove existence of these functions is introduced, and necessary conditions for this existence are derived. The results are general and apply to all transforms with product-type kernels.
A finite-difference approach based upon the immersed interface method is used to analyze the mode structure of Bragg fibers with arbitrary index profiles. The method allows general propagation constants and eigenmodes to be calculated to a high degree of accuracy, while computation times are kept to a minimum by exploiting sparse matrix algebra. The method is well suited to handle complicated structures comprised of a large number of thin layers with high-index contrast and simultaneously determines multiple eigenmodes without modification.
The concept of self-Fourier functions, i.e., functions that equal their Fourier transform, is almost always associated with specific functions, the most well known being the Gaussian and the Dirac delta comb. We show that there exists an infinite number of distinct families of these functions, and we provide an algorithm for both generating and characterizing their distinct classes. This formalism allows us to show the existence of these families of functions without actually evaluating any Fourier or other transform-type integrals, a task often challenging and frequently not even possible.
We extend the perturbation theory of the nonlinear Schrödinger equation for the study of perturbed (nonintegrable) forms of the vector equation. We derive a set of linear equations that describe the radiation field shed by the soliton as it propagates down a birefringent optical fiber. The formalism is applied to the case when strong birefringence and higher-order dispersion are present in the fiber and to the study of polarization mode dispersion. Finally we discuss an analytical treatment of the mechanism that generates the soliton shadow.