Browsing by Author "Eti, Neslihan"

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Classical and Quantum Euler equation
(Izmir Institute of Technology, 2007) Eti, Neslihan; Pashaev, Oktay
In the present thesis we give generalization of analytical mechanics to describe dynamical systems with dissipation. The Lagrangian function in this case is determined by nonstationary pseudo-Riemannian metric for the kinetic energy, and by general quadratic form, nondiagonal in the generalized coordinates and velocities. Skew symmetric nondiagonal terms in our approach play the role of dissipation coefficients. As an application we study in details the classical damped harmonic oscillator. We show that two known formulations of this oscillator, the Bateman dual and the Caldirola Kanai formulations are particular realizations of our general approach. The Hamiltonian formulation and quantization of the model in both representations are given. Moreover Ostrogradsky generalization of Lagrangian and Hamiltonian formalism for description of systems with higher order derivatives and its application to the constant coefficient equations of an arbitrary order are considered. We construct related with the last one the Euler differential equation of an arbitrary order and its Lagrangian and Hamiltonian structure. Quantum Euler systems are introduced and solved for the stationary Schrodinger picture. Nonstationary nonlinear quantum models corresponding to arbitrary Euler Hamiltonian are solved exactly in the Heisenberg picture.
Mathematical modelling of light propagation in pohotonic crystal waveguides
(Izmir Institute of Technology, 2014) Eti, Neslihan; Sözüer, Hüseyin Sami
Photonic crystals are artificially engineered materials where the dielectric constant varies periodically. A photonic band gap can be created by scattering at the dielectric interfaces, which forbids propagation of light in a certain frequency range of light. This property enables us to control light, which is normally impossible with conventional optics. Moreover, by placing a linear defect into the photonic crystal, one can construct a waveguide, which keeps light inside the waveguide in the desired direction. Thus, by using photonic crystal waveguides one can control light propagation in integrated circuit devices. The goal of this work is to provide a comprehensive understanding of how to bend light using photonic crystal waveguides. The purpose is to create a 90◦ bend for line defect photonic crystal assisted waveguides and present fully three-dimensional calculations with optimized geometrical parameters that minimize the bending loss. The scheme uses one-dimensional photonic crystal slab waveguides for straight sections, and a corner element that employs a square photonic crystal with a band gap at the operating frequency.. The two different structures, with either silicon-silica or with silicon-air are used in the guiding photonic crystal layer. Furthermore, the guiding layer is sandwiched between either air on both top and bottom, or between air on top and silica substrate at the bottom, to serve as the ”cladding” medium. Calculations are presented for the transmission values of TE-like modes where the electric field is strongly transverse to the direction of propagation, with and without the photonic crystal corner element for comparison. We find that the bending loss can be reduced to under 2%.