Browsing by Subject "Wave equations"
Now showing 1 - 4 of 4
- Results Per Page
- Sort Options
Item Open Access An exponential stability result for the wave equation(Elsevier, 2002) Morgül, Ö.We consider a system described by the one-dimensional linear wave equation in a bounded domain with appropriate boundary conditions. To stabilize this system, we propose a dynamic boundary controller applied at the free end of the system. The transfer function of the proposed controller is a proper rational function which consists of a strictly positive real function and some poles on the imaginary axis. We then show that under some conditions the closed-loop system is exponentially stable. © 2002 Published by Elsevier Ltd.Item Open Access The Fractional Fourier transform and harmonic oscillation(Springer, 2002) Kutay, M. A.; Özaktaş, Haldun M.The ath-order fractional Fourier transform is a generalization of the ordinary Fourier transform such that the zeroth-order fractional Fourier transform operation is equal to the identity operation and the first-order fractional Fourier transform is equal to the ordinary Fourier transform. This paper discusses the relationship of the fractional Fourier transform to harmonic oscillation; both correspond to rotation in phase space. Various important properties of the transform are discussed along with examples of common transforms. Some of the applications of the transform are briefly reviewed.Item Open Access Plane-wave dynamics of optical parametric oscillation with simultaneous sum-frequency generation(Institute of Electrical and Electronics Engineers, 1999-06) Dikmelik, Y.; Akgün, G.; Aytür, O.This paper presents a theoretical analysis of sum-frequency generating optical parametric oscillators where a single nonlinear crystal is used for both parametric generation and sum-frequency generation. In these devices, the parametric and sum-frequency generation processes are both phase matched for the same direction of propagation inside the crystal. Different polarization geometries for which this simultaneous phase-matching condition can potentially be satisfied are identified and categorized, for both birefringent and quasi-phase-matching methods. Plane-wave coupled-mode equations are presented for each of these categories. Solutions of these coupled mode equations and calculation of the single-pass saturated signal gain are outlined. Intracavity signal photon flux density calculations based on these solutions lead to stable steady-state upconversion, multistability, and chaos. The dependence of the photon conversion efficiency on various design parameters are investigated.Item Open Access Polarization of radiation in multipole Jaynes-Cummings model(Taylor & Francis Ltd, 2002) Can, M.A.; Shumovsky, A.S.We discuss the spatial properties of quantum radiation emitted by a multipole transition in a single atom. It is shown that the polarization of multipole radiation and quantum fluctuations of polarization change with distance from the source. In the case of a transition specified by a given quantum number m, the quantum noise of polarization contains contributions coming from the modes with m′ ≠ m as well.