Research Project: Ters Saçılma Kuramı Karmaşık Enerjiye Bağlı Potansiyeller, ve Optik Uygulamaları
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Contributors
Funders
ID
TB.00119
Authors
Mostafazadeh, Ali
Faculty Member
Publications
Adiabatic approximation, semiclassical scattering, and unidirectional invisibility
(Institute of Physics (IOP) Publishing, 2014) Mostafazadeh, Ali; Department of Mathematics; Yes; College of Sciences
The transfer matrix of a possibly complex and energy-dependent scattering potential can be identified with the S-matrix of a two-level time-dependent non-Hermitian Hamiltonian H(tau). We show that the application of the adiabatic approximation to H(tau) corresponds to the semiclassical description of the original scattering problem. In particular, the geometric part of the phase of the evolving eigenvectors of H(tau) gives the pre-exponential factor of the WKB wave functions. We use these observations to give an explicit semiclassical expression for the transfer matrix. This allows for a detailed study of the semiclassical unidirectional reflectionlessness and invisibility. We examine concrete realizations of the latter in the realm of optics.
Active invisibility cloaks in one dimension
(American Physical Society (APS), 2015) Mostafazadeh, Ali; Department of Mathematics; Department of Physics; Yes; College of Sciences
We outline a general method of constructing finite-range cloaking potentials which render a given finite-range real or complex potential, v(x), unidirectionally reflectionless or invisible at a wave number, k(0), of our choice. We give explicit analytic expressions for three classes of cloaking potentials which achieve this goal while preserving some or all of the other scattering properties of v(x). The cloaking potentials we construct are the sum of up to three constituent unidirectionally invisible potentials. We discuss their utility in making v(x) bidirectionally invisible at k(0) and demonstrate the application of our method to obtain antireflection and invisibility cloaks for a Bragg reflector.
Unidirectionally invisible potentials as local building blocks of all scattering potentials
(American Physical Society (APS), 2014) Mostafazadeh, Ali; Department of Mathematics; Yes; College of Sciences
We give a complete solution of the problem of constructing a scattering potential v(x) that possesses scattering properties of one's choice at an arbitrary prescribed wave number. Our solution involves expressing v(x) as the sum of at most six unidirectionally invisible finite-range potentials for which we give explicit formulas. Our results can be employed for designing optical potentials. We discuss its application in modeling threshold lasers, coherent perfect absorbers, and bidirectionally and unidirectionally reflectionless absorbers, amplifiers, and phase shifters.
Unidirectional reflectionlessness and invisibility in the TE and TM modes of a PT-symmetric slab system
(American Physical Society (APS), 2017) Sarısaman, Mustafa; Department of Mathematics; Department of Physics; No; College of Sciences
Unidirectional invisibility of a PT-symmetric optical system is of great interest, but challenging as well since it is infeasible to fulfill it through wide optical frequency ranges in all angular directions. Accordingly we study reflectionless and invisible patterns in the TE and TM modes of an optical slab system consisting of an adjacent or separated pair of balanced gain and loss layers with a gap. We provide a comprehensive study of one of the simplest experimentally accessible examples of a unidirectionally reflectionless and invisible PT-symmetric optical slab system. We obtain the physically optimal conditions for the realization of these phenomena. We derive analytic expressions, and show that only certain gain amounts restricted to take values between certain minimum and maximum values give rise to uni- or bidirectionally invisible configurations. The size of gap decides the measure of reflectionlessness and invisibility parameters, especially on gain value and incident angle.
Physics of spectral singularities
(Springer, 2015) Mostafazadeh, Ali; N/A; Department of Mathematics; Yes; College of Sciences
Spectral singularities are certain points of the continuous spectrum of generic complex scattering potentials. We review the recent developments leading to the discovery of their physical meaning, consequences, and generalizations. In particular, we give a simple definition of spectral singularities, provide a general introduction to spectral consequences of PT-symmetry (clarifying some of the controversies surrounding this subject), outline the main ideas and constructions used in the pseudo-Hermitian representation of quantum mechanics, and discuss how spectral singularities entered in the physics literature as obstructions to these constructions. We then review the transfer matrix formulation of scattering theory and the application of complex scattering potentials in optics. These allow us to elucidate the physical content of spectral singularities and describe their optical realizations. Finally, we survey some of the most important results obtained in the subject, drawing special attention to the remarkable fact that the condition of the existence of linear and nonlinear optical spectral singularities yield simple mathematical derivations of some of the basic results of laser physics, namely the laser threshold condition and the linear dependence of the laser output intensity on the gain coefficient.
