Spectral Singularities, Unidirectional Invisibility, and Dynamical Formulation of One-Dimensional Scattering Theory

Spectral Singularities, Unidirectional Invisibility, and Dynamical Formulation of One-Dimensional Scattering Theory

Ali Mustafazade

Koç Unıversity, Physics Deptartment

Abstract: Complex scattering potentials have surprising properties that real scattering potentials lack. Among these are spectral singularities and unidirectional invisibility. In the first part of this talk, I will survey the recent development in the study of physical meaning and applications of spectral singularities. In particular, I show that they provide the basic mathematical framework for all lasing and antilasing systems. In the second part of the talk, I outline a dynamical theory of potential scattering in one-dimension and offer an inverse scattering scheme for the construction of scattering potentials with desirable properties at a prescribed wavelength. This is based on the curious observation that given a possibly complex scattering potential v(x) we can construct a two-level non-stationary and non-Hermitian Hamiltonian H(t) whose S-matrix coincides with the transfer matrix of v(x). We use this approach to develop a complete perturbative description of the phenomenon of unidirectionally invisibility, construct multi-mode unidirectionally invisible potentials with wavelength-dependent direction of invisibility, and show that the application of the adiabatic approximation for H(t) coincides with the semiclassical (WKB) treatment of the scattering problem. A remarkable outcome of the latter result is the identification of the geometric part of the phase of the adiabatically evolving states with the pre-exponential factor of the WKB wave functions. If time permits, we will also outline a recent solution of a local inverse scattering problem that allows for a exact and explicit construction of scattering potentials with given scattering properties at any prescribed wavelength. This construction has direct applications in optical design.


A. Mostafazadeh, Phys. Rev. Lett., 102, 220402 (2009), arXiv:0901.4472.
A. Mostafazadeh, Phys. Rev. Lett. 110, 260402 (2013); arXiv: 1303.2501.
A. Mostafazadeh, Ann. Phys. (N.Y.) 341, 77-85 (2014); arXiv:1310.0592.
A. Mostafazadeh, Phys. Rev. A 89, 012709 (2014); arXiv: 1310.0619.
A. Mostafazadeh, J. Phys. A 47, 125301 (2014); arXiv: 1401.4315.
A. Mostafazadeh, Phys. Rev. A 90, 023833 (2014); arXiv: 1407.1760

Yer : MSGSÜ Bomonti Binası, Fizik Bölümü
Tarih : 16 Ekim 2014 Perşembe, 15:00

%d blogcu bunu beğendi: