Transfer Matrices as Non-Unitary S-Matrices, Multimode Unidirectional Invisibility, and Perturbative Inverse Scattering
| Autor: | Ali Mostafazadeh |
|---|---|
| Přispěvatelé: | Mostafazadeh, Ali (ORCID 0000-0002-0739-4060 & YÖK ID 4231), College of Sciences, Department of Department of Mathematics |
| Jazyk: | angličtina |
| Rok vydání: | 2013 |
| Předmět: |
High Energy Physics - Theory
FOS: Physical sciences symbols.namesake Matrix (mathematics) Quantum mechanics Non-hermitian hamiltonians Klein-gordon fields Quantum-mechanics Pseudo-hermiticity Pt-symmetry Exceptional points Hilbert-space Approximation Formulation Absorption Born approximation Mathematical Physics S-matrix Physics Quantum Physics Mathematical Physics (math-ph) Transfer matrix Atomic and Molecular Physics and Optics Condensed Matter - Other Condensed Matter High Energy Physics - Theory (hep-th) Inverse scattering problem symbols Scattering theory Hamiltonian (quantum mechanics) Series expansion Quantum Physics (quant-ph) Optics Other Condensed Matter (cond-mat.other) Optics (physics.optics) Physics - Optics |
| Zdroj: | Physical Review E |
| Popis: | We show that in one dimension the transfer matrix M of any scattering potential v coincides with the S matrix of an associated time-dependent non-Hermitian 2 x 2 matrix Hamiltonian H(tau). If v is real valued, H(tau) is pseudo-Hermitian and its exceptional points correspond to the classical turning points of v. Applying time-dependent perturbation theory to H(tau) we obtain a perturbative series expansion for M and use it to study the phenomenon of unidirectional invisibility. In particular, we establish the possibility of having multimode unidirectional invisibility with wavelength-dependent direction of invisibility and construct various physically realizable optical potentials possessing this property. We also offer a simple demonstration of the fact that the off-diagonal entries of the first-order Born approximation for M determine the form of the potential. This gives rise to a perturbative inverse scattering scheme that is particularly suitable for optical design. As a simple application of this scheme, we construct an infinite-range unidirectionally invisible potential. Scientific and Technological Research Council of Turkey (TÜBİTAK); Turkish Academy of Sciences (TÜBA) |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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