Publication: Solving scattering problems in the half-line using methods developed for scattering in the full line
dc.contributor.department | Department of Mathematics | |
dc.contributor.department | Department of Physics | |
dc.contributor.kuauthor | Mostafazadeh, Ali | |
dc.contributor.schoolcollegeinstitute | College of Sciences | |
dc.date.accessioned | 2024-11-09T12:45:05Z | |
dc.date.issued | 2019 | |
dc.description.abstract | We reduce the solution of the scattering problem defined on the half-line [0,∞) by a real or complex potential v(x) and a general homogeneous boundary condition at x=0 to that of the extension of v(x) to the full line that vanishes for x<0. We find an explicit expression for the reflection amplitude of the former problem in terms of the reflection and transmission amplitudes of the latter. We obtain a set of conditions on these amplitudes under which the potential in the half-line develops bound states, spectral singularities, and time-reversed spectral singularities where the potential acts as a perfect absorber. We examine the application of these results in the study of the scattering properties of a δ-function potential and a finite barrier potential defined in [0,∞), discuss optical systems modeled by these potentials, and explore the configurations in which these systems act as a laser or perfect absorber. In particular, we derive an explicit formula for the laser threshold condition for a slab laser with a single mirror and establish the surprising fact that a nearly perfect mirror gives rise to a lower threshold gain than a perfect mirror. We also offer a nonlinear extension of our approach which allows for utilizing a recently developed nonlinear transfer matrix method in the full line to deal with finite-range nonlinear scattering interactions defined in the half-line. | |
dc.description.fulltext | YES | |
dc.description.indexedby | WOS | |
dc.description.indexedby | Scopus | |
dc.description.openaccess | YES | |
dc.description.publisherscope | International | |
dc.description.sponsoredbyTubitakEu | TÜBİTAK | |
dc.description.sponsorship | Scientific and Technological Research Council of Turkey (TÜBİTAK) | |
dc.description.sponsorship | Turkish Academy of Sciences (TÜBA) | |
dc.description.version | Author's final manuscript | |
dc.description.volume | 411 | |
dc.identifier.doi | 10.1016/j.aop.2019.167980 | |
dc.identifier.embargo | NO | |
dc.identifier.filenameinventoryno | IR02472 | |
dc.identifier.issn | 0003-4916 | |
dc.identifier.quartile | Q2 | |
dc.identifier.scopus | 2-s2.0-85074093723 | |
dc.identifier.uri | https://hdl.handle.net/20.500.14288/2427 | |
dc.identifier.wos | 502886800027 | |
dc.keywords | Coherent perfect absorber | |
dc.keywords | Complex potential | |
dc.keywords | Point interaction | |
dc.keywords | Quantum scattering theory | |
dc.keywords | Spectral singularity | |
dc.keywords | Transfer matrix | |
dc.language.iso | eng | |
dc.publisher | Elsevier | |
dc.relation.grantno | 114F357 | |
dc.relation.ispartof | Annals of Physics | |
dc.relation.uri | http://cdm21054.contentdm.oclc.org/cdm/ref/collection/IR/id/9109 | |
dc.subject | Physics | |
dc.title | Solving scattering problems in the half-line using methods developed for scattering in the full line | |
dc.type | Journal Article | |
dspace.entity.type | Publication | |
local.contributor.kuauthor | Mostafazadeh, Ali | |
local.publication.orgunit1 | College of Sciences | |
local.publication.orgunit2 | Department of Physics | |
local.publication.orgunit2 | Department of Mathematics | |
relation.isOrgUnitOfPublication | 2159b841-6c2d-4f54-b1d4-b6ba86edfdbe | |
relation.isOrgUnitOfPublication | c43d21f0-ae67-4f18-a338-bcaedd4b72a4 | |
relation.isOrgUnitOfPublication.latestForDiscovery | 2159b841-6c2d-4f54-b1d4-b6ba86edfdbe | |
relation.isParentOrgUnitOfPublication | af0395b0-7219-4165-a909-7016fa30932d | |
relation.isParentOrgUnitOfPublication.latestForDiscovery | af0395b0-7219-4165-a909-7016fa30932d |
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