Publication:
Solving scattering problems in the half-line using methods developed for scattering in the full line

dc.contributor.departmentDepartment of Mathematics
dc.contributor.departmentDepartment of Physics
dc.contributor.kuauthorMostafazadeh, Ali
dc.contributor.schoolcollegeinstituteCollege of Sciences
dc.date.accessioned2024-11-09T12:45:05Z
dc.date.issued2019
dc.description.abstractWe 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.fulltextYES
dc.description.indexedbyWOS
dc.description.indexedbyScopus
dc.description.openaccessYES
dc.description.publisherscopeInternational
dc.description.sponsoredbyTubitakEuTÜBİTAK
dc.description.sponsorshipScientific and Technological Research Council of Turkey (TÜBİTAK)
dc.description.sponsorshipTurkish Academy of Sciences (TÜBA)
dc.description.versionAuthor's final manuscript
dc.description.volume411
dc.identifier.doi10.1016/j.aop.2019.167980
dc.identifier.embargoNO
dc.identifier.filenameinventorynoIR02472
dc.identifier.issn0003-4916
dc.identifier.quartileQ2
dc.identifier.scopus2-s2.0-85074093723
dc.identifier.urihttps://hdl.handle.net/20.500.14288/2427
dc.identifier.wos502886800027
dc.keywordsCoherent perfect absorber
dc.keywordsComplex potential
dc.keywordsPoint interaction
dc.keywordsQuantum scattering theory
dc.keywordsSpectral singularity
dc.keywordsTransfer matrix
dc.language.isoeng
dc.publisherElsevier
dc.relation.grantno114F357
dc.relation.ispartofAnnals of Physics
dc.relation.urihttp://cdm21054.contentdm.oclc.org/cdm/ref/collection/IR/id/9109
dc.subjectPhysics
dc.titleSolving scattering problems in the half-line using methods developed for scattering in the full line
dc.typeJournal Article
dspace.entity.typePublication
local.contributor.kuauthorMostafazadeh, Ali
local.publication.orgunit1College of Sciences
local.publication.orgunit2Department of Physics
local.publication.orgunit2Department of Mathematics
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