On the Coupled Maxwell–Bloch System of Equations With Nondecaying Fields at Infinity.
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| Title: | On the Coupled Maxwell–Bloch System of Equations With Nondecaying Fields at Infinity. |
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| Authors: | Li, Sitai1 (AUTHOR) sitaili@xmu.edu.cn, Biondini, Gino2 (AUTHOR), Kovačič, Gregor3 (AUTHOR) |
| Source: | Studies in Applied Mathematics. May2025, Vol. 154 Issue 5, p1-54. 54p. |
| Subjects: | Nonlinear optics, Inverse scattering transform, Solitons, Optical spectra, Optical materials, Nonlinear optical techniques, Boundary value problems |
| Abstract: | We study an initial‐boundary‐value problem (IBVP) for a system of coupled Maxwell–Bloch equations (CMBE) that model two colors or polarizations of light resonantly interacting with a degenerate, two‐level, active optical medium with an excited state and a pair of degenerate ground states. We assume that the electromagnetic field approaches nonvanishing plane waves in the far past and future. This type of interaction has been found to underlie nonlinear optical phenomena including electromagnetically induced transparency, slow light, stopped light, and quantum memory. Under the assumptions of unidirectional, lossless propagation of slowly modulated plane waves, the resulting CMBE become completely integrable in the sense of possessing a Lax pair. In this paper, we formulate an inverse scattering transform (IST) corresponding to these CMBE and their Lax pair, allowing for the spectral line of the atomic transitions in the active medium to have a finite width. The scattering problem for this Lax pair is the same as for the Manakov system. The main advancement in this IST for CMBE is calculating the nontrivial spatial propagation of the spectral data and determining the state of the optical medium in the distant future from that in the distant past, which is needed for the complete formulation of the IBVP. The Riemann–Hilbert problem is used to extract the spatio‐temporal dependence of the solution from the evolving spectral data. We further derive and analyze several types of solitons and determine their velocity and stability, as well as find dark states of the medium, which fail to interact with a given pulse. [ABSTRACT FROM AUTHOR] |
| Copyright of Studies in Applied Mathematics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Items | – Name: Title Label: Title Group: Ti Data: On the Coupled Maxwell–Bloch System of Equations With Nondecaying Fields at Infinity. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Li%2C+Sitai%22">Li, Sitai</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> sitaili@xmu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Biondini%2C+Gino%22">Biondini, Gino</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Kovačič%2C+Gregor%22">Kovačič, Gregor</searchLink><relatesTo>3</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Studies+in+Applied+Mathematics%22">Studies in Applied Mathematics</searchLink>. May2025, Vol. 154 Issue 5, p1-54. 54p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Nonlinear+optics%22">Nonlinear optics</searchLink><br /><searchLink fieldCode="DE" term="%22Inverse+scattering+transform%22">Inverse scattering transform</searchLink><br /><searchLink fieldCode="DE" term="%22Solitons%22">Solitons</searchLink><br /><searchLink fieldCode="DE" term="%22Optical+spectra%22">Optical spectra</searchLink><br /><searchLink fieldCode="DE" term="%22Optical+materials%22">Optical materials</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+optical+techniques%22">Nonlinear optical techniques</searchLink><br /><searchLink fieldCode="DE" term="%22Boundary+value+problems%22">Boundary value problems</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We study an initial‐boundary‐value problem (IBVP) for a system of coupled Maxwell–Bloch equations (CMBE) that model two colors or polarizations of light resonantly interacting with a degenerate, two‐level, active optical medium with an excited state and a pair of degenerate ground states. We assume that the electromagnetic field approaches nonvanishing plane waves in the far past and future. This type of interaction has been found to underlie nonlinear optical phenomena including electromagnetically induced transparency, slow light, stopped light, and quantum memory. Under the assumptions of unidirectional, lossless propagation of slowly modulated plane waves, the resulting CMBE become completely integrable in the sense of possessing a Lax pair. In this paper, we formulate an inverse scattering transform (IST) corresponding to these CMBE and their Lax pair, allowing for the spectral line of the atomic transitions in the active medium to have a finite width. The scattering problem for this Lax pair is the same as for the Manakov system. The main advancement in this IST for CMBE is calculating the nontrivial spatial propagation of the spectral data and determining the state of the optical medium in the distant future from that in the distant past, which is needed for the complete formulation of the IBVP. The Riemann–Hilbert problem is used to extract the spatio‐temporal dependence of the solution from the evolving spectral data. We further derive and analyze several types of solitons and determine their velocity and stability, as well as find dark states of the medium, which fail to interact with a given pulse. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Studies in Applied Mathematics is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1111/sapm.70055 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 54 StartPage: 1 Subjects: – SubjectFull: Nonlinear optics Type: general – SubjectFull: Inverse scattering transform Type: general – SubjectFull: Solitons Type: general – SubjectFull: Optical spectra Type: general – SubjectFull: Optical materials Type: general – SubjectFull: Nonlinear optical techniques Type: general – SubjectFull: Boundary value problems Type: general Titles: – TitleFull: On the Coupled Maxwell–Bloch System of Equations With Nondecaying Fields at Infinity. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Li, Sitai – PersonEntity: Name: NameFull: Biondini, Gino – PersonEntity: Name: NameFull: Kovačič, Gregor IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Text: May2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 00222526 Numbering: – Type: volume Value: 154 – Type: issue Value: 5 Titles: – TitleFull: Studies in Applied Mathematics Type: main |
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