Brewster solitons and omnidirectional solitons in one-dimensional optical structures involving Kerr-type nonlinear materials
The possibility of exciting stationary solitons due to the Brewster effect is investigated. The analysis is performed by computing the transmission coefficient of an electromagnetic monochromatic wave obliquely incident on the optical system and linearly polarized with the transverse-electric polari...
- Autores:
-
Posada Loaiza, Jonathan
- Tipo de recurso:
- Trabajo de grado de pregrado
- Fecha de publicación:
- 2025
- Institución:
- Universidad de Antioquia
- Repositorio:
- Repositorio UdeA
- Idioma:
- eng
- OAI Identifier:
- oai:bibliotecadigital.udea.edu.co:10495/45760
- Acceso en línea:
- https://hdl.handle.net/10495/45760
- Palabra clave:
- Efecto Kerr
Kerr effect
Solitones
Solitons
Ondas electromagnéticas - Transmisión
Electromagnetic waves - Transmission
Ondas electromagnéticas - Polarización
Electromagnetic waves - Polarization
Óptica no lineal
Nonlinear optics
Brewster angle
Total transmission
Linear layer
Nonlinear layer
http://id.loc.gov/authorities/subjects/sh85072072
http://id.loc.gov/authorities/subjects/sh85124672
http://id.loc.gov/authorities/subjects/sh85042183
http://id.loc.gov/authorities/subjects/sh85042181
http://id.loc.gov/authorities/subjects/sh85092328
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by-nc-sa/4.0/
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Brewster solitons and omnidirectional solitons in one-dimensional optical structures involving Kerr-type nonlinear materials |
| title |
Brewster solitons and omnidirectional solitons in one-dimensional optical structures involving Kerr-type nonlinear materials |
| spellingShingle |
Brewster solitons and omnidirectional solitons in one-dimensional optical structures involving Kerr-type nonlinear materials Efecto Kerr Kerr effect Solitones Solitons Ondas electromagnéticas - Transmisión Electromagnetic waves - Transmission Ondas electromagnéticas - Polarización Electromagnetic waves - Polarization Óptica no lineal Nonlinear optics Brewster angle Total transmission Linear layer Nonlinear layer http://id.loc.gov/authorities/subjects/sh85072072 http://id.loc.gov/authorities/subjects/sh85124672 http://id.loc.gov/authorities/subjects/sh85042183 http://id.loc.gov/authorities/subjects/sh85042181 http://id.loc.gov/authorities/subjects/sh85092328 |
| title_short |
Brewster solitons and omnidirectional solitons in one-dimensional optical structures involving Kerr-type nonlinear materials |
| title_full |
Brewster solitons and omnidirectional solitons in one-dimensional optical structures involving Kerr-type nonlinear materials |
| title_fullStr |
Brewster solitons and omnidirectional solitons in one-dimensional optical structures involving Kerr-type nonlinear materials |
| title_full_unstemmed |
Brewster solitons and omnidirectional solitons in one-dimensional optical structures involving Kerr-type nonlinear materials |
| title_sort |
Brewster solitons and omnidirectional solitons in one-dimensional optical structures involving Kerr-type nonlinear materials |
| dc.creator.fl_str_mv |
Posada Loaiza, Jonathan |
| dc.contributor.advisor.none.fl_str_mv |
Reyes Gómez, Ernesto Amador Mazo Vásquez, Juan Diego |
| dc.contributor.author.none.fl_str_mv |
Posada Loaiza, Jonathan |
| dc.contributor.jury.none.fl_str_mv |
Osorio Guillén, Jorge Mario Álvarez Quiceno, Juan Camilo |
| dc.subject.lcsh.none.fl_str_mv |
Efecto Kerr Kerr effect Solitones Solitons Ondas electromagnéticas - Transmisión Electromagnetic waves - Transmission Ondas electromagnéticas - Polarización Electromagnetic waves - Polarization Óptica no lineal Nonlinear optics |
| topic |
Efecto Kerr Kerr effect Solitones Solitons Ondas electromagnéticas - Transmisión Electromagnetic waves - Transmission Ondas electromagnéticas - Polarización Electromagnetic waves - Polarization Óptica no lineal Nonlinear optics Brewster angle Total transmission Linear layer Nonlinear layer http://id.loc.gov/authorities/subjects/sh85072072 http://id.loc.gov/authorities/subjects/sh85124672 http://id.loc.gov/authorities/subjects/sh85042183 http://id.loc.gov/authorities/subjects/sh85042181 http://id.loc.gov/authorities/subjects/sh85092328 |
| dc.subject.proposal.eng.fl_str_mv |
Brewster angle Total transmission Linear layer Nonlinear layer |
| dc.subject.lcshuri.none.fl_str_mv |
http://id.loc.gov/authorities/subjects/sh85072072 http://id.loc.gov/authorities/subjects/sh85124672 http://id.loc.gov/authorities/subjects/sh85042183 http://id.loc.gov/authorities/subjects/sh85042181 http://id.loc.gov/authorities/subjects/sh85092328 |
| description |
The possibility of exciting stationary solitons due to the Brewster effect is investigated. The analysis is performed by computing the transmission coefficient of an electromagnetic monochromatic wave obliquely incident on the optical system and linearly polarized with the transverse-electric polarization. The optical system is supposed to be surrounded by a vacuum. Two different optical systems are studied. First, the system under consideration is assumed to be composed of the junction of a single dispersive layer with a linear electromagnetic response and a single nonlinear layer exhibiting Kerr nonlinearity. The obtained results suggest the excitation of stationary solitons in the nonlinear layer induced by the occurrence of the Brewster phenomenon in the linear medium. The second system is considered as a single Kerr nonlinear layer. The Brewster effect is observed for both self-focusing and self-defocusing nonlinearities, which leads to the excitation of soliton states within the nonlinear layer. The Brewster-angle dependence of the intensity of the incident electromagnetic wave is also shown. Finally, the excitation of omnidirectional solitons in the case of single nonlinear layers is discussed. It is shown that matching the magnetic permeability of the surrounding medium and the nonlinear layer leads to maximum transmission states, independent of the incidence angle, for the input-intensity value that causes the homogenization of the electric permittivity. |
| publishDate |
2025 |
| dc.date.accessioned.none.fl_str_mv |
2025-04-29T20:47:48Z |
| dc.date.issued.none.fl_str_mv |
2025 |
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Trabajo de grado - Pregrado |
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Text |
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info:eu-repo/semantics/draft |
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Posada Loaiza, J., Mazo Vásquez, J., y Reyes Gómez, E.A. “Brewster solitons and omnidirectional solitons in onedimensional optical structures involving Kerr-type nonlinear materials”, artículo de investigación, Física, Universidad de Antioquia, Medellín, 2025. |
| dc.identifier.uri.none.fl_str_mv |
https://hdl.handle.net/10495/45760 |
| identifier_str_mv |
Posada Loaiza, J., Mazo Vásquez, J., y Reyes Gómez, E.A. “Brewster solitons and omnidirectional solitons in onedimensional optical structures involving Kerr-type nonlinear materials”, artículo de investigación, Física, Universidad de Antioquia, Medellín, 2025. |
| url |
https://hdl.handle.net/10495/45760 |
| dc.language.iso.none.fl_str_mv |
eng |
| language |
eng |
| dc.relation.references.none.fl_str_mv |
D. Brewster, Philosophical Transactions of the Royal Society of London 105, 125 (1815). Y. Tamayama, T. Nakanishi, K. Sugiyama, and M. Kitano, Phys. Rev. B 73, 193104 (2006). X. Lin, Y. Shen, I. Kaminer, H. Chen, and M. Soljačić, Phys. Rev. A 94, 023836 (2016). K. V. Sreekanth, M. ElKabbash, R. Medwal, J. Zhang, T. Letsou, G. Strangi, M. Hinczewski, R. S. Rawat, C. Guo, and R. Singh, ACS Photonics 6, 1610 (2019). B. G. Jungk, Philosophical Magazine B 70, 493 (1994). A. G. Aronov and V. M. Gasparian, Solid State Communications 73, 61 (1990). A. A. Asatryan, L. C. Botten, M. A. Byrne, V. D. Freilikher, S. A. Gredeskul, I. V. Shadrivov, R. C. McPhedran, and Y. S. Kivshar, Phys. Rev. Lett. 99, 193902 (2007). D. Mogilevtsev, F. A. Pinheiro, R. R. dos Santos, S. B. Cavalcanti, and L. E. Oliveira, Phys. Rev. B 82, 081105 (2010). S. B. Cavalcanti, P. A. Brandão, A. Bruno-Alfonso, and L. E. Oliveira, Opt. Lett. 39, 178 (2014). R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker, Inc., 2003), ISBN 0-8247-4243-5. Y. S. Kivshar and G. P. Agrawal, Optical solitons: from fibers to photonic crystals (Academic Press, 2003), ISBN 0124105904. S. B. Cavalcanti, M. de Dios-Leyva, E. Reyes-Gómez, and L. E. Oliveira, Phys. Rev. B 74, 153102 (2006). L. M. Hincapie-Zuluaga, J. D. Mazo-Vásquez, C. A. Betancur-Silvera, and E. Reyes-Gómez, EPL (Europhysics Letters) 134, 54002 (2021). C. A. Betancur-Yepes, J. D. Mazo-Vásquez, and E. Reyes Gómez, The European Physical Journal D 78, 94 (2024). R. S. Hegde and H. G. Winful, Opt. Lett. 30, 1852 (2005). E. Reyes-Gómez, S. Cavalcanti, and L. Oliveira, Superlattices and Microstructures 90, 1 (2016). W. Chen and D. L. Mills, Phys. Rev. B 35, 524 (1987). |
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Attribution-NonCommercial-ShareAlike 4.0 International |
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Universidad de Antioquia |
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Física |
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Instituto de Física |
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Medellín, Colombia |
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Facultad de Ciencias Exactas y Naturales |
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Campus Medellín - Ciudad Universitaria |
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Universidad de Antioquia |
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Reyes Gómez, Ernesto AmadorMazo Vásquez, Juan DiegoPosada Loaiza, JonathanOsorio Guillén, Jorge MarioÁlvarez Quiceno, Juan Camilo2025-04-29T20:47:48Z2025Posada Loaiza, J., Mazo Vásquez, J., y Reyes Gómez, E.A. “Brewster solitons and omnidirectional solitons in onedimensional optical structures involving Kerr-type nonlinear materials”, artículo de investigación, Física, Universidad de Antioquia, Medellín, 2025.https://hdl.handle.net/10495/45760The possibility of exciting stationary solitons due to the Brewster effect is investigated. The analysis is performed by computing the transmission coefficient of an electromagnetic monochromatic wave obliquely incident on the optical system and linearly polarized with the transverse-electric polarization. The optical system is supposed to be surrounded by a vacuum. Two different optical systems are studied. First, the system under consideration is assumed to be composed of the junction of a single dispersive layer with a linear electromagnetic response and a single nonlinear layer exhibiting Kerr nonlinearity. The obtained results suggest the excitation of stationary solitons in the nonlinear layer induced by the occurrence of the Brewster phenomenon in the linear medium. The second system is considered as a single Kerr nonlinear layer. The Brewster effect is observed for both self-focusing and self-defocusing nonlinearities, which leads to the excitation of soliton states within the nonlinear layer. The Brewster-angle dependence of the intensity of the incident electromagnetic wave is also shown. Finally, the excitation of omnidirectional solitons in the case of single nonlinear layers is discussed. It is shown that matching the magnetic permeability of the surrounding medium and the nonlinear layer leads to maximum transmission states, independent of the incidence angle, for the input-intensity value that causes the homogenization of the electric permittivity.PregradoFísico10 páginasapplication/pdfengUniversidad de AntioquiaFísicaInstituto de FísicaMedellín, ColombiaFacultad de Ciencias Exactas y NaturalesCampus Medellín - Ciudad Universitariahttp://creativecommons.org/licenses/by-nc-sa/4.0/info:eu-repo/semantics/openAccessAttribution-NonCommercial-ShareAlike 4.0 Internationalhttp://purl.org/coar/access_right/c_abf2Efecto KerrKerr effectSolitonesSolitonsOndas electromagnéticas - TransmisiónElectromagnetic waves - TransmissionOndas electromagnéticas - PolarizaciónElectromagnetic waves - PolarizationÓptica no linealNonlinear opticsBrewster angleTotal transmissionLinear layerNonlinear layerhttp://id.loc.gov/authorities/subjects/sh85072072http://id.loc.gov/authorities/subjects/sh85124672http://id.loc.gov/authorities/subjects/sh85042183http://id.loc.gov/authorities/subjects/sh85042181http://id.loc.gov/authorities/subjects/sh85092328Brewster solitons and omnidirectional solitons in one-dimensional optical structures involving Kerr-type nonlinear materialsTrabajo de grado - Pregradohttp://purl.org/coar/resource_type/c_7a1fhttp://purl.org/redcol/resource_type/TPTexthttp://purl.org/coar/version/c_b1a7d7d4d402bcceinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/draftD. Brewster, Philosophical Transactions of the Royal Society of London 105, 125 (1815).Y. Tamayama, T. Nakanishi, K. Sugiyama, and M. Kitano, Phys. Rev. B 73, 193104 (2006).X. Lin, Y. Shen, I. Kaminer, H. Chen, and M. Soljačić, Phys. Rev. A 94, 023836 (2016).K. V. Sreekanth, M. ElKabbash, R. Medwal, J. Zhang, T. Letsou, G. Strangi, M. Hinczewski, R. S. Rawat, C. Guo, and R. Singh, ACS Photonics 6, 1610 (2019).B. G. Jungk, Philosophical Magazine B 70, 493 (1994).A. G. Aronov and V. M. Gasparian, Solid State Communications 73, 61 (1990).A. A. Asatryan, L. C. Botten, M. A. Byrne, V. D. Freilikher, S. A. Gredeskul, I. V. Shadrivov, R. C. McPhedran, and Y. S. Kivshar, Phys. Rev. Lett. 99, 193902 (2007).D. Mogilevtsev, F. A. Pinheiro, R. R. dos Santos, S. B. Cavalcanti, and L. E. Oliveira, Phys. Rev. B 82, 081105 (2010).S. B. Cavalcanti, P. A. Brandão, A. Bruno-Alfonso, and L. E. Oliveira, Opt. Lett. 39, 178 (2014).R. L. Sutherland, Handbook of Nonlinear Optics (Marcel Dekker, Inc., 2003), ISBN 0-8247-4243-5.Y. S. Kivshar and G. P. Agrawal, Optical solitons: from fibers to photonic crystals (Academic Press, 2003), ISBN 0124105904.S. B. Cavalcanti, M. de Dios-Leyva, E. Reyes-Gómez, and L. E. Oliveira, Phys. Rev. B 74, 153102 (2006).L. M. Hincapie-Zuluaga, J. D. Mazo-Vásquez, C. A. Betancur-Silvera, and E. Reyes-Gómez, EPL (Europhysics Letters) 134, 54002 (2021).C. A. Betancur-Yepes, J. D. Mazo-Vásquez, and E. Reyes Gómez, The European Physical Journal D 78, 94 (2024).R. S. Hegde and H. G. Winful, Opt. Lett. 30, 1852 (2005).E. Reyes-Gómez, S. Cavalcanti, and L. Oliveira, Superlattices and Microstructures 90, 1 (2016).W. Chen and D. L. Mills, Phys. Rev. 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