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...

Full description

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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oai_identifier_str oai:bibliotecadigital.udea.edu.co:10495/45760
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network_name_str Repositorio UdeA
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dc.title.eng.fl_str_mv 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
dc.type.none.fl_str_mv Trabajo de grado - Pregrado
dc.type.coar.none.fl_str_mv http://purl.org/coar/resource_type/c_7a1f
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dc.type.content.none.fl_str_mv Text
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dc.identifier.citation.none.fl_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.
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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dc.publisher.department.none.fl_str_mv Instituto de Física
dc.publisher.place.none.fl_str_mv Medellín, Colombia
dc.publisher.faculty.none.fl_str_mv Facultad de Ciencias Exactas y Naturales
dc.publisher.branch.none.fl_str_mv Campus Medellín - Ciudad Universitaria
publisher.none.fl_str_mv Universidad de Antioquia
institution Universidad de Antioquia
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spelling 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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