Bogdanov Map for Modelling a Phase-Conjugated Ring Resonator

Bogdanov Map for Modelling a Phase-Conjugated Ring Resonator

In this paper, we propose using paraxial matrix optics to describe a ring-phase conjugated resonator that includes an intracavity chaos-generating element; this allows the system to behave in phase space as a Bogdanov Map. Explicit expressions for the intracavity chaos-generating matrix elements wer...

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Main Authors: Vicente Aboites, David Liceaga, Rider Jaimes-Reátegui, Juan Hugo García-López
Format: Article
Language:English
Published: MDPI AG 2019-04-01
Series:Entropy
Subjects:
spatial dynamics
Bogdanov Map
chaos
laser
resonator
Online Access:https://www.mdpi.com/1099-4300/21/4/384
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spelling doaj-51fe19bdd6af4a51984509731a3877072020-11-25T00:58:53ZengMDPI AGEntropy1099-43002019-04-0121438410.3390/e21040384e21040384Bogdanov Map for Modelling a Phase-Conjugated Ring ResonatorVicente Aboites0David Liceaga1Rider Jaimes-Reátegui2Juan Hugo García-López3Centro de Investigaciones en Óptica, Loma del Bosque 115, 37150 León, MexicoDivisión de Ciencias e Ingenierías, Universidad de Guanajuato, Loma del Bosque 107, 37150 León, MexicoCentro Universitario de los Lagos, Universidad de Guadalajara, Enrique Diaz de León 1144, Paseos de la Montaña, Lagos de Moreno, 47460 Jalisco, MexicoCentro Universitario de los Lagos, Universidad de Guadalajara, Enrique Diaz de León 1144, Paseos de la Montaña, Lagos de Moreno, 47460 Jalisco, MexicoIn this paper, we propose using paraxial matrix optics to describe a ring-phase conjugated resonator that includes an intracavity chaos-generating element; this allows the system to behave in phase space as a Bogdanov Map. Explicit expressions for the intracavity chaos-generating matrix elements were obtained. Furthermore, computer calculations for several parameter configurations were made; rich dynamic behavior among periodic orbits high periodicity and chaos were observed through bifurcation diagrams. These results confirm the direct dependence between the parameters present in the intracavity chaos-generating element.https://www.mdpi.com/1099-4300/21/4/384spatial dynamicsBogdanov Mapchaoslaserresonator
collection DOAJ
language English
format Article
sources DOAJ
author Vicente Aboites
David Liceaga
Rider Jaimes-Reátegui
Juan Hugo García-López
spellingShingle Vicente Aboites
David Liceaga
Rider Jaimes-Reátegui
Juan Hugo García-López
Bogdanov Map for Modelling a Phase-Conjugated Ring Resonator
Entropy
spatial dynamics
Bogdanov Map
chaos
laser
resonator
author_facet Vicente Aboites
David Liceaga
Rider Jaimes-Reátegui
Juan Hugo García-López
author_sort Vicente Aboites
title Bogdanov Map for Modelling a Phase-Conjugated Ring Resonator
title_short Bogdanov Map for Modelling a Phase-Conjugated Ring Resonator
title_full Bogdanov Map for Modelling a Phase-Conjugated Ring Resonator
title_fullStr Bogdanov Map for Modelling a Phase-Conjugated Ring Resonator
title_full_unstemmed Bogdanov Map for Modelling a Phase-Conjugated Ring Resonator
title_sort bogdanov map for modelling a phase-conjugated ring resonator
publisher MDPI AG
series Entropy
issn 1099-4300
publishDate 2019-04-01
description In this paper, we propose using paraxial matrix optics to describe a ring-phase conjugated resonator that includes an intracavity chaos-generating element; this allows the system to behave in phase space as a Bogdanov Map. Explicit expressions for the intracavity chaos-generating matrix elements were obtained. Furthermore, computer calculations for several parameter configurations were made; rich dynamic behavior among periodic orbits high periodicity and chaos were observed through bifurcation diagrams. These results confirm the direct dependence between the parameters present in the intracavity chaos-generating element.
topic spatial dynamics
Bogdanov Map
chaos
laser
resonator
url https://www.mdpi.com/1099-4300/21/4/384
work_keys_str_mv AT vicenteaboites bogdanovmapformodellingaphaseconjugatedringresonator
AT davidliceaga bogdanovmapformodellingaphaseconjugatedringresonator
AT riderjaimesreategui bogdanovmapformodellingaphaseconjugatedringresonator
AT juanhugogarcialopez bogdanovmapformodellingaphaseconjugatedringresonator
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