Polarization dynamics in twisted fiber amplifiers: a non-Hermitian nonlinear dimer model

Huerta-Morales, José D.; Rodríguez-Lara, B. M.; Malomed, Boris A.

doi:10.1364/ol.42.004402

Cited by 8 publications

(6 citation statements)

References 27 publications

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“…Generalized Viviani curves appear naturally in the description of a range of physical phenomena, including the Bose-Hubbard dimer [48], which as discussed earlier presents mathematical analogies with the aberrated cavity [24]. In optics, generalized Viviani curves describe polarization evolution in nonlinear birefringent fibers (also analogous to the Bose-Hubbard dimer) [49], and the subset of the generalized Viviani curves that are eight-shaped (with c + R = 1) describe the polarization evolution for linearly polarized light traversing a rotating waveplate, or conversely the polarization states explored by a rotating-waveplate polarimeter [50].…”

Section: Poincaré Path As a Generalized Vivani Curvementioning

confidence: 96%

Ray and caustic structure of Ince-Gauss beams

Gutiérrez-Cuevas,

Dennis,

Alonso

2024

New J. Phys.

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The Ince-Gauss beams, separable in elliptic coordinates, are studied through a ray-optical approach. Their ray structure can be represented over a ray-Poincaré sphere by generalized Viviani curves (intersections of a cylinder and a sphere). This representation shows two topologically different regimes, in which the curve is composed of one or two loops. The overall beam shape is described by the ray caustics that delimit the beams’ bright regions. These caustics are inferred from the generalized Viviani curve through a geometric procedure that reveals connections with other physical systems and geometrical constructions. Depending on the regime, the caustics are composed either of two confocal ellipses or of segments of an ellipse and a hyperbola that are confocal. The weighting of the rays is shown to follow the two-mode meanfield Gross-Pitaevskii equations, which can be mapped to the equation of a simple pendulum. Finally, it is shown that the wave field can be accurately estimated from the ray description.

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Section: Poincaré Path As a Generalized Vivani Curvementioning

confidence: 96%

Ray and caustic structure of Ince-Gauss beams

Gutiérrez-Cuevas,

Dennis,

Alonso

2024

New J. Phys.

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“…Equations ( 16) result from the model of a birefringent single-mode fibre amplifier with a saturable nonlinearity [20]:…”

Section: The Systemmentioning

confidence: 99%

“…The literature suggests several recipes for preventing the blow-up in dimers, including linear vs nonlinear gain-loss competition [18,19] and nonlinear gain-loss saturation [12,20]. This paper explores cross-stimulation-an alternative mechanism that, in addition to ensuring nonsingular evolution, conserves the norm |u| 2 + |v| 2 (interpreted as the total power of light in the optical context).…”

Section: Introductionmentioning

confidence: 99%

Integrability and trajectory confinement in -symmetric waveguide arrays

Barashenkov

Smuts

Chernyavsky

2023

J. Phys. A: Math. Theor.

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We consider $\mathcal{PT}$-symmetric ring-like arrays of optical waveguides with purely nonlinear  gain and loss. Regardless of the value of the gain-loss coefficient, these systems are protected from spontaneous $\mathcal{PT)$-symmetry breaking.  If the nonhermitian part of the array matrix has cross-compensating structure,  the total power in such a system remains bounded --- or even constant --- at all times.  We identify two-, three-, and four-waveguide arrays with cross-compensatory nonlinear gain and lossthat constitute completely integrable Hamiltonian systems.

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“…[8,9]). The generality of the underlying model, consisting of coupled-mode equations, suggests its applicability to a wide class of isomorphic non-Hermitian dimers, describing other photonic systems such as twisted fiber amplifiers [10] as well as quantum systems [11,12].…”

Section: Introductionmentioning

confidence: 99%

Enhanced stability, bistability, and exceptional points in saturable active photonic couplers

et al. 2019

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A generic photonic coupler with active and lossy parts, gain saturation and asymmetric characteristics is examined. Saturable activity is shown to be able to enhance the overall stability of the steady states, prevent evolution to undesirable unbounded modes and allow for bistable operation in specific regions of parametric space. Both stability and bistability are studied in the phase space of the system, where the basins of attraction of each state are identified, providing an accurate description of the dependence of the electric fields on the initial conditions. Continuous families of exceptional points are detected via suitable regulation of the coupling and asymmetry features of the configuration. In this way, a complete description of the nonlinear dynamics landscape is provided, which should be crucial for multiple application-driven designs incorporating such a ubiquitous optical component. *

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Polarization dynamics in twisted fiber amplifiers: a non-Hermitian nonlinear dimer model

Cited by 8 publications

References 27 publications

Ray and caustic structure of Ince-Gauss beams

Ray and caustic structure of Ince-Gauss beams

Integrability and trajectory confinement in -symmetric waveguide arrays

Enhanced stability, bistability, and exceptional points in saturable active photonic couplers

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