Centrally Coupled Circular Array of Optical Waveguides: The Existence of Stable Steady-State Continuous Waves and Breathing Modes

Hizanidis, Kyriakos; Droulias, Sotiris; Tsopelas, Ilias; Efremidis, Nikolaos K.; Christodoulides, D.N.

doi:10.1238/physica.topical.107a00013

Cited by 16 publications

(14 citation statements)

References 19 publications

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“…The spectra of "+" and "−"labeled supermodes Z (±) m are obtained, correspondingly, from + and − branches of Eq. (11):…”

Section: A Spectrum and Supermodesmentioning

confidence: 99%

“…The problem of energy transfer management in circular fiber arrays has always been in the focus of attention of 063845-3 communication optics, especially in connection with the search for the ways of all-optical switching and routing [11,20]. In a general context this can be seen as the steps towards implementation of the so-called guidonics [21].…”

Section: Energy Transfer In a Double-ring Arraymentioning

confidence: 99%

“…The question of light's propagation in such arrays with various geometries has been addressed in a number of papers, including both classical works [9,10] and more recent studies [11]. Practical interest in such arrays is concerned with their application for creation of cylindrical beams [12].…”

Section: Introductionmentioning

confidence: 99%

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Energy transfer, orbital angular momentum, and discrete current in a double-ring fiber array

2011

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We study energy transfer and orbital angular momentum of supermodes in a double-ring array of evanescently coupled monomode optical fibers. The structure of supermodes and the spectra of their propagation constants are obtained. The geometrical parameters of the array, at which the energy is mostly confined within the layers, are determined. The developed method for finding the supermodes of concentric arrays is generalized for the case of multiring arrays. The orbital angular momentum carried by a supermode of a double-ring array is calculated. The discrete lattice current is introduced. It is shown that the sum of discrete currents over the array is a conserved quantity. The connection of the total discrete current with orbital angular momentum of discrete optical vortices is made.

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“…The spectra of "+" and "−"labeled supermodes Z (±) m are obtained, correspondingly, from + and − branches of Eq. (11):…”

Section: A Spectrum and Supermodesmentioning

confidence: 99%

Section: Energy Transfer In a Double-ring Arraymentioning

confidence: 99%

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Energy transfer, orbital angular momentum, and discrete current in a double-ring fiber array

2011

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“…Refs. [20,21] studied a model related to the DNLS, the discrete Ginzburg-Landau equation, and how localization can arise through instabilities for solutions where all ring-sites have the same amplitude.…”

Section: Introductionmentioning

confidence: 99%

Discrete breathers for a discrete nonlinear Schrödinger ring coupled to a central site

Jason

Johansson

2016

Phys. Rev. E

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We examine the existence and properties of certain discrete breathers for a discrete nonlinear Schrödinger model where all but one site are placed in a ring and coupled to the additional central site. The discrete breathers we focus on are stationary solutions mainly localized on one or a few of the ring sites and possibly also the central site. By numerical methods, we trace out and study the continuous families the discrete breathers belong to. Our main result is the discovery of a split bifurcation at a critical value of the coupling between neighboring ring sites. Below this critical value, families form closed loops in a certain parameter space, implying that discrete breathers with and without central-site occupation belong to the same family. Above the split bifurcation the families split up into several separate ones, which bifurcate with solutions with constant ring amplitudes. For symmetry reasons, the families have different properties below the split bifurcation for even and odd numbers of sites. It is also determined under which conditions the discrete breathers are linearly stable. The dynamics of some simpler initial conditions that approximate the discrete breathers are also studied and the parameter regimes where the dynamics remain localized close to the initially excited ring site are related to the linear stability of the exact discrete breathers.

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“…53,54, and the results indicated fascinating new features (compared with both infinite photonic lattices and single core fibers). Mathematical models of MCFs are based on the nonlinear Schrödinger equation 4,53,54 or the nonlinear complex GinzburgLandau equation 27,28,55,56 . The latter model describes an active MCF media with loss and gain effects included during light propagation.…”

Section: Introductionmentioning

confidence: 99%

Stable optical vortices in nonlinear multicore fibers

et al. 2015

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The multicore fiber (MCF) is a physical system of high practical importance. In addition to standard exploitation, MCFs may support discrete vortices that carry orbital angular momentum suitable for spatial-division multiplexing in high-capacity fiber-optic communication systems. These discrete vortices may also be attractive for high-power laser applications. We present the conditions of existence, stability, and coherent propagation of such optical vortices for two practical MCF designs. Through optimization, we found stable discrete vortices that were capable of transferring high coherent power through the MCF. Keywords: coherent energy propagation; multicore fibers; nonlinear vortices INTRODUCTION Vortex structures are widespread in nature and are found in both macroscopic atmospheric phenomena, such as tornadoes and the Great Red Spot of Jupiter, and microscopic-scale objects in quantum physics. Mathematically, vortices are related to topological defects, the accumulation of geometrical phases, and the phase singularity of a complex linear or nonlinear field (see, e.g., Refs. 1-8 and references therein).Optical vortices present a fascinating and expanding area of research that combines fundamental theoretical and mathematical science and maturing applied technologies (see recent review 4 ). Optical vortices are characterized by a wave field with zero intensity, an undefined phase in the vortex center (pivot point) and the presence of a screw dislocation of the wave front 5,6 . All transmutations of vortices in linear and nonlinear fields obey the conservation of the topological charge S, which is defined as the total change of the phase along a closed curve surrounding the pivotal point of the vortex divided by 2p. The special behavior of the phase and amplitude near the vortex pivot point results in the circular flow of energy in optical vortices [7][8][9][10] . This property is closely related to the ability of optical vortices to carry orbital angular momentum and energy [11][12][13][14] . This property is interesting for various applications, such as in optical traps [15][16][17] , information transmission 18-20 , astrophysics 21,22 , microscopy 23,24 , and laser micromachining 25,26 .In nonlinear media, optical vortices are treated as (topological) vortex solitons 4,27,28 . Such topologically stable pulses can act as information carriers 4,[29][30][31] . It is important that continuum vortex solitons are highly sensitive to azimuthal instability. Stabilization is possible by applying optically induced photonic lattices, which lead to a discrete optical vortex field. Different types of discrete lattice vortex solitons were theoretically predicted in the Refs. 32-35 and experimentally demonstrated in the Refs. 36,37. Discrete vortex solitons can also be created in photonic crystal fibers and other types of photonic lattices 38,39 . Discrete vortex solitons are frequently associated with soliton clusters, which feature interesting mobility properties and

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Centrally Coupled Circular Array of Optical Waveguides: The Existence of Stable Steady-State Continuous Waves and Breathing Modes

Cited by 16 publications

References 19 publications

Energy transfer, orbital angular momentum, and discrete current in a double-ring fiber array

Energy transfer, orbital angular momentum, and discrete current in a double-ring fiber array

Discrete breathers for a discrete nonlinear Schrödinger ring coupled to a central site

Stable optical vortices in nonlinear multicore fibers

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