1,721,024 research outputs found
Pure quartic traveling wave solutions: a numerical study
No full textWe study a family of periodic traveling wave solution of a pure quartic generalized nonlinear Schrödinger equation (NLSE). We focus on dn-oidal-like solutions with a nonzero average component. After numerically finding a one-parameter family of solutions and comparing it to their conventional NLSE counterpart, we numerically solve the corresponding modulational instability problem. This shows a nontrivial trend, where the instability occurs in specific intervals of the parameter separated by stability islands. Numerical simulations confirm the soundness of this result, thus proving that high-order dispersion terms in an optical waveguide allow to observe the propagation of regular and stable comb-like spectra
Modelling and Characterization of Guiding Micro-structured Devices for Integrated Optics
No full textIn this thesis we show several modelling tools which are used to study nonlinear photonic
band-gap structures and microcavities. First of all a nonlinear CMT and BPM were implemented
to test the propagation of spatial solitons in a periodic device, composed by an array
of parallel straight waveguides. In addition to noteworthy theoretical considerations, active
functionalities are possible by exploiting these nonlinear regimes. Another algorithm was developed
for the three-dimensional modelling of photonic cavities with cylindrical symmetry,
such as microdisks. This method is validated by comparison with FDTD. We also show the
opportunity to confine a field in a region of low refractive index lying in the centre of a silicon
microdisk. High Q-factor and small mode volumes are achieved. Finally the characterization
of microdisks in SOI with Q-factor larger than 50000 is presente
Nonlinear modulational instability: is it really a Fermi-Pasta-Ulam-Tsingou phenomenon?
No full textThe nonlinear Schrödinger equation models mixing phenomena such as modulational instability in fibers. I ts r egular b ehavior w as a ssociated t o Fermi-Pasta-Ulam-Tsingou recurrence. We rigorously compare their behaviors and clarify this analogy, set-tling a long-lasting debated problem
Recurrent nonlinear modulational instability in the beta-FPUT chain
No full textWe address the fully nonlinear stage of seeded modulational instability in the Fermi-Pasta–Ulam-Tsingou chain with quartic interaction potential (??-FPUT) subject to periodic boundary conditions. In particular, we investigate quantitatively the validity of the continuous approximation that describes the evolution of a narrow band of normal modes in terms of the ubiquitous nonlinear Schrödinger equation (NLSE) or its generalizations. By injecting three normal modes comprising a pair of unstable sidebands, we find that the FPUT chain exhibits, for weak enough nonlinear interaction, recurrent evolutions (though of different nature compared with the original work by FPUT). Such recurrences generally preserve the homoclinic structure of nonlinear modulational instability ruled by the NLSE, with generated higher order-modes being essentially enslaved to the unstable pair. Under some circumstance, we find that pseudo-random separatrix crossing events may occur even for a very weak interaction strength.
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Collective modulation instability of multiple four-wave mixing
No full textWe investigate the modulation instability of multiple four-wave mixing arising from a dual-frequency pump
in a single-mode fiber or waveguide. By applying the Floquet theory on account of the periodic nature of
four-wave mixing, we reveal a collective type of instability occurring in the anomalous dispersion regime. Our
interpretation of the linear stability analysis is validated by the numerical solution of the nonlinear Schroedinger
equation
Suppression of transverse instabilities of dark solitons and their dispersive shock waves
No full textWe investigate the impact of nonlocality, owing to diffusive behavior, on transverse instabilities of a dark
stripe propagating in a defocusing cubic medium. The nonlocal response turns out to have a strongly stabilizing
effect both in the case of a single soliton input and in the regime where dispersive shock waves develop
multisoliton regime. Such conclusions are supported by the linear stability analysis and numerical simulation
of the propagation
Advancement optimization in multihop wireless networks
No full textIn this paper, we consider advancement as the metric to be used in making routing decisions. The advancement provided by a relay node is defined as the difference between the distance of the transmitting node to its intended destination, minus the distance between the relay node and the destination, multiplied by the probability of a successful transmission from the transmitting node to the relay. By analysis, we provide results about the advancement as a function of the relay's location, as well as the average optimum advancement for a given relay population. Our results are useful in making routing decisions where one would like to choose the next hop so as to minimize the remaining distance to the final destination. This metric can also be incorporated as part of more sophisticated routing schemes, which take into account other considerations, e.g., energy or delay
Comparative Analysis of a Planar Slotted Microdisk Resonator
No full textWe analyze a microdisk resonator of sub-micrometer radius where confinement is obtained in a vertical sandwich characterized by a central slot of lower refractive index material. The properties of the antiguiding even modes characterized by TM fields peaked in the slot are analyzed with specific reference to the resonant wavelengths, the quality factor, the mode confinement properties, and the Purcell factor. It is shown, by means of a comparative analysis, that, for a small disk radius a full vectorial approach is required in order to properly account for the hybrid nature of the modes. This reflects on the dependence of such figures of merit upon geometrical parameters of the structure
Modellizzazione di solitoni di gap spaziali in array di guide non lineari
No full textIl self-trapping in file di guide ottiche parallele accoppiate in modo evanescente e' analizzato secondo due approcci di diversa accuratezza. I risultati mostrano che le equazioni dei modi accoppiati descrivano accuratamente le soluzioni auto-confinate nel gap fotonico, che si generano per interferenza di due fasci all'angolo di Bragg
Modeling of spatial gap solitons in nonlinear waveguide arrays
No full textWe discuss the modeling of self-trapping in arrays of evanescently coupled optical waveguides with Kerr nonlinear response, contrasting two different approaches. Our results show that the coupled mode equations describe with good accuracy, in a wide range of the parameter values of physical interest, the gap soliton self-trapped solutions that can propagate from beams interfering at Bragg angles
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