M.Sc Student | Eyal Ben-Bassat |
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Subject | Spontaneous Pattern Formation upon Incoherent Waves and Rabi-Oscillations between Discrete Solitons |

Department | Department of Physics |

Supervisor | ? 18? Segev Mordechai |

Full Thesis text |

Spontaneous pattern formation is a phenomenon where a nonlinear system, becomes unstable, and spontaneously forms self-organized well-defined structures. In optics this phenomenon is called modulation instability (MI). Modulation instability is a process through which small intensity perturbations grow rapidly as a result of the interplay between dispersion and nonlinearity, and it is manifested, for example, in the breakup of an optical beam into filaments. Originally, MI was thought of as a fully coherent phenomenon. One decade ago, it has been shown that MI can also exist with partially-spatially-incoherent light, and later on, in light that is both spatially and temporally incoherent.

**In the first part of my thesis** I present an analytic model of
incoherent MI as a phase-matching process. I show, theoretically and experimentally,
that in a specific realization of partially-spatially incoherent light with a
ring-shaped spatial power-spectrum, a specific resonant spatial frequency
arises during the MI process. I analyze these resonances for a general
realization of a partially-spatially incoherent light, and show that their
resonant frequency and gain can be predicted from the geometry of the spatial
power-spectrum.

The second part of my thesis deals with discrete solitons in nonlinear periodic media. A soliton is a self-trapped wave-packet, which propagates in a stable manner while maintaining its shape. Its natural tendency to expand while propagating, due to the linear dispersion/diffraction, is balanced by nonlinearity. The idea of spatial optical solitons was suggested in 1962, and it was first observed experimentally a few years later. Later on, solitons were also found in periodic optical systems, where they are called discrete solitons. On a different front, it has been recently shown that in a photonic lattice, power can be transferred from one linear Bloch mode to another, through the mechanism of Rabi oscillations, by introducing an appropriate periodic modulation of the refractive index in the propagation direction.

**In the second part of my thesis,** I present a formalism for
describing discrete solitons of a general periodic structure, as well as other
nonlinear defect modes. I then describe the phenomenon of Rabi-oscillations
between gap solitons: power oscillation between two discrete solitons. I
investigate the conditions for efficient power transfer between the two
gap-solitons. Finally, I show that by manipulating the unit-cell of a periodic
structure, we can achieve the required control over the band-structure,
facilitating efficient power transfer between the two solitons.