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Register a new userExtreme events in forced oscillatory media in 0, 1 and 2 dimensions
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One of the open questions in the field of optical rogue waves is the relevance of the number of spatial dimensions in which waves propagate. Here we review recent results on extreme events obtained in 0, 1 and 2 spatial dimensions in the specific context of forced oscillatory media. We show that some dynamical scenarii can be relevant from 0 to 2D while others can take place only in sufficiently large number of spatial dimensions.
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Both the group velocity and phase velocity of two solitons can be synchronized by a Kerr-effect mediated interaction, causing what is known as soliton trapping. Trapping can occur when solitons travel through single-pass optical fibers or when circulating in optical resonators. Here, we demonstrate and theoretically explain a new manifestation of soliton trapping that occurs between counter-propagating solitons in microresonators. When counter-pumping a microresonator using slightly detuned pump frequencies and in the presence of backscattering, the group velocities of clockwise and counter-clockwise solitons undergo periodic modulation instead of being locked to a constant velocity. Upon emission from the microcavity, the solitons feature a relative oscillatory motion having an amplitude that can be larger than the soliton pulse width. This relative motion introduces a sideband fine structure into the optical spectrum of the counter-propagating solitons. Our results highlight the significance of coherent pumping in determining soliton dynamics within microresonators and add a new dimension to the physics of soliton trapping.
We report on the experimental study of an optically driven multimode semiconductor laser with 1~m cavity length. We observed a spatiotemporal regime where real time measurements reveal very high intensity peaks in the laser field. Such a regime, which coexists with the locked state and with stable phase solitons, is characterized by the emergence of extreme events which produce a heavy tail statistics in the probability density function. We interpret the extreme events as collisions of spatiotemporal structures with opposite chirality. Numerical simulations of the semiconductor laser model, showing very similar dynamical behavior, substantiate our evidences and corroborate the description of such interactions as collisions between phase solitons and transient structures with different phase rotations.
Ring dark and anti-dark solitons in nonlocal media are found. These structures have, respectively, the form of annular dips or humps on top of a stable continuous-wave background, and exist in a weak or strong nonlocality regime, defined by the sign of a characteristic parameter. It is demonstrated analytically that these solitons satisfy an effective cylindrical Kadomtsev-Petviashvilli (aka Johnsons) equation and, as such, can be written explicitly in closed form. Numerical simulations show that they propagate undistorted and undergo quasi-elastic collisions, attesting to their stability properties.
We investigate the breathing of optical spatial solitons in highly nonlocal media. Generalizing the Ehrenfest theorem, we demonstrate that oscillations in beam width obey a fourth-order ordinary differential equation. Moreover, in actual highly nonlocal materials, the original accessible soliton model by Snyder and Mitchell [Science textbf{276}, 1538 (1997)] cannot accurately describe the dynamics of self-confined beams as the transverse size oscillations have a period which not only depends on power but also on the initial width. Modeling the nonlinear response by a Poisson equation driven by the beam intensity we verify the theoretical results against numerical simulations.
The extreme magnetoelectric medium (EME medium) is defined in terms of two medium dyadics, $alpha$, producing electric polarization by the magnetic field and $beta$, producing magnetic polarization by the electric field. Plane-wave propagation of time-harmonic fields of fixed finite frequency in the EME medium is studied. It is shown that (if $omega eq 0$) the dispersion equation has a cubic and homogeneous form, whence the wave vector $k$ is either zero or has arbitrary magnitude. In many cases there is no dispersion equation (NDE medium) to restrict the wave vector in an EME medium. Attention is paid to the case where the two medium dyadics have the same set of eigenvectors. In such a case the $k$ vector is restricted to three eigenplanes defined by the medium dyadics. The emergence of such a result is demonstrated by considering a more regular medium, and taking the limit of zero permittivity and permeability. The special case of uniaxial EME medium is studied in detail. It is shown that an interface of a uniaxial EME medium appears as a DB boundary when the axis of the medium is normal to the interface. More in general, EME media display interesting wave effects that can potentially be realized through metasurface engineering.
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