Soliton-comb structures in ring-shaped optical microresonators: generation, reconstruction and stability

Abstract

Characteristic features of soliton-comb structures in optical microresonators are investigated in normal and anomalous dispersion regimes, when the detuning parameter is varied over a broad range of values. The study rests on the assumption that soliton combs are self-organized ensemble of co-propagating coherently entangled states of light, and depending on the group-velocity dispersion they can result from space-division multiplexing of single-bright and singledark solitons. Their analytical and numerical reconstruction schemes are discussed, while a linear-stability analysis leads to a 2 × 2 Lamé eigenvalue problem whose boundstate spectrum is composed of a Goldstone-type translation mode and stable internal modes, as well as unstable decaying modes and growing modes. A power-spectral analysis of the three distinct possible soliton crystals enables us probe their inner structures in the frequency domain, and unveil the existence of structural defects in their power spectra. PACS 42.60.DaRing-shaped microresonators · 42.65.TgOptical Solitons · 42.65.SfDynamics of Nonlinear Optical Systems 1 IntroductionFrequency combs [1] have attracted a great deal of attention in the recent past because of their numerous potential applications in optical metrology [2,3,4], where they introduce the possibility to accurately measure time and frequency using optical comb structures. A frequency comb is an optical device composed of millions of equidistant modes laser that can achieve one octave-spanning spectrum. Thus an

Quantum-tunneling transitions and exact statistical mechanics of bistable systems with parametrized Dikandé-Kofané double-well potentials

“…The decay of metastable states over an energy barrier is a physical process inherent to a large number of systems, and particularly those undergoing phase transitions [51,52,53]. It is observed in the motion of atoms trapped in the field of force of a multi-well potential [52], the motion of kinks and dislocations across the Peierls-Nabarro barrier [54,55], the excitations of Cooper pairs in a Josephson loop [56], the dynamics of macromolecules in DNA strands and other molecular chains across hydrogen bridges and so on. In a pioneer study Kramers [51] suggested that the lifetime of a classical particle in a metastable state, separated from a stable equilibrium state by an energy barrier, would obey Arrhenius law.…”

Using dark solitons from a Bose–Einstein condensate necklace to imprint soliton states in the spectral memory of a free boson gas

“…In this case the 'tanh' soliton solution of the GP equation becomes unstable. However besides this hyperbolic kink-soliton solution, the Nonlinear Schrödinger equation with self-defocusing nonlinearity can also admit a periodic-soliton structure which is represented by a Jacobi elliptic function [29,32,35,36]. This last periodic solution is the kind of soliton structure we are interested in, in connection with its periodic feature we can readily assume that it forms in a BEC with a ring shape of effective length L. Seeking for the periodic-soliton solution of the GP equation ( 1), we consider a wave function that describes a stationary state.…”

“…Assuming the BEC to be of finite length L, the application of periodic boundary conditions favored soliton solutions represented by the Jacobi Elliptic function of the snoidal type. In [32], we established that the snoidal function is a 'crystal' of 'tanh-shaped kink-antikink' solitons. Using the matter-wave dark soliton crystal found, the linear Schrödinger equation for the free boson gas was shown to reduce to the Lamé equation of an arbitrary order ν.…”

“…In our study we shall focus on the bound-state spectrum for the eigenvalue problem induced by the periodic dark-soliton structure from the repulsive BEC with finite size, in the free boson system. However, unlike [20], here the discrete spectrum of the free boson system will emerge to be more rich and complex, given that the periodic dark soliton is a 'crystal' of entangled 'tanh' dark solitons [32] and the correlations of centers of mass of these entangled 'tanh' modes broaden the internal-mode spectrum, promoting a multitude of degenerate states.…”

Soliton‐mode proliferation induced by cross‐phase modulation of harmonic waves by a dark‐soliton crystal in optical media

“…Substituting this in Equation (), we find that the wave amplitude must obey the first‐integral equation: with an energy constant determining shape profile of . Solving Equation () with periodic boundary conditions, 33–36 the pump amplitude is found to be the following nonlocalized periodic pattern of time‐entangled dark solitons: where () is a Jacobi elliptic function of modulus (with ), and: The amplitude of the periodic dark soliton () is represented in Figure 1, for (left graph) and (right graph). Note that when the Jacobi elliptic function , corresponding to the dark soliton pump obtained in Ref.…”