The focusing nonlinear Schrödinger equation (NLSE) describes propagation of quasimonochromatic waves in weakly nonlinear media. The aim of this study is to determine conditions of soliton synchronization in the NLSE in terms of the solitons' position and phase parameters. For this purpose, the concept of asymptotic middle states of solitons in the NLSE is first introduced. With soliton solutions of the NLSE, it is shown that soliton synchronization can be achieved by synchronizing the asymptotic middle states of the solitons, and conditions of soliton synchronization in terms of the solitons' position and phase parameters are given. Although the interaction of the solitons is nonlinear, the conditions are linear equations. Then, aided with the synchronization conditions, simple initial conditions are presented for producing synchronized interaction of solitons without the need to obtain analytic expressions for the synchronized interaction of the solitons. The initial conditions are summations of fundamental solitons with no mutual overlap, so they might be convenient to implement in applicative contexts.
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Sci Rep
November 2024
Laser Spectroscopy Group, Faculty of Electronics, Photonics and Microsystems, Wroclaw University of Science and Technology, Wyb. Wyspianskiego 27, Wroclaw, 50-370, Poland.
We demonstrate the first successful stabilization of a dissipative soliton resonance (DSR) mode-locked (ML) laser source using straightforward techniques. Our setup employed a figure-8 (F8) resonator configuration and a nonlinear optical loop mirror (NOLM) to achieve stable mode-locking, generating 1064 nm rectangular pulses with a 3 ns duration at a repetition frequency of ~ 1 MHz. The pulses were boosted in an all-fiber amplifier chain and reached 30 µJ and 10 kW peak power per pulse at 30 W average output power.
View Article and Find Full Text PDFNano Lett
November 2024
State Key Laboratory of Surface Physics, Institute for Nanoelectronic Devices and Quantum Computing, and Department of Physics, Fudan University, Shanghai 200438, China.
It is widely acknowledged that quantum entities with minimal mass cannot undergo spontaneous symmetry breaking due to strong quantum fluctuations. Here, we report the discovery of a positionally settled single electric dipole that can be manipulated and electrically polarized in a monolayer CoCl-graphite heterostructure, which demonstrates an unprecedented example of spontaneous lattice-translational-symmetry breaking. Scanning tunneling microscopy and atomic force microscopy show that the solitons are intrinsic paraelectric dipoles driven by synchronous charge-lattice distortion around individual CoCl octahedrons.
View Article and Find Full Text PDFChaos
August 2024
Department of Physics, The University of Adelaide, Adelaide 5005, Australia.
We consider systems of N particles interacting on the unit circle through 2π-periodic potentials. An example is the N-rotor problem that arises as the classical limit of coupled Josephson junctions and for various energies is known to have a wide range of behaviors such as global chaos and ergodicity, together with families of periodic solutions and transitions from order to chaos. We focus here on selected initial values for generalized systems in which the second order Euler-Lagrange equations reduce to first order equations, which we show by example can describe an ensemble of oscillators with associated emergent phenomena such as synchronization.
View Article and Find Full Text PDFI present what is believed to be the first demonstration of using the cross-phase modulation (XPM) effect to achieve high-precision, all-optical synchronization and stabilization of the pulse repetition rate of a dissipative soliton resonance (DSR) mode-locked (ML) fiber laser working in the 1.06 µm wavelength range. Nanosecond 1.
View Article and Find Full Text PDFPhys Rev E
June 2024
The Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 9190401, Israel.
Microresonator frequency comb generation from Kerr solitons has become a cutting edge technology, but challenges remain in creating, maintaining, and controlling the solitons. Pump modulation and dual pumping are promising techniques for meeting these challenges. Here we derive the equation of motion of solitons interacting with a modulated pump in the framework of synchronization theory.
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