arXiv subjects

Stefan Wabnitz

Publications and source records attributed to Stefan Wabnitz.

At least 73 records · Page 4Linked to original sources

arXiv2015

Frequency comb generation beyond the Lugiato-Lefever equation: multi-stability and super cavity solitons

The generation of optical frequency combs in microresonators is considered without resorting to the mean-field approximation. New dynamical regimes are found to appear for high intracavity power that cannot be modeled using the Lugiato-Lefever equation. Using the Ikeda map we show the existence of multi-valued stationary states and analyse their stability. Period doubled patterns are considered and a novel type of super cavity soliton associated with the multi-stable states is predicted.

physics.optics↗

arXiv2015

Baseband Modulation Instability as the Origin of Rogue Waves

We study the existence and properties of rogue wave solutions in different nonlinear wave evolution models that are commonly used in optics and hydrodynamics. In particular, we consider Fokas-Lenells equation, the defocusing vector nolinear Schrödinger equation, and the long-wave-short-wave resonance equation. We show that rogue wave solutions in all of these models exist in the subset of parameters where modulation instability is present, if and only if the unstable sideband spectrum also contains cw or zero-frequency perturbations as a limiting case (baseband instability). We numerically confirm that rogue waves may only be excited from a weakly perturbed cw whenever the baseband instability is present. Conversely, modulation instability leads to nonlinear periodic oscillations.

nlin.SI↗

arXiv2015

Bragg grating rogue wave

We derive the rogue wave solution of the classical massive Thirring model, that describes nonlinear optical pulse propagation in Bragg gratings. Combining electromagnetically induced transparency with Bragg scattering four-wave mixing, may lead to extreme waves at extremely low powers.

nlin.PS↗

arXiv2014

Dispersive wave emission in dual concentric core fiber: the role of soliton-soliton collisions

Soliton-soliton collisions have a crucial role in enhancing the spectrum of dispersive waves in optical fibers and collisions among in-phase solitons lead to a dramatic enhancement of the dispersive wave power, as well as to its significant spectral reshaping. We obtained a simple analytical model to estimate the spectral position, width and amplitude of the dispersive waves induced by a collision of two in-phase solitons. We tested our theory in the case of a dual concentric core microstructured fiber.

physics.optics↗

arXiv2014

Mid-Infrared Soliton and Raman Frequency Comb Generation in Silicon Microrings

We numerically study the mechanisms of frequency comb generation in the mid-infrared spectral region from cw pumped silicon microring resonators. Coherent soliton comb generation may be obtained even for a pump with zero linear cavity detuning, through suitable control of the effective lifetime of free-carriers from multiphoton absorption, which introduces a nonlinear cavity detuning via free-carrier dispersion. Conditions for optimal octave spanning Raman comb generation are also described.

physics.optics↗

arXiv2014

Instability and noise-induced thermalization of Fermi-Pasta-Ulam recurrence in the nonlinear Schrödinger equation

We investigate the spontaneous growth of noise that accompanies the nonlinear evolution of seeded modulation instability into Fermi-Pasta-Ulam recurrence. Results from the Floquet linear stability analysis of periodic solutions of the three-wave truncation are compared with full numerical solutions of the nonlinear Schrödinger equation. The predicted initial stage of noise growth is in good agreement with simulations, and is expected to provide further insight in the subsequent dynamics of the field evolution after recurrence breakup.

nlin.PS↗

arXiv2014

Vector Rogue Waves and Baseband Modulation Instability in the Defocusing Regime

We report and discuss analytical solutions of the vector nonlinear Schrödinger equation that describe rogue waves in the defocusing regime. This family of solutions includes bright-dark and dark-dark rogue waves. The link between modulational instability (MI) and rogue waves is displayed by showing that only a peculiar kind of MI, namely baseband MI, can sustain rogue wave formation. The existence of vector rogue waves in the defocusing regime is expected to be a crucial progress in explaining extreme waves in a variety of physical scenarios described by multi-component systems, from oceanography to optics and plasma physics.

nlin.SI↗

arXiv2013

Optical tsunamis: shoaling of shallow water rogue waves in nonlinear fibers with normal dispersion

In analogy with ocean waves running up towards the beach, shoaling of prechirped optical pulses may occur in the normal group-velocity dispersion regime of optical fibers. We present exact Riemann wave solutions of the optical shallow water equations and show that they agree remarkably well with the numerical solutions of the nonlinear Schrödinger equation, at least up to the point where a vertical pulse front develops. We also reveal that extreme wave events or optical tsunamis may be generated in dispersion tapered fibers in the presence of higher-order dispersion.

physics.optics↗

arXiv2013

Shallow water rogue wavetrains in nonlinear optical fibers

In addition to deep-water rogue waves which develop from the modulation instability of an optical CW, wave propagation in optical fibers may also produce shallow water rogue waves. These extreme wave events are generated in the modulationally stable normal dispersion regime. A suitable phase or frequency modulation of a CW laser leads to chirp-free and flat-top pulses or flaticons which exhibit a stable self-similar evolution. Upon collision, flaticons at different carrier frequencies, which may also occur in wavelength division multiplexed transmission systems, merge into a single, high-intensity, temporally and spatially localized rogue pulse.

nlin.PS↗

arXiv2012

Bragg-Scattering conversion at telecom wavelengths towards the photon counting regime

We experimentally study Bragg-scattering four-wave mixing in a highly nonlinear fiber at telecom wavelengths using photon counters. We explore the polarization dependence of this process with a continuous wave signal in the macroscopic and attenuated regime, with a wavelength shift of 23 nm. Our measurements of mean photon numbers per second under various pump polarization configurations agree well with the theoretical and numerical predictions based on classical models. We discuss the impact of noise under these different polarization configurations.

quant-ph↗

arXiv2012

Trapping polarization of light in nonlinear optical fibers: An ideal Raman polarizer

The main subject of this contribution is the all-optical control over the state of polarization (SOP) of light, understood as the control over the SOP of a signal beam by the SOP of a pump beam. We will show how the possibility of such control arises naturally from a vectorial study of pump-probe Raman interactions in optical fibers. Most studies on the Raman effect in optical fibers assume a scalar model, which is only valid for high-PMD fibers (here, PMD stands for the polarization-mode dispersion). Modern technology enables manufacturing of low-PMD fibers, the description of which requires a full vectorial model. Within this model we gain full control over the SOP of the signal beam. In particular we show how the signal SOP is pulled towards and trapped by the pump SOP. The isotropic symmetry of the fiber is broken by the presence of the polarized pump. This trapping effect is used in experiments for the design of new nonlinear optical devices named Raman polarizers. Along with the property of improved signal amplification, these devices transform an arbitrary input SOP of the signal beam into one and the same SOP towards the output end. This output SOP is fully controlled by the SOP of the pump beam. We overview the sate-of-the-art of the subject and introduce the notion of an "ideal Raman polarizer".

physics.optics↗

arXiv2012

Theory of Polarization Attraction in Parametric Amplifiers Based on Telecommunication Fibers

We develop from first principles the coupled wave equations that describe polarization-sensitive parametric amplification based on four-wave mixing in standard (randomly birefringent) optical fibers. We show that in the small-signal case these equations can be solved analytically, and permit us to predict the gain experienced by the signal beam as well as its state of polarization (SOP) at the fiber output. We find that, independently of its initial value, the output SOP of a signal within the parametric gain bandwidth is solely determined by the pump SOP. We call this effect of pulling the polarization of the signal towards a reference SOP as polarization attraction, and such parametric amplifier as the FWM-polarizer. Our theory is valid beyond the zero polarization mode dispersion (PMD) limit, and it takes into account moderate deviations of the PMD from zero. In particular, our theory is capable of analytically predicting the rate of degradation of the efficiency of the parametric amplifier which is caused by the detrimental PMD effect.

physics.optics↗

arXiv2012

Deterministic Vector Freak Waves

We construct and discuss a semi-rational, multi-parametric vector solution of coupled nonlinear Schrödinger equations (Manakov system). This family of solutions includes known vector Peregrine solutions, bright-dark-rogue solutions, and novel vector unusual freak waves. The vector freak (or rogue) waves could be of great interest in a variety of complex systems, from optics to Bose-Einstein condensates and finance.

nlin.SI↗

arXiv2010

Theory of Fiber Optic Raman Polarizers

The theoretical description of a Raman amplifier based on the vector model of randomly birefringent fibers is proposed and applied to the characterization of Raman polarizers. The Raman polarizer is a special type of Raman amplifier with the property of producing a highly repolarized beam when fed by relatively weak and unpolarized light.

physics.optics↗

arXiv2010

Theoretical study of optical fiber Raman polarizers with counterpropagating beams

The theory of two counter-propagating polarized beams interacting in a randomly birefringent fiber via the Kerr and Raman effects is developed and applied to the quantitative description of Raman polarizers in the undepleted regime. Here Raman polarizers, first reported by Martinelli et. al. [Opt. Express. 17, 947 (2009)], are understood as Raman amplifiers operating in the regime in which an initially weak unpolarized beam is converted into an amplified fully polarized beam towards the fiber output. Three parameters are selected for the characterization of a Raman polarizer: the degree of polarization of the outcoming beam, its state of polarization, and its gain. All of these parameters represent quantities that are averaged over all random polarization states of the initially unpolarized signal beam. The presented theory is computer friendly and applicable to virtually all practically relevant situations, including the case of co-propagating beams, and in particular to the undepleted as well as the depleted regimes of the Raman polarizer.

physics.optics↗

arXiv2010

Maxwell-Drude-Bloch dissipative few-cycle optical solitons

We study the propagation of few-cycle pulses in two-component medium consisting of nonlinear amplifying and absorbing two-level centers embedded into a linear and conductive host material. First we present a linear theory of propagation of short pulses in a purely conductive material, and demonstrate the diffusive behavior for the evolution of the low-frequency components of the magnetic field in the case of relatively strong conductivity. Then, numerical simulations carried out in the frame of the full nonlinear theory involving the Maxwell-Drude-Bloch model reveal the stable creation and propagation of few-cycle dissipative solitons under excitation by incident femtosecond optical pulses of relatively high energies. The broadband losses that are introduced by the medium conductivity represent the main stabilization mechanism for the dissipative few-cycle solitons.

physics.optics↗

arXiv2007

Parametric Frequency Conversion of Short Optical Pulses Controlled by a CW Background

We predict that parametric sum-frequency generation of an ultra-short pulse may result from the mixing of an ultra-short optical pulse with a quasi-continuous wave control. We analytically show that the intensity, time duration and group velocity of the generated idler pulse may be controlled in a stable manner by adjusting the intensity level of the background pump.

physics.optics↗

arXiv2006

Inelastic Scattering and Interactions of Three-Wave Parametric Solitons

We study the excitation, decay and interactions of novel, velocity locked three-wave parametric solitons in a medium with quadratic nonlinearity and dispersion. We analytically describe the particle-like scattering between stable or unstable soliton triplets with linear waves in terms of explicit solutions featuring accelerated or decelerated solitons.

physics.optics↗