Two-soliton and three-soliton molecules in optical fibers

Rohrmann, Philipp; Hause, A.; Mitschke, F.

doi:10.1103/physreva.87.043834

Cited by 79 publications

(70 citation statements)

References 47 publications

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“…Eventually, the solitons overlap in the temporal domain which makes solitons' energies split: M1(A) and M1(B) arise 19 . In analogy to the energy splitting in molecules, M1(A) and M1(B) can be regarded as a common soliton molecule state M1 [43][44][45][46][47][48] . For exactly 0 = 0.54 W, we observe a perfect oscillation-free Akhmediev breather which manifests inself in a thin line that parts the collective soliton state from the state of soliton molecules in Fig.…”

Section: Akhmediev Breather As Initial Conditionmentioning

confidence: 99%

Soliton radiation beat analysis of optical pulses generated from two continuous-wave lasers

Zajnulina

Böhm

Blow

et al. 2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We propose a fibre-based approach for generation of optical frequency combs (OFC) with the aim of calibration of astronomical spectrographs in the low and medium-resolution range. This approach includes two steps: in the first step, an appropriate state of optical pulses is generated and subsequently moulded in the second step delivering the desired OFC. More precisely, the first step is realised by injection of two continuous-wave (CW) lasers into a conventional single-mode fibre, whereas the second step generates a broad OFC by using the optical solitons generated in step one as initial condition. We investigate the conversion of a bichromatic input wave produced by two initial CW lasers into a train of optical solitons which happens in the fibre used as step one. Especially, we are interested in the soliton content of the pulses created in this fibre. For that, we study different initial conditions (a single cosine-hump, an Akhmediev breather, and a deeply modulated bichromatic wave) by means of Soliton Radiation Beat Analysis and compare the results to draw conclusion about the soliton content of the state generated in the first step. In case of a deeply modulated bichromatic wave, we observed the formation of a collective soliton crystal for low input powers and the appearance of separated solitons for high input powers. An intermediate state showing the features of both, the soliton crystal and the separated solitons, turned out to be most suitable for the generation of OFC for the purpose of calibration of astronomical spectrographs.Optical frequency combs constitute a discrete optical spectrum with lines that are equidistantly positioned. Frequency combs generated in modelocked lasers have been proposed and already successfully tested as calibration sources for high-resolution astronomical spectrographs. However, there is a variety of novel astronomical instruments that operate in the low-and medium resolution range. They also would profit from the deployment of frequency combs as calibration marks. We propose a fibre-based approach for optical frequency comb generation that is specifically suitable for spectrographs with low and medium resolution. This approach consists of two fibres fed with two continuouswave lasers. To be able to generate broadband, stable, and low-noise frequency combs, we need to understand the optical pulse formation in different fibre stages. In this paper, we focus our attention on the pulse build-up in the first fibre stage of the proposed approach and study it numerically by means of the Soliton Radiation Beat Analysis.

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Section: Akhmediev Breather As Initial Conditionmentioning

confidence: 99%

Soliton radiation beat analysis of optical pulses generated from two continuous-wave lasers

Zajnulina

Böhm

Blow

et al. 2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

show abstract

“…In reality, the continuous emission of linear waves from the soliton during its propagation along the fiber and some inevitable perturbations make the experimental observation of the higher-order equilibria of soliton molecules rather challenging. Thus far, only the stable ground state for the opposite-phase soliton pairs [2,[9][10][11] and the unstable ground state for the in-phase soliton pairs [11] were experimentally observed. We employ the Gauss-Hermite trial functions, which are good for analytic calculations but insufficiently accurate for detecting the higher-order equilibria of soliton molecules.…”

Section: Introductionmentioning

confidence: 95%

“…The proof-of-principle demonstration of the data transmission via optical fiber using the extended alphabet [logical zero, one (single soliton), two (two-soliton molecule), and three (three-soliton molecule)] was recently reported in Refs. [9,10]. The quaternary coding scheme doubles the rate of information transfer compared to the binary case according to the law ∼log 2 M, where M is the number of "letters" in the alphabet.…”

Section: Introductionmentioning

confidence: 99%

“…The binding mechanism of temporal soliton molecules allows to calculate the potential of interaction as a function of the separation between solitons using the perturbation theory [8,10]. The position of the minimum and the depth of the potential correspond, respectively, to the equilibrium separation and the binding energy of the molecule.…”

Section: Introductionmentioning

confidence: 99%

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Averaged dynamics of soliton molecules in dispersion-managed optical fibers

2014

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The existence regimes and dynamics of soliton molecules in dispersion-managed (DM) optical fibers have been studied. Initially we develop a variational approximation to describe the periodic dynamics of a soliton molecule within each unit cell of the dispersion map. The obtained system of coupled equations for the pulse width and chirp allows to find the parameters of DM soliton molecules for the given dispersion map and pulse energy. Then by means of a scaling transformation and averaging procedure we reduce the original nonlinear Schrödinger equation (NLSE) with piecewise-constant periodic dispersion to its counterpart with constant coefficients and additional parabolic potential. The obtained averaged NLSE with expulsive potential can explain the essential features of solitons and soliton molecules in DM fibers related to their energy loss during propagation. Also, the model of averaged NLSE predicts the instability of the temporal position of the soliton, which may lead to difficulty in holding the pulse in the middle of its time slot. All numerical simulations are performed using the parameters of the existing DM fiber setup and illustrated via pertinent examples.

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“…For larger separations, there is attraction, for smaller, repulsion: it is a stable equilibrium. Soliton molecules also exist for more than two DM solitons and have been discussed as information carriers in data transmission [44,45]. As it turns out, there can be several equilibrium positions [46].…”

Section: Soliton Moleculesmentioning

confidence: 99%

Soliton Content of Fiber-Optic Light Pulses

2017

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This is a review of fiber-optic soliton propagation and of methods to determine the soliton content in a pulse, group of pulses or a similar structure. Of central importance is the nonlinear Schrödinger equation, an integrable equation that possesses soliton solutions, among others. Several extensions and generalizations of this equation are customary to better approximate real-world systems, but this comes at the expense of losing integrability. Depending on the experimental situation under discussion, a variety of pulse shapes or pulse groups can arise. In each case, the structure will contain one or several solitons plus small amplitude radiation. Direct scattering transform, also known as nonlinear Fourier transform, serves to quantify the soliton content in a given pulse structure, but it relies on integrability. Soliton radiation beat analysis does not suffer from this restriction, but has other limitations. The relative advantages and disadvantages of the methods are compared.

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Two-soliton and three-soliton molecules in optical fibers

Cited by 79 publications

References 47 publications

Soliton radiation beat analysis of optical pulses generated from two continuous-wave lasers

Soliton radiation beat analysis of optical pulses generated from two continuous-wave lasers

Averaged dynamics of soliton molecules in dispersion-managed optical fibers

Soliton Content of Fiber-Optic Light Pulses

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