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Group interactions of dissipative solitons in a laser cavity: the case of 2+1

Philippe Grelu and Nail Akhmediev

Open Access Open Access

Abstract

What can be the outcome of the interaction between a dissipative soliton pair and a soliton singlet? We report an experimental observation of “elastic” collisions as well as “inelastic” formation of triplet soliton states in a fiber laser setup. These observations are supported with the numerical simulations based on the dispersion (parameter) managed cubic-quintic Ginzburg-Landau equation model.

©2004 Optical Society of America

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Supplementary Material (2)

Media 1: MOV (1475 KB)     
Media 2: MOV (1497 KB)     

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Figures (7)
Fig. 1.
Fig. 1. Fiber ring laser experimental setup. WDM-IS: polarization-insensitive coupler isolator.

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Fig. 2.
Fig. 2. (a) “Collisions”: the QuickTime video file (1475 Kb) presents live recording of the oscilloscope trace featuring a doublet and a moving singlet soliton. (b) “Collisions and triplets”: the QuickTime video file (1497 Kb) presents formation and decomposition of stable triplet soliton, when cavity losses are slightly changed back and forth. Note that the small sub peaks of amplitude around or less than one division are electronic artifacts due to imperfect impedance matching.

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Fig. 3.
Fig. 3. Autocorrelation traces taken from (a) the variable output coupler and (b) the 10% coupler. In blue: doublet and singlet in endlessly relative motion. In red: when the triplet soliton state is formed.

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Fig. 4.
Fig. 4. Recorded optical spectrum (in blue line) and its baseline (in magenta dotted line), for doublet and singlet solitons in endlessly relative motion.

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Fig. 5.
Fig. 5. Dispersion map and values of parameters used in the simulation

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Fig. 6.
Fig. 6. Formation of stable soliton pairs in the interaction plane. R represents the separation between the two solitons, whereas ϕ is their relative phase.

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Fig. 7.
Fig. 7. “Elastic” collision of a pair of coupled dissipative solitons with a soliton singlet.

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Equations (1)

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i ψ z + D 2 ψ tt + ∣ ψ ∣ 2 ψ + ν ∣ ψ ∣ 4 ψ = i δ ψ + i ε ∣ ψ ∣ 2 ψ + i β ψ tt + i μ ∣ ψ ∣ 4 ψ ,
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