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Timestamp: 2019-04-23 06:28:44+00:00

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Dissipative Kerr solitons have paved the way to broadband and fully coherent optical frequency combs in microresonators. Here, we demonstrate numerically that slow frequency tuning of the pump laser in conjunction with phase or amplitude modulation corresponding to the free spectral range of the microresonator, provides reliable convergence of an initially excited chaotic comb state to a single dissipative Kerr soliton (DKS) state. The efficiency of this approach depends on both frequency tuning speed and modulation depth. The relevance of the proposed method is confirmed experimentally in a MgF2 microresonator.
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Fig. 1 Probability p of the final number of solitons distribution for different modulation amplitudes ε and scan speeds α. Final detuning is ζ0 = 18 for the phase and ζ0 = 15 for the amplitude modulation. In each case F ≈ 4.11 and 100 realizations were generated.
Fig. 2 Field distribution evolution inside microresonator for different values of phase modulation depth (α = 0.002, F ≈ 4.11): (a) ε = 0 (no modulation); (b,c) ε = 0.04; (d) ε = 0.08; (e) ε = 0.5; (f) fractional modulation frequency Ω = D1/3, ε = 1.5, α = 0.0004, F = 5.
Fig. 3 Field distribution evolution inside microresonator for different values of amplitude modulation depth (α = 0.002): (a,b) ε = 0.04; (c) ε = 0.08; (d,e) ε = 0.5; (f) ε = 1.0. Dashed line indicates the halt of frequency scan.
Fig. 4 Distribution of number of solitons generated by phase-modulated pump for different values of Δ and ε at α = 0.001, D 2 κ ≈ 0.01. Final detuning is ζ0 = 18: (a) ε = 0.3; (b) ε = 0.6; (c) ε = 1.0.
Fig. 5 Probabilities of realizations obtained via pump phase modulation resulting in generation of 1 or 0 solitons (a) vs. thermal nonlinearity coefficient, (b–c) vs. modulation depth and (d) vs thermal relaxation time. In all cases D 2 κ ≈ 0.01, α = 0.002 and Δ = 0. Final detuning is ζ0 = 18.
Fig. 6 Experimental measurement of soliton formation upon phase modulation and laser detuning. (a) experimental setup (AFG, arbitrary function generator; CW laser, continuous wave narrow linewidth tunable laser; FPC, fiber polarization controller, EDFA, Erbium-doped fiber amplifier; WGM, whispering gallery mode MgF2 crystalline microresonator; FBG, Fiber Bragg grating filter; PD, photodiode; OSA, optical spectrum analyzer; OSC, oscilloscope); (b) statistics for 100 oscilloscope traces at scan repetition rate of 100 Hz for the output power versus laser detuning without modulation. (c) statistics of traces at 100 Hz with phase modulation, the zero soliton probability is 0.5, one soliton – 0.4, two solitons – 0.1; the inset shows one-soliton spectrum with sech2(x) envelope, spectrum width is 35 nm, line spacing is 12.1 GHz; (d) statistics of 100 traces with amplitude modulation, scan repetition rate is 5 Hz, zero soliton probability – 0.4, one soliton – 0.6.
(1) ∂ a μ ∂ τ = − ( 1 + ζ μ ) a μ + i ∑ μ ′ , μ ″ a μ ′ a μ ″ a μ ′ + μ ″ − μ * + f μ exp ( i μ Δ τ ) .

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