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Journals >Photonics Research >Volume 9 >Issue 8 >Page 1432 > Article

Photonics Research
Vol. 9, Issue 8, 1432 (2021)

Vector harmonic mode-locking by acoustic resonance

Sergey Sergeyev^*, Stanislav Kolpakov, and Yury Loika

Author Affiliations

Aston Institute of Photonic Technologies, Aston University, Birmingham, B4 7ET, UK

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DOI: 10.1364/PRJ.424759 Cite this Article Set citation alerts

Sergey Sergeyev, Stanislav Kolpakov, Yury Loika. Vector harmonic mode-locking by acoustic resonance[J]. Photonics Research, 2021, 9(8): 1432 Copy Citation Text

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Abstract

For an Er-doped fiber laser, for the first time, to the best of our knowledge, we demonstrate both experimentally and theoretically a novel mechanism of harmonic mode-locking based on the electrostriction effect leading to excitation of the torsional acoustic modes in the transverse section of the laser. The exited torsional acoustic modes modulate the fiber birefringence that results in synchronization of oscillations at the harmonic modes and the linewidth narrowing with the increased signal-to-noise ratio of 30 dB. By adjusting the in-cavity birefringence based on tuning the polarization controller, we enable the selection of the harmonic mode to be stabilized.

S_{0} = I_{x} + I_{y}, S_{1} = I_{x} - I_{y}, S_{2} = 2 \sqrt{I_{x} I_{y}} \cos ϕ, S_{3} = 2 \sqrt{I_{x} I_{y}} \sin ϕ, s_{i} = S_{i} / \sqrt{S_{1}^{2} + S_{2}^{2} + S_{3}^{2}}, i = 1, 2, 3, DOP = \sqrt{S_{1}^{2} + S_{2}^{2} + S_{3}^{2}} / S_{0} .

(1)

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d S / d t = R \cdot W \cdot S .

(2)

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R = [\begin{matrix} \cos [ζ (t)] & - \sin [ζ (t)] & 0 \\ \sin [ζ (t)] & \cos [ζ (t)] & 0 \\ 0 & 0 & 1 \end{matrix}],

(3)

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\frac{d S_{0}}{d t} = (\frac{2 α_{1} f_{1}}{1 + Δ^{2}} - 2 α_{2}) S_{0} + \frac{2 α_{1} f_{2}}{1 + Δ^{2}} S_{1} + \frac{2 α_{1} f_{3}}{1 + Δ^{2}} S_{2}, \frac{d S_{1}}{d t} = γ S_{2} S_{3} + \frac{2 α_{1} f_{2}}{1 + Δ^{2}} S_{0} + (\frac{2 α_{1} f_{1}}{1 + Δ^{2}} - 2 α_{2}) S_{1} - β_{C} S_{2} - {\frac{2 α_{1} f_{3} Δ}{1 + Δ^{2}} - β_{L} \sin [ζ (t)]} S_{3} + σ_{1}, \frac{d S_{2}}{d t} = - γ S_{1} S_{3} + \frac{2 α_{1} f_{3}}{1 + Δ^{2}} S_{0} + β_{C} S_{1} + (\frac{2 α_{1} f_{1}}{1 + Δ^{2}} - 2 α_{2}) S_{2} + {\frac{2 α_{1} f_{2} Δ}{1 + Δ^{2}} - β_{L} \cos [ζ (t)]} S_{3} + σ_{2}, \frac{d S_{3}}{d t} = {\frac{2 α_{1} Δ f_{3}}{1 + Δ^{2}} - β_{L} \sin [ζ (t)]} S_{1} - {\frac{2 α_{1} Δ f_{2}}{1 + Δ^{2}} - β_{L} \cos [ζ (t)]} S_{2} + (\frac{2 α_{1} f_{1}}{1 + Δ^{2}} - 2 α_{2}) S_{3} + σ_{3}, \frac{d f_{1}}{d t} = ε [\frac{(χ_{s} - 1) I_{p}}{2} - 1 - (1 + \frac{I_{p} χ_{p}}{2} + d_{1} S_{0}) f_{1} - (d_{1} S_{1} + \frac{I_{p} χ_{p}}{2} \frac{1 - δ^{2}}{1 + δ^{2}}) f_{2} - d_{1} S_{2} f_{3}], \frac{d f_{2}}{d t} = ε [\frac{1 - δ^{2}}{1 + δ^{2}} \frac{I_{p} (χ_{s} - 1)}{4} - (\frac{I_{p} χ_{p}}{2} + 1 + d_{1} S_{0}) f_{2} - (\frac{1 - δ^{2}}{1 + δ^{2}} \frac{I_{p} χ_{p}}{2} + d_{1} S_{1}) \frac{f_{1}}{2}], \frac{d f_{3}}{d t} = - ε [\frac{d_{1} S_{2} f_{1}}{2} + (\frac{I_{p} χ_{p}}{2} + 1 + d_{1} S_{0}) f_{3}] .

(C1)

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⟨ σ_{i} {(t) ⟩}_{t} = 0, ⟨ σ_{i} (t) σ_{j} {(t - τ) ⟩}_{t} = Σ^{2} δ_{i, j} δ (τ), δ_{i, j} = {\begin{matrix} 1, i = j, \\ 0 i \neq j, \end{matrix} δ (τ) = {\begin{matrix} \infty, τ = 0, \\ 0 τ \neq 0 . \end{matrix}

(C2)

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n (θ) = \frac{n_{0}}{2} + \sum_{k = 1}^{\infty} n_{1 k} \cos (k θ) + \sum_{k = 1}^{\infty} n_{2 k} \sin (k θ), f_{1} = (χ \frac{n_{0}}{2} - 1) + χ \frac{n_{12}}{2}, f_{2} = (χ \frac{n_{0}}{2} - 1) - χ \frac{n_{12}}{2}, f_{3} = χ \frac{n_{22}}{2} .

(C3)

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Sergey Sergeyev, Stanislav Kolpakov, Yury Loika. Vector harmonic mode-locking by acoustic resonance[J]. Photonics Research, 2021, 9(8): 1432

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