Effects of gain nonlinearities in an optically injected gain lever semiconductor laser

J. M. Sarraute; K. Schires; S. LaRochelle; F. Grillot

doi:10.1364/PRJ.5.000315

Journals >Photonics Research >Volume 5 >Issue 4 >Page 315 > Article

Photonics Research
Vol. 5, Issue 4, 315 (2017)

Effects of gain nonlinearities in an optically injected gain lever semiconductor laser | On the Cover

J. M. Sarraute^1,2,*, K. Schires¹, S. LaRochelle², and F. Grillot^1,3

Author Affiliations

¹LTCI, Télécom Paristech, Université Paris-Saclay, 46 rue Barrault, 75013 Paris, France

²COPL, Université Laval, 2375 rue de la Terrasse, Québec, Québec G1V 06A, Canada

³Center for High Technology Materials, University of New Mexico, 1313 Goddard SE, Albuquerque, New Mexico 87106-4343, USA

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DOI: 10.1364/PRJ.5.000315 Cite this Article Set citation alerts

J. M. Sarraute, K. Schires, S. LaRochelle, F. Grillot, "Effects of gain nonlinearities in an optically injected gain lever semiconductor laser," Photonics Res. 5, 315 (2017) Copy Citation Text

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Abstract

The effects of gain compression on the modulation dynamics of an optically injected gain lever semiconductor laser are studied. Calculations reveal that the gain compression is not necessarily a drawback affecting the laser dynamics. With a practical injection strength, a high gain lever effect and a moderate compression value allow us to theoretically predict a modulation bandwidth four times higher than the free-running one without a gain lever, which is of paramount importance for the development of directly modulated broadband optical sources compatible with short-reach communication links.

Keywords

Lasers, injection-locked Modulation transfer function Nonlinear optics, integrated optics Semiconductor lasers

G_{k} (N_{k}, S, ϵ) = \frac{G_{k, 0}}{1 + ϵ S} \ln (\frac{N_{k} + N_{s}}{N_{tr} + N_{s}}),

(1)

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\frac{d N_{k}}{d t} = \frac{J_{k}}{eV} - \frac{N_{k}}{τ_{c, k}} - G_{k} S, k \in [a, b], k \in Z,

(2a)

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\frac{d S}{d t} = G S + 2 k_{c} \sqrt{S_{inj} S} \cos (ϕ) + R_{sp},

(2b)

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\frac{d ϕ}{d t} = G \frac{α_{H}}{2} - Δ ω_{inj} - k_{c} \sqrt{\frac{S_{inj}}{S}} \sin (ϕ),

(2c)

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d X = X_{1} e^{ı ω t},

(3a)

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d G_{k} = \frac{G_{k, 0}^{'}}{1 + ϵ S^{0}} d N_{k} - \frac{ϵ G_{k}}{1 + ϵ S^{0}} d S,

(3b)

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i ω [\begin{matrix} N_{a, 1} \\ N_{b, 1} \\ S_{1} \\ ϕ_{1} \end{matrix}] = M [\begin{matrix} N_{a, 1} \\ N_{b, 1} \\ S_{1} \\ ϕ_{1} \end{matrix}] + [\begin{matrix} J_{a, 1} / (e V) \\ J_{b, 1} / (e V) \\ 0 \\ 0 \end{matrix}],

(4)

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{| R (f) |}^{2} = \frac{B_{0}^{2} [{(η - A_{2}^{'} f^{2})}^{2} + {(A_{1}^{'} f)}^{2}]}{{[B_{1} f - B_{3} f^{3}]}^{2} + {[η B_{0} - B_{2} f^{2} + f^{4}]}^{2}},

(5)

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χ = \frac{ϵ S^{0}}{1 + ϵ S^{0}} [\frac{1}{τ_{p}} - 2 η \cos (ϕ^{0})] \cdot A_{0}^{ϵ} = \frac{χ}{16 π^{6}} {(γ_{b})}^{2} g Z_{ϕ, α_{H}}, A_{1}^{ϵ} = \frac{χ}{8 π^{3}} [γ_{b} (g + 1) η Z_{ϕ, α_{H}} + {(γ_{b})}^{2} g] A_{2}^{ϵ} = \frac{χ}{4 π^{2}} [η Z_{ϕ, α_{H}} + γ_{b} (g + 1)], A_{3}^{ϵ} = \frac{χ}{2 π}

(6)

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A_{0} = \frac{η {(γ_{b})}^{2} g}{16 π^{4}} + \frac{γ_{b} g Z_{ϕ, α_{H}} σ}{16 π^{4}}, A_{1}^{'} = \frac{2 π}{Z_{ϕ, α_{H}}} + \frac{2 π η}{γ_{b}}, A_{1} = [γ_{b} (g + 1) η^{2} + 2 η \cos (ϕ^{0}) {(γ_{b})}^{2} g + σ (γ_{b} g + η Z_{ϕ, α_{H}})] \frac{1}{8 π^{3}}, A_{2} = [η^{2} + 2 η \cos (ϕ^{0}) γ_{b} (g + 1) + {(γ_{b})}^{2} g + σ] \frac{1}{4 π^{2}}, A_{3} = [2 η \cos (ϕ^{0}) + γ_{b} (g + 1)] \frac{1}{2 π}, A_{2}^{'} = \frac{4 π^{2}}{γ_{b} Z_{ϕ, α_{H}}}, Z_{ϕ, α_{H}} = \cos (ϕ^{0}) - α_{H} \sin (ϕ^{0}), η = k_{c} \sqrt{K}, γ_{k} = \frac{1}{1 + ϵ S^{0}} (\frac{1}{τ_{c, k}} + G_{k, 0}^{'} S_{0}) + \frac{ϵ S^{0}}{τ_{c, k} (1 + ϵ S^{0})}, K = \sqrt{\frac{S_{inj}}{S_{0}}} σ = \frac{1}{1 + ϵ S^{0}} (\frac{1}{τ_{p}} - 2 η \cos (ϕ^{0})) (γ_{b} - \frac{1}{τ_{c, b}}), g = \frac{γ_{a}}{γ_{b}} .

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J. M. Sarraute, K. Schires, S. LaRochelle, F. Grillot, "Effects of gain nonlinearities in an optically injected gain lever semiconductor laser," Photonics Res. 5, 315 (2017)

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