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[J]. Photonics Research, 2017, 5(4): 315 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}} .

(7)

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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[J]. Photonics Research, 2017, 5(4): 315

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