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Journals >Chinese Optics Letters >Volume 13 >Issue Suppl. >Page S21405 > Article

Chinese Optics Letters
Vol. 13, Issue Suppl., S21405 (2015)

Control of the polarization switching and the nonlinear dynamic behaviors of vertical cavity surface-emitting lasers with external optical injection

Dongzhou Zhong

Author Affiliations

School of Information Engineering, Wuyi University, Jiangmen 529020, China

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DOI: 10.3788/COL201513.S21405 Cite this Article Set citation alerts

Dongzhou Zhong. Control of the polarization switching and the nonlinear dynamic behaviors of vertical cavity surface-emitting lasers with external optical injection[J]. Chinese Optics Letters, 2015, 13(Suppl.): S21405 Copy Citation Text

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Abstract

For polarization switching (PS) and nonlinear dynamic behaviors (NDBs) of an optically injected laser system composed of a master vertical-cavity surface-emitting laser (VCSEL) and a slave VCSEL, we put forward a novel manipulation scheme by means of electro-optic (EO) modulation with quasi-phase matched technology. It is found that the PS of the slave VCSEL subject to parallel or orthogonal optical injection takes on a change of periodic oscillation with the applied transverse electric field. The optically injected slave VCSEL can experience different NDBs evolutions when the light from the master laser is modulated by the linear EO effect.

\frac{d}{d t} (\begin{matrix} E_{M x} (t) \\ E_{M y} (t) \end{matrix}) = k (1 + i a) [N_{M} (t) - 1] (\begin{matrix} E_{M x} (t) \\ E_{M y} (t) \end{matrix}) \pm i k (1 + i a) n_{M} (t) (\begin{matrix} E_{M y} (t) \\ E_{M x} (t) \end{matrix}) \mp (γ_{a} + i γ_{p}) (\begin{matrix} E_{M x} (t) \\ E_{M y} (t) \end{matrix}) + (\begin{matrix} {[β_{s p} (N_{M} (t) + n_{M} (t)) / 2]}^{1 / 2} \\ - i {[β_{s p} (N_{M} (t) + n_{M} (t)) / 2]}^{1 / 2} \end{matrix}) ξ_{1} + (\begin{matrix} {[β_{s p} (N_{M} (t) - n_{M} (t)) / 2]}^{1 / 2} \\ i {[β_{s p} (N_{M} (t) - n_{M} (t)) / 2]}^{1 / 2} \end{matrix}) ξ_{2},

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\frac{d N_{M} (t)}{d t} = - γ_{e} {N_{M} (t) - μ_{M} + N_{M} (t) ({| E_{M x} (t) |}^{2} + {| E_{M y} (t) |}^{2}) + i n_{M} (t) [E_{M y} (t) E_{M x}^{*} (t) - E_{M x} (t) E_{M y}^{*}],

(2)

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\frac{d n_{M} (t)}{d t} = - γ_{s} n_{M} (t) - γ_{e} {n_{M} (t) ({| E_{M x} (t) |}^{2} + {| E_{M y} (t) |}^{2}) + i N_{M} (t) [E_{M y} (t) E_{M x}^{*} (t) - E_{M x} (t) E_{M y}^{*} (t)]},

(3)

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U_{x, y} (0, t - τ) = \sqrt{\frac{ℏ ω_{0} V}{S T_{L} C n_{1, 2}}} E_{M x, M y} (t - τ),

(4)

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\frac{d U_{x} (t, x)}{d x} = - i d_{1} U_{y} (t, x) \exp (i Δ k x) - i d_{2} U_{x} (t, x),

(5)

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\frac{d U_{y} (t, x)}{d x} = - i d_{3} U_{x} (t, x) \exp (- i Δ k x) - i d_{4} U_{y} (t, x),

(6)

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d_{1} = k_{0} r_{eff 1} E_{0} f_{1} / 2 \sqrt{n_{1} n_{2}}, d_{3} = k_{0} r_{eff 1} E_{0} f_{- 1} / 2 \sqrt{n_{1} n_{2}},

(7)

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d_{2} = k_{0} r_{eff 2} E_{0} f_{0} / 2 n_{1}, d_{4} = k_{0} r_{eff 3} E_{0} f_{0} / 2 n_{2} .

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r_{eff 1} = \sum_{j, k, l} (ε_{j j} ε_{k k}) a_{j} r_{j k l} b_{k} c_{l},

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r_{eff 2} = \sum_{j, k, l} (ε_{j j} ε_{k k}) a_{j} r_{j k l} a_{k} c_{l},

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r_{eff 2} = \sum_{j, k, l} (ε_{j j} ε_{k k}) b_{j} r_{j k l} b_{k} c_{l},

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E_{P x, P y} (t - τ) = \sqrt{\frac{S T_{L} C n_{1, 2}}{ℏ ω_{0} V}} u_{x, y} (t - τ, L) .

(12)

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\frac{d}{d t} (\begin{matrix} E_{S x} (t) \\ E_{S y} (t) \end{matrix}) = k (1 + i a) [N_{S} (t) - 1] (\begin{matrix} E_{S x} (t) \\ E_{S y} (t) \end{matrix}) \pm i k (1 + i a) n_{S} (t) (\begin{matrix} E_{S y} (t) \\ E_{S x} (t) \end{matrix}) \mp (γ_{a} + i γ_{p}) (\begin{matrix} E_{S x} (t) \\ E_{S y} (t) \end{matrix}) + (\begin{matrix} {[β_{s p} (N_{S} (t) + n_{S} (t)) / 2]}^{1 / 2} \\ - i {[β_{s p} (N_{S} (t) + n_{S} (t)) / 2]}^{1 / 2} \end{matrix}) ξ_{1} + (\begin{matrix} {[β_{s p} (N_{S} (t) - n_{S} (t)) / 2]}^{1 / 2} \\ i {[β_{s p} (N_{S} (t) - n_{S} (t)) / 2]}^{1 / 2} \end{matrix}) ξ_{2} + k_{i n j} [\begin{matrix} E_{P x} (t - τ) \\ E_{P y} (t - τ) \end{matrix}] \exp (- i ω_{0} τ + i Δ ω t),

(13)

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\frac{d N_{S} (t)}{d t} = - γ_{e} {N_{S} (t) - μ_{S} + N_{S} (t) ({| E_{S x} (t) |}^{2} + {| E_{S y} (t) |}^{2}) + i n_{S} (t) [E_{S y} (t) E_{S x}^{*} (t) - E_{S x} (t) E_{S y}^{*}],

(14)

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\frac{d n_{S} (t)}{d t} = - γ_{s} n_{S} (t) - γ_{e} {n_{S} (t) ({| E_{S x} (t) |}^{2} + {| E_{S y} (t) |}^{2}) + i N_{S} (t) [E_{S y} (t) E_{M x}^{*} (t) - E_{S x} (t) E_{S y}^{*} (t)]},

(15)

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{PD}_{1, 2} = \frac{〈 I_{1 x, 2 x} (t) 〉 - 〈 I_{1 y, 2 y} (t) 〉}{〈 I_{1 x, 2 x} (t) 〉 + 〈 I_{1 y, 2 y} (t) 〉},

(16)

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Dongzhou Zhong. Control of the polarization switching and the nonlinear dynamic behaviors of vertical cavity surface-emitting lasers with external optical injection[J]. Chinese Optics Letters, 2015, 13(Suppl.): S21405

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