Analysis of the time domain characteristics of tapered semiconductor lasers

Desheng Zeng; Li Zhong; Suping Liu; Xiaoyu Ma

doi:10.1088/1674-4926/41/3/032305

Journals >Journal of Semiconductors >Volume 41 >Issue 3 >Page 032305 > Article

Journal of Semiconductors
Vol. 41, Issue 3, 032305 (2020)

Analysis of the time domain characteristics of tapered semiconductor lasers

Desheng Zeng^1、2, Li Zhong¹, Suping Liu¹, and Xiaoyu Ma^1、2

Author Affiliations

¹National Engineering Center for Optoelectronic Device, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China

²University of Chinese Academy of Sciences, Beijing 100049, China

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DOI: 10.1088/1674-4926/41/3/032305 Cite this Article

Desheng Zeng, Li Zhong, Suping Liu, Xiaoyu Ma. Analysis of the time domain characteristics of tapered semiconductor lasers[J]. Journal of Semiconductors, 2020, 41(3): 032305 Copy Citation Text

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Abstract

We use traveling wave coupling theory to investigate the time domain characteristics of tapered semiconductor lasers with DBR gratings. We analyze the influence of the length of second order gratings on the power and spectrum of output light, and optimizing the length of gratings, in order to reduce the mode competition effect in the device, and obtain the high power output light wave with good longitudinal mode characteristics.

$ \left( {\frac{1}{{{{{v}}_{\rm{g}}}}} \frac{\partial }{{\partial t}} + \frac{\partial }{{\partial z}}} \right)R = [g - a - \varepsilon (z)]R + [i \kappa (z) - \varepsilon (z)]S + {\Phi _{\rm{R}}} \tag{1a},$

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$ \left( {\frac{1}{{{{{v}}_{\rm{g}}}}} \frac{\partial }{{\partial t}} - \frac{\partial }{{\partial z}}} \right)S =[g - a - \varepsilon (z)]S + [i \kappa (z) - \varepsilon (z)]R + {\Phi _{\rm{S}}} \tag{1b},$

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$ {{g}}(t,z) = \frac{{G(z,t)}}{2} (1 - i \alpha ), $

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$ G(z,t) = A (N(z,t) - {N_0}), $

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$\begin{split} & \left\langle {{\Phi _i}(z,t){\Phi _i}(z',t')} \right\rangle = \delta (z - z') \frac{{{\text{π}} \Delta \upsilon }}{2}{{\rm{e}}^{ - {\text{π}} \Delta \upsilon \left| {t - t'} \right|}} \\ & \qquad\!\! \qquad\qquad\qquad \times (G {n_{\rm{sp}}}(z) hv \frac{{{w_{\rm{act}}}}}{{{W^2}}}), \end{split}$

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$ {n_{\rm{sp}}}(z) = \frac{1}{{1 - \exp \left\{ {[{{hv + {E_{\rm{FV}}}(z) - {E_{\rm{FC}}}(z)]} / {{k_{\rm{B}}}T}}} \right\}}}. $

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$ \frac{{\partial N(z,t)}}{{\partial t}} = \frac{{{\eta _i}}}{e}J(z,t) - \Re (N) - \frac{G}{{hv}}({\left| R \right|^2} + {\left| S \right|^2}), $

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$\begin{array}{l} R(t + \Delta t,z + \Delta z) - R(t,z)\\ \;\;= R(t + \Delta t,z + \Delta z) - R(t,z + \Delta z) + R(t,z + \Delta z) - R(t,z)\\ \;\; = \dfrac{{\partial R}}{{\partial t}}\left| {_{z + \Delta z} } \right.\Delta t + \dfrac{{\partial R}}{{\partial z}}\left| {_t} \right. \Delta z\\ \;\; = \dfrac{{\partial R}}{{\partial t}}\left| {_{z + \Delta z}} \right. \Delta t - \dfrac{{\partial R}}{{\partial t}}\left| {_z} \right. \Delta t + \dfrac{{\partial R}}{{\partial t}}\left| {_z} \right. \Delta t + \dfrac{{\partial R}}{{\partial z}}\left| {_{\Delta t} \Delta z} \right. \\ \;\; = \dfrac{{{\partial ^2}R}}{{\partial {z^2}}} {v_{\rm{g}}} \Delta t \Delta z + \left( {\dfrac{1}{{{v_{\rm{g}}}}} \dfrac{{\partial R}}{{\partial t}} + \dfrac{{\partial R}}{{\partial z}}} \right) \Delta z. \end{array}$

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$ R(k + 1,m + 1) = R(k,m) + \Delta z {\Psi _R}, \tag{7a}$

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$ S(k + 1,m - 1) = S(k,m) + \Delta z {\Psi _S}, \tag{7b}$

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$ \frac{{\rm{d}}}{{{\rm{d}}z}}\left[ {\begin{array}{*{20}{c}} {\bar R}\\ {\bar S} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} {g - a - \varepsilon } & {i \kappa - \varepsilon }\\ { - i \kappa + \varepsilon } & { - g + a + \varepsilon } \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {\bar R}\\ {\bar S} \end{array}} \right]. $

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Desheng Zeng, Li Zhong, Suping Liu, Xiaoyu Ma. Analysis of the time domain characteristics of tapered semiconductor lasers[J]. Journal of Semiconductors, 2020, 41(3): 032305

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