Theoretical investigation of state bistability between pure- and mixed-mode states in a 1550-nm VCSEL under parallel optical injection
Theoretical investigation of state bistability between pure- and mixed-mode states in a 1550-nm VCSEL under parallel optical injection
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平行光注入下 1550 nm VCSEL 纯模态和混合模态之间的态双稳定性理论研究
DOI：
10.1109/access.2018.2820678
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发表时间：
2018
期刊：
影响因子：
3.9
通讯作者：
Zheng-Mao Wu
中科院分区：
文献类型：
--
作者：
Dan Wang;Guang-Qiong Xia;Yu-Shuang Hou;Wen-Yan Yang;Elumalai Jayaprasath;Jian-Jun Chen;Zheng-Mao Wu
基于自旋翻转模型，对平行光注入下1550 nm垂直腔面发射激光器的纯模态和混合模态之间的状态双稳态（SB）进行了理论研究。模拟结果表明，当注入光频率（<inline-formula> <tex-math notation="LaTeX">$v_{\textrm {inj}}$ </tex-math></inline-formula>）小于自由运行激光的主模频率（<inline-formula> <tex-math notation="LaTeX">$v_{e}$时，可以观察到两种类型的SB </tex-math></inline-formula>）。对于 I 型 SB，通过固定 <inline-formula> <tex-math notation="LaTeX">$v_{\textrm {inj}}$ </tex-math></inline-formula> 和扫描注入功率 (<inline-formula> <tex-math notation="LaTeX">$P_{\textrm {inj}}$ </tex-math></inline-formula>) 沿着不同的路线发生，存在两个激光器在纯模或混合模状态下工作的磁滞回线，取决于<inline-formula> <tex-math notation="LaTeX">$P_{\textrm {inj}}$ </tex-math></inline-formula>的变化路线，并且磁滞回线宽度随着<inline-formula> <tex-math notation="LaTeX">$\vert \Delta \nu \vert $的增加而急剧增加</tex-math></inline-formula> (<inline-formula> <tex-math notation="LaTeX">$\Delta v = v_{\textrm {inj}}- v_{e}$ </tex-math></inline-formula>) 具有相对较强的 <inline-formula> <tex-math notation="LaTeX">$P_{\textrm {inj}}$ </tex-math></inline-formula> 而相对较弱的 <inline-formula> <tex-math notation="LaTeX">$P_{\textrm {inj}}$ </tex-math></inline-formula> 循环宽度缓慢增加，与我们最近的实验报告一致。此外，还通过固定 <inline-formula> <tex-math notation="LaTeX">$P_{\textrm {inj}}$ </tex-math></inline-formula> 并沿不同路径扫描 <inline-formula> <tex-math notation="LaTeX">$v_{\textrm {inj}}$ </tex-math></inline-formula> 来研究类型 II SB。还存在两个磁滞回线，其中激光器可以在纯模式或混合模式状态下工作。随着<inline-formula> <tex-math notation="LaTeX">$P_{\textrm {inj}}$ </tex-math></inline-formula>的增加，位于<inline-formula> <tex-math notation="LaTeX">$\vert \Delta \nu \vert $ </tex-math></inline-formula>处的磁滞回线宽度急剧增加，达到最大值后又减小。然而，对于位于较高 <inline-formula> <tex-math notation="LaTeX">$\vert \Delta \nu \vert $ </tex-math></inline-formula> 处的磁滞回线，回线宽度随着 <inline-formula> <tex-math notation="LaTeX">$P_{\textrm {inj}}$ </tex-math></inline-formula> 的增大而逐渐增大。
Based on the spin-flip model, state bistability (SB) between pure- and mixed-mode states in a 1550-nm vertical-cavity surface-emitting laser under parallel optical injection is theoretically investigated. The simulated results show that two types of SB can be observed when the injection light frequency (<inline-formula> <tex-math notation="LaTeX">$v_{\textrm {inj}}$ </tex-math></inline-formula>) is smaller than the dominant mode frequency of the free-running laser (<inline-formula> <tex-math notation="LaTeX">$v_{e}$ </tex-math></inline-formula>). For type-I SB, which occurs through fixing <inline-formula> <tex-math notation="LaTeX">$v_{\textrm {inj}}$ </tex-math></inline-formula> and scanning injection power (<inline-formula> <tex-math notation="LaTeX">$P_{\textrm {inj}}$ </tex-math></inline-formula>) along different routes, there exist two hysteresis loops in which the laser operates at pure- or mixed-mode state, depending on the variation route of <inline-formula> <tex-math notation="LaTeX">$P_{\textrm {inj}}$ </tex-math></inline-formula>, and the hysteresis loop width increases sharply for increasing <inline-formula> <tex-math notation="LaTeX">$\vert \Delta \nu \vert $ </tex-math></inline-formula> (<inline-formula> <tex-math notation="LaTeX">$\Delta v = v_{\textrm {inj}}- v_{e}$ </tex-math></inline-formula>) with relatively strong <inline-formula> <tex-math notation="LaTeX">$P_{\textrm {inj}}$ </tex-math></inline-formula> whereas the loop width increases slowly for relatively weak <inline-formula> <tex-math notation="LaTeX">$P_{\textrm {inj}}$ </tex-math></inline-formula>, in agreement with our recent experimental report. Furthermore, type-II SB is also investigated through fixing <inline-formula> <tex-math notation="LaTeX">$P_{\textrm {inj}}$ </tex-math></inline-formula> and scanning <inline-formula> <tex-math notation="LaTeX">$v_{\textrm {inj}}$ </tex-math></inline-formula> along different routes. There also exist two hysteresis loops in which the laser may operate at a pure- or mixed-mode state. With an increase of <inline-formula> <tex-math notation="LaTeX">$P_{\textrm {inj}}$ </tex-math></inline-formula>, the hysteresis loop width located at lower <inline-formula> <tex-math notation="LaTeX">$\vert \Delta \nu \vert $ </tex-math></inline-formula> increases sharply and then decreases after reaching a maximum. However, for the hysteresis loop located at higher <inline-formula> <tex-math notation="LaTeX">$\vert \Delta \nu \vert $ </tex-math></inline-formula>, the loop width gradually increases with the increase of <inline-formula> <tex-math notation="LaTeX">$P_{\textrm {inj}}$ </tex-math></inline-formula>.