1.The CAS Key Laboratory of Solid State Optoelectronics Information Technology, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China 2.College of Materials Science and Opto-Electronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China 3.College of Future Technology, University of Chinese Academy of Sciences, Beijing 101408, China 4.The State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China
Fund Project:Project supported by the National Key Research and Development Program of China (Grant Nos. 2016YFB0401804, 2016YFB0401003, 2016YFA0301102) and the National Natural Science Foundation of China (Grant Nos. 91850206, 61535013)
Received Date:06 September 2019
Accepted Date:15 October 2019
Available Online:01 January 2020
Published Online:20 January 2020
Abstract:The non-Hermitian description is of great significance for open systems, and the Hamiltonian which satisfies parity-time symmetry can make the energy have real eigenvalue within a certain range. The properties of parity-time symmetry have bright application prospects in optical systems. For semiconductor lasers, the parity-time symmetry can be constructed by adjusting the level of electrical injection to help achieve better mode control. Electric injection is easier to realize than optical pump when the device size is small and the structure is complex. Therefore, we hope to analyze the characteristics of the laser that satisfies the parity-time symmetry condition under the condition of electric injection. In this paper, we simulate the effects of different set loss values on parity-time symmetry. It is found that with the increase of set loss value, the imaginary part of the refractive index of the gain cavity corresponding to the parity-time symmetry breaking point so-called exceptional point will decrease, and the imaginary part of the characteristic frequency corresponding to the exceptional point will also decrease. We also simulate the effect of structural size ratio of gain region and loss region on parity-time symmetry. On condition that the total cavity length and the imaginary part of the refractive index of the loss region remain unchanged, as the gain cavity becomes longer and the loss cavity becomes shorter, the imaginary part of the refractive index of the gain cavity corresponding to the exceptional point will increase, and the imaginary part of the characteristic frequency corresponding to the exceptional point will also increase. And we qualitatively explain the above phenomenon through the coupled mode equations. Through experiments, metal organic chemical vapor deposition (MOCVD) and standard lithography techniques are used to fabricate asymmetric ridge lasers. Under thermoelectric cooler (TEC) refrigeration and by controlling the injection level of the gain area, the doubled mode spacing and halved mode number of ridge waveguide are found for the first time due to the parity-time symmetry breaking under the condition of electric injection. We believe that the study of parity-time symmetry in ridge laser under the condition of electric injection will be of great help in implementing the mode control. Keywords:parity-time symmetry/ electric injection/ semiconductor laser/ mode control
通过标准的光刻工艺制备条形激光器, 为了满足PT对称条件, 使其中一部分能够通过电注入对激光器提供增益, 作为增益区; 另一部分为了避免载流子扩散带来的影响, 将这部分区域的高掺层通过电感耦合等离子体(inductively coupled plasma, ICP)工艺刻蚀掉, 然后由SiO2覆盖, 起到绝缘层的效果, 由于本征吸收的存在, 这部分吸收区可以作为损耗区, 结构如图2所示. 图 2 器件结构图, 其中黄色部分为增益区, 蓝色部分为损耗区 Figure2. Device structure diagram, the yellow part is the gain region and the blue part is the loss region.
图 4 折射率虚部为${n_{{\rm{Ir}}}} = - 0.01$和${n_{{\rm{Ir}}}} = - 0.05$时, 波长与${n_{{\rm{Il}}}}$的关系图 Figure4. Relationship between wavelength and ${n_{{\rm{Il}}}}$ when ${n_{{\rm{Ir}}}} = - 0.01$ and ${n_{{\rm{Ir}}}} = - 0.05$.
图 5 折射率虚部为nIr = –0.01以及nIr = –0.05时, 特征频率虚部与${n_{{\rm{Il}}}}$的关系图 Figure5. Relationship between the imaginary part of the characteristic frequency and ${n_{{\rm{Il}}}}$ when ${n_{{\rm{Ir}}}} = - 0.01$ and ${n_{{\rm{Ir}}}} = - 0.05$.
${\beta _{\rm{r}}}$为传播常数的实部, 显然在PT对称破缺点时, 增益损耗$({{{\gamma _{1 - }}{\gamma _2}}})/{2}$与耦合系数$\kappa $之间要满足一定的比例关系[25,26], 使$ \pm \sqrt {{\kappa ^2} - {{\displaystyle\left( {\frac{{{\gamma _1} - {\gamma _2}}}{2}} \right)}^2}} $项带来的虚部刚好为0, 当固定损耗增加时, PT对称破缺点对应的增益数值下降. 并且破缺点处对应的虚部数值$({{{\gamma _1} + {\gamma _2}}})/{2}$, 由于γ1数值减小以及γ2的减小(固定损耗增大), 也会明显减小. 本文还对器件结构对称性的影响进行了模拟分析, 分别模拟了增益区与损耗区长度比例为5∶5, 7∶3以及8∶2时的结果, 如图6—图8所示. 图 6 增益区和损耗区长度比为5∶5, 7∶3以及8∶2时的结构图 Figure6. Simulation structure of ridged waveguide when length ratio of gain region and loss region is 5∶5, 7∶3, and 8∶2.
图 8 长度比为5∶5, 7∶3以及8∶2时, 特征频率虚部与${n_{{\rm{Il}}}}$的关系图 Figure8. Relationship between the imaginary part of the characteristic frequency and ${n_{{\rm{Il}}}}$ when the length ratio is 5∶5, 7∶3, and 8∶2.
图6为增益区与损耗区长度比例分别为5∶5, 7∶3以及8∶2时的结构图, 图7和图8为固定损耗区虚部为–0.05时模拟结果. 其中图7为${n_{{\rm{Il}}}}$和波长的关系曲线, 图8为${n_{{\rm{Il}}}}$和特征频率虚部的关系曲线. 图中, 黑线和红线、蓝线和绿线、紫线和棕线分别对应增益区与损耗区长度比例为5∶5, 7∶3以及8∶2时的发射模式以及吸收模式. 由于模拟结构的总长度不变, 非对称性的增加, 在这里可以理解为损耗腔损耗的减小, 增益腔带来的增益与损耗腔带来的损耗$({{{\gamma _1} - {\gamma _2}}})/{2}$与耦合系数$\kappa $之间仍然要满足耦合模方程中PT对称破缺点时对应的关系, 损耗的减小会导致PT对称破缺点处对应增益的变大, 且破缺点处对应的特征频率虚部数值变大. 图 7 长度比为5∶5, 7∶3以及8∶2时, 波长与${n_{{\rm{Il}}}}$的关系图 Figure7. Relationship between wavelength and ${n_{{\rm{Il}}}}$ when the length ratio is 5∶5, 7∶3, and 8∶2.
3.实验结果在激射条件下, 通过对注入电流的控制来实现增益的调制, 将激光器的输出在热电制冷器(thermoelectric cooler, TEC)制冷的条件下由光纤导入光谱仪中, 测试了其腔模(非激射模)与注入电流大小的关系, 发现当电流达到PT对称破缺(约320 mA)后, 发生模式简并现象, 测试结果如图9所示. 图 9 腔模强度与波长关系 (a)注入电流为100 mA; (b)注入电流分别为310 mA(黑线)、320 mA(红线)以及330 mA(蓝线) Figure9. Relationship between the normalized intensity and wavelength of cavity modes: (a) The injection current is 100 mA; (b) the injection current is 310 mA (black line), 320 mA (red line) and 330 mA (blue line), respectively.
图 1 外延片结构图
图 2 器件结构图, 其中黄色部分为增益区, 蓝色部分为损耗区
图 3 条型波导模拟结构图
图 4 折射率虚部为
图 5 折射率虚部为nIr = –0.01以及nIr = –0.05时, 特征频率虚部与
图 6 增益区和损耗区长度比为5∶5, 7∶3以及8∶2时的结构图
图 8 长度比为5∶5, 7∶3以及8∶2时, 特征频率虚部与
图 7 长度比为5∶5, 7∶3以及8∶2时, 波长与
图 9 腔模强度与波长关系 (a)注入电流为100 mA; (b)注入电流分别为310 mA(黑线)、320 mA(红线)以及330 mA(蓝线)
