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首页> 外文期刊>Optical and quantum electronics >Mathematical analysis of the lasing eigenvalue problem for the optical modes in a layered dielectric cavity with a quantum well and distributed Bragg reflectors
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Mathematical analysis of the lasing eigenvalue problem for the optical modes in a layered dielectric cavity with a quantum well and distributed Bragg reflectors

机译：具有量子阱和分布式布拉格反射器的层状介电腔中光学模式的激光本征值问题的数学分析

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摘要

Optical modes and associated linear threshold values of material gain bringing them to lasing are investigated for a VCSEL-type cavity with a quantum well, sandwiched between two distributed Bragg reflectors. They are found as solutions to a specific novel eigenvalue problem with the "active" imaginary part of the quantum well refractive index. For the calculation of the Bragg mirror reflection coefficients, well-established method of the transfer matrices is used. The presented results accurately quantify intuitively predictable lowering of the modal thresholds for the modes whose lasing frequencies lay inside the reflectors rejection bands. Besides, they demonstrate that this approach automatically incorporates the account of overlapping between the active region and the modal E-field patterns and its effect on the thresholds.
机译：对于夹在两个分布式布拉格反射器之间的具有量子阱的VCSEL型腔，研究了将其激发的光模和相关的材料增益线性阈值。发现它们是解决特定新颖特征值问题的方法，该问题具有量子阱折射率的“活动”虚部。为了计算布拉格镜面反射系数，使用了行之有效的传递矩阵方法。对于激光频率位于反射器抑制带内的模态，给出的结果准确地量化了模态阈值的直观可预测的降低。此外，他们证明了这种方法会自动考虑有效区域和模态电场模式之间的重叠及其对阈值的影响。

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