Theoretical study on optical process in nanomaterial by using nonlinear susceptibility without cancellation terms

在光学非线性极化率的序数表达式中，许多项是相互抵消的。如果我们离开抵消项，非线性极化率发散在一个整体极限。为了避免这种非物理的结果，我们应该仔细对待取消问题。到目前为止，石原和赵在一个简单的模型中完全处理了取消问题。然而，在第一原理计算中，用非线性极化率的序数表达式来消除抵消项几乎是不可能的，在本项目中，我们成功地推导出了一个不含抵消项的非线性极化率的一般表达式。该表达式有助于我们计算非线性极化率的尺寸依赖性，而不需要考虑相互抵消项。迄今为止，腔系统的光学非线性都是在半经典条件下研究的。然而，我们已经表明，腔量子电动力学（腔QED）是必不可少的，以研究腔系统的光学非线性。然后，我们研究了腔QED处理中的各种非线性过程：1.推导了微腔中单个量子点实现大光学非线性的最佳条件; 2.研究了微腔中量子阱和量子点的超参量过程产生纠缠光子的过程.由于腔效应的存在，产生的效率显著提高。我们也找到了产生纠缠光子的最佳条件。从腔QED的特征出发，定性地理解了这些最优条件。

In the ordinal expression of optical nonlinear susceptibility, many terms are cancelled with each other. If we leave the cancellation terms, the nonlinear susceptibility diverges in a bulk limit. In order to avoid this unphysical result, we should treat the cancellation problem carefully. So far, the cancellation problem was exactly treated in a simple model by Ishihara and Cho. However, it is almost impossible to remove the cancellation terms in the first principle calculation by usin the ordinal expression of the nonlinear susceptibility.In this project, we have succeeded to derive a general expression of nonlinear susceptibility without cancellation terms in advance. The general expression helps us to calculate size dependence of nonlinear susceptibility without attention to the cancellation terms.We have also studied optical nonlinear response of excitons in microcavity. So far, the optical nonlinearities of cavity systems were studied in a semiclassical treatment. However, we have shown that cavity quantum electrodynamics (cavity QED)is indispensable in order to study the optical nonlinearity of the cavity systems. Then, we study various nonlinear processes in the cavity QED treatment.1.We have derived optimal conditions for achieving large optical nonlinearity of a single quantum dot in microcavity.2.We have studied entangled photon generation due to the hyper-parametric process from a quantum well and quantum dot in microcavity. The efficiency of the generation is dramatically enhanced due to the cavity effect. We have also found optimal conditions for the entangled photon generation. These optimal conditions are qualitatively understood from the characteristic feature of the cavity QED.