Nonlinear and quantum optics of multidimensional and multiperiodic structures

在本研究中，我们首先分析了可在半导体衬底上制造的光子晶体板的色散关系和光子带的寿命，以及赝隙中局域缺陷模的频率和品质因子。澄清了金属光子晶体等离子体光子带的色散关系和对称性，并期望在等离子体光子晶体中实现非常小的群光速。其次，我们选取了正交相位压缩作为利用二阶非线性光学效应的量子光学现象的一个代表性例子。利用格林函数法的近似解，阐明了小群速度的增强效应。我们还提出了一种线性近似下处理电磁场量子涨落的数值方法，并将其应用于光子晶体板。此外，我们还分析了超辐射，这是一种物质的相干偏振协同发光，并研究了大拉比分裂，电子系统的部分弛豫，以及光子带隙引起的超辐射脉冲形状的异常原子数依赖性。另一方面，我们与美国代顿大学合作，用离子交换法制备了具有二阶非线性磁化率的LiNbO3波导。我们进一步在波导上制备了光阻剂的一维和二维周期图案，以制作弱调制光子晶体板，并研究了它们的特性。我们还合成了具有大二阶非线性磁化率的新型有机材料。我们出版了施普林格Verlag和Morikita Publishing的两本书，其中收集了首席研究员近十年的主要作品，包括上述研究。

In this research, firstly we analyzed the dispersion relation and the lifetime of photonic bands, and the frequency and the quality factor of localized defect modes in the pseudo-gap for photonic crystal slabs that can be fabricated on semiconductor substrates. We clarified the dispersion relation and the symmetry of photonic bands originating from plasmons for metallic photonic crystals in which very small group velocity of light is expected to be realized. Secondly we picked up the quadrature-phase squeezing as a representative example of quantum optical phenomena utilizing the second-order nonlinear optical effect. We clarified the enhancement effect due to the small group velocity by means of an approximate solution obtained by the Green function method. We also developed a numerical method to deal with the quantum fluctuation of the electromagnetic field in the linear approximation, and applied it to the photonic crystal slab.In addition, we analyzed the superradiance, which is a cooperative light emission by a coherent polarization of matter, and examined the large Rabi splitting, partial relaxation of the population inversion of the electronic system, and the extraordinary atom-number dependence of the superradiant pulse shape caused by the photonic band gap. On the other hand, in cooperation with Dayton University, we fabricated waveguides made of LiNbO3 by the ion exchange method that has the second-order nonlinear susceptibility. We further fabricated one-and two-dimensional periodic patterns of a photoresist on the waveguide to make weakly modulated photonic crystal slabs, and examined their characteristics. We also synthesized new organic materials with the large second-order nonlinear susceptibility. We published two books from Springer Verlag and Morikita Publishing, in which the major works of the head investigator in the last ten years including the above-mentioned studies were collected.