The dispersion relation and the optical transmittance of a two-dimensional photonic crystal composed of the hexagonal array of cylindrical air holes fabricated in a dielectric slab were analyzed by group theory and the numerical calculation based on the finite-difference time-domain method. The decay rate of the leaky modes that exist above the light line (the dispersion relation in air) in the band diagram was also evaluated, from which the absence of the coupling between certain internal eigenmodes and the external radiation field was shown. This phenomenon was related to symmetry mismatching by the group-theoretical argument. It was also shown that a certain leaky band has a quality factor as large as 3000 over its entire spectral range. These features as well as the opaque frequency regions due to symmetry mismatching were clearly demonstrated by the calculated optical transmission spectra.

Making use of a droplet-epitaxial technique, we realize nanometer-sized quantum ring complexes, consisting of a well-defined inner ring and an outer ring. Electronic structure inherent in the unique quantum system is analyzed using a microphotoluminescence technique. One advantage of our growth method is that it presents the possibility of varying the ring geometry. Two samples are prepared and studied: a single-wall ring and a concentric double ring. For both samples, highly efficient photoluminescence emitted from a single quantum structure is detected. The spectra show discrete resonance lines, which reflect the quantized nature of the ring-type electronic states. In the concentric double ring, the carrier confinement in the inner ring and that in the outer ring are identified distinctly as split lines. The observed spectra are interpreted on the basis of single electron effective mass calculations.

The photonic bands of two-dimensional triangular and square lattices composed of circular rods were classified by means of the group theory based on the symmetry of the lattice structure. According to this classification, it was shown that the uncoupled mode, or the mode that cannot be excited by an external plane wave, which we previously found for the triangular lattice by the numerical calculation of the transmittance, is an antisymmetric mode under the relevant mirror reflection, and this fact is consistent with the observation by Robertson et al. It was also shown that triangular and square lattices with ${\mathit{C}}_{6\mathit{v}}$ or ${\mathit{C}}_{4\mathit{v}}$ symmetry have many other uncoupled modes with relatively low eigenfrequencies and some of them can be easily identified as the spectral ranges of total reflection in spite of their nonzero state density.

An ideal emitter of entangled photon pairs combines the perfect symmetry of an atom with the convenient electrical trigger of light sources based on semiconductor quantum dots. Our source consists of strain-free GaAs dots self-assembled on a triangular symmetric (111)$A$ surface. The emitted photons reveal a fidelity to the Bell state as high as 86($\pm 2$)% without postselection. We show a violation of Bell's inequality by more than five times the standard deviation, a prerequisite to test a quantum cryptography channel for eavesdropping. Due to the strict nonlocal nature the source can be used for real quantum processing without any postprocessing. The remaining decoherence channel of the photon source is ascribed to random charge and nuclear spin fluctuations in and near the dot.