The physical origin of the ultrafast response of nonlinear photonic crystal (PC) atoms to the excitation of ultrashort pulses is investigated in detail. It is found that the dynamic shift of PC defect modes is responsible for the dramatic shortening of the photon lifetime in nonlinear PC atoms. The transmission spectra for nonlinear PC atoms that resulted from the dynamic shift are calculated and they are in good agreement with the simulation results.

We investigate, experimentally and theoretically, the influence of disordered defects on the transmission properties of optical delay lines based on coupled cavity waveguides (CCW's). Also, the modification of transmission for a line-defect waveguide in a two-dimensional (2D) photonic crystal (PC) upon bending is examined by numerical simulation. We reveal that the effect of waveguide bending on the transmission properties of PC circuits is very similar to that of disordered defects on the transmission properties of CCW's. It is shown that the broad impurity band of a one-dimensional CCW will evolve into sharp defect modes upon increasing the disorder. Using a symmetric Mach-Zehnder structure formed in a 2D PC as an example, we show that a PC circuit containing multiple bends and branches of different properties generally gives rise to sharp resonant modes whose linewidth is inversely proportional to the size of the PC circuit. This might be an intrinsic problem in realizing PC circuits.

Coupling of defects in one-dimensional (1D) and two-dimensional (2D) photonic crystals (PC's) is analyzed theoretically and investigated numerically using the transfer-matrix method and the finite-difference timedomain technique. Basically, the coupling behavior of defects is reflected in the spectra of PC molecules formed by two identical PC atoms (single defects). In both 1D and 2D cases, PC atoms can be roughly classified into two types based on the spectral shape of the resulting PC molecules. One type of PC atom generates clear bonding and antibonding states in the spectra of PC molecules. In contrast, the other type of PC atom creates PC molecules whose spectra are nearly flat on top. It is shown that this kind of PC atom is crucial for the construction of coupled cavity waveguides with quasiflat impurity bands. More accurately, we use a quantity related to the valley depth in the spectra of PC molecules to describe the coupling behavior of PC atoms. The dependence of this quantity on the properties of individual PC atoms is investigated in detail. It is revealed that the coupling of PC atoms is governed by the linewidth (δω) and the frequency shift of the PC atoms (Δω) upon increasing the confine (δω) ment. The factor (Δω/δω)2 is confirmed by theoretical analysis and numerical calculation to be a universal criterion to characterize the coupling behavior of both 1D and 2D PC defects.

On self-assembled InxGa12xAs/GaAs(311)B quantum dots (QD's), photocurrent in the plane of QD arrays was measured under irradiation with wavelengths longer than 850 nm (1.46 eV). A sample with rather inhomogeneous QD sizes shows hopping conduction, indicating the localization of carriers in individual QD's. A two-dimensional QD superlattice, consisting of highly ordered and homogeneously sized QD's, exhibits negative differential conductance (NDC), i.e., photocurrent decrease with increasing applied voltage, in a limited electric-field range. The pre-NDC conduction is argued to arise from the miniband, which is evidenced by the photoluminescence, while the post-NDC conduction is found to be hopping as in a localized QD system, suggesting a miniband destruction under an in-plane electric field as low as～103Vcm-1. The miniband transport is likely controlled by two-dimensional acoustic-phonon scattering.

We propose a new mechanism for constructing waveguide intersections with broad bandwidth and low cross talk in photonic crystal (PC) circuits. The intersections are created by combination of coupled-cavity waveguides (CCWs) with conventional line-defect waveguides. This mechanism utilizes the strong dependence of the defect coupling on the field pattern in the defects and the alignment of the defects (i.e., the coupling angle) in CCWs. By properly designing the defect mode, we demonstrate through numerical imulation the establishment of such a waveguide intersection in one of the most useful PCs, which is based on a two-dimensional triangular lattice of air holes made in a dielectric material. The transmission of a 500-fs pulse at 1.3mm is simulated by use of the finite-difference time-domain method, showing negligible distortion and low cross talk.