Excitation of gap solitons, soliton trains, and soliton sets in finite-sized two-dimensional photonic crystals

We study in detail the excitation of gap solitons in finite-sized two-dimensional photonic crystals under various kinds of source configuration, including two external beams along different incident directions and a point source at different locations inside the sample. We find different types of gap solitons, such as soliton trains along different symmetry axes of the photonic crystal and soliton sets with a higher rotational symmetry. In the case of a single external beam, we find the existence of an optimal beamwidth $d_{\mathrm{opt}}$ for the excitation of gap solitons, and the value of $d_{\mathrm{opt}}$ is close to the diameter of single localized envelopes of the excitation. In the case of a point source, it is found that the excitation threshold depends only on the distance between the source and the nearest cylinder, and its value increases nearly exponentially with distance.