Principle of beam generation in on-chip 2D beam pattern projecting lasers.

Integrable spatial-phase-modulating surface-emitting lasers, which utilize the band edge mode of two-dimensional photonic-crystals as resonators, project static arbitrary two-dimensional beam patterns from on-chip size. In this device, holes shifting from the lattice point of a two-dimensional photonic crystal provide spatial phase modulation to light waves, which form standing waves in the resonator. Thus far, the origin of the beam patterns has not been studied, especially the formation of subsidiary beam patterns against the designed beam pattern. In this work, we clarify the origin of beam patterns in two types of spatial phase modulating method, which impose in-plane shifting of holes according to circular and linear shift methods. Based on a theoretical study of spatial phase modulation, we reveal that the circular shift method provides a symmetric beam pattern, while the linear shift method causes an asymmetric beam pattern. Consequently, we demonstrated the asymmetric two-dimensional beam pattern by the linear shift method for the first time.