The photonic band gap ͑PBG͒ effect and its isotropy of sunflower-type circular photonic crystal ͑CPC͒ are obtained and investigated from the transmission spectra performed by finite-difference time-domain ͑FDTD͒ method. The PBG directional width variation is found to be only 6.7%. A well-confined whispering gallery mode ͑WGM͒ with azimuthal number of 6 is obtained by FDTD simulation from the CPC microcavity formed by seven missing air holes ͑C2͒. Ascribed to the deep and isotropic PBG confinement, the WGM lasing with very-low threshold ͑ϳ0.13 mW͒ and very-high-quality ͑Q͒ factor ͑Ͼ10 000͒ is obtained from well-fabricated CPC C2 microcavity lasers.
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Dodecagonal (12-fold) quasiperiodic photonic crystal (DQPC) microcavity lasers sustaining whispering gallery mode (WGM) are fabricated. Lasing characteristics of DQPC D2 microcavity lasers are obtained and compared with triangular lattice D2 photonic crystal (PC) lasers, and ultralow threshold is obtained. The strong WGM mode dependence on 12 nearest airholes of DQPC D2 microcavity and its fabrication tolerance is investigated and discussed by randomly varying the lattice of two separate regions. This mode dependence also indicates that one can enhance a WGM in different PC microcavities by modifying the cavity boundary to be circular.
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