Planar photonic crystal (PPC) cavities with high quality (Q) factors were currently designed by missing or moving air holes. Here, we propose that cutting air holes in PPC into semicircles could be considered as another strategy to realize and optimize cavities, presenting superiorities over cavities with missed or moved air holes in a higher Q factor and a smaller mode volume (Vmode). Examples are demonstrated: (1) in a PPC lattice, cutting two adjacent air holes promises a cavity mode with a Q exceeding 200,500 and an ultrasmall mode volume Vmode < 0.329(λ/2 n)3; (2) in a PPC waveguide, cutting two air holes on opposite sides of the waveguide supports a cavity mode with a Q exceeding 104,600 and a Vmode < 1.22(λ/2 n)3; (3) cutting the two air holes at the edges of an L3-type PPC cavity, the Q factor is optimized from 5500 to 124,700, with an almost constant Vmode. The concept of cutting air holes to introduce defects in PPC also promises the design of PPC also waveguides with an engineered transmission loss and dispersion.
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