“…where n is the average refractive index of BPs, a is the lattice constant of BPs, (hkl) is the Miller indices representing the crystal orientation, and θ is the propagation angle of light in BPs with respect to the normal direction of a Miller plane. Because of the external stimuli-responsivity of BPs, they can be easily switched and tuned by controlling temperature [6,7], by applying an electric field [7][8][9][10][11], and by illuminating light [12,13], making them applicable to various photonic applications such as displays [14], photonic crystal lasers [6,[15][16][17][18], biosensors [19,20], optical filters [21], polarization converters [22], and diffractive optics with the capability of nonmechanical beam steering [23,24]. Despite the technological potential of BPs, several issues have been raised to achieve tailored light-matter interaction for practical applications.…”