Fig. 3: Calculated radiation constants for dually modulated photonic crystals by a three-dimensional coupled wave theory.

a Radiation constants of band-edges A–D with respect to the amplitude of position modulation \(|{\mathrm{\Delta }}{\mathbf{d}}|\), where the amplitude of size modulation \({\mathrm{\Delta }}S\) is fixed to \(0.03a^2\). b Radiation constants with respect to the amplitude of size modulation \({\mathrm{\Delta }}S\), where the amplitude of position modulation \(|{\mathrm{\Delta }}{\mathbf{d}}|\) is fixed to 0.08a. Throughout these calculations, the polar emission angle \(\theta\) and azimuthal emission angle \(\phi\) are fixed to \(36^\circ\) and \(0^ \circ /180^ \circ\), respectively.