Study on the similarity of photonic crystal ring resonator cavity modes and whispering-gallery-like modes in order to design more efficient optical power dividers

In this study, we discuss the wave pattern characteristics of confined cavity modes inside photonic crystal ring resonators (PCRRs). Despite different physical origins, these cavity modes are analogous to the whispering-gallery (WG-like) modes. Because of the absence of perfectly circular symmetry in our PC cavity, the WG-like modes are not degenerate, but they form a close doublet in which the field pattern of each of these doublets repeats itself by \(180^{\circ }/m\) where “m” is the azimuthal index number of WG-like modes. The cavity modes are named according to their symmetric field pattern, and WG-like ones are named by their azimuthal mode numbers “m.” Based on the study of these similarities, we propose a \(1\times 2\) and a \(1\times 4\) T-junction- like power dividers. Through study of the similar properties of these cavity modes with WG-like modes, we have enhanced the output power of both dividers to 49.6 and 24.5 %, respectively. The permittivity of the hexagonal photonic crystal rod is \(\varepsilon _{h}= 12.04\) surrounded by air as the background medium. For our PCRR, the dominant resonating mode is the cavity mode with hexapole field pattern or equivalently WG-like mode with azimuthal mode number of \(m\,=\,6\). The normalized frequencies for this mode and its doublet are \(a/\lambda = 0.348066\) and 0.348301, respectively. The photonic band structure, PC waveguide guided mode and electric field patterns of the confined cavity modes inside the PCRR are calculated using the PWE method, and the transmission spectra are calculated by means of 2D-FDTD simulation method.