Resonant frequencies and quality factors for optical equilateral triangle resonators calculated by FDTD technique and the Pade approximation

The mode wavelength and quality factor (Q-factor) for resonant modes in optical equilateral triangle resonators (ETR´s) are calculated by the finite-difference time-domain (FDTD) technique and the Pade approximation. For an ETR with the side length of 3 μm and the refractive index of 3.2, we get the mode wavelength interval of about 70 nm and the Q-factor of the fundamental mode over 10³. The results show that the ETR is suitable to realize single-mode operation, and that the radiation loss in the corner regions of ETR is rather low. In addition, the numerical results of the mode wavelength agree very well with our analytical formula.