Mode characteristics for equilateral triangle optical resonators

Mode characteristics of equilateral triangle resonators (ETRs) are analyzed based on the symmetry operation of the point group C_3v. The results show that doubly degenerate eigenstates can be reduced to the A₁ and A₂ representations of C_3v, if the longitudinal mode number is a multiple of 6; otherwise, they form the E irreducible representation of C_3v. And the one-period length for the mode light ray is half of the perimeter of the ETR. Mode Q-factors are calculated by the finite-difference time-domain (FDTD) technique and compared with those calculated from far-field emission based on the analytical near-field pattern for TE and TM modes. The results show that the far-field emission based on the analytical field distribution can be used to estimate the mode Q-factor, especially for TM modes. FDTD numerical results also show that Q-factor of TE modes reaches maximum value as the longitudinal mode number is a multiple of 7. In addition, photoluminescence spectra and measured Q-factors are presented for fabricated ETR with side lengths of 20 and 30 μm, and the mode wavelength intervals are compared with the analytical results.