Mode Analysis and $Q$-Factor Enhancement Due to Mode Coupling in Rectangular Resonators

Modes in rectangular resonators are analyzed and classified according to symmetry properties, and quality factor ( $Q$-factor) enhancement due to mode coupling is observed. In the analysis, mode numbers $p$ and $q$ are used to denote the number of wave nodes in the direction of two orthogonal sides. The even and odd mode numbers correspond to symmetric and antisymmetric field distribution relative to the midlines of sides, respectively. Thus, the modes in a rectangle resonator can be divided into four classes according to the parity of $p$ and $q$. Mode coupling between modes of different classes is forbidden; however, anti-crossing mode coupling between the modes in the same class exists and results in new modes due to the combination of the coupled modes. One of the combined modes has very low power loss and high $Q$-factor based on far-field emission of the analytical field distribution, which agrees well with the numerical results of the finite-difference time-domain (FDTD) simulation. Both the analytical and FDTD results show that the $Q$-factors of the high $Q$-factor combined modes are over one order larger than those of the original modes. Furthermore, the general condition required to achieve high-$Q$ modes in the rectangular resonator is given based on the analytical solution.