The authors propose a new cross-energy scalar product to normalize and compare resonant (quasi-normal) modes of optical resonators using their radiation fields. This method avoids the complications of divergent modal fields outside the resonator. The theory is applied to whispering gallery modes in a disk resonator, where JCMsuite's finite element method solver was used to compute the complex eigenfrequencies and spatial field profiles of the resonant modes, which are essential for evaluating the proposed scalar product.
M. Paszkiewicz-Idzik, et al. Scalar product for the radiation of resonant modes. Phys. Rev. A 112, 013518 (2025).
DOI: 10.1103/1rhp-ts2q