Reformulation of the Fourier–Bessel steady state mode solver

• Reformulation of the Fourier–Bessel mode solver using Ampere's and Faraday's law..
• Simpler and fewer expressions required for system matrix building.
• Converged results generally achieved using fewer terms in expansion basis series.
• Mode family symmetry facilitates system matrix order reduction.
• Two forms of the system matrix are provided with advantages and disadvantages to each indicated.
• Two application examples are presented, one for a dielectric SNAP resonator with material variations in the permittivity only, the other for a quasi-crystal containing variations in both permittivity and permeability.
• The simplified nature of the reformulated Fourier–Bessel numerical solver makes it attractive to all researchers with a moderately performant desktop PC.

The Fourier–Bessel resonator state mode solver is reformulated using Maxwell's field coupled curl equations. The matrix generating expressions are greatly simplified as well as a reduction in the number of pre-computed tables making the technique simpler to implement on a desktop computer. The reformulation maintains the theoretical equivalence of the permittivity and permeability and as such structures containing both electric and magnetic properties can be examined. Computation examples are presented for a surface nanoscale axial photonic resonator and hybrid {ε,μ}{ε,μ} quasi-crystal resonator.