Fig. 1. 3-D configuration of a double confocal waveguide

Fig. 2. The diagram of the modes in a double confocal waveguide （a） Superposition mode; （b） Ring mode

Fig. 3. Confocal waveguide with spherical reflectors

Fig. 4. The magnitude of electric field of the superposition modes in a double confocal waveguide （a）, （b）, （c） and （d） are the results simulated by commercial CST software; （e）, （f）, （g） and （h） are the theoretical results.

Fig. 5. Normalized beam-wave coupling coefficient versus R_b.

Fig. 6. Coordinate systems for the ring mode

Fig. 7. The magnitude of the electric field of the ring mode,（a） and （b） are the results from the commercial CST software; （c） and （d） are the theoretical results.

Fig. 8. Dispersion curve.（a） Dispersion curve in a cylindrical waveguide. （b） Dispersion curve in a single confocal waveguide. （c） Dispersion curve in a double confocal waveguide.

Fig. 9. Variation of diffraction losses of the anti-phase superposition mode TE₀₆ mode with the aperture size.