Spontaneous emission dynamics in an omnidirectional waveguide made of photoniccrystals

Abstract

The spontaneous emission dynamics of atoms embedded in an omnidirectional waveguide(ODWG), a novel optical waveguide, is studied on the basis of the complete reflectionof one-dimensional photonic crystals. With the dispersion curve of the singlewaveguide mode within the photonic band gap and various extents of backgrounddissipation, we characterize the photon–atom interaction in the ODWG. Thephoton emitter of the system is a two-level atom embedded in the low-indexmedium of the multilayer-film ODWG or the atom–ODWG system. Fractionalcalculus, an innovative mathematical method in optical systems, is applied to solvethe equation of motion for this atom–ODWG system. Two kinds of states withdifferent group velocities exhibit totally distinctive dynamical behavior. The highfrequency waveguide mode with a fast group velocity shows fast exponential decayin propagation while the band-edge mode with a slow group velocity displaysnon-Markovian dynamics with non-exponential oscillating time evolution. We thereforesuggest different functions of this atom–ODWG system for these two kinds ofstates. The richness of the physical content of the system is also revealed throughinvestigating the dynamical behavior of the band-edge mode. These results aid infurther application and fundamental understanding of the atom–ODWG system.