Full electromagnetic Green's dyadic of spherically symmetric open optical systems and elimination of static modes from the resonant-state expansion

Abstract

A general analytic form of the full 6x6 dyadic Green's function of a spherically symmetric open optical system is presented, with an explicit solution provided for a homogeneous sphere in vacuum. Different spectral representations of the Green's function are derived using the Mittag-Leffler theorem, and their convergence to the exact solution is analyzed, allowing us to select optimal representations. Based on them, more efficient versions of the resonant-state expansion (RSE) are formulated, with a particular focus on the static mode contribution, including versions of the RSE with a complete elimination of static modes. These general versions of the RSE, applicable to non-spherical optical systems, are verified and illustrated on exactly solvable examples of a dielectric sphere in vacuum with perturbations of its size and refractive index, demonstrating the same level of convergence to the exact solution for both transverse electric and transverse magnetic polarizations.

arXiv comment26 pages, 5 figures

References in corpus (17)

• Light interaction with photonic and plasmonic resonances
• Spontaneous decay in the presence of dispersing and absorbing bodies: general theory and application to a spherical cavity
• Rigorous modal analysis of plasmonic nanoresonators
• Brillouin-Wigner perturbation theory in open electromagnetic systems
• Exact mode volume and Purcell factor of open optical systems
• Resonant state expansion applied to three-dimensional open optical systems
• Quasinormal mode solvers for resonators with dispersive materials
• Resonant state expansion applied to two-dimensional open optical systems
• Resonant-state expansion of dispersive open optical systems
• Resonant-state expansion for open optical systems: Generalization to magnetic, chiral, and bi-anisotropic materials
• Riesz-projection-based theory of light-matter interaction in dispersive nanoresonators
• How to calculate the pole expansion of the optical scattering matrix from the resonant states
• Resonant-state expansion of three-dimensional open optical systems: Light scattering
• Resonant-state expansion applied to three-dimensional open optical systems: A complete set of static modes
• Resonant-state expansion of light propagation in non-uniform waveguides
• Resonant-state expansion for planar photonic-crystal structures
• Applying the resonant-state expansion to realistic materials with frequency dispersion

Cited by in corpus (7)

• Normalization, orthogonality and completeness of quasinormal modes of open systems: the case of electromagnetism
• First-order perturbation theory of eigenmodes for systems with interfaces
• Optical resonances in graded index spheres: A resonant-state expansion study and analytic approximations
• Varying the medium surrounding an optical resonator: An efficient and rigorous way to calculate its spectral changes
• Exceptional points in perturbed dielectric spheres: A resonant-state expansion study
• Rigorous theory of coupled resonators
• Extending completeness of the eigenmodes of an open system beyond its boundary, for Green's function and scattering-matrix calculations