Lamb shift multipolar analysis

Abstract

International audienc

Interplay between spontaneous decay rates and Lamb shifts in open photonic systems

“…In contrast, for dissipative systems characterized by Im(V α ) = 0 [5], Eqs. (8) and (9) reveal an interplay between the "Hermitian" decay rates γ H α and Lamb shifts ∆ω H α . This constitutes our first result.…”

“…As an example, let us apply Eqs. (8) and (9) to two situations of a QE coupled to an open photonic system: (i) dielectric silicon (Si) nanosphere with no absorption (and no dispersion) and (ii) plasmonic silver (Ag) nanosphere with absorption (and dispersion) (see insets in Fig. 1 (ac)).…”

“…Therefore, for spherical resonators the sums over α in Eqs. (8) and (9) become: α → q,n,m,l . Moreover, for a given set of {q, n, l}, the QNMs with a different number m are degenerate (i.e.…”

“…Moreover, for a given set of {q, n, l}, the QNMs with a different number m are degenerate (i.e. have the same complex frequency ω q,n,m,l ), and the sum can be recast in the form q,n,l with "effective" mode volumes defined as 1/V q,n,l ≡ m 1/V q,n,m,l (see Appendix E in [6] and also [8]).…”

“…(6), and appearing in the QNM formulas Eqs. (8) and (9), are computed using the analytical expressions of the QNM fields E α derived for a spherical resonator shape in [14] for non-dispersive materials (i.e. with a constant permittivity) and in [6] for dispersive materials (i.e.…”