Ultrahigh Purcell factors and Lamb shifts in slow-light metamaterial waveguides

Abstract

Employing a medium-dependent quantum optics formalism and a Green function solution of Maxwell's equations, we study the enhanced spontaneous emission factors (Purcell factors) and Lamb shifts from a quantum dot or atom near the surface of a slow-light metamaterial waveguide. Purcell factors of approximately 250 and 100 are found at optical frequencies for p−polarized and s−polarized dipoles respectively placed 28 nm (0.02 λ0) above the slab surface, including a realistic metamaterial loss factor of γ/2π = 2 THz. For smaller loss values, we demonstrate that the slowlight regime of odd metamaterial waveguide propagation modes can be observed and related to distinct resonances in the Purcell factors. Correspondingly, we predict unusually large and rich Lamb shifts of approximately −1 GHz to −6 GHz for a dipole moment of 50 Debye. We also make a direct calculation of the far field emission spectrum which contains direct measurable access to these enhanced Purcell factors and Lamb shifts.

Optical forces between coupled plasmonic nanoparticles near metal surfaces and negative index material waveguides

“…We consider ω = ω SP P = ω LSP and add the first particle at r 1 = r and the second particle at r 2 = (0, 0.05 λ SSP , h). When there are no particles in the system, we can see that the imaginary part of the LDOS (red-dark dashed curve) diverges, which would lead to an infinite LDOS for an excited emitter; although this effect may seem surprising, such a divergence always happens above a lossy structure 20,55 [Eq. (A10)].…”

“…This optical quenching is a result of the intrinsic material loss which, in principle, can be tuned in metamaterial systems. For metals, the quasi-static approximation is also typically used 26,27 for small objects approaching the surface (kh < 1, where k is the wavevector in the background medium containing the object and h is the height above the surface), but for NIMs, such an approximation does not necessarily hold even for kz ∼ 0.03 20 .…”

“…However, slow light modes could, in principle, propagate for much longer distances. Also, the typical scaling laws associated with the quasi-static approximation are not reached, even very close to the slab 20 (because of the strong magnetic resonance). Thus for our study, we are never really in the quasi-static regime above a NIM slab and we must consider retardation effects.…”

“…al. 20 examined the enhancement of the spontaneous emission rate (Purcell Factor 21 ) above a NIM slab which supports a collection of slow-light modes in the region of negative index 18,22 ; related Purcell factor enhancements in NIM waveguides have been found by Xu et al 23 and Li et al 24 . In the slow light region, very large field enhancements can be obtained similar to the enhancements found in plasmonic structures.…”

“…Detailed descriptions of the exact corresponding complex band structure and Purcell effect are given by Yao et al 20 for the same parameters as given above. Here, we briefly point out a few features of interest for this study.…”