Superemitters in hybrid photonic systems: A simple lumping rule for the local density of optical states and its breakdown at the unitary limit

We theoretically investigate how the enhancement of the radiative decay rate of a spontaneous emitter provided by coupling to an optical antenna is modified when this “superemitter” is introduced into a complex photonic environment that provides an enhanced local density of optical states (LDOS) itself, such as a microcavity or stratified medium. We show that photonic environments with increased LDOS further boost the performance of antennas that scatter weakly, for which a simple multiplicative LDOS lumping rule holds. In contrast, enhancements provided by antennas close to the unitary limit, i.e., close to the limit of maximally possible scattering strength, are strongly reduced by an enhanced LDOS of the environment. Thus, we identify multiple scattering in hybrid photonic systems as a powerful mechanism for LDOS engineering.

Figure 1

(a) Left: Sketch of a superemitter formed by two silver spheres. The fluorescent source is located between the two particles with its dipole moment along the symmetry axis. Right: Hybrid photonic system composed of a superemitter embedded in a background system formed by a dielectric sphere. Red and blue colors illustrate fields of a whispering-gallery mode. (b) Dashed line: polarizability of a single antenna particle in vacuum. Solid line: antenna enhancement factor for the superemitter sketched in (a) in vacuum. (c) Dashed line: Extinction efficiency of a dielectric sphere showing narrow Mie resonances. Solid line: Purcell factor of the Mie sphere 50 nm from its surface.

Figure 2

(a) Solid line (hybrid system): Decay rate of the source in the gap of the superemitter next to the Mie sphere normalized to the rate of the source in vacuum. Dashed line (superemitter in vacuum): Decay rate of the source in the gap of the superemitter in vacuum normalized to the rate of the source in vacuum. At the Mie resonances, the hybrid LDOS is drastically modified compared to that of the antenna in vacuum. (b) Solid line (hybrid system): Decay rate enhancement in hybrid system [solid line in (a)], normalized to the rate enhancement in the superemitter in vacuum [dashed line in (a)]. Off antenna resonance, the superemitter benefits from the LDOS enhancement offered by the sphere (dashed line), while on antenna resonance the enhancement is suppressed by the inverse of the sphere's LDOS (dotted line).

Figure 3

(a) Real (solid) and imaginary (dashed) parts of the radial component of the Green function of the Mie sphere 50 nm from sphere's surface. These terms enter the radiation correction to ${\mathit{\alpha }}_{\mathrm{Mie}}$. (b) Solid line: Radial component of the antenna polarizability ${\mathit{\alpha }}_{\mathrm{Mie}}$ when located 50 nm from the Mie sphere. Dash dotted line: ${\mathit{\alpha }}_{\mathrm{vac}}$ for the same antenna in vacuum. While ${\mathit{\alpha }}_{\mathrm{vac}}$ is limited by the inverse vacuum LDOS (dashed line), ${\mathit{\alpha }}_{\mathrm{Mie}}$ is bounded by the inverse of the sphere's LDOS (dotted line), which leads to the suppression of ${\mathit{\alpha }}_{\mathrm{Mie}}$ close to the antenna resonance.

Figure 4

Relative LDOS enhancement for the superemitter as a function of distance to a near-perfect mirror. (a) Superemitter oriented parallel to the mirror surface (see inset). Solid line: A superemitter with source far below antenna resonance [$\omega =4.0\times {10}^{15}{\text{s}}^{-1}$, cf. Fig. 1b] traces the LDOS of the mirror (dashed line), except at small superemitter-mirror separations. A source close to antenna resonance (long dashed line, $\omega =4.5\times {10}^{15}{\text{s}}^{-1}$) traces the inverse of the mirror LDOS (dotted line), except at small separations. (b) Same as (a) for the superemitter perpendicular to the mirror (see inset).