Fluorescence in nonlocal dissipative periodic structures

We present an approach for the description of fluorescence from optically active materials embedded in layered periodic structures. Based on an exact electromagnetic Green's tensor analysis, we determine the radiative properties of emitters such as the local photonic density of states, Lamb shifts, linewidths, etc. for a finite or infinite sequence of thin alternating plasmonic and dielectric layers. In the effective-medium limit, these systems may exhibit hyperbolic dispersion relations so that the large wave-vector characteristics of all constituents and processes become relevant. These include the finite thickness of the layers, the nonlocal properties of the constituent metals, and local-field corrections associated with an emitter's dielectric environment. In particular, we show that the corresponding effects are nonadditive and lead to considerable modifications of an emitter's luminescence properties.

Figure 1

Within the real-cavity model the emitter is placed in vacuum and a spherical cavity is carved inside the host dielectric material. This is a simple description of realistic situation where the emitter is embedded into the lattice formed by the atoms (molecules) of the host material [14]. The cavity radius is determined by the average distance between the emitter and the nearest atoms (molecules) of the host material.

Figure 2

Sketch of the layered material considered in this work. A central dielectric layer (thickness $D$, white shading) is sandwiched between a finite or infinite number of identical bilayers (total thickness $p=p_1+p_2$) consisting of a plasmonic (thickness $p_2$, red shading) and a dielectric layer (thickness $p_1$, white shading). All dielectric layers are made from the same material [permittivity $\epsilon \left(\omega \right)$]. The plasmonic layers are identical and different material models are considered. For the infinite system, the dashed region delineates the unit cell. See text for further details.

Figure 3

Top row: Lateral wave-vector dependence of the imaginary part of the reflection coefficients for $p$-polarized light for a infinite number of silver/silica bilayers (left panel) and a thin silver layer on top of a silica half space (right panel). The frequency is fixed to $\omega =0.2{\omega }_p$ and the thickness of the silica and silver layers are $p_1=0.2c/{\omega }_p\sim 4.4$ nm and $p_2=0.1c/{\omega }_p\sim 2.2$ nm, respectively (see Fig. 2). Bottom row: Same as the top row but for $s$-polarized light. In each plot, the different curves correspond to different material models for silver: The nonlocal SCIB model based on the Boltzmann equation (blue solid line), the local Drude model (purple dashed line) and the nonlocal hydrodynamic model (red solid line). For comparisons with the case of the periodic structure, also the predictions of the effective-medium approximation (EMA, black dashed line) [2] are depicted.

Figure 4

Spontaneous emission enhancement factor derived from the orthogonal (left) and parallel (right) components of the scattering Green's tensor of an infinite sequence of alternating silver and silica layers. The different curves correspond to different material models for silver: The nonlocal SCIB model based on the Boltzmann equation (blue solid line), the local Drude model (purple dashed line) and the nonlocal hydrodynamic model (red solid line). In order to highlight the impact of the local-field corrections, the same computations have been carried out for the same parameters except for replacing silica by vacuum. The results are displayed in the semitransparent curves. In particular, the incorporation of local-field corrections, which take into account dissipation in silica, leads to a significant broadening of the plasmon resonance. The gray dashed lines indicate the position of the odd bulk plasmon resonance as give in Eq. (60) (${\omega }_{2n+1}^{\mathrm{B}}$). See the text for details regarding the geometric and material parameters.

Figure 5

Bulk plasmon resonances in the orthogonal enhancement of the spontaneous decay of an emitter located in a cavity formed by two thin metallic layers. The position and behavior of these resonances is similar in all configurations considered in this work. The different curves correspond to different material models for silver: The local Drude model (purple dashed line), the nonlocal hydrodynamic model (red solid line) and the SCIB model based on the Boltzmann equation (blue solid line). See the text for details regarding the geometric and material parameters. In order to highlight the impact of the local-field corrections, the same computations have been carried out for the same parameters except for replacing silica by vacuum. The results are depicted in the semitransparent curves.

Figure 6

Geometric frequency shift for an emitter in a silica nanocavity sandwiched between infinite sequences of alternating silver and silica layers. The parameters and the models are the same as those used for describing the spontaneous decay (see main text). The values are normalized to $U_0=-\hslash {\omega }_p({\alpha }_g{\omega }_p^3/c^3){\left(2\pi {\epsilon }_0\right)}^{-1}$ and depicted as a functions of the emitter's transition frequency. The different curves correspond to different material models for silver: The local Drude model (purple dashed line), the nonlocal hydrodynamic model (red solid line) and the SCIB model based on the Boltzmann equation (blue solid line). See the text for details regarding the geometric and material parameters. In order to highlight the impact of the local-field corrections, the same computations have been carried out for the same parameters except for replacing silica by vacuum. The results are depicted in the semitransparent curves. The local-field corrections significantly reduce the magnitude of these geometry-induced shifts relative to vacuum.

Figure 7

Spontaneous emission enhancement factor derived from the orthogonal (left) and parallel (right) components of the scattering Green's tensor of composite slab structure consisting of a central silica layer sandwiched between two silver layers and completely embedded in silica. The emitter is located in the center of central silica layer. The different curves correspond to different material models for silver: The nonlocal SCIB model based on the Boltzmann equation (blue solid line), the local Drude model (purple dashed line) and the nonlocal hydrodynamic model (purple solid line). In order to highlight the impact of the local-field corrections, the same computations have been carried out for the same parameters except for replacing silica by vacuum. The results are displayed in the semitransparent curves. In particular, the incorporation of local-field corrections, which take into account dissipation in silica, leads to a significant broadening of the plasmon resonance. The gray dashed lines indicate the position of the odd bulk plasmon resonance as given in Eq. (60) (${\omega }_{2n+1}^{\mathrm{B}}$). See text for details regarding the geometric and material parameters.