Confinement of gigahertz sound and light in Tamm plasmon resonators

We demonstrate theoretically and by pump-probe picosecond acoustics experiments the simultaneous confinement of light and gigahertz sound in Tamm plasmon resonators, formed by depositing a thin layer of Au onto a GaAs/AlGaAs Bragg reflector. The cavity has InGaAs quantum dots (QDs) embedded at the maximum of the confined optical field in the first GaAs layer. The different sound generation and detection mechanisms are theoretically analyzed. It is shown that the Au layer absorption and the resonant excitation of the QDs are the more efficient light-sound transducers for the coupling of near-infrared light with the confined acoustic modes, while the displacement of the interfaces is the main back-action mechanism at these energies. The prospects for the compact realization of optomechanical resonators based on Tamm plasmon cavities are discussed.

Figure 1

(a) Schematic diagram of the planar Tamm plasmon resonator with embedded QDs localized at the maximum of the confined optical field. (b) Amplitude of the electromagnetic field $E$ (red curve) and lattice displacement $u$ (blue curve) for the first confined optical and acoustic phonon modes, respectively. The calculation assumes incidence from the substrate (air side) of amplitude 1 for the acoustic (optical) case. (c) Detail of the electromagnetic field $E$ corresponding to the Tamm optical mode. (d) Strain distribution $(du/dz)$ corresponding to the first (20 GHz, solid) and third (60 GHz, dash-dotted) order acoustic confined modes.

Figure 2

(a) Optical reflectivity as a function of wavelength (incidence of amplitude 1 from the air side) and (b) surface displacement as a function of frequency (incidence of amplitude 1 from the substrate side), for the bare DBR (shaded curves) and the Tamm resonator, that is, the same DBR with the added Au layer (red curves).

Figure 3

Color map corresponding to the optical reflectivity as a function of wavelength for incidence of amplitude 1 from the air side (a), and surface displacement as a function of frequency for incidence of amplitude 1 from the substrate side (b) for varying Au layer thickness of the Tamm resonator. The white arrow in (a) indicates the optical Tamm plasmon mode. Note that the displacement is presented in logarithmic scale.

Figure 4

Amplitude of the numerical Fourier transform of picosecond acoustic traces taken with the laser resonant with the Tamm optical mode at room temperature (top) and 80 K (middle). Black curves are experimental; blue dash-dotted curves are the calculated spectra (see text for details). The bottom panel shows the corresponding dispersion of the folded acoustic phonons of the bare DBR. The top smaller panels show the calculated spatial distribution of the first observed zone edge (confined) and zone center (DBR-like) phonons.

Figure 5

Calculated pump-probe spectra for different generation and detection mechanisms. The left (right) panels correspond to photoelastic (interface displacement) detection processes. Spectra are calculated with finite generation efficiency $(K=1)$ either in the Au layer, InGaAs QDs, or GaAs layers of the DBR (indicated in each panel), and 0 otherwise.