Time-resolved dynamics of GaN waveguide polaritons

Abstract

We implement a new experimental approach to directly measure the lifetime of guided polaritons arising from the strong-coupling of GaN excitons and the guided photonic modes of a slab waveguide. Using a Fourier imaging setup, combined with spatial filtering of the emission, the emission associated to polaritonic modes with well-defined propagation constants can be selectively analyzed in the temporal domain. By directing it to the entrance slit of a streak camera, time-resolved photoluminescence (TRPL) measurements along the polariton dispersion branch were performed at 40 K, enabling to assess the time decay of polariton modes. By combining this information with the photonic/excitonic fraction corresponding to each polariton mode, extracted from a coupled-oscillators model that indicate a Rabi splitting of $Ω$ = 80 meV, we could extract the photon lifetime in the waveguide $τ_γ\, =\, 3\pm 1$ ps. This corresponds to a record $Q$-factor in the UV of 16 000. The excitonic reservoir lifetime, which contributes to polariton formation, was determined through TRPL measurements on excitonic luminescence. Finally, measurements conducted at lower temperature highlight secondary feeding mechanisms for the guided polaritonic mode, either via photon recycling from the AlGaN cladding layer or through resonant injection of photons from transitions below the band gap.

Figures (8)

• Figure 1: (a) Schematic representation of the studied sample. Blue regions correspond to GaN layers (150 nm and 3.5 µm). Purple region represents AlGaN lower cladding (1.5 µm) and black region displays the sapphire substrate (thicknesses are not at scale). The excitation laser beam and a grating are also representated. Two guided modes with different in-plane wavevectors are extracted by the grating with different emission angle to illustrate the Bragg's diffraction law (eq.\ref{['eq:Bragglaw']}). (b) Scanning electron microscope (SEM) image showing the gratings elaborated by electron beam lithography on top of the structure. (c) Scanning electron microscope (SEM) image showing grating lines, the good periodicity prevents the detection of ghost lines in angle-resolved photoluminescence measurements.
• Figure 2: Left panel: Measurement of the polariton dispersion curve under the excitation spot without spatial filtering (S.F.). Right panel: Measurement of the dispersion curve after shifting the excitation spot above the extraction grating and using a pinhole to apply spatial filtering, analyzing only a 20 µm-diameter region at the center of the extraction grating. In this configuration, only one propagation direction of the polaritons is collected, and nearly all of the sample's direct luminescence is filtered out, as illustrated by the inset white graph. This graph displays the integrated intensity over both images within a wavelength range of 358.0 ± 0.2 nm.
• Figure 3: Left panel: experimental measurement of the lower polariton branch (LPB) for a temperature of T = 40.9 K and a laser excitation power of 10 mW at 349 nm (the color scale corresponds to a logarithmic intensity scale). The solid white line represents the theoretical calculation of the polaritonic dispersion using a quasiparticle model. The dashed white lines correspond to the dispersion of the photonic mode propagating in the waveguide ($\mathrm{TE_0}$) and the excitonic resonance in the material at 3.4948 eV. The second mode observable above 3.46 eV, displaying a lower effective mass, corresponds to the $\mathrm{TM_0}$ mode strongly-coupled to GaN C exciton, as confirmed by polarization-resolved dispersion measurements. Right panel: temporal decay of polaritonic states (a), (b), (c), and (d) highlighted in the left panel. The gray squares represent the experimental data, and the colored lines correspond to fits of the decays using equation \ref{['eq4']}.
• Figure 4: Top panel: time-resolved photoluminescence (TRPL) measurement as a function of excitation power for the free exciton transition X (colored squares) and the neutral donor bound exciton transition $\mathrm{D^\circ X}$ (colored circles). The black lines correspond to the fitting of these decays using a biexponential model for the three lowest excitation powers (from 100 µW to 1 mW) and a monoexponential model for the higher excitation powers (5 mW and 10 mW). Bottom panel: decay times obtained by fitting the experimental decays for the free exciton (red square) and bound exciton (black circle). Only the shortest decay time is shown, as it corresponds to the excitonic population in the thin surface GaN layer. The baseline of each spectrum is shifted vertically for clarity.
• Figure 5: The red circles correspond to the polariton lifetimes experimentally determined as a function of the energy of the studied polariton state. The blue, green, and red regions correspond to the theoretical calculation of the polariton lifetime using equation \ref{['eqtpol']} and varying the photon lifetime between 2.0 ps and 4.0 ps, the Rabi splitting between 60 and 80 meV, and the excitonic reservoir decay time between 100 and 160 ps, respectively. The yellow dashed line corresponds to the polariton lifetime adjusted to the experimental results, which allows determining the following parameters: $\Omega$ = 80 meV, $\tau_X$ = 130 ps, $\tau_\gamma$ = 2.8 ps.