Optical cavity mode dynamics and coherent phonon generation in high-$Q$ micropillar resonators

We study the temporal dynamics of photoexcited carriers in distributed Bragg reflector based semiconductor micropillars at room temperature. Their influence on the process of coherent phonon generation and detection is analyzed by means of pump-probe microscopy. The dependence of the measured mechanical signatures on laser-cavity detuning is explained through a model that accounts for the varying light-cavity coupling existent during the ultrashort times that pump and probe pulses dwell within the structure. To do so, we first explain the optical mode dynamics with an electron-hole diffusion model that accounts for the escape of carriers from the probed area, as well as their recombination in the bulk and on the free surfaces. We thus show that the latter is the most influential factor for pillars below $\sim 10\mu \mathrm{m}$, where 3D confinement of the optical and mechanical fields becomes relevant.

Figure 1

Top: Pump-probe microscopy experimental setup. The polarizing beam splitter allows us to separate the reflections corresponding to pump and probe pulses, which are cross-polarized. The reflected probe pulse is guided either to a photodiode (to measure the differential reflectivity) or to a spectrometer (to measure the reflectivity spectrum). Bottom: Outline representing the effect the optical cavity mode has on the reflected probe spectra (left) and how the shifting mode changes the differential reflectivity measurement (right), which is based on the spectral integral of the reflected probe pulse. The reflectivity is minimum when the optical cavity mode is better coupled with the laser and the sample absorbs more. Any phonons present will also modulate the reflectivity [11].

Figure 2

(a) Optical mode spectral position and reflectivity as a function of time (map). The encircled numbers mark the spectral position of the optical mode for 4 characteristic times. (b) Differential reflectivity ($\mathrm{\Delta }R/R_0$) as a function of time. The black encircled numbers mark the same times and spectral positions as in (a). Inset: Pulsed laser spectrum (orange line). The red arrows are guides to the eye showing the spectral path followed by the optical mode between the characteristic times.

Figure 3

Differential reflectivity as a function of time for pillars of different side lengths. The curves with the same color correspond to the same pillar at different detunings. The curves corresponding to different pillars are vertically shifted with respect to the rest for clarity. The gray dashed line marks the characteristic recovery time ${\tau }_e$.

Figure 4

Differential reflectivity oscillations due to the fundamental acoustical cavity mode ($\sim 19$ GHz) for square section pillars of different sizes. Only the trace corresponding to optimum detuning is shown for each pillar. The curves corresponding to different pillars are vertically shifted with respect to the rest for clarity. The gray dashed line marks the characteristic recovery time ${\tau }_e$. The black circles mark the phase shift time $t_{\pi }$, corresponding to a $\pi$ phase change in the oscillations.

Figure 5

Optical mode characteristic recovery time ${\tau }_e$ as a function of the side length L. Measurements (yellow circles) and theory (red dashed line).

Figure 6

Fundamental acoustic cavity mode dependence with laser wavelength for square pillars with side length of $3\mu \mathrm{m}$, $5\mu \mathrm{m}$, $10\mu \mathrm{m}$, and $60\mu \mathrm{m}$. The gray dotted line is a guide to the eye showing the approximate spectral position of the optical cavity mode. The curves were vertically shifted for clarity.

Figure 7

Top: Generation (red) and detection (black) functions as calculated with the proposed model. Bottom: $\sim 19$ GHz acoustical cavity mode relative intensity as a function of optical mode detuning (${\lambda }_0-{\lambda }_{\mathrm{laser}}$) for a $3\mu \mathrm{m}$ square pillar (circles). The red dashed line corresponds to the theoretical calculation, given by the product between the generation (Gen) and detection (Det) functions.

Figure 8

Outline of the fundamentals of the experiment. The pump pulses (top) are blocked intermittently, while the probe pulses (center) are not. Because of this, the optical cavity mode, marked with an asterisk, is in different positions, and the probe pulses reflected from the sample (bottom) present a different spectrum, with a periodicity given by the modulation of the pump pulses. Since during the experiment we integrate during a timescale much longer than the period of the modulation, the measured spectra (bottom, right) are given by the average between the excited and unexcited reflectivity.

Figure 9

The right panel shows the reflectivity spectrum as a function of time during the 200 ps previous to the pump excitation, and the 400 ps posterior to it. The left panel displays the temporal dependence of the real (top) and imaginary (bottom) components of the refractive index, as extracted from the reflectivity spectra.

Figure 10

$5\mu \mathrm{m}$ square section pillar differential reflectivity measurement (black dots) and fit (red dashed line).

Figure 11

Scheme of the distribution of the electron-hole pairs excited by the pump pulse (left), after diffusing for a short time (center), and a long time (right). The drawing is not to scale.

Figure 12

Calculation of the temporal dependence of the optical cavity mode (normalized by the maximum shift) using Eq. (C9) (black thick line) and an exponential decay fit with a characteristic recovery time ${\tau }_e\approx 1.3$ ns (red dotted line).