1. INTRODUCTION

Brillouin scattering [1,2], the inelastic interaction of light with acoustic phonons, has been exploited successfully for a large number of applications [3–8]. These range from novel approaches for all-optical data storage based on long-lived acoustic modes [3], to the tailored generation of optical frequency combs in periodically patterned semiconductor waveguides [4], and narrowband Brillouin lasers in fibers [5] and semiconductors [6]. These applications require intense optical fields to enter the regime of stimulated Brillouin scattering and a good mode overlap between the optical and acoustic fields for the scattering process to be efficient. Therefore, many realizations of Brillouin scattering generators rely on optical fibers [9–11] or photonic waveguides [6,12,13] providing lateral confinement on a micrometer scale over a large interaction length in a centimeter range. Much effort has been devoted to the generation or mitigation of tailored Brillouin spectra in these devices, either by introducing periodic patterns along the fiber using, for instance, the concept of distributed Bragg reflectors (DBRs) [14–16], or through specialized cross sections in photonic crystal fibers [17,18] and suspended waveguides [12]. With these approaches, effective control over acoustic phonons can be achieved up to a few tens of GHz, a limit imposed by the minimum achievable feature size, which needs to be on the length scale of the phonon wavelength. In addition, these approaches to engineering the phonon spectrum have to take into account the simultaneous modifications introduced to the optical dispersion relation of the waveguides [12]; this imposes some constraints on their versatility.

A very different class of devices that are employed for the generation and enhancement of Raman and Brillouin signals are resonant microstructures such as silica microspheres [19] or planar Fabry–Perot semiconductor microcavities [20–23] grown by molecular-beam epitaxy. In contrast to single-pass fibers and waveguides, a larger effective interaction length is achieved in resonant microcavities of equal geometric extent through the $Q$-factor of the optical cavity. More importantly, semiconductor planar microcavities have been used to embed ultra-high-frequency multilayer nanophononic resonators confining acoustic phonon modes in the 100 GHz–1 THz range [20,24–28]. This approach allows independent design of the acoustic and optical densities of states. The acoustic multilayer only acts as an effective medium for the optical fields. However, these structures are, by definition, extended in the lateral dimension.

Here, we transfer the concept of nested, independently tunable optophononic resonators to three-dimensional semiconductor micropillars [22,23,29–32]. We thus combine the advantages of resonant cavities and transversal optical field confinement in a fiber, yet with minimum vertical feature sizes well below 10 nm. We develop an optical free-space technique to characterize spontaneous Brillouin scattering in such a monolithic device hosting a nanophononic interface mode at 320 GHz. We furthermore demonstrate a measurement protocol that allows us to maximize the Brillouin generation efficiency in the presence of optically induced thermal effects. The compact and versatile optophononic micropillar resonators could be integrated with existing fibered and on-chip architectures, opening a wide range of future applications. The high phonon frequency range explored in this work might even allow preparing our devices in the acoustic quantum mechanical ground state of motion at liquid-helium temperatures. This might substantially increase their usefulness for applications such as the manipulation of the quantum states of light and of mechanical motion through optomechanical interactions.

2. BRILLOUIN SPECTROSCOPY ON MICROPILLARS

The sample under study is grown on a (001)-oriented GaAs substrate by molecular-beam epitaxy. It consists of an optical microcavity with two DBRs enclosing a resonant spacer with an optical path length of $2.5\lambda$ at a resonance wavelength of around $\lambda =890\mathrm{nm}$. The top (bottom) optical DBR is formed by 14 (18) periods of Ga_0.9Al_0.1As/Ga_0.05Al_0.95As bilayers optimized to confine an optical mode with typical $Q$-factors of 2000. The optical spacer of the cavity is composed of two concatenated acoustic superlattices (SLs) with the top (bottom) acoustic SL formed by 16 periods of 7.3 nm/9.8 nm (8.5 nm/8.2 nm) GaAs/AlAs layers. This acoustic structure is designed to confine acoustic phonons at 300 GHz at the interface between the two SLs based on their different topological properties [26,33–35]. From this nested planar optophononic cavity, 30 μm pitched arrays of square and circular micropillars with various lateral sizes are fabricated by optical lithography and inductively coupled plasma etching. Scanning electron microscope (SEM) images of an array of micropillar resonators and a zoomed-in view of a single square micropillar with a lateral extent of 4.5 μm are shown in Figs. 1(a) and 1(b), respectively. We numerically calculate the electric field distribution of the fundamental optical mode in a circular micropillar resonator through the finite-element method (FEM) as shown in Fig. 1(c). In the optical domain, the high-frequency acoustic resonator behaves as an effectively homogeneous medium with optical properties modulated on a deep sub-wavelength scale. The micropillar thus behaves as a three-dimensional resonator with wavelength-scale optical confinement in all three dimensions of space, resulting in a discrete spectrum of optical modes. In the vertical direction, the resonant cavity confinement leads to an exponentially decaying envelope of the optical mode in both DBRs. In the radial direction, the refractive index contrast between the semiconductor materials and vacuum leads to an additional in-plane confinement of the mode with a Bessel-type envelope [23,29,36] much like for an optical fiber.

 

Fig. 1. SEM images of (a) an array of circular and square micropillar resonators, and (b) a single square micropillar with a lateral extent of 4.5 μm. The top layer is SiN deposited as part of dry etching. (c) FEM simulation of the fundamental optical mode in a circular micropillar, showing the absolute value of the electric field. The resonant optical spacer is composed of two nanoacoustic SLs. (d) Setup in reflection geometry: the reflected optical signal comprises a pronounced pattern of diffracted laser light (red) and the Brillouin beam (blue) with a Gaussian spatial pattern dictated by the optical micropillar modes. A spatial filter optimizes the relative collection ratio of the Brillouin signal. (f) Experimental reflectivity spectrum of a micropillar with a Lorentzian resonance dip at 902 nm. (e) Corresponding experimental diffraction patterns as a function of wavelength. The pattern changes markedly at the resonance wavelength. The blue circle indicates the position and size of the spatial filter applied for Brillouin spectroscopy.

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To probe the Brillouin spectrum of individual micropillars, we use a backscattering geometry as sketched in Fig. 1(d). An incident laser beam (mode-hop-free cw Ti:Sa laser, M2 SolsTiS) resonant with the fundamental optical micropillar mode is focused to a spot of roughly 10 μm size (FWHM) on the sample surface and centered on a pillar. Excitation and collection are realized through the same optical elements under normal incidence. The main obstacle in Brillouin scattering measurements on wavelength-scale objects is stray-light rejection. Usually, there is a compromise between the minimum size of the studied object (source of stray light) and the minimum Brillouin frequency that can be accessed stray-light-free. We overcome this experimental challenge by actively using the spatial mode mismatch between the incoming laser beam and the optical micropillar modes as a signal filtering method, as sketched in Fig. 1(d). Three contributions emerge from the sample: the reflection of the excitation laser from the substrate surface, the reflection of laser light from the micropillar, and the Brillouin signal. In contrast to the other two, the Brillouin signal originates solely from the fraction of laser light coupled into the micropillar and interacting with the nanoacoustic structure constituting the resonant optical spacer. It hence emerges from the micropillar through its optical modes, with a spatial pattern approximated by a Gaussian beam (blue). In a plane behind the collection lens, the directly reflected contributions lead to the formation of a pronounced diffraction pattern. Here, we exploit the different spatial patterns of the micropillar mode and the scattered contributions upon laser excitation for signal filtering by inserting a spatial filter behind the collection lens, exclusively transmitting in a node of the diffraction pattern where the contribution emerging from the cavity dominates. In Fig. 1(f), we show an optical reflectivity curve of a micropillar. Around 902 nm, a Lorentzian dip in reflectivity is observed, showing the presence of the optical micropillar mode with a quality factor of $Q\sim 1500$. In Fig. 1(e), we show corresponding laser diffraction patterns recorded with a camera placed in the same plane, in which a spatial filter was applied for Brillouin spectroscopy. The position and size of the filter are marked with a blue circle. We observe that the diffraction pattern changes substantially with wavelength when crossing the optical resonance of 1 nm width (901.5–902.5 nm). In contrast, the pattern hardly changes outside the resonance, i.e., for the wavelength intervals of 899–901 nm and 903–905 nm. This difference highlights that the diffraction pattern originates from an interference between a component directly reflected by the sample substrate and another component that has interacted with the micropillar. Across the optical resonance, this second contribution undergoes a phase shift of $\pi$. Therefore, the radial positions of the interference maxima and minima are inverted in the pattern exactly on resonance. Figure 2(a) presents the Brillouin signal obtained using the spatial filtering method described above, recorded on a 4.5 μm square micropillar. It exhibits three pronounced peaks at acoustic frequencies of around 280, 320, and 360 GHz, labeled A, B, and C, respectively.

 

Fig. 2. (a) Anti-Stokes Brillouin spectrum measured on the micropillar resonator shown in Fig. 1(b). The spectrum exhibits three pronounced peaks (A–C). (b) Brillouin spectrum measured on a planar resonator with an identical vertical structure (solid black curve). A photoelastic model calculation (dashed red curve) well accounts for the three-peaked structure of the spectrum. (c) Simulated phonon modes corresponding to the three main peaks in panels (a) and (b). The absolute value of the mechanical displacement $u(z)$ is displayed.

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Here, we note that acoustic characterization of semiconductor micropillars working at 20 GHz has been performed previously by means of impulsive coherent phonon generation and detection [22,37]. Although a powerful characterization tool, it is, however, not applicable for the investigation of spontaneous Brillouin scattering. With standard Brillouin or Raman scattering techniques, the frequency range explored in this work is usually inaccessible in micro-objects due to insufficient stray-light rejection. Also, standard radio frequency noise spectroscopy often used with optomechanical microresonators, is usually limited to a few GHz. The present observations thus represent the first Brillouin scattering measurement on a micrometer-size acoustic resonator in the frequency range of 100 GHz.

To understand the origin and nature of the observed peaks, Brillouin spectra are also measured on the planar microcavity, not etched into pillar shapes. In this case, perfect spatial filtering of the reflected light can be achieved by simply blocking the reflected beam in the collection path (see Supplement 1). By furthermore taking advantage of the angular dispersion of the planar microcavity, a simultaneous incoming–outgoing optical resonance condition can be established [24,26,38]. A Brillouin spectrum of the planar cavity is shown in Fig. 2(b), which shows very similar peaks as the micropillar. In the case of a planar structure, the corresponding high-frequency acoustic modes can be modeled by means of transfer-matrix calculations [39]. The calculation results shown in Fig. 2(c) confirm that the strongest, central, peak in the Brillouin spectrum is caused by the topological phononic interface state that presents the largest overlap with the optical cavity mode. In contrast, the two other peaks correspond to propagating modes extending over the full acoustic structure. These latter modes are a general feature of Brillouin scattering of periodic SLs [40,41]. All experiments reported here were performed in a backscattering configuration, labeled $z(x,x)\overline{z}$ in conventional Brillouin/Raman notation [42]. In this configuration, Brillouin active modes comply with the condition $k_p=2k_l$, whereas for forward scattering, labeled $z(x,x)z$, the active modes fulfill the condition $k_p=0$. Here, $k_p$ is the (quasi-) momentum of the phonon and $k_l$ is the momentum of the laser. Since we are studying an optical cavity here, both types of modes are optically accessible in a backscattering configuration. For both types of modes, the polarization of the incident laser is preserved (see Supplement 1). Note that for the band structure of an acoustic SL, the condition $k_p=2k_l$ is fulfilled in each band folded back into the first Brillouin zone. The modes A and C are the backscattering modes associated with the second and third acoustic bands of SL1 and SL2, respectively. The backscattering peak from the lowest acoustic band occurs at a frequency of 30–40 GHz, which is, however, too close to the laser line to be resolved in our experiments (see Supplement 1). To fully account for the shape and relative composition of the observed Brillouin spectrum, we furthermore perform calculations for the anti-Stokes Brillouin scattering cross section based on a 1D photoelastic model [dashed red curve in Fig. 2(b); see Supplement 1] [41]. Note that at room temperature, the fundamental electronic transition in GaAs is at 1.52 eV, such that the experiments are performed under nearly resonant conditions. The Brillouin spectrum is thus dominated by the photoelastic contributions from the GaAs layers. The results of the calculation shown in Fig. 2(b) reproduce well the measured Brillouin spectrum. The larger peak width in the experimental spectra is a consequence of the finite spectral resolution of approximately 13 GHz in our setup [26].

The close similarity between the Brillouin spectra of the micropillar and the planar cavity is a direct consequence of the high acoustic resonance frequencies of around 300 GHz explored here. These frequencies correspond to acoustic wavelengths of around 10 nm, which are roughly one order of magnitude smaller than the optical wavelengths involved in the Brillouin scattering process. In the acoustic domain, the micropillar therefore confines longitudinal acoustic phonons to a wavelength-scale dimension along the vertical direction. However, since the characteristic wavelength of the confined mechanical mode is much smaller than the lateral size of the micropillar, the system effectively behaves as an infinitely extended planar acoustic structure in the lateral direction. We have observed systematically that the intensity of the signals collected from the micropillars is similar to the intensity of the ones collected from the planar microcavities, and are, thus, typical of spontaneous Brillouin scattering in semiconductor cavities. The collected signal can be further optimized by shaping the spatial filter to match the ring pattern.

3. OPTIMIZING BRILLOUIN SCATTERING IN THE PRESENCE OF THERMAL EFFECTS

Although the Brillouin spectra in the planar and micropillar resonators studied here are spectrally very similar, striking differences are observed in their dependence on laser power. We recorded optical reflectivity spectra as a function of power for the micropillar resonator shown in Fig. 1. The results for laser powers between 1 and 34 mW incident on the focusing lens are displayed in Fig. 3(a). For 1 mW, we find a symmetric reflectivity dip centered at 892.3 nm with a minimum of 65% in normalized reflectivity and a $Q$-factor of 2000. The contrast is mainly limited by the mode mismatch between the excitation laser and the fundamental micropillar mode [43] (see Fig. 1). With increasing laser power, the reflectivity minimum shifts to larger wavelengths, reaching a maximum shift of $\mathrm{\Delta }{\lambda }_{\mathrm{res}}=0.4\mathrm{nm}$ [see Fig. 3(c)]. Furthermore, the shape of the reflectivity becomes asymmetric, with a steeper slope at the long-wavelength end. Note that in all the curves, the laser was scanned from a short to a long wavelength. For comparison, we performed an equivalent experiment on the planar, not etched, portion of the microcavity [gray crosses in Fig. 3(c)]. Here, the power-dependent shift in resonance wavelength is almost absent. These observations are attributed to power-dependent thermal effects in micropillars. Indeed, working relatively close to the band edge in GaAs at room temperature, heating and subsequent modification of the electronic band structures of the materials are expected with increasing excitation power. Whereas in the case of a planar microcavity heat can be dissipated rapidly through both the substrate and in the lateral direction, the finite lateral size of a micropillar implies a limited conduction of heat toward the substrate, and a much more pronounced light-induced rise in temperature.

 

Fig. 3. (a) Optical reflectivity of the micropillar resonator shown in Fig. 1, recorded at laser powers of 1, 9, 18, 27, and 34 mW. With increasing laser power, absorption-induced heating leads to a systematic red shift of the optical resonance. (c) For an excitation wavelength of 892.7 nm [dashed line in panel (a)], an overall power-dependent red shift of 0.4 nm is found. On a planar cavity with the same vertical structure, a shift of only 0.05 nm is found under equal excitation conditions (gray crosses). (b) Simulated reflectivity spectra based on a self-consistent one-oscillator model [30]. (d) Simulated power dependence of cavity resonance extracted from the modeling results in panel (b).

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With increasing temperature, the refractive indices of GaAs and AlAs rise [44], resulting in an increase of the optical path length through the cavity and, hence, an effective red shift of the resonance wavelength. For each power and wavelength, the system acquires a stationary equilibrium in which the absorbed optical power and the dissipated heat flow into the substrate are of equal magnitude. We describe this self-consistent problem in terms of a Lorentzian resonator with power-dependent resonance energy [30] based on the parameters deduced from the experimental reflectivity curves in Figs. 3(a) and 3(c). The calculation results are displayed in Figs. 3(b) and 3(d). We observe that a simple one-resonator model can consistently reproduce both the shapes of the reflectivity spectra and the power-dependent resonance shifts.

These drastic changes in the properties of the optical device due to laser-induced heating will affect its operation as a Brillouin generator. Indeed, the Brillouin scattering cross section strongly depends on the coupling between the excitation laser and the optical cavity mode. Building upon the results presented in Fig. 3, we measure the power-dependent Brillouin spectra for both the micropillar resonator and a planar microcavity with an identical vertical structure. For the micropillar, we tune the laser to 892.7 nm (dashed vertical lines in Fig. 3)—that is, the wavelength is chosen such that the excitation is off-resonant at low power, but becomes on-resonant at high power through optical heating. The quantity plotted in Fig. 4(a) is the integrated area under the central Brillouin peak (see upper inset) normalized to the incident laser power. We furthermore set the area measured at a power of 1 mW to unity. Therefore, a linear power dependence of the spontaneous Brillouin signal is represented by a constant value of unity. However, for the micropillar (black circles), we observe an increase in Brillouin efficiency by a factor of 25. For comparison, we perform an equivalent measurement on a planar cavity (gray crosses) resulting in an almost power-independent normalized Brillouin efficiency around unity. These observations arise from the absorption-induced temperature changes discussed above and the related red shift of the optical micropillar resonance. We perform corresponding photoelastic model calculations using the experimentally determined power-dependent shift in the optical resonance wavelength [Fig. 3(c)] to calculate the power-dependent laser and scattered fields. The calculated Brillouin spectra are then processed in exactly the same manner as their experimental counterparts. To reach the quantitative agreement shown in Fig. 4(b), we furthermore make the assumption that the laser field and the scattered Brillouin field are equally enhanced upon the power-dependent red shift of the micropillar mode. Although the measured enhancement in the Brillouin signal is very reminiscent of the onset of stimulated Brillouin scattering, our modeling conclusively demonstrates that thermal effects on the optical cavity mode fully account for our experimental observations.

 

Fig. 4. (a) Power-dependent Brillouin spectra recorded on the micropillar shown in Fig. 1 (circles), with the excitation laser red-detuned by 0.4 nm from optical resonance at 1 mW of power [dashed vertical line in Fig. 3(a)]. Plotted is the area under the central Brillouin peak (upper inset) normalized to laser power. The area measured at 1 mW is set to unity. The normalized signal increases 25-fold when the laser power is increased to 35 mW. On a planar cavity with the same vertical structure (gray crosses), increase in the normalized signal is almost absent. (b) Photoelastic model calculation based on the structure in Fig. 2 and experimentally measured power-dependent resonance shifts [Fig. 3(c)]. Resonant optical excitation and collection are assumed.

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4. DISCUSSION AND CONCLUSIONS

The present results demonstrate that optical micropillar cavities are an interesting platform for the generation of high-frequency Brillouin spectra. An apparent difficulty of using a micrometer-size platform arises from the inevitable generation of stray light, which we overcome here by proposing a spatial filtering technique. This allows lifting the usual trade-off between object size and the minimum accessible frequency in the Brillouin spectrum. The proposed structure also offers great versatility since any planar multilayer structure that shapes the acoustic phonon spectrum, such as mirrors, filters, resonators, and coupled cavity systems [20,45–53], could be embedded in the optical cavity if its characteristic feature size is small enough for it to act as an effective optical medium, i.e., working at ultrahigh phononic frequencies [20,26,27,54]. We have shown furthermore that one can exploit the heating effects induced by the excitation laser to lock the optical cavity mode at a given spectral position for a given power and to optimize the Brillouin scattering signal by initially detuning the excitation laser from the unperturbed cavity mode.

Building upon these results, several possible routes could be followed to enter the stimulated Brillouin regime: Since the monolithic cavity studied here is based on DBRs, the optical quality factor could be enhanced by orders of magnitude by increasing the number of DBR layers to access Brillouin lasing [6]. Likewise, the acoustic quality factor may be raised to target phonon lasing [55]. In the phonon lasing regime, our devices could constitute a novel type of on-chip phonon lasers as building blocks for phononic nanocircuitry. Moving the resonance of the optical cavity closer to the electronic band gap in the materials of the nanoacoustic structure, the photoelastic interaction can be increased resulting in resonant Brillouin scattering [21]. Finally, the compactness and the waveguiding structure allow integration of our device with existing fibered and on-chip architectures [56,57].