High-frequency GaAs optomechanical bullseye resonator Open Access

The engineering of light–matter interaction in optomechanical devices has allowed the observation of very relevant fundamental phenomena such as gravitational waves¹ and ground-state cooling² and, consequently, has enabled important developments in information science technology.^3,4 For the past decade, silicon has been the material of choice for most on-chip optomechanics experiments. However, as we move toward high power efficiency and quantum-level control, device design becomes more challenging and material properties become more restrictive, which have driven intense research on alternative materials.^5–8 Therefore, gallium arsenide (GaAs) arises as a mature platform with the potential to match or overcome silicon in many properties, such as light confinement and optomechanical coupling strength, due to its high refractive index and large photo-elastic coefficients.⁹ Moreover, the optical losses that often impair the performance of GaAs have been mitigated by improved etching and surface passivation techniques, leading to optical quality factors (Q_opt) of over a million.¹⁰ 

Developing optomechanical resonators based on III–V materials would not only allow for their disruptive integration with coherent light sources and single quantum emitters but also opens a route to explore the interplay of gain and loss in non-Hermitian physical systems.^11,12 Besides its advantageous optoelectronic properties, GaAs also has other valuable characteristics, such as piezoelectricity, revealing its suitability for wavelength conversion mediated by piezo-optomechanics,¹³ thus enabling the ultimate integration and control of charge carriers, light, sound, and microwave fields.

To unleash the outstanding properties of GaAs and enable an optomechanical device operation in the resolved-sideband regime, a design supporting high mechanical frequencies must be devised. In simple microdisks, this is limited by the resonator radius, which turns out to be unpractically small.^14–16 Also, it becomes relatively complex in optomechanical crystals, which require complicated designs.⁹ Despite recent efforts with nanobeam cavities showing impressive optomechanical coupling rates, mechanical frequencies have not exceeded 2.8 GHz in GaAs.^17,18 In this work, we demonstrate GaAs optomechanical devices built using a bullseye design that allows for very high mechanical quality factors and measured mechanical modes up to 3.4 GHz, with the potential to explore even higher frequency modes, according to simulations. Our design allows for optimizing the optical and mechanical resonances independently, offering to couple several high-quality factor optical modes with a single mechanical mode, which can be interesting for the exploration of multi-mode optomechanical experiments.

Our samples were fabricated using a technique that allows different etching depths to be obtained in a single-step lithography process. The mechanical performance of our device was investigated by cooling it to liquid nitrogen temperatures and by characterizing typical sources of mechanical dissipation, revealing that the mechanical quality factor is only limited by temperature-dependent effects, which can be circumvented under cryogenic conditions. We also show that our GaAs samples are strongly affected by the material elastic anisotropy and numerically evaluate their implications, obtaining a good match between experimental data and simulations. The devices achieved optomechanical coupling rates and mechanical quality factors up to 39 kHz and 4000 (at ∼80 K), respectively, operating just above the resolved sideband limit.

The bullseye geometry, originally devised by Santos et al.¹⁹ using silicon, consists of a ring-type cavity resonator obtained by patterning a nano-structured circular grating over a microdisk, as shown in Fig. 1(a1). In this design, the mechanical waves are confined to the outermost ring using a radial phononic shield, which also isolates the ring cavity from the supporting pedestal, inhibiting anchor losses and, therefore, enabling very high mechanical quality factors. A key advantage of the bullseye design, compared to nanobeams or optomechanical crystal devices, is the complete decoupling between optical and mechanical resonance frequencies. The former is mostly influenced by the radius of the disk, R in Fig. 1(a1), whereas the latter will be defined by the external ring width (w_ring). In this way, mechanical frequencies can be increased by narrowing down the external ring, with minimal impact on the optical frequencies, as long as w_ring ≳ 500 μm.¹⁹ 

Our GaAs bullseye project was based on a nominal geometry with a disk radius of 6 µm and grating dimensions set to a = 600 nm, w = 120 nm, and t = 50 nm, as shown in Fig. 1(a1). This grating is designed as a phononic shield to confine dilatational mechanical waves propagating in the radial direction and, as long as their wavelengths are small compared to the ring radius, one can neglect its curvature and approximate it to a linear crystal¹⁹ [see the inset of Fig. 1(b)]. Using the 2D cartesian Finite Element Method (FEM), we modeled a linear grating with the geometrical parameters mentioned above, obtaining a band diagram as in Fig. 1(b). Such an approximation revealed a partial phononic bandgap for longitudinal (x-polarized) and vertical shear waves (z-polarized), represented by the blue lines in Fig. 1(b), where shear-horizontal waves (y-polarized) are also shown in yellow. It resulted in two mechanical frequency stopbands in the ranges between ∼2 GHz–3 GHz and ∼3 GHz–4 GHz, being able to constrain radial dilatational mechanical waves to the edge of the disk.

The optomechanical coupling rate, g₀/(2π), for the full bullseye structure is shown in Fig. 1(c). Our simulations (2D-axisymmetric) show that three mechanical modes couple to the (whispering gallery-type) optical field, as highlighted by the gray dashed lines between 2 GHz and 5 GHz. The mechanical displacement profiles of these modes are shown in Fig. 1(a2), followed by the first radial-order transverse electric (TE) optical mode to which they are coupled [see Fig. 1(a3)]. This reveals that C is the desired ring-type breathing mode, while A is a flexural ring mode, and B is a grating mode that is almost independent of the external ring size. Unlike GaAs disk resonators with similar dimensions, the g₀ for the first-order ring dilatational mechanical mode is dominated by the photo-elastic effect; precisely, our calculations for a 740 nm w_ring show that the moving boundaries²⁰ and photo-elastic²¹ optomechanical coupling rates are 12 kHz and 129 kHz, respectively, resulting in a total g₀/(2π) of 141 kHz.

The devices were fabricated from a GaAs/Al_0.7Ga_0.3As stack (250 nm/2000 nm) that was grown over a GaAs substrate by molecular beam epitaxy (Canadian Photonics Fabrication Centre). In contrast to the previous silicon bullseye, which was fabricated with an optical stepper, the GaAs structure was defined by electron beam lithography.²² The fabrication steps of the GaAs bullseye samples are summarized in Fig. 2(a1). The devices were patterned on the top of the GaAs wafer through a single plasma etching step. We used a positive electroresist (ZEP-520A) and managed to define grating grooves and remove all the material outside the microdisk region using the aspect-ratio dependent etching, where the etching rate of narrower gaps is lower in comparison to wider regions [Fig. 2(a2)].^23,24 The bullseye disks were then released from the substrate by selective wet etching of the AlGaAs buffer layer with hydrofluoric acid (HF), followed by standard organic cleaning. This advantageous technique avoided the need for multiple lithography steps that would introduce complex alignment procedures.

Figures 2(b) and 2(c) present scanning electron microscope images of exemplar samples. The former shows the final device surrounded by the parking lot, which was designed to support the fiber loop. Top-view images, such as in Fig. 2(c), were used to characterize the dimensions of the devices. The disk radius (R), w_ring, a, and w were measured through this method, whereas t was only estimated from the etching rate, which was calibrated before the fabrication of the devices. Electron beam proximity effects caused the first outer groove [w₁ in Fig. 2(a3)] to have a narrower width in comparison to the inner grooves (w). Nevertheless, we obtained very regular and sharp grooves that are only slightly angled. Section S1 of the supplementary material discusses in detail the impact of the verticality of the sidewalls and the depth of the grooves on the mechanical grating structure. Finally, in Sec. S2, both w₁ and t were found by matching the measured and simulated values for the optical mode dispersion of our device. All those geometrical values were then used in the FEM simulations of Fig. 3.

The optomechanical properties of the resonators were characterized in the setup schematically represented in Fig. 3(a). The bullseye microcavity was probed via evanescent coupling with a tapered fiber loop continuously fed by a tunable C-band laser (New Focus TLB-6728). The transmitted optical signal was then split and simultaneously measured by using a slow and a fast detector. The DC component gave information about the optical response of the cavity, while the fast signal was measured by using an electrical spectrum analyzer (ESA) that read out the mechanical mode signatures imparted on the transmitted optical signal.

We experimentally investigated two devices with different w_ring sizes: 700 nm and 740 nm at room temperature and atmospheric pressure. The optical spectrum of the 740 nm sample is displayed in Fig. 3(b). The inset has a mode doublet (counter-propagating whispering gallery modes) presenting total linewidths, κ/(2π), of ∼6 GHz (Q_opt ∼3 × 10⁴), which was a typical value measured in our samples. These modes provided the strongest readout of the mechanical modes and were found to be second radial-order modes with quasi-TE polarization (major component along the radial direction). The identification was based on the comparison between the measured and simulated frequency dependence of the free spectral range (due to group velocity dispersion;²⁵ see S2 of the supplementary material for details).

The optomechanical coupling with the second radial-order TE optical mode is very similar to its fundamental counterpart [Fig. 1(c)] and predicts g₀/(2π) = 136 kHz for the sample with a ring size of 740 nm. The complete 2D simulation for this optical mode structure as a function of the w_ring size can be found in S2 of the supplementary material. Although a slightly larger g₀ is expected for the optomechanical coupling through the first radial-order mode, our measurement scheme was sensitive to $g02/κ$ and, therefore, the detection of the mechanical interaction with such optical modes was compromised by their larger linewidths. Similar conclusions have been reported for microdisks in Ref. 26.

A 3.29 GHz mechanical resonance was measured in the 740 nm w_ring and shown in Fig. 3(c). The Lorentzian fit gave a mechanical quality factor (Q_m) of 900 and the calibration of g₀—through the comparison between the phase modulator (PM) RF-tone and the optical transduction of the cavity²⁸—resulted in an optomechanical coupling rate of g₀/(2π) = 34 kHz. Analogously, we obtained a Q_m of 1200 and a g₀/(2π) = 39 kHz for a 3.13 GHz mode of the 700 nm w_ring sample. Numerical simulations of g₀ for the 740 nm w_ring are shown in Figs. 3(d1)–3(d3). Also, Fig. 3(d4) presents a 1 GHz-broad experimental mechanical spectrum—raw and Savitzky–Golay filtered.²⁷ The data used to obtain the optomechanical coupling rates were not filtered.

The lower g₀ and the multiple peaks observed in the experimental spectra of Fig. 3(d4) are not consistent with axisymmetric simulations that predict a single peak for each mechanical mode [A, B, and C in Fig. 1(a1)]. Therefore, we employed a three-dimensional FEM model to account for the well-known elastic anisotropy of GaAs and precisely identify the mechanical modes. Indeed, as the material anisotropy is gradually increased in the 3D simulations, a clear degeneracy lifting of the mechanical mode frequencies is observed, as shown in Figs. 3(d1)–3(d3), by sweeping the anisotropy parameter η. Here, η = 0 corresponds to an isotropic device and η = 1 is the full anisotropic case according to the relation $c44*(η)=ηc44+(1−η)((c11+c22)/2)$ for the GaAs stiffness tensor component.

The isotropic mechanical displacement profile shown in Fig. 3(d5) (η = 0) corresponds to the prominent bar in Fig. 3(d1). It demonstrates that only the C-mode is optomechanically coupled to the second radial-order optical mode. Indeed, despite the modification of the mode structure after the loss of symmetry in the material, the measured mechanical mode, highlighted in shaded orange in Fig. 3(d4), can still be related to the C-mode (external ring breathing mode), as shown in Fig. 3(d5) (η = 1), which corresponds to the highest bar in (d3). The 3D modeling also shows that the mechanical grating isolation is resilient to the anisotropy but predicts a reduced g₀ when compared to the 2D simulations with isotropic material elasticity. Thus, when η = 1, it foresees a g₀/(2π) of up to 53 kHz (33 kHz due to the photo-elastic effect and 20 kHz associated with the moving boundaries contribution—see Secs. S2 and S3 of the supplementary material), which agrees reasonably well with the calibrated data presented in Fig. 3(c). Moreover, such a result is still above the achievable g₀ for the fundamental radial breathing mechanical mode in GaAs disks with the same radius and thickness [$g0(disk)/(2π)∼(ω0/R)xzpf=$12 kHz, where ω₀ is the angular optical frequency and x_zpf is the zero-point amplitude fluctuation of a 230 MHz mode], with the benefit of having mechanical GHz frequencies not yet reported in any GaAs optomechanical structure operating at telecom wavelengths.

In order to investigate the role of the mechanical grating in inhibiting clamping losses, thermal channels of dissipation had to be suppressed. Therefore, our samples were cooled down to the temperature of liquid nitrogen. Figure 4(a1) contains the measured mechanical C-mode of the 700 nm w_ring. At a temperature of ∼80 K, a Q_m of 4 × 10³ was measured, which is an improvement of over three times in comparison to room temperature data. To observe the behavior of the mechanical linewidth (Γ_m) as a function of the cavity input power, we performed a laser power sweep—frequency tuned for maximum optomechanical transduction—on the blue side of the optical resonance. As the power was increased, we noticed a simultaneous increase in the mechanical linewidth and a redshift, Δf = f − f₀, where f₀ is the initial mechanical mode frequency and f is its frequency at a given optical input power, as shown in Fig. 4(a2).

In Fig. 4(b), we show that Δf goes down a few MHz when approaching 1 mW of the optical input power. This effect is explained by the cavity heating, which causes the material to expand, modifying the mode frequency.²⁹ We calculated this shift and plotted it against the data by assuming that at a very low power, this heating was negligible, i.e., Δf = 0, and that the initial reading of the temperature sensor was a good approximation for the cavity temperature. Then, it was possible to estimate a linear relationship between the temperature and the input power to the resonator, which was done by comparing the measured power induced frequency shift to the expected shift caused by thermal expansion.

We also measured the decrease in Q_m with power, as displayed in Fig. 4(c), that contains the data of Figs. 4(a1) and 4(a2) in the extreme input power values, highlighted in light blue (low power) and light red (high power), respectively. In order to understand this behavior, we included other loss mechanisms to the mechanical linewidth. When neglecting anchor losses, the linewidth broadening of nanomechanical resonators is then, in general, dominated by phonon–phonon interactions and scattering by defects. The former can introduce losses via relaxation of thermal phonons, whereas the second dissipates the mechanical energy by coupling strain waves to two-level systems (TLS).^30,31

To estimate the linewidth of our sample, we calculated the anharmonic and the TLS mechanical attenuation through the methods described in Ref. 32 (see S4 of the supplementary material). From 300 K to 80 K, our bullseye resonators fall into the Akhiezer regime,³³ ω_mτ_ph ≲ 1, where τ_ph is the phonon relaxation time for this channel and ω_m is the mechanical resonator angular frequency. Thermoelastic losses obtained from FEM were found to be several orders of magnitude lower than the Akhiezer damping and are neglected in this analysis. The double-well potential parameters of our TLS dissipation model were obtained from Ref. 34, where GaAs microdisks were investigated; as such values are highly material dependent and do not change significantly with a small variation in geometry, they serve as a reasonable approximation for our devices. The results are displayed in Fig. 4(d), where the inset includes a direct comparison of the measured mechanical quality factors (3.1 GHz mode) to the theory, which predicts that Q_m ∼12 × 10³ at 20 K. It is important to notice that, at very low temperatures, scattering by defects is the main dissipation mechanism, and thus, predictions may not be so accurate in this regime.

The measurement of Q_m as the input laser power was increased gives a hint about the accuracy of our mechanical dissipation model, which correctly predicts the Q_m optical power dependence, as shown in Fig. 4(c). The total model not only accounted for the thermal sources of mechanical dissipation (Akhiezer and TLS) but also included the linewidth modification expected from the optomechanical backaction. If the measured Q_m was dominated by optomechanical dynamics, an opposite trend should be observed with the increase in (decrease in) the Q-factor (Γ_m) for a higher input power. Therefore, we can see that optomechanical antidamping does not play a significant role in the mechanical linewidth, indicating that it is dominated by temperature-dependent dissipation. Moreover, the 3D calculation including mechanical clamping and perfectly matched layers predicted mechanical Q-factors between 10⁴ and 10⁷ for the ring modes, which are at least one order of magnitude higher than the measured values [Fig. 4(d)], thus suggesting that our device is not limited by anchor losses.

In summary, we designed a GaAs bullseye resonator with a phononic grating operating between 3 GHz and 4 GHz. The fabricated devices show modes ranging between ∼3.0 GHz and 3.4 GHz with optomechanical coupling rates of up to 39 kHz and a mechanical quality factor of 4000 when cooled down to the temperature of liquid nitrogen, rendering an optomechanical cooperativity of C_om ∼ 0.05 at 80 K (0.8 mW of cavity input power). In order to harness the full potential of the GaAs bullseye resonators, the regime of high cooperativity must be accessible and, thus, higher optical and mechanical Q-factors must be achieved. The former could be obtained by minimizing roughness²² and surface absorption¹⁰ with electroresist thermal reflow and alumina passivation (Q_opt ∼ 10⁵ − 10⁶). Additionally, mechanical dissipation is expected to be drastically reduced at lower temperatures,¹⁸ as thermal anharmonic losses are reduced (Q_m ∼ 14 × 10³). Under the above conditions, unitary C_om is reachable with the same 0.8 mW or less power. Incorporating III–V quantum emitters to the bullseye cavity would also enable the study of active optomechanics, opening a plethora of possibilities, including the creation of an alternative approach for hybrid systems that couple single emitters to mechanical strain³⁵ and the realization of mechanically modulated light sources.³⁶ Microwave to optical conversion, on the other hand, could take advantage of higher mechanical frequencies enabled by narrower w_ring’s or exploring higher-order mechanical modes. Finally, the bullseye design was shown to be robust across different material platforms and could be extended to other semiconductor materials with lower non-linear optical losses, such as GaP.^37,38

See the supplementary material for details on the fabrication of the devices (S1), the characterization of the optical modes through the frequency dependence of the free spectral range (S2), the effect of the elastic anisotropy on the optomechanical coupling rate (S3), and the modeling of the mechanical dissipation (S4).

The authors acknowledge CCSNano-UNICAMP for providing the micro-fabrication infrastructure and CMC Microsystems for providing access to MBE epitaxy and the GaAs wafers. This work was supported by the São Paulo Research Foundation (FAPESP) under Grant Nos. 2017/19770-1, 2016/18308-0, 2018/15580-6, 2018/15577-5, and 2018/25339-4, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Brasil (Finance Code 001), the Financiadora de Estudos e Projetos, and the National Sciences and Engineering Research Council (NSERC) of Canada.

The data that support the findings of this study are available from the corresponding author upon reasonable request.