Strong coherent interactions between colocalized optical and mechanical eigenmodes of various cavity optomechanical systems have been explored intensively toward quantum information processing using both photons and phonons. In contrast to localized modes, propagating mechanical waves are another form of phonons that can be guided and manipulated like photons in engineered phononic structures. Here, we demonstrate sideband-resolved coupling between multiple photonic nanocavities and propagating surface acoustic waves up to 12 GHz. Coherent and strong photon–phonon interaction is manifested with electro-optomechanically induced transparency, absorption, and amplification, and phase-coherent interaction in multiple cavities. Inside an echo chamber, it is shown that a phonon pulse can interact with an embedded nanocavity for multiple times. Our device provides a scalable platform to optomechanically couple phonons and photons for microwave photonics and quantum photonics.
© 2015 Optical Society of America
Strong coherent interactions between colocalized optical and mechanical eigenmodes of various cavity optomechanical systems have been explored intensively toward quantum information processing using both photons and phonons [1–5]. To achieve this, optomechanically induced transparency (OMIT) [6–8], backaction cooling [9,10], and light squeezing [11,12] have been demonstrated. To this end, the optomechanical interaction between the localized mechanical modes and confined optical modes of the cavity system is exploited to obtain strong photon–phonon coupling. In contrast to localized motion, however, the more ubiquitous form of phonons are various types of mechanical waves that freely propagate in the bulk or on the surface of solids. Propagating mechanical waves can strongly interact with light through elasto-optic effects and have been utilized in various acousto-optic devices [13,14]. In optical fibers [15–18] and more recently in integrated waveguides [19–23] and in whispering-gallery-mode cavities [24–27], mechanical waves can also be stimulated optically and lead to strong Brillouin scattering between phase-matched optical modes. Much like photons, these mechanical waves, or itinerant phonons, can be confined and guided in planar phononic waveguides to propagate over long distances so that their coupling with photonic modes are highly scalable [28–30]. Furthermore, phononic crystals and cavities can also be implemented to confine and store phonons to achieve an extended lifetime [31–33]. The quantum nature of those itinerant mechanical states has been revealed recently .
While both propagating and localized mechanical modes can be stimulated optically, they can be more efficiently excited electromechanically so that the amplitude or number of phonons can be pumped to a very high level without the need of a strong pump laser. Such an approach has been employed in electro-optomechanical systems that can directly couple microwave signals with optical signals [35–37]. Mechanical waves can also be excited with electromechanical transducers in monolithic devices. Representative types of mechanical waves include bulk acoustic waves, Rayleigh surface acoustic waves (SAWs), Lamb waves, and flexural plate waves. Rayleigh SAWs are particularly interesting because the displacement is confined on the surface of the substrate and it can be conveniently excited with planar transducers. Acoustic wave devices have long been applied for wireless communication and signal-processing applications [38,39]. In quantum physics, single quanta of a SAW have been detected with single-electron transistors and superconducting qubits, manifesting that propagating phonons can be viable quantum information carriers [34,40]. In photonics, we showed previously that a microwave frequency SAW can efficiently modulate photonic waveguide modes . In this work, we present a new type of cavity optomechanical system consisting of high- photonic crystal nanocavities integrated with SAW transducers working at frequencies up to 12 GHz, entering the microwave Ku band. At this very high frequency, the optomechanical interaction in the new system reaches the sideband-resolved regime and enables electro-optomechanically induced transparency, absorption, and amplification. To establish the propagating feature of mechanical waves, we demonstrate the phase-coherent optomechanical modulation of multiple nanocavities and an echo chamber inside which an acoustic pulse travels for multiple roundtrips to interact with an embedded nanocavity.
2. DEVICE DESIGN AND EXPERIMENTS
A. Device Design and Characterizations
Both the photonic crystal nanocavities and the SAW transducers are integrated on a 330 nm thick aluminum nitride (AlN) film, which provides strong piezoelectricity for efficient excitation of SAWs and a high refractive index for optical confinement. As illustrated in Fig. 1(a), the nanocavity is formed in a nanobeam inscribed with a one-dimensional photonic crystal shallow-etched in the AlN layer. The nanocavity can be coupled with a waveguide either on the side or at the ends. An interdigital transducer (IDT) is configured to launch a SAW propagating in the transverse direction to the nanobeam. The aperture of the IDT (100 μm) is designed to be much larger than the mode size of the nanocavity with a 24 μm FWHM of the Gaussian intensity profile, as shown in Fig. 1(b). Therefore, the nanocavity undergoes approximately uniform deformation when the acoustic wave passes. The wavelength of the acoustic wave that is excited is determined by the period of the IDT, whereas the frequencies of the modes are strongly dependent on their dispersion properties in the multilayer substrate. The scanning electron microscope image in Fig. 1(c) shows the IDT electrodes with a period of 450 nm and a linewidth of 112.5 nm (see Appendix A for details of the fabrication methods.) To achieve a high optical quality factor and a strong optomechanical interaction, we optimized the photonic crystal nanocavity design such that the electric field of the fundamental dielectric mode  is well confined inside the AlN structures with an effective mode index of . (The design of the photonic crystal nanocavity is discussed in Supplement 1).
Figure 1(d) displays the measured transmission spectrum of the nanocavity side-coupled with a waveguide, showing the fundamental and first-order cavity modes as dips. The quality factor of the waveguide-loaded fundamental mode is , corresponding to a linewidth of [Fig. 1(e)]. To characterize the SAW modes, the reflection coefficient () of the IDT was measured with a vector network analyzer (VNA) and is plotted in Fig. 1(f). (Detailed descriptions of the measurement setup are provided in Appendix B.) When an acoustic wave is excited, the reflection spectrum also shows a negative peak as the microwave signal is converted to outgoing waves so less reflected. Prominent resonance peaks corresponding to high-order Rayleigh modes, as marked in Fig. 1(f), can be observed in the reflection spectrum. These high-order modes are more interesting than the low-order modes because mechanical energy is more confined in the AlN layer rather than in so that their overlap with the cavity optical mode is more significant, inducing a stronger optomechanical coupling . The inset in Fig. 1(f) shows the simulated mode profile of Rayleigh mode R14 with more than 20% mechanical energy confined in the AlN layer. Its frequency is , entering the microwave Ku band. The linewidth of the mode resonance is [Fig. 1(g)]. We note that one feature of our platform is that the electromechanical transducer is separated from the photonic cavity, allowing the mechanical frequency to be freely engineered and the photonic cavity to be optimized independently. (More simulation results of the SAW modes are included in Supplement 1).
B. Sideband-resolved Optomechanical Coupling
To characterize the optomechanical coupling between the nanocavity and the SAWs, a laser source, with a variable detuning from the fundamental cavity mode, was sent into the input waveguide with 22 μW power. The transmitted optical power was measured with a high-speed photodetector (PD), which was connected to the VNA and the overall system transmission coefficient was measured as a function of the excitation frequency at the IDT. The broadband optical spectrum is shown in Fig. 2(a). It can be seen that in addition to the Rayleigh modes (R11–R16) observable in , optical also detects additional modes (R4–R10) that are not visible in the spectrum. A comparison of the two spectra demonstrates that the high- nanocavity provides optical detection of acoustic waves with a broader bandwidth and a higher sensitivity. The amplitudes of the peaks are proportional to the modal overlaps of the Rayleigh modes with the cavity mode. Figure 2(b) shows a zoom-in of the and of the R14 mode. Since the frequency of the mechanical mode  is considerably greater than the dissipation rate of the nanocavity mode , their optomechanical coupling is in the sideband-resolved regime, a prerequisite condition for phenomena such as induced transparency and strong coupling. Figure 2(c) shows the peak amplitude of the R14 mode as a function of varying laser-cavity detuning, displaying the characteristic line shape of sideband-resolved cavity optomechanical coupling. Fitting the results with the theoretical model and calibrating the transducing factors of the system provide the optomechanical coupling coefficient of the system, , expressed in terms of the power of the SAW as . (More details are provided in Supplement 1).
C. Electro-optomechanically Induced Transparency, Absorption, and Amplification by a SAW
Coherent interactions between cavity photons and propagating phonons generate Stokes and anti-Stokes photons, which can interfere with probe photons constructively (destructively) to induce optical transparency (absorption). This three-wave nonlinear process is illustrated in the diagram in Fig. 3(a). Different from optically stimulated phonons in conventional cavity optomechanics and stimulated Brillouin scattering in optical fibers, here the phonons are electromechanically excited nonlocally and are propagating on the surface. We investigate the coherent photon–phonon interaction in our system using the setup depicted in Fig. 3(b). Briefly, a laser is detuned from the cavity resonance by exactly the SAW mode frequency () to provide the control light at a frequency of and is modulated with an electro-optic modulator to generate sidebands, with the upper one at a frequency of used as the probe light. With this scheme, the transmission spectrum of the cavity can be measured by varying the modulation frequency to scan and by detecting the beating signal between the transmitted probe light and the control light.
The result is displayed by gray symbols in Fig. 3(c), showing a transmission dip, which can be understood as cavity absorption. When the modulation signal is also sent to drive the IDT, a SAW of the same frequency is excited and propagates to the nanocavity to couple with the control light. This optomechanical coupling leads to three-wave mixing between the control, probe, and SAW. Depending on the SAW phase, which can be controlled with a phase shifter, the interference of waves leads to transparency or absorption. When the interference is constructive (destructive), a transparency (absorption) window is observed within the cavity resonance, shown as a red peak (blue dip) in Fig. 3(c). Because in this homodyne measurement scheme the mechanical frequency and the probe detuning are synchronized, the transparency (absorption) window width agrees with the SAW IDT bandwidth [Fig. 2(b)]. Fixing the control light power, the SAW can be excited to a high amplitude to compensate for the cavity loss and even to amplify the probe light with a considerable gain, as shown in Fig. 3(d). When the gain is high, and so the original cavity absorption is negligible, it is proportional to the SAW power (or the number of propagating phonons), as shown in Fig. 3(f). In addition to transparency or absorption, the three-wave mixing process is controlled by the phase of the SAW relative to the probe. The columns in Fig. 3(e) show the situations when the phase shift is set to 0, , , and , so that the interference is tuned from constructive to destructive and displays Fano-resonance-like line shapes in between. We note that in our system SAW electro-optomechanically induces transparency and absorption [35,36], which is different from OMIT where mechanical motion is stimulated optically [6,7].
D. Coherent SAW Interaction with Multiple Cavities
Besides the phenomena observable in sideband-resolved cavity optomechanics, an important feature of our new platform is that the propagating mechanical wave can interact with multiple cavities in a coherent fashion. This scalability will be important, for example, to wavelength-multiplexed coupling and conversion between microwave and optical photons. We demonstrate scalability by placing three nanocavities in the path of the SAW as shown in Fig. 4(a). These cavities are end-coupled with the waveguides and the SAW transducers operate at a lower frequency of 1.75 GHz. As the beam of SAW propagates, it also undergoes diffraction, which can be described by integrating the Lamb’s point source solution along all the IDT finger pairs , each of which is treated as an effective line source. Overlaid in Fig. 4(a) is the calculated displacement field amplitude of the propagating SAW, showing its diffraction pattern. Counterintuitively, as shown in Fig. 4(b), the displacement amplitude of the SAW changes nonmonotonically along the central line of the IDT where the nanocavities lie. This is confirmed in the optical spectra measured from the three cavities, as shown in Fig. 4(c), in which the farthest cavity (1.5 mm from the IDT) shows almost equally strong modulation as the second cavity (0.5 mm from the IDT). On the other hand, the phases of the optomechanical modulation of the three cavities are coherent with incremental time delays due to the propagation of the SAW. The group delay as a function of the distance of the three cavities from the IDT transducers is plotted in Fig. 4(d). The slope in the plot indicates the group velocity of the SAW to be . The coupling demonstrated between multiple cavities and the SAW with well-understood diffraction can be utilized to implement multiplexed microwave signal processing in the optical domain.
E. SAW Interaction with a Cavity in an Acoustic Echo Chamber
Finally, propagating phonons can be guided and confined in a fashion much like photons, with phononic structures such as one- or two-dimensional phononic crystals. Here we use acoustic Bragg reflectors to build a planar phononic cavity, or an acoustic echo chamber, inside which a photonic nanocavity is inserted to enable cavity-enhanced photon–phonon interaction. An optical image of the device is displayed in Fig. 5(a). Figure 5(b) shows the optical spectra measured with the nanocavities inside phononic cavities of different lengths of , 0.6, and 0.9 mm. The spectra show additional peaks within the IDT bandwidth, corresponding to the acoustic resonances of the phononic cavity. Similarly to an optical Fabry–Perot cavity, the spacing between the peaks, or the free spectral range, , decreases with increasing cavity length as given by , where is the roundtrip time, is the group velocity of the SAW, and is the effective extra cavity length due to the Bragg reflectors. The nanocavity provides highly sensitive and broadband detection of the acoustic wave traveling inside the echo chamber. By performing a time-domain measurement, we show that the nanocavity can “hear” multiple echoes of an acoustic pulse bouncing inside the chamber, as displayed in Fig. 5(c). The acoustic pulse is first excited by a 40 ns microwave burst sent to the IDT (orange). Due to electrical and optical delay, after , the pulse was detected by the nanocavity for the first time. The pulse then propagates back and forth between the reflector and the IDT. It passes and is detected by the nanocavity four times, as is most obvious in the top panel, before its amplitude decays below the noise floor. From the arrival times and signal amplitudes of multiple echoes, shown in Figs. 5(d) and 5(e), we can observe that other than linear propagation delay and loss, an extra delay of 100 ns (corresponding to ) and a loss of 8 dB occur during each roundtrip. Those are attributed to the Bragg reflector of finite length and can be optimized with a more advanced design of low-loss phononic reflectors.
In conclusion, we have demonstrated a planar cavity optomechanical platform on which propagating acoustic waves can be generated, confined, and guided to interact with photonic cavities integrated in the same layer of AlN. By using high-resolution electron-beam lithography, IDTs can be patterned to excite acoustic waves at frequencies into the microwave Ku band. We expect it to be straightforward to further increase the frequency by using more advanced nanofabrication techniques such as nanoimprint lithography. In addition to high frequency, an important feature of a propagating mechanical wave is its scalability—multiple photonic cavities can be coupled. In contrast to other cavity optomechanical systems that include a mechanical resonator, the SAW in our current system is freely propagating and is not confined in a high- cavity. As a result, prominent optomechanical backaction effects such as optical spring, cooling, and amplification cannot be achieved with such an open SAW system. However, high- acoustic cavities can be obtained if the acoustic loss can be reduced by removing substrate leakage, reducing diffraction via acoustic waveguides [32,44], and suppressing intrinsic material loss at cryogenic temperatures . More recently, a SAW cavity with a quality factor of up to has been demonstrated at a cryogenic temperature . Therefore, it is promising to achieve photon–phonon interaction in the regime of strong coupling on a SAW-based platform as a scalable modality of quantum optomechanics.
APPENDIX A: DEVICE FABRICATION
The devices were fabricated from a -axis oriented, 330 nm thick piezoelectric AlN thin film sputtered (OEM Group, AZ) on a silicon wafer with a 3 μm buried silicon dioxide layer. The photonics layer was first patterned by electron-beam lithography (Vistec EBPG-5000+) using ZEP-520A resist followed by chlorine-based reactive-ion etching. The AlN layer was etched down by 200 nm, leaving a 130 nm thick AlN slab for the SAW to propagate without significant reflection and loss. The SAW IDT electrodes and contact pads were fabricated by electron-beam lithography, followed by 35 nm Ti/Au deposition and a liftoff process.
APPENDIX B: MEASUREMENT SETUP
An external cavity tunable semiconductor laser was used as the laser source with its output power stabilized using a feedback loop. A 20 GHz electro-optic power modulator (EOM) was used to generate the probe sidebands for the observation of electro-optomechanically induced transparency, absorption, and amplification. The laser (and the probe sidebands, if present) was further conditioned with a fiber polarization controller and a variable optical attenuator before being coupled into and out of the photonic crystal nanocavity via the on-chip grating couplers and waveguides. The output laser from the nanocavity was amplified with an erbium-doped fiber amplifier, filtered with an optical tunable bandpass filter, and measured with a high-speed PD (New Focus 1474-A).
In frequency-domain measurement, a VNA (Agilent E8362B) was used to measure the frequency response of the system. For measurement, VNA Port 1 was directly connected to the on-chip IDT through an RF probe. For measurements, the RF power output from VNA Port 1 was split into two paths with an RF power splitter. One path was connected to the on-chip IDT through the RF probe. The other path was connected to the EOM to generate the optical probe sidebands only for the measurement of SAW-induced transparency, absorption, and amplification. For all other measurements, the latter path was disconnected and the EOM did not modulate the input laser. Both paths were properly conditioned with RF amplifiers, tunable attenuators, and/or tunable delay lines used as phase shifters. The output from the PD was amplified before being sent into VNA Port 2. In time-domain measurements, RF bursts were generated by gating a continuous-wave RF source with a pulse generator and a high-speed RF switch. The RF source and the pulse generator were properly synchronized to minimize phase jitter, which was crucial to ensure excellent identicalness of all the RF bursts. The RF bursts generated were sent to the on-chip IDT through the RF probe. The output of the PD was amplified and measured with an oscilloscope, which was synchronously triggered by the pulse generator. To achieve a high signal-to-noise ratio, the device responses shown in Fig. 5 were averaged for 2 s.
Air Force Office of Scientific Research (AFOSR) (FA9550-12-1-0338); National Science Foundation (NSF) (ECCS-1307601).
We thank Dr. Changling Zou for helpful discussions.
See Supplement 1 for supporting content.
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