The exploitation of Brillouin scattering, the scattering of light by sound, has led to demonstrations of a broad spectrum of novel physical phenomena and device functionalities for practical applications. Compared with optomechanical excitation by optical forces, electromechanical excitation of acoustic waves with transducers on a piezoelectric material features intense acoustic waves sufficient to achieve near-unity scattering efficiency within a compact device footprint, which is essential for practical applications. Recently, it has been demonstrated that gigahertz acoustic waves can be electromechanically excited to scatter guided optical waves in integrated photonic waveguides and cavities, leading to intriguing phenomena such as induced transparency and nonreciprocal mode conversion, and advanced optical functionalities. The new integrated electromechanical Brillouin devices, utilizing state-of-the-art nanofabrication capabilities and piezoelectric thin film materials, succeed guided wave acousto-optics with unprecedented device integration, ultrahigh frequency, and strong light-sound interaction. Here, we experimentally demonstrate large-angle (60°) acousto-optic beam deflection of guided telecom-band light in a planar photonics device with electromechanically excited gigahertz (∼11 GHz) acoustic Lamb waves. The device consists of integrated transducers, waveguides, and lenses, all fabricated on a 330 nm thick suspended aluminum nitride membrane. In contrast, conventional guided-wave acousto-optic devices can only achieve a deflection angle of a few degrees at most. Our work shows the promises of such a new acousto-optic device platform, which may lead to potential applications in on-chip beam steering and routing, optical spectrum analysis, high-frequency acousto-optic modulators, RF or microwave filters and delay lines, as well as nonreciprocal optical devices such as optical isolators.
INTRODUCTION
The exploitation of Brillouin scattering, the scattering of light by sound, has led to demonstrations of a broad spectrum of novel physical phenomena in various optical systems and device functionalities for practical applications.1–8 The acoustic waves involved in the Brillouin scattering process can be thermally excited or optomechanically stimulated by radiation pressure and electrostriction.9–11 It is the most pronounced in stimulated Brillouin scattering (SBS) in fiber optics12–15 and integrated waveguides,16–18 as well as in cavity optomechanical systems,19–22 which feature many intriguing interactions between light and mechanical motions.23 Alternatively, the acoustic waves can be electromechanically excited with transducers on a piezoelectric material. With efficient transducers,24–26 the intensity of the excited acoustic wave can be sufficiently high to achieve near-unity scattering efficiency within a compact device footprint,27,28 which is essential for practical applications (in this context, we define the electromechanical Brillouin scattering efficiency as the power ratio between the deflected and input light). For electromechanical excitation of acoustic waves via piezoelectric effects, near-unity transduction efficiency, from RF power to acoustic power, can be achieved within a millimeter-sized or even smaller device, leading to high acoustic wave intensity that is unachievable for practical optomechanical excitation. Meanwhile, in a typical SBS process, each pump photon (at least terahertz frequency) can generate at most one phonon (at most gigahertz frequency), leading to power efficiency generally smaller than 10−3. Recently, it has been demonstrated that gigahertz frequency acoustic waves can be electromechanically excited to scatter guided optical waves in integrated photonic waveguides and cavities.29–38 In these integrated electromechanical Brillouin devices, intriguing phenomena such as induced transparency32 and nonreciprocal mode conversion,34 and advanced optical functionalities27,29,30,35,36,38 have been demonstrated. Also, it has been proposed and theoretically investigated that electromechanical Brillouin scattering can be employed to scatter light from on-chip optomechanical antennas into a steerable free-space optical beam.39
The new integrated electromechanical Brillouin devices succeed guided wave acousto-optics6,40–44 with significant technological advances. Utilizing state-of-the-art nanofabrication capabilities and piezoelectric thin film materials, electromechanical Brillouin devices advance acousto-optics to an unprecedented regime of device integration, ultrahigh frequency, and strong light-sound interaction. The frequency of the acoustic waves excited on this platform can be well above 10 GHz and the wavelength well below the optical wavelength, which is a one or two orders of magnitude improvement, compared with conventional guided-wave acousto-optic devices. In this regime, the acousto-optic interaction, that is, the Brillouin scattering, can be drastically enhanced by (1) co-confinement for both the acoustic waves and optical waves in one-dimensional (1D) and two-dimensional (2D) subwavelength optomechanical waveguides with an optimal modal overlap and (2) satisfying momentum and energy conservation of photons and phonons in engineered devices. Realizing strong Brillouin scattering of light with a ultrahigh frequency acoustic wave potentially results in steering the optical beam over a large deflection angle and shifting optical frequency over a wide bandwidth.
Here, we experimentally demonstrate acousto-optic beam deflection of telecom-band light in a planar photonics device using Brillouin scattering with gigahertz acoustic waves. The device consists of integrated interdigital transducers (IDTs), waveguides, and lenses, all fabricated on a 330 nm thick suspended aluminum nitride (AlN) membrane. Acoustic Lamb wave mode33 near 11 GHz is electromechanically excited in the piezoelectric membrane to deflect the guided optical beam in the 2D waveguide by 60°. Both Stokes and anti-Stokes sidebands due to the Brillouin frequency shift have been separately observed in two different scattering configurations.
Because their acoustic wave frequency is generally in the hundreds of megahertz range, conventional guided-wave acousto-optic devices can only achieve a deflection angle of a few degrees at most.6,44 Furthermore, the optical waveguides formed by the ion diffusion process in conventional guided-wave acousto-optic devices has a low refractive index contrast to only produce weakly guided optical modes that have a typical mode size of micrometers.6,44 This leads to a poor mode overlap between the optical modes and the acoustic wave modes. In our design, in contrast, the suspended AlN membrane strongly confines both the acoustic Lamb wave mode and the optical slab mode, providing optimal acousto-optic mode overlap. Gigahertz acoustic Lamb waves are electromechanically excited with nanofabricated IDTs, resulting in an acoustic wavelength comparable to that of the guided optical slab mode in the optical telecom-band, therefore enabling large-angle beam deflection that is an order of magnitude higher than that achievable in conventional guided-wave acousto-optic devices.
Because in this work we only consider electromechanical Brillouin scattering (EBS), which does not include the stimulated process in stimulated Brillouin scattering (SBS), we oftentimes use the terms “Brillouin scattering” (BS) and EBS interchangeably, which should not cause confusion. Although in recent nonlinear optics and optomechanics literature, BS and SBS are used interchangeably, in established historical literature on acousto-optics,1,3–6 the original meaning of BS does not involve the stimulated process, which justifies our use of the term BS.
OPERATION PRINCIPLES
The schematic diagram of our prototype is shown in Fig. 1(a). It consists of four sets of rib waveguides and integrated planar lenses,45 and a split-finger IDT46,47 with an etched-through trench reflector and two contact pads. All the device components are on the suspended AlN membrane, except the contact pads for the radio-frequency (RF) probe, which are supported by a solid silicon substrate underneath the AlN membrane. Within each set of waveguide and lens, which forms an optical port for the device, one end of the waveguide is located at the focal point of the lens, while the other end is terminated by a grating coupler (not shown) and accessible by a fiber array. The angles between the axes of adjacent lenses and the IDT are all of them 60°. The trench reflector at the back end of the IDT reflects the backward propagating acoustic wave into the forward direction, thereby doubling the maximum IDT efficiency when perfectly impedance-matched.
Prototype device operation principles. (a) Schematic diagram of the prototype device. P1-4: Ports 1–4. [(b) and (c)] Wave vector diagrams of the Stokes and anti-Stokes scattering, respectively. [(d)–(f)] FEM simulation results of the acoustic S0 and optical TE0 modes in the x-z plane in the AlN membrane with a wavelength of 1 μm. The propagation directions of the acoustic and optical modes are both +x in the simulation. (d) Mechanical displacement in the S0 mode. The color represents the vertical displacement. (e) Piezoelectric potential in the S0 mode. (f) Transverse electric field in the TE0 mode.
Prototype device operation principles. (a) Schematic diagram of the prototype device. P1-4: Ports 1–4. [(b) and (c)] Wave vector diagrams of the Stokes and anti-Stokes scattering, respectively. [(d)–(f)] FEM simulation results of the acoustic S0 and optical TE0 modes in the x-z plane in the AlN membrane with a wavelength of 1 μm. The propagation directions of the acoustic and optical modes are both +x in the simulation. (d) Mechanical displacement in the S0 mode. The color represents the vertical displacement. (e) Piezoelectric potential in the S0 mode. (f) Transverse electric field in the TE0 mode.
As shown in Fig. 1(a), in one representative scattering configuration, a collimated acoustic beam is launched from the IDT, while the optical wave is launched and collimated from Port 1, and focused and collected into Port 3. A portion of the collimated light is deflected by the acoustic wave by 60° due to Brillouin scattering, and subsequently focused and collected by Port 4. The deflected light is also red-shifted by the acoustic frequency and forms a Stokes sideband with respect to the input light. Similarly, if the optical beam is input from Port 2, it will be output to Port 4, and the deflected light will be collected into Port 3, blue-shifted by the acoustic frequency and forms an anti-Stokes sideband with respect to the input light.
In such configurations, the wave vectors of the phase-matched Stokes and anti-Stokes Brillouin scattering form equilateral triangles, as shown in Figs. 1(b) and 1(c), which requires that the wavelengths of the acoustic and optical waves should be equal. Both the acoustic fundamental symmetric Lamb (S0) mode and optical fundamental TE (TE0) mode within one full wavelength of 1 μm in the AlN membrane is calculated from Finite Element Method (FEM, COMSOL Multiphysics) simulations and visualized in Figs. 1(d)–1(f). Our acoustic mode simulation takes into account the full anisotropic mechanical and piezoelectric properties of AlN, resulting in both the mechanical displacement and the piezoelectric potential distributions. The membrane vertically extends and compresses periodically along the propagation direction, shown in Fig. 1(d), which accordingly induces piezoelectric potential with periodically alternating polarity, shown in Fig. 1(e). Because the AlN thin film used is polycrystalline with highly aligned c-axis in the out-of-the-plane direction, its properties relevant to the acoustic mode are isotropic in the plane, which is assumed in the simulation. Meanwhile, Fig. 1(f) shows the transverse electric field component Ey of the optical TE0 mode in the AlN membrane.
Brillouin scattering occurs due to the change of the refractive index distribution induced by the acoustic wave. In AlN membranes, two major contributions that modulate the waveguide refractive index distribution should be considered. The first major contribution is the photoelastic effect in the waveguide material, including both the primary and the secondary effects. The primary photoelastic effect, usually known simply as the photoelastic effect, is the change of the refractive index directly due to strain. However, this is accurate only in optically isotropic materials. In optically anisotropic materials, such as AlN and lithium niobate (LiNbO3), the refractive index changes due to the pure rotation of material, which is ubiquitous in the acoustic modes but not represented in the strain, may not be negligible.48,49 The secondary photoelastic effect is through the piezoelectric and electro-optic effects, whereby the piezoelectric field in the acoustic mode changes the refractive index. The second major contribution is the deformation of the waveguide material, whereby the refractive index changed by the photoelastic effects is further redistributed.
DEVICE DESIGN AND FABRICATION
Figure 2 shows the scanning electron microscope (SEM) images of the prototype device, fabricated with standard electron-beam lithography, dry etching, metal deposition, and lift-off processes, from a 330 nm thick c-axis-oriented polycrystalline piezoelectric AlN thin film sputtered on silicon wafers, purchased from OEM Group, LLC, AZ. First, the optical components, including the lenses, rib waveguides, and the grating couplers, were patterned and etched down by 200 nm into the 330 nm thick AlN layer. Second, the IDT with contact pads, which consists of 140 nm of aluminum and 25 nm of gold, was patterned, deposited, and lifted-off on top of the AlN layer. The gold layer deposited on top of the aluminum layer is meant to passivate its top surface from oxidation, and hence, to reduce the resistance of both the IDT fingers and contact pads. Third, the six triangular releasing windows and the acoustic trench reflector were patterned and etched through the AlN layer. Fourth, to further reduce the contact resistance, the IDT contact pads were thickened to be ∼600 nm by an additional step of metal deposition on top of the gold layer, which consists of ∼20 nm of aluminum, ∼365 nm of copper, and ∼50 nm of aluminum. The first layer of aluminum is used to improve the adhesion between copper and gold, while the last layer of aluminum is used to passivate copper to survive the subsequent XeF2 etching. As the final step, the sample was etched in XeF2 gas to remove the silicon substrate underneath the AlN layer. The undercut was monitored and controlled so that most area of the IDT contact pads was still supported by the silicon substrate. Therefore, RF probes could be used to engage the pads and drive the IDT without damaging the suspended membrane. No attack of AlN due to the XeF2 etching was observed from SEM images or optical reflection spectrum measurement.
SEM images showing the prototype design. The shallow-etched areas are colorized blue to improve contrast. (a) Overview of the entire device without the grating couplers. (b) IDT fingers and contact pads, where Λ ≈ 2.7 μm. (c) IDT fingers and the back-end trench reflector. (d) Taper structure at the end of the rib waveguides, where w = 800 nm. (e) The optional acoustic trench reflector at the opposite side of the IDT across the hexagonal membrane.
SEM images showing the prototype design. The shallow-etched areas are colorized blue to improve contrast. (a) Overview of the entire device without the grating couplers. (b) IDT fingers and contact pads, where Λ ≈ 2.7 μm. (c) IDT fingers and the back-end trench reflector. (d) Taper structure at the end of the rib waveguides, where w = 800 nm. (e) The optional acoustic trench reflector at the opposite side of the IDT across the hexagonal membrane.
The suspended membrane in the center of the device, where the collimated optical beam is scattered by the collimated acoustic beam, is a regular hexagon. The distance between the lenses on the opposite sides of the hexagon is 200 μm, as shown in Fig. 2(a). We adopted a simple parabolic design for the integrated planar lenses,45 taking advantage of the effective index contrast between the shallow-etched (130 nm thick) and unetched (330 nm thick) areas on the AlN membrane. The wavelength of the optical TE0 mode in the telecom-band in this AlN membrane is near 0.9 μm. Accordingly, as shown in Figs. 2(b) and 2(c), the period (Λ) of the split-finger IDT46,47 is designed to be varied near 2.7 μm so that the wavelength and frequency of the third spatial harmonic acoustic S0 mode are varied near 0.9 μm and 11 GHz, respectively. The third spatial harmonic of split-finger IDTs is widely used due to its design simplicity, high efficiency, and ease of fabrication. The final IDT consists of 35 periods, each of which contains 4 fingers, or two sets of split fingers. We have not implemented additional impedance matching circuits on our device or taken other special measures to preferentially excite the third harmonic or suppress the first (fundamental) harmonic. Figure 2(c) also shows the trench reflector at the back end of the IDT. The phase velocity of the S0 mode is ∼10 km/s, which is significantly higher than the bulk acoustic velocity in common substrate materials such as SiO2 and Si. Therefore, suspension of the AlN thin film is essential to support a guided S0 mode. Within each optical port, the end of the rib waveguide is smoothly transitioned into the slab waveguide with a compact taper structure that facilitates mode conversion, as shown in Fig. 2(d). As a variation of the device shown in Fig. 2(a), we also fabricated devices with an acoustic trench reflector at the opposite side of the IDT across the hexagonal membrane, as shown in Fig. 2(e).
OPTICAL AND ACOUSTIC CHARACTERIZATIONS
We validate our optical port designs, including the parabolic lens in Fig. 2(a) and the rib waveguide taper in Fig. 2(d) using full three-dimensional (3D) Finite Difference Time Domain (FDTD, Lumerical FDTD Solutions) method. To save computation resources and time, we simulated a smaller version of the lens, with a focal length of 20 µm, shown in Fig. 3(a), where the optical field launched from the rib waveguide diverges into the slab waveguide with minimal reflections and is subsequently collimated by the lens. In the actual devices, where the lens focal length is 100 µm, we characterize the optical ports by measuring the transmission spectra through pairs of grating couplers with and without a pair of optical ports in between. As shown in Fig. 3(b), the inclusion of a pair of optical ports, which face straight to each other, for example, Ports 1 and 3, introduces an extra 13 dB of optical loss, which is largely due to the mode conversion loss of the integrated planar lenses and the rib waveguide tapers. From the experimental data of our previous work on the same AlN material,31,33 the optical propagation loss in the slab and rib waveguides in our device, which are hundreds of micrometers long, should be insignificant.
Optical and acoustic characterizations of the prototype device. (a) FDTD simulation of the integrated planar lens and the rib waveguide taper. The field shown is Hz. The focal lengths of the simulated and actual lenses are 20 μm and 100 μm, respectively. (b) Transmission spectrum of the prototype device compared with that of only a pair of grating couplers. GC: grating coupler. (c) Equivalent circuit of the IDT. The circuit component values are from the curve fitting of the measured reflection coefficient. (d) Measured IDT reflection coefficient and extracted IDT efficiency.
Optical and acoustic characterizations of the prototype device. (a) FDTD simulation of the integrated planar lens and the rib waveguide taper. The field shown is Hz. The focal lengths of the simulated and actual lenses are 20 μm and 100 μm, respectively. (b) Transmission spectrum of the prototype device compared with that of only a pair of grating couplers. GC: grating coupler. (c) Equivalent circuit of the IDT. The circuit component values are from the curve fitting of the measured reflection coefficient. (d) Measured IDT reflection coefficient and extracted IDT efficiency.
To characterize the IDT performance, we measured its RF reflection coefficient S11 with a vector network analyzer (VNA) and a calibrated RF probe, and subsequently extracted the electromechanical power transduction efficiency from the equivalent circuit model shown in Fig. 3(c) by curve fitting. The measurement results are shown in Fig. 3(d). The resistor Rs accounts for the total series resistance between the RF probe and the IDT fingers. The shunt resistor Rl and the capacitor Ce account for the effective leakage resistance and electrode capacitance between the IDT fingers, respectively. The electromechanical response of the transducer is modeled with a complex and frequency-dependent admittance Ya, generalized from the Butterworth Van Dyke (BVD) model.50,51 The electrical power dissipated on Ya is transduced into acoustic power. From the curve fitting results, at the desired S0 mode with a wavelength of 0.9 µm, the third IDT spatial harmonic, the electromechanical transduction efficiency is ∼17%, which is about two times of that at the S0 mode with a wavelength of 2.7 µm, the first (fundamental) IDT spatial harmonic, due to better impedance matching with the 50 Ω RF source.
LARGE-ANGLE BEAM DEFLECTION DEMONSTRATION
Next, we went on to measure the Brillouin scattering in the prototype device. In the first scattering configuration in Fig. 4(a), light of 10 dBm power is input from Port 1, while the IDT is driven by an RF power of 20 dBm. The deflected light collected into Port 4 was measured by an optical spectrum analyzer (OSA) with 0.02 nm wavelength resolution, which was small enough to clearly separate the scattered Stokes sidebands from the input light, shown in Fig. 4(b). Meanwhile, in the second scattering configuration in Fig. 4(d), light is input from Port 2, and the deflected light, collected into Port 3 and measured by the same OSA, forms the anti-Stokes sideband, shown in Fig. 4(e). The center peaks in Figs. 4(b) and 4(e) are due to diffraction and Rayleigh scattering of the input light. The Brillouin scattering efficiency can be calculated from the sideband peak power, taking into account the calibrated grating coupler and port losses.
Large-angle beam deflection using Brillouin scattering. [(a), (d), and (g)] Three different scattering configurations. [(b), (e), and (h)] Spectra of the deflected light measured by an OSA, for configurations (a), (d), and (g), respectively. SSB: Stokes sideband. ASB: anti-Stokes sideband. [(c) and (f)] The apparent dependence of the Brillouin scattering efficiency on the input laser wavelength and the RF frequency, for configurations (a) and (d), respectively. The green dashed lines are guide-for-the-eye phase-matching curves.
Large-angle beam deflection using Brillouin scattering. [(a), (d), and (g)] Three different scattering configurations. [(b), (e), and (h)] Spectra of the deflected light measured by an OSA, for configurations (a), (d), and (g), respectively. SSB: Stokes sideband. ASB: anti-Stokes sideband. [(c) and (f)] The apparent dependence of the Brillouin scattering efficiency on the input laser wavelength and the RF frequency, for configurations (a) and (d), respectively. The green dashed lines are guide-for-the-eye phase-matching curves.
To investigate the apparent dependence of the Brillouin scattering efficiency, defined as the power ratio between the deflected and input light, we varied both the input laser wavelength and the RF frequency and mapped out the efficiency in Figs. 4(c) and 4(f). The horizontal lines in Fig. 4(f) are caused by the fluctuations of the device optical insertion loss as a function of laser wavelength, which are Fabry-Perot noise due to the multireflections and interference within the device. The maximum efficiency achieved so far is ∼3.0 × 10−5, which occurred for the anti-Stokes sideband at the wavelength of 1540 nm and RF frequency of 11.055 GHz. The low Brillouin scattering efficiency in our preliminary prototype devices, on the order of 10−5, may be due to one or more of the following reasons and is expected to be significantly improved after thorough device optimization. First and foremost, the acousto-optic interaction area may be too small for efficient Brillouin scattering to occur. For a fixed total acoustic power, a larger acoustic aperture and/or a wider optical beam profile will generally lead to higher Brillouin scattering efficiency. Increasing the interaction area to millimeter size should lead to Brillouin scattering efficiency acceptable for practical applications, which we elaborate in the Appendix. Second, the deflected light may not have the optimal beam profile to be properly focused by the integrated lens and efficiently coupled into the rib waveguide. Generally, the efficient focusing of free-space light into single-mode optical fibers depends sensitively on the beam profile and lens alignment. In our planar integrated device, such dependence should also be very sensitive. Therefore, we may have underestimated the Brillouin scattering efficiency because we assumed that the deflected light had the same beam profile as that of the collimated input light. Third, the acoustic propagation loss may be higher than what we expected, which requires dedicated effort on systematic characterization and optimization.
The phase matching curves cannot be clearly extracted from Figs. 4(c) and 4(f) due to limited IDT and grating coupler bandwidths, which are only ∼120 MHz and ∼35 nm (full width at half maximum), shown in Figs. 3(d) and 3(b), respectively. Nevertheless, the guide-for-the-eye phase-matching curves in Figs. 4(c) and 4(f) go through the point at 1540 nm and 11.055 GHz, with a slope of −110 nm/GHz. From COMSOL simulations, the optical effective and group indices (ne and ng) of the TE0 mode in the suspended AlN slab waveguide at vacuum wavelength (λ0) of 1540 nm are 1.72 and 2.17, respectively, while the phase and group velocities (vp and vg) of the S0 mode at RF frequency (f) of 11.055 GHz are 10.7 km/s and 10.0 km/s, respectively. Because the position and slope at every point on the phase-matching curve should satisfy the following equations, it is straightforward to verify that the experiment (left-hand side) and simulation (right-hand side) match well
Furthermore, when a trench reflector is present at the exit of the acoustic wave on the hexagonal membrane, as shown in Fig. 4(g), both the anti-Stokes and Stokes sidebands are observed in the deflected light in Fig. 4(h), clearly indicating the reflection of the acoustic wave back to the hexagonal membrane. The anti-Stokes sideband, scattered by the original acoustic beam, is ∼7.5 dB higher than the Stokes sideband, scattered by the reflected acoustic beam, which is expected to be weaker than the original one due to propagation loss and diffraction, and hence, scatters less light. When the RF power that drives the IDT is turned off, the sidebands disappear but the center peak remains almost unchanged, further confirming that the observed sidebands are due to Brillouin scattering. The power of both sidebands measured in this device is about 10 dB lower than their counterparts in the device without the additional trench reflector, probably due to the following reasons. The additional trench reflector introduced extra deformation of the AlN thin film, which may have compromised the alignment between the lens and the rib waveguide and caused extra insertion loss. In addition, other random fabrication variations may also have contributed to the discrepancies between the sideband powers measured in different devices.
CONCLUSION AND FUTURE PERSPECTIVES
In conclusion, we have experimentally demonstrated large-angle optical beam deflection using electromechanical Brillouin scattering in suspended AlN membranes. The current device only deflects the input light into a fixed angle. To steer the optical beam over a large angle range, IDTs with varying periods and directions will need to be integrated in future devices. There is a myriad of existing solutions for optical beam steering, switching, routing, and modulation, which generally fall into four categories, namely, microelectromechanical, electro-optic, acousto-optic, and thermo-optic devices. Compared with the existing solutions, our device, once fully optimized, could achieve a unique combination of fast and continuous steering over a large angle range with high operation frequency and moderate power consumption.
Our results not only show the promises of such a new acousto-optic device platform but also the necessity that, to improve the device performance, the acousto-optic interactions on this platform be further characterized, modeled, and optimized. It is worth noting that the conventional theories for acousto-optics beam steering only apply for small deflection angles. In the widely used coupled-mode analysis,6 generally the optical beam propagation direction is assumed to be nearly perpendicular to that of the acoustic beam, which is invalid in our device. Therefore, new theoretical and numerical tools will be developed for this new operation regime. The device components, including the integrated planar lenses and the rib waveguide tapers, can be further optimized to reduce optical mode conversion loss. The area where the Brillouin scattering occurs should be increased to millimeter size to improve the Brillouin scattering efficiency. The acoustic propagation loss will be characterized and minimized. Both the optical TE0 and TM0 mode should be investigated and compared. New acousto-optic materials such as LiNbO3 thin films will be explored and compared. New material systems that do not require the suspension of thin membranes to guide both the acoustic and optical modes are also appealing due to their improved power handling capabilities and mechanical robustness. Nevertheless, we believe that our work here is the first step toward a new generation of integrated planar photonic devices based on electromechanical Brillouin scattering, for potential applications in on-chip beam steering and routing, optical spectrum analysis, high-frequency acousto-optic modulators, RF or microwave filters and delay lines, as well as nonreciprocal optical devices such as optical isolators.
ACKNOWLEDGMENTS
We acknowledge the funding support from the National Science Foundation (NSF) (Grant Nos. EFMA-1641109 and EFMA-1741656). Parts of this work were carried out in the Minnesota Nano Center, which is supported by the National Science Foundation through the National Nano Coordinated Infrastructure Network (NNCI) under Award No. ECCS-1542202, and the Washington Nanofabrication Facility/Molecular Analysis Facility, a National Nanotechnology Coordinated Infrastructure (NNCI) site at the University of Washington, which is supported in part by funds from the National Science Foundation (Award Nos. NNCI-1542101, 1337840, and 0335765), the National Institutes of Health, the Molecular Engineering & Sciences Institute, the Clean Energy Institute, the Washington Research Foundation, the M. J. Murdock Charitable Trust, Altatech, ClassOne Technology, GCE Market, Google, and SPTS.
APPENDIX: ESTIMATION OF THE BRILLOUIN SCATTERING EFFICIENCY
Systematic theoretical modeling or simulation of our device is quite challenging and requires dedicated effort. On one hand, the size of the device, hence the required three-dimensional (3D) simulation domain, is hundreds of wavelengths in the two in-plane dimensions and a few wavelengths in the out-of-plane dimension. Direct simulation of such a large 3D domain is computationally prohibitive. On the other hand, the conventional analytical formulation, the coupled-mode analysis, for guided-wave acousto-optic devices, is only applicable for small deflection angles; hence, it cannot be used in our case, where the deflection angle is 60°. Ultimately, the quantitative prediction of the performance of such devices will require a combination of analytical and numerical calculations, which are still yet to be developed. Moreover, the AlN physical properties used in the simulations, including the mass density, elasticity tensor, piezoelectricity tensor, dielectricity tensor, optical relative permittivity tensor, photoelastic tensor, and electro-optic tensor, are obtained from the literature and may not be accurate for our specific AlN thin film and experimental conditions. In sum, it is our future goal to develop analytical and numerical tools to systematically model and simulate our devices.
Nevertheless, we were able to simulate a significantly simplified case to show the potential of our device using COMSOL. Here, we assume that the acoustic wave is a perfect and lossless plane wave, which induces a static optical phase grating in the infinitely large suspended AlN thin film due to the photoelastic effects and the material deformation. Due to the presence of the grating, there exist optical eigenmodes which possess a complex wave vector in the direction normal to the acoustic wave front, , and a real wave vector in the direction tangential to the acoustic wave front, k∥. The imaginary part of k⊥, namely, , quantifies the reflectivity of the grating, which, for a fixed acoustic power density, reaches maximum when the Bragg condition is satisfied, namely, , where ka is the acoustic wave vector.
In the experiment, the acoustic power launched by the IDT is ∼17 mW, the IDT acoustic aperture is 60 μm, and so the acoustic power density is ∼0.28 mW/μm. The acoustic wavelength is ∼900 nm. The angle between the acoustic and optical wave vectors is 60° so that . By solving for the complex band structure, we found that reaches maximum, ∼1 mm−1, when the optical vacuum wavelength is ∼1543 nm. This suggests that, along the direction normal to the acoustic wave front, the optical power decays to 1/e every ∼1 mm due to the grating deflection.
It is worth noting that is proportional to the refractive index change induced by the acoustic wave, which is proportional to the square root of the acoustic power density. This is an important scaling law for integrated acousto-optics, which leads to the following two rules of thumb. First, when the total acoustic power is fixed, it is beneficial to spread it out across a large acoustic aperture, A, such that the traversing optical beam will accumulate more optical phase change, which is ∝A0.5, and hence, will be more efficiently deflected. When the Brillouin scattering efficiency is fixed, using a larger acoustic aperture will reduce the required total acoustic power, which is ∝A−0.5. From another point of view, when the acoustic and the optical beams are wider, their power is more delocalized in real space, and hence, more localized in the reciprocal space. Therefore, wider acoustic and optical beams possess better defined wave vectors that can satisfy the phase-matching conditions, which will generally lead to higher Brillouin scattering efficiency for a fixed total acoustic power.
Based on the above simulation and the scaling laws, we believe increasing the acousto-optic interaction area to millimeter size should lead to significant reduction of power consumption, compared with conventional acousto-optic devices, as well as Brillouin scattering efficiency suitable for practical applications. Further increasing the interaction area may cause difficulties in the fabrication process. For example, if the acoustic aperture is 3 mm, then for a total acoustic power of 30 mW, the acoustic power density will be 0.01 mW/μm. According to the scaling laws, will become ∼0.2 mm−1, which suggests that, along the direction normal to the acoustic wave front, the optical power decays to 1/e over a distance of ∼5 mm. In contrast, commercially available acousto-optic devices using bulk crystals require a few watts of acoustic power to achieve comparable performance. This estimation is further justified by considering that scaling down the bulk crystal in one dimension from millimeter size to submicrometer size, while keeping the acoustic power density per unit area in the wave front constant, should lead to orders of magnitude reduction of the total acoustic power without significant changes of the Brillouin scattering efficiency because the reflectivity of the optical phase grating induced by the acoustic wave should remain almost the same.