Microwave-to-optical conversion using lithium niobate thin-film acoustic resonators

LINBO SHAO, MENGJIE YU, SMARAK MAITY, NEIL SINCLAIR, LU ZHENG, CLEAVEN CHIA, AMIRHASSAN SHAMS-ANSARI, CHENG WANG, MIAN ZHANG, KEJI LAI, AND MARKO LONČAR John A. Paulson School of Engineering and Applied Sciences, Harvard University, 29 Oxford Street, Cambridge, Massachusetts 02138, USA Division of Physics, Mathematics and Astronomy, and Alliance for Quantum Technologies (AQT), California Institute of Technology, 1200 E. California Blvd., Pasadena, California 91125, USA Department of Physics, University of Texas at Austin, Austin, Texas 78712, USA Department of Electrical Engineering & State Key Laboratory of THz and Millimeter Waves, City University of Hong Kong, Kowloon, Hong Kong, China HyperLight Corporation, 501 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA e-mail: shaolb@seas.harvard.edu e-mail: loncar@seas.harvard.edu


INTRODUCTION
Conversion of information between the microwave and optical domains is a key ingredient for classical and quantum hybrid signal processing, computing, and networking [1][2][3][4][5]. Among the many approaches to achieve coherent quantum transduction, electrically coupled optomechanical systems have emerged as promising candidates [6]. Experimental progress includes suspended structures such as optical waveguides in microwave cavities [7], membranes in free-space Fabry-Perot cavities [8][9][10], and nanoscale piezoelectric optomechanical crystals (OMCs) [11][12][13][14][15][16]. While optical waveguides in bulk microwave cavities benefit from the high quality (Q) factors of microwave resonance, the suspended membranes achieve a high photon number conversion efficiency leveraging a triple resonance of microwave, mechanical, and optical fields. Large-scale integration of these devices is, however, challenging and has not been demonstrated yet. On the other hand, OMCs [17][18][19][20][21][22] provide a fully integrated platform featuring gigahertz mechanical frequencies, and megahertz optomechanical coupling strengths, while limitations due to surface effects are becoming better understood [17].
To address the weak microwave-to-mechanical conversion of current integrated devices, we use freestanding LN thin-film acoustic (i.e., mechanical) resonators with low-loss optical resonators. Using an interdigital transducer (IDT), our acousto-optic devices demonstrate up to 50% coupling efficiency from microwave inputs to acoustic resonator modes, thereby enabling efficient optical modulation using Mach-Zehnder interferometers (MZIs) and racetrack cavities. Our approach benefits from the strong piezoelectricity and electro-optic effects of LN [23][24][25] in conjunction with the photoelastic effect to achieve microwave-to-optical conversion. Specifically, using a 100 μmlong optical waveguide embedded within a 3.33 GHz acoustic resonator with a Q factor of 3600, our MZI exhibits a low half-wave voltage V π of 4.6 V. Moreover, the half-wave-voltagelength product V π L, the figure of merit for optical modulators, is as low as 0.046 V · cm, which is a 50-fold reduction over state-ofthe-art electro-optic modulators [26]. This low V π L comes at the expense of reduced microwave-to-optical conversion bandwidth of around 1 MHz, which is significantly smaller than that of electro-optic MZI approaches [26]. Nonetheless, it is much greater than what has previously been demonstrated using a microwave, mechanical, and optical triple resonance [8]. Our racetrack cavity features an optical Q factor of over 2 × 10 6 , thereby enabling single optical sideband conversion with an effective V π of 0.77 V, a photon number conversion efficiency of 0.0017% for an optical power of 1 mW, and an acousto-optic (i.e., optomechanical) coupling strength of 1.1 kHz. Though this acoustooptic coupling strength is lower than that of state-of-the-art OMCs, the overall microwave-to-optical conversion efficiency is improved due to the enhanced microwave-to-mechanical coupling. Finally, to illustrate its efficient microwave-to-optical conversion, we demonstrate a loss-less microwave-photonic link with a ∼50 mW optical power routing on chip.

DEVICE DESIGN AND FABRICATION
IDTs are periodically spaced metal electrodes placed on piezoelectric materials and provide efficient transduction between alternating electric fields and acoustic waves when the electrode spacing matches the wavelength of the acoustic wave. We utilize IDTs to drive our acoustic resonators due to their efficient electromechanical coupling and ease of fabrication. Notably, IDTs are widely used in electro-acoustic signal processing at up to hypersonic (greater than 1 GHz) frequencies [27]. Furthermore, they have been used in optical applications to diffract guided beams [28][29][30], modulate cavities [31], drive photonic molecules [32], and even break time-reversal symmetry [33]. Therefore, integration of IDT-coupled acoustic resonators [34,35] with highperformance optical devices fabricated in LN [36,37] offers the possibility for efficient acoustically mediated microwave-tooptical conversion.
Figures 1(a) and 1(b) shows our acousto-optic devices in the MZI and the racetrack cavity configurations, respectively.
IDT-coupled acoustic resonators host optical waveguides and modulate the phase acquired by the optical signal propagating in one arm of the MZI, which results in intensity modulation of the transmitted optical signal [ Fig. 1(a)]. A similar effect is responsible for modulating the optical resonance of the racetrack cavity [ Fig. 1(b)]. For our optical components, we employ rib waveguides that are defined by etching a 0.8-μm-thick X-cut LN thin film to a depth of 0.4 μm. The width of the optical waveguide is 0.95 and 1.3 μm in the case of MZI and the racetrack cavity, respectively. In the case of the latter, the larger waveguide cross section is used to reduce the propagating loss due to sidewall roughness. To reduce bending loss and to minimize mode conversion between transverse electric (TE) and transverse magnetic (TM) modes, we employ quadratic Bézier curves for our optical waveguides, which is a generalized form of more conventional Euler curves [38]. To confine the acoustic waves, the LN waveguide is released by removing a sacrificial silicon dioxide layer [ Fig. 1(c)]. The suspended thin-film acoustic resonator is formed by the long slots on both sides of an LN waveguide section. The length of each acoustic resonator is 10 μm, and the width is 100 μm. The electrode width of 90 μm is used to match the impedance of IDT with the 50 Ω impedance of the driving electronics. The electrode pitch and width of IDTs are controlled to allow excitation of acoustic modes at different frequencies.
Specifically, an IDT with four electrodes, a pitch of 0.6 μm, and a width of 0.3 μm is used for the acoustic resonator in the MZI configuration. This allows the coupling to acoustic modes in the range of 1-4.5 GHz, with peak coupling efficiency occurring around 3 GHz. In the racetrack cavity configuration, we use an IDT featuring a pitch of 0.86 μm, a width of 0.43 μm, and the same number of electrodes (four). This allows the highest coupling efficiency to acoustic modes around 2 GHz.
To fabricate each device, three layers of electron beam lithography are used to define the LN optical waveguides, the opening slots for the acoustic resonator and the release of the LN layer, and the metal electrodes needed for IDT. The LN is etched using reactive ion etching, and the fabricated devices feature a sidewall angle of 70°. The metal electrodes are defined using a lift-off process: PMMA resist is patterned as a sacrificial layer, then a 100 µm  75-nm-thick gold layer with an 8-nm-thick chromium adhesion layer is deposited using electron-beam evaporation, and the device is immersed in a solvent to lift off the resist. Finally, the release of the LN device from the substrate is achieved using buffered oxide etchant, which removes the sacrificial oxide layer underneath through the completely etched slots of the LN layer.

DESCRIPTION OF ACOUSTICALLY MEDIATED MICROWAVE-TO-OPTICAL CONVERSION
Our acoustic resonator mediates the microwave-to-optical conversion by coupling to the microwave input via the IDT and modulating light due to acoustic modes [ Fig. 2(a)]. The optical modulation is enabled by a generalized acousto-optic interaction that comprises conventional optomechanical couplings of photoelastic and weak moving boundary effects, as well as cascading piezoelectric and electro-optic effects, which feature a coupling strength comparable to photoelastic alone. We perform simulations to understand and engineer the interplay among these three effects in order to maximize the overall acousto-optic interaction.
The coupling strength of each interaction is evaluated using a two-dimensional (2D) numerical model based on the device cross section and crystal orientation shown in Fig. 2(b). To avoid double-counting the coupling strength, we use photoelastic (electro-optic) coefficients under a constant electric field (strain, i.e., clamped) condition following that presented in Refs. [25,39]. Owing to the LN crystal orientation chosen for our device, the generalized acousto-optic interaction is much stronger for the guided TE mode [ Fig. 2(c)] than for the TM mode at 1550 nm, due to the strong electro-optic and photoelastic coefficients, r 33 and p 31 , respectively, for TE polarization. The electro-optic coefficients form a third-order tensor, and r 33 relates n Z Z , the optical index change of the crystal Z Z component (indicated by the first 3 in the subscript), to E Z , the electrical field in the Z direction (indicated by the first 3 in the subscript). The photoelastic coefficients form a fourth-order tensor, and p 31 relates n Z Z to s X X , the strain of the crystal X X component (indicated by the 1 in the subscript). Thus, the strain s X X (or s yy in the simulation coordinate) contributes most to the photoelastic interaction. Detailed discussions are provided in Supplement 1. Figures 2(d) and 2 (e) plot the simulated acoustic strain s yy and electric field E x of a 3.24 GHz mode, both of which have the same sign across the optical waveguide region, thus contributing constructively to the overall modulation to the optical refractive index.
The contributions of moving boundary, electro-optic, and photoelastic effects are calculated by integrating the products of the acoustic and optical field components with the corresponding coupling matrices. Acousto-optic interaction strengths between various acoustic modes and optical TE or TM mode are summarized in Table S1 of Supplement 1. For the 3.24 GHz acoustic mode, Figs. 2(f ) and 2(g) show the induced refractive index changes of the TE mode by the photoelastic and electro-optic effects. Based on this result, we extract an acoustooptic single-photon coupling strength g 0 1.6 kHz for the racetrack cavity geometry. For the acousto-optic MZI, the half-wave voltage-length product V π L depends on the acoustic Q factor and microwave-to-acoustic coupling efficiency, where we use experimental values to avoid overestimation by the 2D simulation. A half-wave voltage-length product V π L 0.045 V · cm for the acousto-optic MZI is extracted based on the simulated interaction strength, as well as the acoustic Q of 2000 and electrical-toacoustic coupling efficiency of 0.5 (corresponding to a -3 dB dip in the S 11 spectrum) from typical experimental measurements. Details are provided in Section 1 of Supplement 1.

ACOUSTO-OPTIC MZI
We experimentally characterize our acousto-optic MZI using a tunable C-band laser, a vector network analyzer (VNA), and a photoreceiver that features a sensitivity of ∼800 V∕W [ Fig. 3(a)].

Research Article
We use lensed fiber to couple light into and out of our structures with a fiber-to-fiber insertion loss of 10 dB (< 5 dB∕facet) for our suspended LN chip. The periodic variation of optical transmission with wavelength at 10 nm intervals is consistent with the optical path difference in the MZI [ Fig. 3(b)]. To optimize the microwave-to-optical conversion efficiency, the laser wavelength is chosen to be 1534 nm, corresponding to 50% transmission and indicating a π∕2 phase difference between two optical paths. We evaluate the acoustic resonances and the microwave-toacoustic coupling of our devices by measuring the microwave reflection (S 11 ) of the IDT. Our acoustic resonator exhibits multiple resonances in the range between 1.0 and 4.5 GHz. To correlate measured acoustic modes with that of our simulations, the acoustic-electric field profiles are experimentally measured using transmission-mode microwave impedance microscopy [40,41]; see Section 4 of Supplement 1. We measure acoustic Q factors of up to 3600 [ Fig. 3(c)], similar to the LN OMC devices [12,18], and our resonance at the microwave frequency of 3.273 GHz yields a state-of-the-art frequency-quality-factor product of f Q > 10 13 at room temperature [35].
We characterize the optical modulation induced by the acoustic resonance by the optoacoustic S 21 spectrum, where the driving Port 1 of the VNA is connected to the IDT of the acoustic resonator and the detecting Port 2 is connected to the photoreceiver [ Fig. 3(a)]. The S 21 spectrum shown in Fig. 3(d) features several peaks indicating enhanced microwave-to-optical conversion at acoustic resonances, with the strongest responses measured at the 2.24 and 3.33 GHz acoustic modes, in agreement with our simulations (Table S1). The microwave-to-optical conversion efficiency indicated by the S 21 depends on both the acoustic Q factor and the overlap between the acoustic mode and the optical mode. We extract the half-wave voltage V π of our acousto-optic MZI from the experimental measurements of the S 21 spectrum.
Under the conditions of our measurement, the MZI half-wave voltage V π is related to the S 21 by in which R PD (I rec 0.25 mW) is the sensitivity of (optical power at) the photoreceiver, with derivation given in Section 2 of Supplement 1. We find V π 4.6 V (5.8 V) using S 21 −17.4 dB (-19.3 dB) at the resonance frequency of 3.33 GHz (2.24 GHz), and due to the 100-μm length of our acoustic resonator, we obtain V π L 0.046 V · cm (0.058 V · cm), which agrees with that predicted by our simulation.

ACOUSTO-OPTIC RACETRACK CAVITY
We can further improve the microwave-to-optical conversion efficiency by using the acoustic-optic racetrack cavity [ Fig. 4(a)]. Compared with MZI, our racetrack cavity features a loaded optical Q factor of 2.2 × 10 6 for TE-polarized light of wavelength 1574.9 nm, corresponding to a linewidth of 95 MHz [ Fig. 4(b)], allowing us to operate in the microwave sideband-resolved regime. With the laser blue-detuned by the acoustic resonant frequency from the optical resonance, we generate an optical sideband by the acoustic resonant mode and enhance it using the racetrack resonator [ Fig. 4(a)]. Consequently, we observe a high S 21 −7.5 dB at the acoustic resonant frequency of 2 GHz, with a total optical power of I rec 0.13 mW measured at the photoreceiver [ Fig. 4(c)]. We note that the S 21 quadratically depends on the optical power, and we should consider S 21 at the same optical power level to compare the conversion efficiency. The S 21 of the racetrack cavity thus results in a much lower effective V π of 0.77 V than does the MZI, as determined by Research Article the small-signal response of an intensity modulator (see Section 2 of Supplement 1). Next, we determine the overall acousto-optic single-photon coupling strength g 0 . In the sideband-resolved regime (Ω m ≫ κ) and for weak microwave inputs, the relation between the S 21 and g 0 is given by where κ (γ) and κ e (γ e ) are the total loss and external coupling rate of the optical (acoustic) mode, respectively. Ω m is the frequency of the acoustic mode, and R load 50 Ω is the impedance of the input microwave source. Equation (2) is derived from the equation of motion for the dynamics of the acousto-optic cavity (see Section 3 of Supplement 1). We estimate the acousto-optic singlephoton coupling strength to be g 0 ∼ 1.1 kHz between the 2.17 GHz acoustic mode and the fundamental TE optical mode, which is in good agreement with our theoretical predictions (see Table S1, Supplement 1). Another important figure of merit is the photon number conversion efficiency η from the microwave frequency to the optical sideband frequency, and it describes the device performance at the single-photon level. From the derivation described in Section 3 of Supplement 1, the photon number conversion efficiency η is given by where C 0 4g 2 0 ∕γκ is the single-photon cooperativity, n cav κ e I opt ∕Ω 2 m ℏω 0 is the intracavity optical photon number for the blue-detuned pump light, and 2κ e ∕κ (2γ e ∕γ) describes the external coupling efficiency of the optical (acoustic) mode. Based on the experimentally extracted rates (Table S2), our acoustooptic cavity features a single-photon cooperativity C 0 4 × 10 −8 and a photon number conversion efficiency η 0.0017% for an optical power of I opt 1 mW. This efficiency could be further improved by acoustic and photonic engineering, as will be discussed later in Section 7.
As shown in Eq. (3), the photon number conversion efficiency depends on both optomechanical cooperativity (C 0 ) and the microwave-to-mechanical coupling strength (described by 2γ e ∕γ). Recent progress of LN OMCs [12] has demonstrated unitary optomechanical cooperativity, but their microwave-to-mechanical coupling strength is as low as 10 −8 , which would limit the overall photon number conversion efficiency. Benefiting from our up to 50% microwave-to-acoustic coupling to the thin-film acoustooptic resonator, this photon number conversion efficiency could be greater than that of the OMCs, even though the acousto-optic coupling strength is weaker than that of the OMCs.

DEMONSTRATION OF A MICROWAVE-PHOTONIC LINK
A microwave-photonic link enables low-loss long-haul transport and flexible manipulation of microwave signals using optical devices by upconverting microwave frequencies to optical frequencies. To benchmark our acousto-optic racetrack device, we demonstrate a narrowband microwave-photonic link using our acousto-optic racetrack cavity, and a link gain of 0 dB is achieved without the need of an optical amplifier within the link (after the modulation of our acousto-optic device), which would significantly increase the noise of the link. The optical pump light is amplified to ∼500 mW by an erbium-doped fiber amplifier and is blue-detuned by the acoustic resonant frequency Ω m from the optical resonance [ Fig. 5(a)]. We estimate that ∼150 mW of optical power is coupled into the suspended LN waveguide, resulting in ∼50 mW reaching the photodiode. Importantly, no damage to the waveguide is observed, indicating the ability of our suspended thin-film LN devices to handle large optical powers. A high-power photodiode, with responsivity R PD of 0.55 A/W (corresponding to a quantum efficiency of 40%), is used to detect and downconvert the optical signal that we generate from our racetrack acousto-optic transducer back to the microwave domain. With these parameters, we measure an overall microwave link gain of 0 dB at 1.572 GHz [ Fig. 5(b)] for a small microwave input signal at -20 dBm. By reducing the fiber-to-chip coupling loss to the previously demonstrated value of 1.7 dB/facet [42], a microwave link with a gain of 6.6 dB may be achieved in principle, with the possibility of a gain of at least 9 dB if tapered fibers are employed [43,44].
Next, we characterize the response at higher powers of microwave input. With increasing microwave powers at the acoustic resonant frequency Ω m ∼ 2 GHz, optical sideband dips are observed in the transmission spectra [ Fig. 5(c)] that agree with  Fig. 4. Characterization of the acousto-optic racetrack cavity. (a) Simplified experimental schematic and illustration of single-sideband microwave-tooptical conversion using an acousto-optic cavity; (b) transmission spectrum of a high-Q optical resonance; (c) acoustic S 11 and opto-acoustic S 21 spectra. A high resolution measurement around 2 GHz is shown in dark blue. The optical pump wavelength is set to maximize the power received at the photoreceiver.
theoretical predictions (Fig. S3, Supplement 1). The redshift of the optical resonance with increasing input microwave powers results from the heating of the acoustic resonator. As a result of the efficient microwave-to-optical conversion, a pair of second-order sideband dips can be observed in the optical transmission spectrum with only 5 mW of microwave input power.
Parking the laser at Ω m detuning from the optical mode, up to third-order harmonic signals are observed at the photodiode output with a microwave power of 5 mW [ Fig. 5(d)]. The additional broad peak observed at 3.85 GHz is a result of the suspended optical racetrack cavity, since it is only observed when the pump laser is close to the optical resonance. We speculate that the acoustic mode along the suspended optical waveguide causes this additional peak by spontaneous Brillouin scattering, as our suspended racetrack cavity has a similar geometry with that in Ref. [45].

CONCLUSIONS AND OUTLOOK
We demonstrate an integrated acousto-optic platform on thinfilm LN, which converts acoustic waves in the microwave domain to optical light by a generalized acousto-optic interaction. The efficient microwave-to-acoustic coupling has been achieved using our IDT-coupled LN thin-film acoustic resonator. This addresses the coupling issue of current OMC-based platforms using mechanically mediated microwave-to-optical converters. To further improve the photon number conversion efficiency, a variety of efforts in acoustic and photonic engineering can be made. For example, the acoustic resonator can be operated under vacuum and cryogenic environments to achieve higher Q factors, and the clamping loss of the suspended structures can be further reduced using phononic crystals [20]. Optical cavities defined by photonic crystal mirrors could improve the acousto-optic coupling strength g 0 with larger overlap with the acoustic resonator, while the presented racetrack cavity only partially sits in the acoustic resonator. Another order-of-magnitude improvement could be obtained by bringing both the pump light and generated optical sideband into resonance [3]. With a double optical resonance, which can be found in coupled cavities or due to scattering in a single ring cavity, the term Ω 2 (∼ GHz) in the denominator of intracavity optical photon number n cav [Eq. (3)] is replaced by the optical cavity loss κ 2 (∼10 s of MHz) and could result in an improvement of 4 orders of magnitude.
Beyond microwave-to-optical conversion, our acousto-optic platform could also find applications in gigahertz frequency optical comb generation [46,47], on-chip optical routing, and optical mode conversion. In these applications, the acoustic resonator could strongly enhance the signal in the microwave domain and allow low microwave power operations. Compared to microwave electromagnetic resonators, the high acoustic f Q product and smaller acoustic mode volume of our on-chip acousto-optic resonator could enable quantum optomechanics at room temperatures with smaller footprints.