Acousto-Optic Modulation and Optoacoustic Gating in Piezo-Optomechanical Circuits

Krishna C. Balram, Marcelo I. Davanço, B. Robert Ilic, Ji-Hoon Kyhm, Jin Dong Song, and Kartik Srinivasan

Phys. Rev. Applied 7, 024008 – Published 9 February 2017

Abstract

Acoustic-wave devices provide a promising chip-scale platform for efficiently coupling radio frequency (rf) and optical fields. Here, we use an integrated piezo-optomechanical circuit platform that exploits both the piezoelectric and photoelastic coupling mechanisms to link 2.4-GHz rf waves to 194-THz (1550 nm) optical waves, through coupling to propagating and localized 2.4-GHz acoustic waves. We demonstrate acousto-optic modulation, resonant in both the optical and mechanical domains, in which waveforms encoded on the rf carrier are mapped to the optical field. We also show optoacoustic gating, in which the application of modulated optical pulses interferometrically gates the transmission of propagating acoustic pulses. The time-domain characteristics of this system under both pulsed rf and pulsed optical excitation are considered in the context of the different physical pathways involved in driving the acoustic waves, and modeled through the coupled mode equations of cavity optomechanics.

Received 26 September 2016

DOI:https://doi.org/10.1103/PhysRevApplied.7.024008

Physics Subject Headings (PhySH)

Acoustic interactions Hybrid quantum systems Integrated optics Optical microcavities Optomechanics Photonic crystals Quantum information processing

Devices

Atomic, Molecular & Optical

Authors & Affiliations

Krishna C. Balram^1,2,*, Marcelo I. Davanço¹, B. Robert Ilic¹, Ji-Hoon Kyhm³, Jin Dong Song⁴, and Kartik Srinivasan^1,†

¹Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
²Maryland NanoCenter, University of Maryland, College Park, Maryland 20742, USA
³Quantum-functional Semiconductor Research Center, Dongguk University, Seoul 04620, South Korea
⁴Center for Opto-Electronic Materials and Devices Research, Korea Institute of Science and Technology, Seoul 136-791, South Korea

^*kcbalram@gmail.com
^†kartik.srinivasan@nist.gov

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Vol. 7, Iss. 2 — February 2017

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Figure 1
(a) Illustration of the piezo-optomechanical circuit platform. A nanobeam optomechanical crystal cavity (OMC) is optically probed through an optical fiber taper waveguide (FTW) and acoustically coupled via a phononic crystal waveguide (PHWG), which in turn is sourced by a radio-frequency (rf) interdigitated transducer (IDT). (b) Schematic depiction of two time-domain processes studied in this work, acousto-optic modulation (top) and optoacoustic gating (bottom). In acousto-optic modulation (top), an rf waveform is mixed with an rf carrier at $Ω_{m}$ and applied to the IDT, while a continuous-wave optical field at $ω_{p}$ , detuned from the optical cavity at $ω_{c}$ by $Ω_{m}$ , is coupled into the FTW. Because of the photoelastic interaction between the displayed 1550-nm optical mode and 2.4-GHz mechanical breathing mode in the nanobeam OMC, the input rf waveform is mapped onto the output optical field. In optoacoustic modulation (bottom), an rf carrier at $Ω_{m}$ is applied to the IDT while a phase-modulated optical pulse (pump at $ω_{p}$ and sideband centered at $ω_{c} = ω_{p} + Ω_{m}$ ) is coupled into the FTW. If the phase between the optical pulse and the rf carrier is set appropriately, this results in a destructive interference in the acoustic domain, with both the output acoustic wave and the optical wave bearing the signature of this interaction. The input and output ports of the FTW and nanobeam OMC indicate the optical and acoustic waveforms in the two different cases, while the relevant sidebands in the optical and acoustic domains are shown on the sides of the central images. In our experiments, we monitor the transmitted optical signal to infer the intracavity phonon population. Although we do not explicitly measure the transmitted acoustic-wave channel, we can infer the transmitted phonon population using the intracavity phonon population and energy conservation.
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Figure 2
(a) Schematic of the experimental setup used for the measurements. AWG, arbitrary waveform generator; DDG, digital delay generator used to synthesize pulses with variable pulse widths and delays with respect to a fixed clock; rfSG, radio-frequency signal generator; EOPM, electro-optic phase modulator; FPC, fiber polarization controller; SCOPE, high-speed digital phosphor oscilloscope; APD, avalanche photodiode; $G$ , rf amplifier; $φ$ , phase shifter; $M 1$ , $M 2$ , rf mixers; SAW, surface acoustic wave; IF, intermediate frequency; LO, local oscillator. (b) Table illustrating the switch configurations for the different experimental scenarios. AOM, acousto-optic modulation; pulsed excitation (rf), response of the optomechanical cavity to rf pulses applied to the IDT; pulsed excitation (OPT), response of the optomechanical cavity to rf pulses applied to the EOPM; OAG, optoacoustic gating.
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Figure 3
(a) Thermal noise spectrum (blue) with Lorentzian fit (red) of the localized breathing mode. (b) Normalized piezo-optic $S_{21}$ spectrum. The resonant peak in (b) corresponds to the peak in (a) showing coherent excitation of the localized mode. (c) Acousto-optic modulation: Square (blue), sine (magneta), and sawtooth (red) modulation are imposed on the optical field using a modulated SAW to drive the mechanical motion (the dashed black lines show the applied modulation patterns for reference). (d) Sideband transmission amplitude for the modulation patterns applied in (c), estimated by solving the coupled equations of cavity optomechanics.
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Figure 4
(a) Measured system response to pulsed excitation. Blue, baseline case in which the system is driven optically and off mechanical resonance; red, on-resonance optically driven motion; and green, rf-driven motion due to the IDT-generated propagating acoustic wave. In comparison to the off-resonance optically driven case, on-resonance optically driven motion has a slower rise time due to the mechanical cavity ring-up. (b) Enlargement of (a) showing the rising edges more clearly. The solid lines in (b) are nonlinear least-squares fits to the data assuming a single exponential decay time. (c) Predicted system response to pulsed off-resonance optical excitation (blue), pulsed on-resonance optical excitation (red), and pulsed rf excitation (green), determined by solving the coupled (optical and mechanical) equations of cavity optomechanics.
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Figure 5
(a) Normalized piezo-optic $S_{21}$ response of the optomechanical cavity for three scenarios (see text for detailed explanation). Red, optomechanically induced transparency (OMIT); blue, acoustic-wave interference; green, electromechanically induced transparency (EMIT). (b) Pulse position modulation (gated interference) of $4 − μ s$ -long acoustic pulses using $1 − μ s$ optical pulses with varying delay between the pulses (a vertical offset between the traces is used for clarity). (c) Mechanical cavity response to simultaneous excitation by acoustic pulses ( $4 − μ s$ length) and optical pulses ( $1 − μ s$ length) with varying rf phase $φ$ between them. The central case shown in (b) corresponds to the blue trace. (d) Predicted system response to the pulses in (c).
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Figure 6
(a) Mechanical-mode thermal noise spectrum with SAW and phase modulator (PM) calibration tones indicated. By comparing the peak heights, we can estimate the modulation index imposed by the SAW. 0 dB is referenced to 1 mW of power (i.e., in dBm). (b) Electrical reflection spectrum of the IDT, with the resonance contrast used to estimate the voltage that is coupled to the IDT and generates a propagating SAW.
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