Taming Brillouin Optomechanics Using Supermode Microresonators

Open Access

Taming Brillouin Optomechanics Using Supermode Microresonators

Min Wang, Zhi-Gang Hu, Chenghao Lao, Yuanlei Wang, Xing Jin, Xin Zhou, Yuechen Lei, Ze Wang, Wenjing Liu, Qi-Fan Yang, and Bei-Bei Li

Phys. Rev. X 14, 011056 – Published 26 March 2024

Abstract

Electrostrictive Brillouin scattering provides a ubiquitous mechanism to optically excite high-frequency ( $> 10 GHz$ ), bulk acoustic phonons that are robust to surface-induced losses. Resonantly enhancing such photon-phonon interactions in high- $Q$ microresonators has spawned diverse applications spanning microwave to optical domains. However, tuning both the pump and scattered waves into resonance usually comes with the cost of photon confinement or modal overlap, leading to limited optomechanical coupling. Here, we introduce Bragg scattering to realize strong bulk optomechanical coupling in the same spatial modes of a micron-sized supermode microresonator. A single-photon optomechanical coupling rate up to 12.5 kHz is demonstrated, showing more than 10 times improvement than other devices. Low-threshold phonon lasing and optomechanical strong coupling are also observed for the 10.2-GHz mechanical mode. Our work establishes a compact and efficient paradigm to optically control bulk acoustic phonons, paving the way toward optomechanical coupling at the single-photon level and providing a powerful engine for large-scale integration of quantum networks in which quantum states are massively transferred and stored.

Received 27 July 2023
Revised 27 November 2023
Accepted 26 February 2024
Corrected 22 April 2024

DOI:https://doi.org/10.1103/PhysRevX.14.011056

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Brillouin scattering & spectroscopy Nonlinear optics Optomechanics Photonics

Cavity resonators

Atomic, Molecular & Optical

Corrections

22 April 2024

Correction: A minor error in Eq. (1) has been fixed. The previously published Fig. 3 contained an error in a label in panel (a) and has been replaced.

Authors & Affiliations

Min Wang ^1,3,*, Zhi-Gang Hu^1,3,*, Chenghao Lao^1,2, Yuanlei Wang^1,2, Xing Jin², Xin Zhou^1,3, Yuechen Lei^1,3, Ze Wang², Wenjing Liu^2,5, Qi-Fan Yang ^2,5,†, and Bei-Bei Li ^1,4,‡

¹Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
²State Key Laboratory for Artificial Microstructure and Mesoscopic Physics and Frontiers Science Center for Nano-optoelectronics, School of Physics, Peking University, Beijing 100871, China
³University of Chinese Academy of Sciences, Beijing 100049, China
⁴Songshan Lake Materials Laboratory, Dongguan 523808, Guangdong, China
⁵Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China

^*These authors contributed equally to this work.
^†leonardoyoung@pku.edu.cn
^‡libeibei@iphy.ac.cn

Popular Summary

When light shines on a solid, it causes the solid to vibrate, generating sound waves. This optomechanical process is known as Brillouin scattering, and it has numerous applications in microscopy, sensing, and lasing. However, Brillouin scattering in bulk materials is often quite weak and requires devices like optical microresonators to enhance it. The strict phase-matching conditions for Brillouin scattering limit the size of microresonators and, in turn, the optomechanical coupling rate. In this work, we develop a new type of microresonator to enhance the Brillouin interaction.

The key novelty of our design is a set of nanometer-scale gratings etched at the edge of the microresonator. When light encounters these gratings, it can be scattered back into opposite directions, creating a coupling between the clockwise and counterclockwise optical modes. This coupling lifts the degeneracy of the two modes and creates two new “supermodes,” or superpositions of the traveling-wave modes. By carefully adjusting the frequency difference between these supermodes to match the acoustic phonon frequency, we achieve ideal phase-matching conditions for Brillouin scattering. This configuration allows Brillouin scattering to occur in much smaller microresonators, greatly enhancing the optomechanical coupling rate. We successfully achieve phonon lasing and optomechanical strong coupling using a silicon dioxide microresonator with a radius of only $20 μ m$ .

This supermode microresonator configuration is also applicable to material platforms with higher Brillouin gain coefficients, such as chalcogenide glass and gallium arsenide. We expect that our device will become a key engine for high-density integration of photonic functionalities enabled by Brillouin scattering.

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Vol. 14, Iss. 1 — January - March 2024

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Images

Figure 1
Brillouin optomechanics in microresonators. (a) Microresonator configurations for efficient bulk Brillouin optomechanics. The resonant structures of the microresonators are plotted on the right. (b) Top: images showing FSR-matched microresonator (left) and supermode microresonators (right). Middle: scanning-electron-microscope image of the supermode microresonator. Bottom: enlarged view of the microresonator boundary.
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Figure 2
Supermode microresonator. (a) Simulated single-photon optomechanical coupling rate ( $g_{0} / 2 π$ ) of different mechanical modes in a microresonator with $20 μ m$ radius. The contributions from the photoelastic effect ( $g_{0}^{pe} / 2 π$ , orange columns) and the moving boundary effect ( $g_{0}^{mb} / 2 π$ , blue columns) are both indicated. (b) Transmission spectrum of a ${SiO}_{2}$ microresonator with $r_{0} = 20 μ m$ and $α \approx 12.6 nm$ , where the target mode has an azimuthal mode number of $m = 101$ . Insets provide enlarged views of the frequency splitting and $Q$ factor.
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Figure 3
Observation of phonon lasing. (a) Schematics of the physical mechanisms of phonon lasing when pumping at the higher-frequency split mode. (b) Optical spectra of stimulated Brillouin scattering (SBS) in both the CW and CCW directions when the pump light is coupled into the higher-frequency split mode in the CW direction. (c) Stokes power in the CW direction ( $P_{S}^{CW}$ ) as a function of the pump power, revealing a threshold power of $P_{th} \approx 8.28 mW$ . Inset: the ratio of the Stokes powers in the CCW and CW directions, which maintains approximately 1. (d) Single-sideband (SSB) frequency noise spectra of phonon lasers with different Stokes powers coupled out of the microresonator. The green, red, orange, and blue curves correspond to the coupled out Stokes power in the CW direction ( $P_{S}^{CW}$ ) of 0.167, 0.289, 1.03, and 3.59 mW, respectively. (e) Phonon linewidth as a function of the coupled out Stokes power in the CCW direction. Inset: electronic spectrum displaying the mechanical frequency at 10.3 GHz.
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Figure 4
Observation of optomechanical strong coupling. (a) Schematic illustrating the resonance structure for the anti-Stokes process. A pump laser with frequency $ω_{pump}$ drives the lower-frequency split mode $a_{-}$ . The higher-frequency sideband of the pump laser, generated by the EOM at a frequency of $ω_{probe}$ , is used to probe the higher-frequency split mode $a_{+}$ . The frequency separation between $a_{+}$ mode and the Brillouin gain peak is denoted as $Δ_{m} = ω_{+} - ω_{pump} - Ω_{m}$ . (b) Power spectra around the high-frequency split mode. As the detuning $ω_{pump} - ω_{-}$ decreases from bottom to top, the intracavity pump power ( $P_{cav}$ ) increases, and the frequency difference between two photonic-phononic hybrid modes first decreases and then increases, showing a trend of avoided mode crossing. (c) Comparison of experimentally measured (top) and theoretically predicted (bottom) spectra as a function of the frequency detuning $ω_{pump} - ω_{-}$ . (d) Optomechanical coupling rate ( $G / 2 π$ ) derived from the measured spectra, plotted as a function of the intracavity pump power ( $P_{cav}$ ).
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Figure 5
Comparison of optomechanical microresonators driven by photoelastic effect. (a) Single-photon optomechanical coupling rate $g_{0} / 2 π$ versus the footprint of the resonator. (b) Single-photon cooperativity $C_{0}$ versus the mechanical frequency.
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