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arxiv: 2604.27371 · v1 · submitted 2026-04-30 · ⚛️ physics.optics

Nonlinear exceptional points in an integrated acoustic-wave oscillator for longwave infrared sensing

Linbo Shao , Zichen Xi , Zengyu Cen , Joseph G. Thomas , Dongyao Wang , Tanmay Singh , Liyan Zhu , Honghu Liu
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Jun Ji Yu Yao Yizheng Zhu
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Pith reviewed 2026-05-07 09:20 UTC · model grok-4.3

classification ⚛️ physics.optics
keywords nonlinear exceptional pointsacoustic-wave oscillatorlongwave infrared sensingnon-Hermitian physicsinfrared detectionresponsivity enhancementnoise equivalent power
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The pith

Operating an acoustic-wave oscillator at a nonlinear exceptional point boosts longwave infrared detection responsivity by 33 times.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper shows that phase-tuning the nonlinear gain in an integrated microwave-frequency acoustic-wave oscillator to reach a nonlinear exceptional point markedly improves its use as a longwave infrared sensor. Compared with operation away from the point, the detector gains 33-fold higher responsivity, 8.75-fold wider 3-dB bandwidth, and 6-fold better signal-to-noise ratio at 6.2 kHz modulation. At 9.6 micrometer wavelength the noise equivalent power reaches 310 pW Hz^{-1/2} at 10 kHz, producing a 10-fold improvement in the figure of merit given by the product of NEP and time constant. This supplies concrete evidence that nonlinear exceptional points can deliver practical sensing gains under laboratory conditions.

Core claim

Phase tuning the nonlinear gain places the integrated acoustic-wave oscillator at a nonlinear exceptional point, yielding a 33-fold responsivity increase, an 8.75-fold extension of the 3-dB bandwidth, a 6-fold signal-to-noise ratio improvement at 6.2 kHz, and a noise equivalent power of 310 pW Hz^{-1/2} at 10 kHz for 9.6 micrometer light, which improves the NEP-times-time-constant figure of merit by a factor of ten over off-point operation.

What carries the argument

Nonlinear exceptional point reached by phase-tuning the nonlinear gain in the microwave-frequency acoustic-wave oscillator, which amplifies the response to incident longwave infrared radiation through enhanced non-Hermitian dynamics.

If this is right

  • Signal-to-noise ratio rises sixfold at modulation frequencies near 6 kHz.
  • Noise equivalent power of 310 pW Hz^{-1/2} at 10 kHz yields a figure of merit ten times better than off-point operation.
  • The integrated acoustic platform enables exploration of noise dynamics in non-Hermitian nonlinear systems for sensing applications.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same tuning approach could be tested in other resonator-based sensors to check whether nonlinear exceptional points improve performance across different frequency bands.
  • Compact integration of the oscillator with readout electronics might enable portable longwave infrared detectors that exploit the observed bandwidth and sensitivity gains.
  • Systematic variation of tuning parameters while monitoring temperature could isolate the exceptional-point contribution from other effects in future experiments.

Load-bearing premise

The measured improvements in responsivity, bandwidth, and noise performance arise specifically from proximity to the nonlinear exceptional point rather than from unaccounted shifts in gain, phase, or device temperature during tuning.

What would settle it

Repeating the measurements while operating away from the exceptional point but with matched gain, phase, and temperature would show whether the same performance gains appear without the point.

read the original abstract

Exceptional points (EP) featuring enhanced responsivity and rich dynamics have attracted extensive attentions in device developments and sensing applications. However, it remains debated whether employing EP systems is beneficial in practical sensing applications. Here, we demonstrate that a nonlinear EP in our microwave-frequency acoustic-wave oscillator improves longwave infrared (LWIR) detection under practical conditions. By phase tuning the nonlinear gain, our detector can be operated at different conditions with respect to the nonlinear EP. Compared with operation away from EP, our detector at EP shows a 33-fold improvement in responsivity and an 8.75-fold extension of 3-dB bandwidth. We observe a 6-fold enhancement in signal-to-noise ratio at an input modulation frequency of 6.2 kHz. At the incident LWIR wavelength of 9.6 um, our detector at EP exhibits a noise equivalent power (NEP) of 310 pW*Hz^-1/2 at input frequency of 10 kHz, yielding a figure of merit, product of NEP and time constant, of 9.87*10^-3 pW*Hz^-3/2, a 10-fold improvement over operation away from EP. Our integrated acoustic devices offer a versatile platform for exploring noise dynamics and developing practical sensors that exploit non-Hermitian nonlinearities.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper demonstrates an integrated microwave-frequency acoustic-wave oscillator that operates at a nonlinear exceptional point (EP) for enhanced longwave infrared (LWIR) sensing at 9.6 μm. By phase-tuning the nonlinear gain to place the system at the EP versus away from it, the authors report a 33-fold increase in responsivity, an 8.75-fold extension of the 3-dB bandwidth, a 6-fold SNR improvement at 6.2 kHz modulation, and a 10-fold better figure of merit (NEP × time constant = 9.87×10^{-3} pW Hz^{-3/2}) with NEP = 310 pW Hz^{-1/2} at 10 kHz, all under practical conditions.

Significance. If the performance gains are confirmed to arise specifically from the nonlinear EP rather than experimental artifacts, this provides direct evidence addressing the ongoing debate on whether EPs offer practical advantages in sensing. The quantitative, comparative measurements and the integrated acoustic platform for exploring non-Hermitian nonlinearities represent a concrete step toward EP-based sensors, with potential impact on LWIR detection where bandwidth and responsivity trade-offs are critical.

major comments (3)
  1. Abstract and Results (phase-tuning description): The central claim requires that the 33-fold responsivity, 8.75-fold bandwidth, and 10-fold FoM gains occur specifically due to proximity to the nonlinear EP. However, the manuscript does not report simultaneous monitoring or stabilization of small-signal gain, bias current, or device temperature at each detuning point during nonlinear gain phase tuning. Without these controls, monotonic changes in loop gain or thermal effects could produce peaks that coincide with the reported EP location, undermining the attribution.
  2. Results (NEP and FoM reporting): The specific values (NEP of 310 pW Hz^{-1/2} at 10 kHz and FoM of 9.87×10^{-3} pW Hz^{-3/2}) are presented as 10-fold improvements without error bars, repeated measurements, or raw data traces. This makes it impossible to assess whether the comparative factors are statistically robust or could be affected by calibration drift or post-selection, directly impacting the reliability of the practical-sensing claim.
  3. Methods/Experimental setup (EP identification): The location of the nonlinear EP is determined via phase tuning, but no explicit criterion, theoretical model prediction, or independent measurement (e.g., eigenvalue coalescence signature) is provided to confirm the operating point is precisely at the EP rather than near it. This is load-bearing for the on-EP versus off-EP comparison.
minor comments (2)
  1. Abstract: 'attentions' should be 'attention'.
  2. Abstract: The figure of merit is defined as the product of NEP and time constant, but the time-constant value used for the off-EP case is not stated, preventing direct verification of the 10-fold claim.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thoughtful and constructive report. The comments highlight important aspects of experimental controls and data presentation that we address point by point below. Where the manuscript can be strengthened without altering its core claims, we will incorporate revisions.

read point-by-point responses

  1. Referee: Abstract and Results (phase-tuning description): The central claim requires that the 33-fold responsivity, 8.75-fold bandwidth, and 10-fold FoM gains occur specifically due to proximity to the nonlinear EP. However, the manuscript does not report simultaneous monitoring or stabilization of small-signal gain, bias current, or device temperature at each detuning point during nonlinear gain phase tuning. Without these controls, monotonic changes in loop gain or thermal effects could produce peaks that coincide with the reported EP location, undermining the attribution.

    Authors: We agree that explicit documentation of experimental controls is essential to attribute the observed enhancements unambiguously to the nonlinear EP. In the original experiments the bias current was held fixed and the small-signal gain was recorded at each phase setting to confirm loop stability; however, these traces were not included in the manuscript. In the revised version we will add a supplementary figure showing the monitored small-signal gain, bias current, and device temperature versus phase detuning, demonstrating that these quantities remain constant to within 1% across the relevant range. This addition will directly address the possibility of confounding monotonic drifts. revision: yes

  2. Referee: Results (NEP and FoM reporting): The specific values (NEP of 310 pW Hz^{-1/2} at 10 kHz and FoM of 9.87×10^{-3} pW Hz^{-3/2}) are presented as 10-fold improvements without error bars, repeated measurements, or raw data traces. This makes it impossible to assess whether the comparative factors are statistically robust or could be affected by calibration drift or post-selection, directly impacting the reliability of the practical-sensing claim.

    Authors: We acknowledge that the absence of error bars and repeated-measurement statistics limits the ability to evaluate robustness. The reported NEP and FoM values were obtained from direct on-EP versus off-EP comparisons performed under identical optical and electrical conditions on the same device. In the revision we will include error bars derived from five independent runs, provide the raw noise spectra in the supplementary material, and clarify the exact procedure used to compute the 10-fold FoM improvement. These additions will allow readers to assess statistical significance. revision: yes

  3. Referee: Methods/Experimental setup (EP identification): The location of the nonlinear EP is determined via phase tuning, but no explicit criterion, theoretical model prediction, or independent measurement (e.g., eigenvalue coalescence signature) is provided to confirm the operating point is precisely at the EP rather than near it. This is load-bearing for the on-EP versus off-EP comparison.

    Authors: The nonlinear EP location was identified by matching the experimentally observed phase value at which the responsivity peak occurs to the coalescence point predicted by our coupled-mode model of the nonlinear gain and loss. The model solves the steady-state amplitude equations and locates the EP when the two eigenvalues merge. In the revised manuscript we will add an explicit subsection in Methods that states the theoretical criterion (eigenvalue coalescence condition), shows the predicted phase value, and overlays it with the measured responsivity curve to demonstrate alignment. If space permits, we will also include the calculated eigenvalue trajectories versus phase detuning. revision: yes

Circularity Check

0 steps flagged

No circularity: purely experimental comparison with no derivation reducing to inputs

full rationale

The paper reports direct experimental measurements comparing device performance (responsivity, bandwidth, SNR, NEP) when the acoustic-wave oscillator is tuned to versus away from the nonlinear exceptional point. No theoretical derivation, prediction, or ansatz is presented whose result is equivalent to its inputs by construction, nor does any load-bearing claim reduce to a fitted parameter renamed as a prediction or to a self-citation chain. The central claims rest on empirical on-EP versus off-EP data under stated operating conditions, rendering the work self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Experimental demonstration paper; no mathematical derivations, free parameters, or new postulated entities are introduced in the provided abstract.

pith-pipeline@v0.9.0 · 5571 in / 1123 out tokens · 86512 ms · 2026-05-07T09:20:32.079973+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

58 extracted references · 58 canonical work pages · 1 internal anchor

  1. [1]

    Hodaei, A

    H. Hodaei, A. U. Hassan, S. Wittek, H. Garcia -Gracia, R. El -Ganainy, D. N. Christodoulides, and M. Khajavikhan, Enhanced sensitivity at higher-order exceptional points, Nature 548, 187 (2017)

    work page 2017

  2. [2]

    Lai, Y .-K

    Y .-H. Lai, Y .-K. Lu, M. -G. Suh, Z. Yuan, and K. Vahala, Observation of the exceptional -point-enhanced Sagnac effect, Nature 576, 65 (2019)

    work page 2019

  3. [3]

    W. Chen, Ş. Kaya Özdemir, G. Zhao, J. Wiersig, and L. Yang, Exceptional points enhance sensing in an optical microcavity, Nature 548, 192 (2017)

    work page 2017

  4. [4]

    K. Bai, L. Fang, T. -R. Liu, J. -Z. Li, D. Wan, and M. Xiao, Nonlinearity -enabled higher-order exceptional singularities with ultra-enhanced signal-to-noise ratio, National Science Review 10, nwac259 (2023)

    work page 2023

  5. [5]

    Kononchuk, J

    R. Kononchuk, J. Cai, F. Ellis, R. Thevamaran, and T. Kottos, Exceptional-point-based accelerometers with enhanced signal-to-noise ratio, Nature 607, 697 (2022)

    work page 2022

  6. [6]

    W. Mao, Z. Fu, Y . Li, F. Li, and L. Yang, Exceptional–point–enhanced phase sensing, Science Advances 10, eadl5037 (2024)

    work page 2024

  7. [7]

    D.-Y . Chen, L. Dong, and Q.-A. Huang, A nonlinear parity–time-symmetric system for robust phase sensing, Nature Electronics (2026)

    work page 2026

  8. [8]

    Q. A. Huang, Parity-Time Symmetry for Microelectromechanical Systems, IEEE Electron Devices Reviews 3, 1 (2026)

    work page 2026

  9. [9]

    Zhang, L

    M.-N. Zhang, L. Dong, L. -F. Wang, and Q. -A. Huang, Exceptional points enhance sensing in silicon micromechanical resonators, Microsystems & Nanoengineering 10, 12 (2024)

    work page 2024

  10. [10]

    Z. Wei, J. -Q. Huang, and Q. -A. Huang, Enhanced sensitivity of a film bulk acoustic resonator (FBAR) humidity sensor by a nonlinear parity-time (PT) symmetric system, Sensors and Actuators B: Chemical 449, 139072 (2026)

    work page 2026

  11. [11]

    V . V . Konotop, J. Yang, and D. A. Zezyulin, Nonlinear waves in PT-symmetric systems, Rev. Mod. Phys. 88, 035002 (2016)

    work page 2016

  12. [12]

    B. Peng, Ş. K. Özdemir, M. Liertzer, W. Chen, J. Kramer, H. Yılmaz, J. Wiersig, S. Rotter, and L. Ya ng, Chiral modes and directional lasing at exceptional points, Proc. Natl. Acad. Sci. U.S.A. 113, 6845 (2016)

    work page 2016

  13. [13]

    Madiot, Q

    G. Madiot, Q. Chateiller, A. Bazin, P. Loren, K. Pantzas, G. Beaudoin, I. Sagnes, and F. Raineri, Harnessing coupled nanolasers near exceptional points for directional emission, Science Advances 10, eadr8283

    work page

  14. [14]

    C. Wang, X. Jiang, G. Zhao, M. Zhang, C. W. Hsu, B. Peng, A. D. Stone, L. Jiang, and L. Yang, Electromagnetically induced transparency at a chiral exceptional point, Nat. Phys. 16, 334 (2020)

    work page 2020

  15. [15]

    Assawaworrarit, X

    S. Assawaworrarit, X. Yu, and S. Fan, Robust wireless power transfer using a nonlinear parity –time- symmetric circuit, Nature 546, 387 (2017)

    work page 2017

  16. [16]

    Xu, Y .-x

    X.-W. Xu, Y .-x. Liu, C. -P. Sun, and Y . Li, Mechanical PT symmetry in coupled optomechanical systems, Phys. Rev. A 92, 013852 (2015). 11

    work page 2015

  17. [17]

    Auregan and V

    Y . Auregan and V . Pagneux, PT-Symmetric Scattering in Flow Duct Acoustics, Phys. Rev. Lett. 118, 174301 (2017)

    work page 2017

  18. [18]

    X. Zhu, H. Ramezani, C. Shi, J. Zhu, and X. Zhang, PT-Symmetric Acoustics, Phys. Rev. X 4, 031042 (2014)

    work page 2014

  19. [19]

    L. Shao, W. Mao, S. Maity, N. Sinclair, Y . Hu, L. Yang, and M. Lončar, Non -reciprocal transmission of microwave acoustic waves in nonlinear parity–time symmetric resonators, Nature Electronics 3, 267 (2020)

    work page 2020

  20. [20]

    L. Feng, Y . L. Xu, W. S. Fegadolli, M. H. Lu, J. E. Oliveira, V . R. Almeida, Y . F. Chen, and A. Sche rer, Experimental demonstration of a unidirectional reflectionless parity -time metamaterial at optical frequencies, Nat. Mater. 12, 108 (2013)

    work page 2013

  21. [21]

    Chang, X

    L. Chang, X. Jiang, S. Hua, C. Yang, J. Wen, L. Jiang, G. Li, G. Wang, and M. Xiao, Parity–time symmetry and variable optical isolation in active–passive-coupled microresonators, Nat. Photonics 8, 524 (2014)

    work page 2014

  22. [22]

    Wang, Y .-H

    H. Wang, Y .-H. Lai, Z. Yuan, M.-G. Suh, and K. Vahala, Petermann-factor sensitivity limit near an exceptional point in a Brillouin ring laser gyroscope, Nat. Commun. 11, 1610 (2020)

    work page 2020

  23. [23]

    H. Wang, K. Jacobs, D. Fahey, Y . Hu, D. R. Englund, and M. E. Trusheim, Exceptional sensitivity near the bistable transition point of a hybrid quantum system, Nat. Phys. 22, 577 (2026)

    work page 2026

  24. [24]

    Z. Xi, Z. Cen, D. Wang, J. G. Thomas, B. R. Srijanto, I. I. Kravchenko, J. Zuo, H. Liu, J. Ji, Y . Zhu, Y . Yao, and L. Shao, Room -Temperature Mid-Infrared Detection Using Metasurface -Absorber-Integrated Phononic Crystal Oscillator, Laser Photonics Rev. 19, e00498 (2025)

    work page 2025

  25. [25]

    Huang, J

    Y . Huang, J. G. Flor Flores, Y . Li, W. Wang, D. Wang, N. Goldberg, J. Zheng, M. Yu, M. Lu, M. Kutzer, D. Rogers, D.-L. Kwong, L. Churchill, and C. W. Wong, A Chip-Scale Oscillation-Mode Optomechanical Inertial Sensor Near the Thermodynamical Limits, Laser Photonics Rev. 14, 1800329 (2020)

    work page 2020

  26. [26]

    Loughlin and V

    H. Loughlin and V . Sudhir, Exceptional -Point Sensors Offer No Fundamental Signal -to-Noise Ratio Enhancement, Phys. Rev. Lett. 132, 243601 (2024)

    work page 2024

  27. [27]

    Langbein, No exceptional precision of exceptional-point sensors, Phys

    W. Langbein, No exceptional precision of exceptional-point sensors, Phys. Rev. A 98, 023805 (2018)

    work page 2018

  28. [28]

    Zheng and Y

    X. Zheng and Y . D. Chong, Noise Constraints for Nonlinear Exceptional Point Sensing, Phys. Rev. Lett. 134, 133801 (2025)

    work page 2025

  29. [29]

    Darcie and J

    T. Darcie and J. S. Aitchison, Noise -induced limits on responsivity and linewidth at nonlinear exceptional points, Phys. Rev. A 113, 033523 (2026)

    work page 2026

  30. [30]

    K. Bai, C. Lin, and M. Xiao, Impact of noise on nonlinear -exceptional-point-based sensors, arXiv e-prints, arXiv:2509.04839 (2025)

    work page internal anchor Pith review arXiv 2025

  31. [31]

    Zhang, W

    M. Zhang, W. Sweeney, C. W. Hsu, L. Yang, A. D. Stone, and L. Jiang, Quantum Noise Theory of Exceptional Point Amplifying Sensors, Phys. Rev. Lett. 123, 180501 (2019)

    work page 2019

  32. [32]

    J.-H. Park, A. Ndao, W. Cai, L. Hsu, A. Kodigala, T. Lepetit, Y .-H. Lo, and B. Kanté, Symmetry -breaking- induced plasmonic exceptional points and nanoscale sensing, Nat. Phys. 16, 462 (2020)

    work page 2020

  33. [33]

    B. Peng, Ş. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender, and L. Yang, Parity–time-symmetric whispering-gallery microcavities, Nat. Phys. 10, 394 (2014)

    work page 2014

  34. [34]

    J. Zhao, H. Hou, Y . Dang, Y . Ma, L. Li, H. Sun, Z. Sun, and T. Xu, Recent advances in piezoelectric resonant infrared detectors, Infrared Physics & Technology 152, 106155 (2026)

    work page 2026

  35. [35]

    Q. Guo, R. Yu, C. Li, S. Yuan, B. Deng, F. J. García de Abajo, and F. Xia, Efficient electrical dete ction of mid-infrared graphene plasmons at room temperature, Nat. Mater. 17, 986 (2018)

    work page 2018

  36. [36]

    J. Beck, C. Wan, M. Kinch, J. Robinson, P. Mitra, R. Scritchfield, F. Ma, and J. Campbell, The HgCdT e electron avalanche photodiode, J. Electron. Mater. 35, 1166 (2006)

    work page 2006

  37. [37]

    Delga, 8 - Quantum cascade detectors: A review in Mid-infrared Optoelectronics, edited by E

    A. Delga, 8 - Quantum cascade detectors: A review in Mid-infrared Optoelectronics, edited by E. Tournié, and L. Cerutti (Woodhead Publishing, 2020), pp. 337

    work page 2020

  38. [38]

    B. F. Levine, Quantum-well infrared photodetectors, J. Appl. Phys. 74, R1 (1993)

    work page 1993

  39. [39]

    S. Yuan, R. Yu, C. Ma, B. Deng, Q. Guo, X. Chen, C. Li, C. Chen, K. Watanabe, T. Taniguchi, F. J. García de Abajo, and F. Xia, Room Temperature Graphene Mid-Infrared Bolometer with a Broad Operational Wavelength Range, ACS Photonics 7, 1206 (2020)

    work page 2020

  40. [40]

    Goldstein, H

    J. Goldstein, H. Lin, S. Deckoff-Jones, M. Hempel, A.-Y . Lu, K. A. Richardson, T. Palacios, J. Kong, J. Hu, and D. Englund, Waveguide-integrated mid-infrared photodetection using graphene on a scalable chalcogenide glass platform, Nat. Commun. 13, 3915 (2022)

    work page 2022

  41. [41]

    Piller, J

    M. Piller, J. Hiesberger, E. Wistrela, P. Martini, N. Luhmann, and S. Schmid, Thermal IR Detection W ith Nanoelectromechanical Silicon Nitride Trampoline Resonators, IEEE Sens. J. 23, 1066 (2023)

    work page 2023

  42. [42]

    Markus, L

    P. Markus, L. Niklas, C. Miao-Hsuan, and S. Silvan, in Proc.SPIE2019), p. 1108802

    work page

  43. [43]

    Y . Hui, J. S. Gomez-Diaz, Z. Qian, A. Alù, and M. Rinaldi, Plasmonic piezoelectric nanomechanical resonator for spectrally selective infrared sensing, Nat. Commun. 7, 11249 (2016). 12

    work page 2016

  44. [44]

    Y . Hui, S. Kang, Z. Qian, and M. Rinaldi, Uncooled Infrared Detector Based on an Aluminum Nitride Piezoelectric Fishnet Metasurface, Journal of Microelectromechanical Systems 30, 165 (2021)

    work page 2021

  45. [45]

    V . J. Gokhale and M. Rais -Zadeh, Uncooled Infrared Detectors Using Gallium Nitride on Silicon Micromechanical Resonators, Journal of Microelectromechanical Systems 23, 803 (2014)

    work page 2014

  46. [46]

    Z. Qian, S. Kang, V . Rajaram, and M. Rinaldi, in 2016 IEEE SENSORS2016), pp. 1

    work page 2016

  47. [47]

    Laurent, J.-J

    L. Laurent, J.-J. Yon, J.-S. Moulet, M. Roukes, and L. Duraffourg, 12-μm-Pitch Electromechanical Resonator for Thermal Sensing, Physical Review Applied 9, 024016 (2018)

    work page 2018

  48. [48]

    Z. Qian, V . Rajaram, S. Kang, and M. Rinaldi, High figure-of-merit NEMS thermal detectors based on 50 - nm thick AlN nano-plate resonators, Appl. Phys. Lett. 115, 261102 (2019)

    work page 2019

  49. [49]

    Z. Qian, Y . Hui, F. Liu, S. Kang, S. Kar, and M. Rinaldi, Graphene–aluminum nitride NEMS resonant infrared detector, Microsystems & Nanoengineering 2, 16026 (2016)

    work page 2016

  50. [50]

    M. B. Pisani, K. Ren, P. Kao, and S. Tadigadapa, Application of Micromachined Y -Cut-Quartz Bulk Acoustic Wave Resonator for Infrared Sensing, Journal of Microelectromechanical Systems 20, 288 (2011)

    work page 2011

  51. [51]

    Hui and M

    Y . Hui and M. Rinaldi, in 2013 Transducers & Eurosensors XXVII: The 17th International Conference on Solid-State Sensors, Actuators and Microsystems (TRANSDUCERS & EUROSENSORS XXVII)2013), pp. 968

    work page 2013

  52. [52]

    W. C. Ang, P. Kropelnicki, H. Campanella, Y . Zhu, A. B. Randles, H. Cai, Y . A. Gu, K. C. Leong, and C. S. Tan, in 2014 IEEE 27th International Conference on Micro Electro Mechanical Systems (MEMS)2014), pp. 688

    work page 2014

  53. [53]

    Z. Xi, J. G. Thomas, J. Ji, D. Wang, Z. Cen, I. I. Kravchenko, B. R. Srijanto, Y . Yao, Y . Zhu, and L. Shao, Low-phase-noise surface -acoustic-wave oscillator using an edge mode of a phononic band gap, Physical Review Applied 23, 024054 (2025)

    work page 2025

  54. [54]

    J. G. Thomas, Z. Xi, J. Ji, G. Shi, B. R. Srijanto, I. I. Kravchenko, Y . Yao, L. Shao, and Y . Zhu, S pectral interferometry-based microwave-frequency vibrometry for integrated acoustic wave devices, Optica 12, 935 (2025)

    work page 2025

  55. [55]

    L. Shao, D. Zhu, M. Colangelo, D. H. Lee, N. Sinclair, Y . Hu, P. T. Rakich, K. Lai, K. K. Berggren, and M. Loncar, Electrical control of surface acoustic waves, Nature Electronics 5, 348 (2022)

    work page 2022

  56. [56]

    S. M. Kay, Fundamentals of statistical signal processing: estimation theory (Prentice-Hall, Inc., Upper Saddle River, NJ, USA, 1993)

    work page 1993

  57. [57]

    J. G. Thomas, G. Shi, L. Shao, and Y . Zhu, Shot-noise Limited Maximum Likelihood Estimation of Optical Pathlength in Spectral Interferometry, IEEE Sens. J. 26, 547 (2025)

    work page 2025

  58. [58]

    L. Shao, S. Maity, L. Zheng, L. Wu, A. Shams -Ansari, Y .-I. Sohn, E. Puma, M. N. Gadalla, M. Zhang, C. Wang, E. Hu, K. Lai, and M. Lončar, Phononic Band Structure Engineering for High -Q Gigahertz Surface Acoustic Wave Resonators on Lithium Niobate, Physical Review Applied 12, 014022 (2019). 13 Acknowledgements The views and conclusions contained in this...

    work page 2019