Abstract

Based on the dispersive interaction between a high quality factor microcavity and nano-objects, whispering-gallery-mode microcavities have been widely used in highly sensitive sensing. Here, we propose a novel method to enhance the sensitivity of the optical frequency shift and reduce the impact of the laser frequency noise on the detection resolution through Brillouin cavity optomechanics in a parity-time symmetric system. The optical spring effect is sensitive to the perturbation of optical modes around the exceptional point. By monitoring the shift of the mechanical frequency, the detection sensitivity for the optical frequency shift is enhanced by 2 orders of magnitude compared with conventional approaches. We find the optical spring effect is robust to the laser frequency noise around the exceptional point, which can reduce the detection limitation caused by the laser frequency instability. Thus, our method can improve the sensing ability for nano-object sensing and other techniques based on the frequency shift of the optical mode.

© 2019 Chinese Laser Press

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References

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2019 (6)

2018 (6)

J. Zhang, B. Peng, S. K. Özdemir, K. Pichler, D. O. Krimer, G. Zhao, F. Nori, Y.-X. Liu, S. Rotter, and L. Yang, “A phonon laser operating at an exceptional point,” Nat. Photonics 12, 479–484 (2018).
[Crossref]

P.-Y. Chen, M. Sakhdari, M. Hajizadegan, Q. Cui, M. M.-C. Cheng, R. El-Ganainy, and A. Alù, “Generalized parity-time symmetry condition for enhanced sensor telemetry,” Nat. Electron. 1, 297–304 (2018).
[Crossref]

S. Wan, R. Niu, H.-L. Ren, C.-L. Zou, G.-C. Guo, and C.-H. Dong, “Experimental demonstration of dissipative sensing in a self-interference microring resonator,” Photon. Res. 6, 681–685 (2018).
[Crossref]

H. Jing, H. Lü, S. Özdemir, T. Carmon, and F. Nori, “Nanoparticle sensing with a spinning resonator,” Optica 5, 1424–1430 (2018).
[Crossref]

B.-B. Li, J. Bilek, U. B. Hoff, L. S. Madsen, S. Forstner, V. Prakash, C. Schäfermeier, T. Gehring, W. P. Bowen, and U. L. Andersen, “Quantum enhanced optomechanical magnetometry,” Optica 5, 850–856 (2018).
[Crossref]

X.-F. Liu, F. Lei, T.-J. Wang, G.-L. Long, and C. Wang, “Gain lifetime characterization through time-resolved stimulated emission in a whispering-gallery mode microresonator,” Nanophotonics 8, 127–134 (2018).
[Crossref]

2017 (11)

J. Ren, H. Hodaei, G. Harari, A. U. Hassan, W. Chow, M. Soltani, D. Christodoulides, and M. Khajavikhan, “Ultrasensitive micro-scale parity-time-symmetric ring laser gyroscope,” Opt. Lett. 42, 1556–1559 (2017).
[Crossref]

J. Li, M.-G. Suh, and K. Vahala, “Microresonator Brillouin gyroscope,” Optica 4, 346–348 (2017).
[Crossref]

Y.-P. Gao, T.-J. Wang, C. Cao, and C. Wang, “Gap induced mode evolution under the asymmetric structure in a plasmonic resonator system,” Photon. Res. 5, 113–118 (2017).
[Crossref]

Z. Yang, W. Zhang, R. Ma, X. Dong, S. L. Hansen, X. Li, and Y. Rao, “Nanoparticle mediated microcavity random laser,” Photon. Res. 5, 557–560 (2017).
[Crossref]

W. Chen, Ş. K. Özdemir, G. Zhao, J. Wiersig, and L. Yang, “Exceptional points enhance sensing in an optical microcavity,” Nature 548, 192–196 (2017).
[Crossref]

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, 187–191 (2017).
[Crossref]

H. Jing, Ş. Özdemir, H. Lü, and F. Nori, “High-order exceptional points in optomechanics,” Sci. Rep. 7, 3386 (2017).
[Crossref]

Y.-L. Liu and Y.-X. Liu, “Energy-localization-enhanced ground-state cooling of a mechanical resonator from room temperature in optomechanics using a gain cavity,” Phys. Rev. A 96, 023812 (2017).
[Crossref]

B. Yao, C. Yu, Y. Wu, S.-W. Huang, H. Wu, Y. Gong, Y. Chen, Y. Li, C. W. Wong, X. Fan, and Y. Rao, “Graphene-enhanced Brillouin optomechanical microresonator for ultrasensitive gas detection,” Nano Lett. 17, 4996–5002 (2017).
[Crossref]

A. Kashkanova, A. Shkarin, C. Brown, N. Flowers-Jacobs, L. Childress, S. Hoch, L. Hohmann, K. Ott, J. Reichel, and J. Harris, “Superfluid Brillouin optomechanics,” Nat. Phys. 13, 74–79 (2017).
[Crossref]

Y. A. Espinel, F. G. Santos, G. O. Luiz, T. M. Alegre, and G. S. Wiederhecker, “Brillouin optomechanics in coupled silicon microcavities,” Sci. Rep. 7, 43423 (2017).
[Crossref]

2016 (6)

Y. Antman, A. Clain, Y. London, and A. Zadok, “Optomechanical sensing of liquids outside standard fibers using forward stimulated Brillouin scattering,” Optica 3, 510–516 (2016).
[Crossref]

W. Yu, W. C. Jiang, Q. Lin, and T. Lu, “Cavity optomechanical spring sensing of single molecules,” Nat. Commun. 7, 12311 (2016).
[Crossref]

J. Su, A. F. Goldberg, and B. M. Stoltz, “Label-free detection of single nanoparticles and biological molecules using microtoroid optical resonators,” Light Sci. Appl. 5, e16001 (2016).
[Crossref]

B. Peng, Ş. K. Özdemir, M. Liertzer, W. Chen, J. Kramer, H. Ylmaz, J. Wiersig, S. Rotter, and L. Yang, “Chiral modes and directional lasing at exceptional points,” Proc. Natl. Acad. Sci. U. S. A. 113, 6845–6850 (2016).
[Crossref]

Y.-F. Xiao and Q. Gong, “Optical microcavity: from fundamental physics to functional photonics devices,” Sci. Bull. 61, 185–186 (2016).
[Crossref]

Z.-P. Liu, J. Zhang, Ş. K. Özdemir, B. Peng, H. Jing, X.-Y. Lü, C.-W. Li, L. Yang, F. Nori, and Y.-X. Liu, “Metrology with PT-symmetric cavities: enhanced sensitivity near the PT-phase transition,” Phys. Rev. Lett. 117, 110802 (2016).
[Crossref]

2015 (4)

X. Jiang, M. Wang, M. C. Kuzyk, T. Oo, G.-L. Long, and H. Wang, “Chip-based silica microspheres for cavity optomechanics,” Opt. Express 23, 27260–27265 (2015).
[Crossref]

C.-H. Dong, Z. Shen, C.-L. Zou, Y.-L. Zhang, W. Fu, and G.-C. Guo, “Brillouin-scattering-induced transparency and non-reciprocal light storage,” Nat. Commun. 6, 6193 (2015).
[Crossref]

J. Kim, M. C. Kuzyk, K. Han, H. Wang, and G. Bahl, “Non-reciprocal Brillouin scattering induced transparency,” Nat. Phys. 11, 275–280 (2015).
[Crossref]

N. Zhang, S. Liu, K. Wang, Z. Gu, M. Li, N. Yi, S. Xiao, and Q. Song, “Single nanoparticle detection using far-field emission of photonic molecule around the exceptional point,” Sci. Rep. 5, 11912 (2015).
[Crossref]

2014 (8)

J. Li, S. Diddams, and K. J. Vahala, “Pump frequency noise coupling into a microcavity by thermo-optic locking,” Opt. Express 22, 14559–14567 (2014).
[Crossref]

H. Jing, S. Özdemir, X.-Y. Lü, J. Zhang, L. Yang, and F. Nori, “Pt-symmetric phonon laser,” Phys. Rev. Lett. 113, 053604 (2014).
[Crossref]

Ş. K. Özdemir, J. Zhu, X. Yang, B. Peng, H. Yilmaz, L. He, F. Monifi, S. H. Huang, G. L. Long, and L. Yang, “Highly sensitive detection of nanoparticles with a self-referenced and self-heterodyned whispering-gallery Raman microlaser,” Proc. Natl. Acad. Sci. U. S. A. 111, E3836–E3844 (2014).
[Crossref]

B.-B. Li, W. R. Clements, X.-C. Yu, K. Shi, Q. Gong, and Y.-F. Xiao, “Single nanoparticle detection using split-mode microcavity Raman lasers,” Proc. Natl. Acad. Sci. U. S. A. 111, 14657–14662 (2014).
[Crossref]

M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391–1452 (2014).
[Crossref]

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, 394–398 (2014).
[Crossref]

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, 524–529 (2014).
[Crossref]

J. Wiersig, “Enhancing the sensitivity of frequency and energy splitting detection by using exceptional points: application to microcavity sensors for single-particle detection,” Phys. Rev. Lett. 112, 203901 (2014).
[Crossref]

2013 (3)

V. R. Dantham, S. Holler, C. Barbre, D. Keng, V. Kolchenko, and S. Arnold, “Label-free detection of single protein using a nanoplasmonic-photonic hybrid microcavity,” Nano Lett. 13, 3347–3351 (2013).
[Crossref]

Y.-W. Hu, Y.-F. Xiao, Y.-C. Liu, and Q. Gong, “Optomechanical sensing with on-chip microcavities,” Front. Phys. 8, 475–490 (2013).
[Crossref]

G. Bahl, K. H. Kim, W. Lee, J. Liu, X. Fan, and T. Carmon, “Brillouin cavity optomechanics with microfluidic devices,” Nat. Commun. 4, 1994 (2013).
[Crossref]

2012 (3)

C. Dong, V. Fiore, M. C. Kuzyk, and H. Wang, “Optomechanical dark mode,” Science 338, 1609–1613 (2012).
[Crossref]

F. Vollmer and L. Yang, “Review label-free detection with high-Q microcavities: a review of biosensing mechanisms for integrated devices,” Nanophotonics 1, 267–291 (2012).
[Crossref]

E. Gavartin, P. Verlot, and T. Kippenberg, “A hybrid on-chip optomechanical transducer for ultrasensitive force measurements,” Nat. Nanotechnol. 7, 509–514 (2012).
[Crossref]

2011 (4)

T. Lu, H. Lee, T. Chen, S. Herchak, J.-H. Kim, S. E. Fraser, R. C. Flagan, and K. Vahala, “High sensitivity nanoparticle detection using optical microcavities,” Proc. Natl. Acad. Sci. U. S. A. 108, 5976–5979 (2011).
[Crossref]

L. He, Ş. K. Özdemir, J. Zhu, W. Kim, and L. Yang, “Detecting single viruses and nanoparticles using whispering gallery microlasers,” Nat. Nanotechnol. 6, 428–432 (2011).
[Crossref]

V. Fiore, Y. Yang, M. C. Kuzyk, R. J. Barbour, L. Tian, and H. Wang, “Storing optical information as a mechanical excitation in a silica optomechanical resonator,” Phys. Rev. Lett. 107, 133601 (2011).
[Crossref]

X. Fan and I. M. White, “Optofluidic microsystems for chemical and biological analysis,” Nat. Photonics 5, 591–597 (2011).
[Crossref]

2010 (2)

S. Weis, R. Rivière, S. Deléglise, E. Gavartin, O. Arcizet, A. Schliesser, and T. J. Kippenberg, “Optomechanically induced transparency,” Science 330, 1520–1523 (2010).
[Crossref]

J. Zhu, S. K. Ozdemir, Y.-F. Xiao, L. Li, L. He, D.-R. Chen, and L. Yang, “On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator,” Nat. Photonics 4, 46–49 (2010).
[Crossref]

2008 (2)

F. Vollmer and S. Arnold, “Whispering-gallery-mode biosensing: label-free detection down to single molecules,” Nat. Methods 5, 591–596 (2008).
[Crossref]

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Figures (5)

Fig. 1.
Fig. 1. (a) Schematic of a Brillouin interaction in the parity-time symmetric system. The modes a2, a3, and b in the lossy cavity represent the anti-Stokes mode, Stokes mode, and mechanical mode, respectively, and the gain microsphere supports the cavity mode a1. The waveguide can couple the light into the cavity and collect the cavity emission power for sensing. (b) The cavity modes and mechanical mode are illustrated in the frequency domain.
Fig. 2.
Fig. 2. Mechanical responses and the supermodes spectrum as a function of γ3. Frequency shifts are plotted in A1 and B1; A2 and B2 denote the optical damping rate Γopt. Here the real and imaginary parts of complex numbers ω± are denoted by the red and blue dashed lines, respectively. A1–A3 indicate the mechanical responses and supermode spectrum with blue-detuned driving. B1–B3 plot the mechanical responses and supermode spectrum in the red sideband driving regime. The parameters used are κ=1  MHz, Pin=17.5  μW, γ2=2.6  MHz, g0=4  Hz, Ωm=50  MHz, Γm=1  kHz, J=κ, δ3=1.95  kHz, and δ1=0.99δ3.
Fig. 3.
Fig. 3. Absolute value of the mechanical frequency shift ΔΩm(ν) and effective linewidth Γ(ν) with the perturbation ν. The red lines show the absolute value of the mechanical frequency shift and the blue dashed lines plot Γ(ν) in (a) and (b) with δ1=δ3=5  kHz. The difference between Abs(ΔΩm(ν)) and Γν are plotted in (c) and (d) with the detuning δ3 and the perturbation ν. The coupling rates J are 0.97κ and 1.01κ in (c) and (d), respectively. Other parameters used here are γ3=1  MHz, κ=0.975γ3, and Γ=5  Hz.
Fig. 4.
Fig. 4. Cavity emission spectrum with the effect of laser frequency noise in (a) and (b). The perturbation ν equals 300 Hz and the mechanical linewidth is 1 Hz. The insets show the mechanical frequency shift induced by laser frequency noise σ. The coupling rate J=0.8κ in (a) and J=κ in (b). (c) We plot η as a function of σ with different coupling rates J. The red line indicates the system is robust to laser frequency noise near the exceptional point. The parameters used here are γ3=1.00  MHz, Δ1=Ωm, Δ3=Ωm, κ=0.985γ3, and Γ=1  Hz.
Fig. 5.
Fig. 5. (a) Normalized output spectra with different optical frequency shifts ν. The black solid line represents the cavity emission spectrum without external perturbation when the mechanical linewidth is 1 Hz. And the output spectrum is normalized to 1 separately. (b) The resolution of ν as a function of the coupling rate J. The red, green, and blue solid lines indicate the minimum detectable optical cavity resonance shift with Γ=2, 1, and 0.5 Hz, respectively. The parameters used here are γ3=1.00  MHz, Δ1=Ωm, Δ3=Ωm, and κ=0.985γ3. And the coupling rate J=κ in (a).

Equations (16)

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H/=H0+HI+Hd,H0=(Δ1+iκ)a1a1(Δ2+iγ2)a2a2(Δ3+iγ3)a3a3+(ωmiΓm2)bb,HI=J(a1a3+a3a1)+g0(a2a3b+a2a3b),Hd=iκex2αL(a2a2),
H0=(Δ1+iκ)a1+a1(Δ3+iγ3)a3+a3+(ωmiΓm2)b+b,HI=G(a3+b++a3b)+J(a1+a3+a3+a1),
G=g0κex2Pin(Δ22+γ22)ω2.
M=(iΔ1+κiJ0iJiΔ3γ3iG0iGiωmΓm2).
Γopt=2G2γ3(δ12+κ2)2J2κ(δ12+κ2)[γ3(δ12+κ2)J2κ]2+[δ3(δ12+κ2)J2δ1]2,
ωopt=G2δ3(δ12+κ2)2J2δ1(δ12+κ2)[γ3(δ12+κ2)J2κ]2+[δ3(δ12+κ2)J2δ1]2,
H13=(ω1+iκJJω3iγ3).
ω±=ω1+ω3+iκiγ3±[ω1ω3+i(κ+γ3)]2+4J22.
ω±=ω3+i2(κγ3)±4J2(κ+γ3)22.
Γ(ν)=Γm2G2γeff(δ+ν)2+γeff2,
Ωm(ν)=ωmG2δ+ν(δ+ν)2+γeff2,
ΔΓ(ν)=2G22γeffδν+γeffν2[(δ+ν)2+γeff2](δ2+γeff2),
ΔΩ(ν)=G2δ2νγeff2ν+δν2[(δ+ν)2+γeff2](δ2+γeff2).
S(ω)=+dteiωtκex3a3(t)a3(0),
ω±=Δ3σ+i2(κγ3)±4J2[iν+(κ+γ3)]22,
S.A.=γ3γeff.