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Measuring deviations from a perfectly circular cross-section of an optical nanofiber at the \r{A}ngstr\"om scale

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Pith's one-line read An optical nanofiber's cross-section is elliptical by only about 2 Å.

desk verdict Careful dual-method measurement of Ångström-scale nanofiber ellipticity: the mechanical mode-splitting relation is parameter-free and solid, the optical birefringence conversion is useful but quantitatively unsettled by a factor of two. read the letter →

arxiv 2505.20476 v1 pith:WFESROQZ submitted 2025-05-26 physics.optics

Jihao Jia , Felix Tebbenjohanns , Thomas Hoinkes , Jürgen Volz , Arno Rauschenbeutel , Philipp Schneeweiss This is my paper · ORCID
classification physics.optics PACS 42.81.-i42.25.Lc
keywords opticalnanofibertaperedfiberlinearbirefringenceflexuralmodesplittingellipticalcross-sectionasymmetryparameterpolarizationeigenaxesÅngström-scaledeviation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper establishes that a tapered optical nanofiber, whose waist is nominally a cylinder with 257 nm radius, actually has a slightly elliptical cross-section whose semi-axes differ by only about 2 Ångströms, a relative deviation of roughly $3.6\times10^{-4}$. The authors show this with two independent in-situ probes: the mechanical flexural modes of the fiber appear as frequency-split doublets whose splitting encodes the ellipticity, and the polarization of guided light, seen through scattered-light imaging, undergoes periodic beating from the resulting linear birefringence. Both methods yield Ångström-scale deviations and, together, fix the orientation of the fiber's polarization eigenaxes. The result matters because such a tiny shape error changes light polarization significantly within millimeters of propagation, affecting quantum memories, frequency conversion, and lasing experiments that require long interaction lengths.

What carries the argument

The key object is the asymmetry parameter $\zeta=(a-b)/(a+b)\ll1$, defined for a slightly elliptical beam with semi-axes $a$ and $b$, which is assumed to stay constant along the entire fiber including the exponential tapers. For flexural modes, the equation of motion of a slightly elliptical beam reduces to a parameter-free relation: the normalized mode splitting $(\Omega_b-\Omega_a)/(\Omega_a+\Omega_b)$ equals $\zeta$, independent of effective length, mode number, and material properties. For the guided light, the elliptical waveguide is treated in elliptical coordinates with Mathieu functions; a first-order Taylor expansion in $\zeta$ gives the linear birefringence $\Delta\beta=(2\pi/\lambda)\times0.176\,\zeta$, with a universal prefactor curve relating geometry to birefringence at any wavelength. The polarization imaging signal is described by the intensity formula $I(\theta_c,\theta_p,z)\propto1-\mathrm{Re}\{e^{i2\theta_p}W\}$ with $W=\cos2\theta_c-i\sin2\theta_c\cos(\Delta\beta z)$, from which a joint fit of two cameras at different angles extracts $\Delta\beta$, the camera angles, and hence the semi-axis difference and the eigenaxis orientation.

What would settle it

A wavelength scan of the beat length on a single fiber, checked against the universal prefactor curve in Fig. 5, would settle whether the optical birefringence is purely geometric ellipticity; if the inferred $\zeta$ changes with wavelength, the semi-axis values derived from the optical method would not represent the fiber's static shape.

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Extended reading notes

Core claim

The central claim is that the nanofiber can be well described as having an elliptical cross-section with a mean radius of $255.6(9)\,\mathrm{nm}$, where the semi-axes differ by only about $2\,\mathrm{\AA}$; equivalently, the relative deviation of the semi-major and semi-minor axis is at the $10^{-4}$ level. The same elliptical geometry, with a fixed eigenaxis orientation, accounts for all of the mechanical resonance data and all of the optical polarization data. The two methods agree on the existence and scale of the asymmetry but give semi-axis differences that differ by about a factor of two ($0.180(2)\,\mathrm{nm}$ from flexural modes versus $0.085(4)\,\mathrm{nm}$ from birefringence), which the authors attribute to adsorption and desorption of surface material between measurements. The paper also introduces a general asymmetry parameter that connects the two observations and determines the orientation of the polarization eigenaxes with respect to the lab frame.

Load-bearing premise

The quantitative semi-axis differences rest on the assumption that both the mechanical mode splitting and the optical birefringence are caused solely by a constant elliptical shape of the glass cross-section, with negligible contributions from surface adsorbates, stress, or shape variations along the taper.

Editorial extensions

If this is right

  • Any experiment that needs a stable linear polarization along a nanofiber must account for a periodic polarization rotation with a beat length of order 14–28 mm, imposed by the measured ellipticity.
  • The mechanical method measures the cross-section asymmetry without any optical calibration, so it can serve as a simple in-situ quality check for any tapered fiber.
  • Determining the eigenaxis orientation allows one to launch light along a principal axis to suppress the polarization beating in practical setups.
  • Since the asymmetry parameter is independent of material properties, the same analysis applies to tapered fibers made from other glasses or with different radii.
  • The observed order-$10^{-4}$ ellipticity challenges the common assumption of perfectly circular nanofiber cross-sections in quantum-optics and optomechanics experiments.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the factor-of-two discrepancy between the two methods is caused by adsorbates, then the optical birefringence, and hence the usable beat length, may drift with vacuum pressure, laser power, and surface conditions; experiments relying on long-term polarization stability would need to monitor it continuously.
  • The universal prefactor curve connecting $\Delta\beta/\zeta$ to $r_0/\lambda$ could be inverted as a design tool: either to minimize ellipticity by feedback during pulling, or to deliberately fabricate polarization-maintaining nanofibers with a specified beat length.
  • The flexural-mode splitting method is essentially a mechanical measurement of geometry at the Ångström scale and could be extended to map shape uniformity along the taper or to detect anisotropic surface layers in other micro-mechanical resonators.
  • A direct wavelength-dependence test of the birefringence, using the predicted prefactor at 1064 nm and 1550 nm, would distinguish a purely geometric ellipticity from stress- or adsorbate-induced contributions.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. The manuscript reports two in-situ methods for measuring deviations from a perfectly circular cross-section of a tapered optical nanofiber. The first method uses the frequency splitting of hundreds of flexural mechanical modes to extract an asymmetry parameter ζ = (a-b)/(a+b) ≈ 3.62(5)×10^-4, corresponding to a semi-axis difference a-b ≈ 0.180(2) nm for a mean radius of 255.6(9) nm. The second method images polarization-dependent Rayleigh scattering along the fiber and fits the visibility to a birefringence model, yielding Δβ = 0.222(9) mm^-1 and a-b ≈ 0.085(4) nm. The authors conclude that the fiber cross-section is elliptical at the Ångström scale, with relative asymmetry at the 10^-4 level, and note a factor-of-two discrepancy between the two methods, which they attribute speculatively to surface adsorbates.

Significance. If the central claim holds, the work is significant: it demonstrates Ångström-level metrology of nanofiber geometry, with direct implications for polarization control in quantum optics and nanophotonics applications. The mechanical analysis is particularly strong: Eq. (4) and Appendix A provide a parameter-free relation between the normalized mode splitting and the asymmetry parameter, and the constant normalized splitting across hundreds of modes (Fig. 2c) is a convincing falsifiable check. The optical analysis is also valuable because it provides the eigenaxis orientation, which the mechanical method cannot. However, the unresolved factor-of-two discrepancy between the two methods means that the quantitative agreement, and hence the optical value of a-b, is not yet fully established.

major comments (2)
  1. [Section d, Eq. (5)] The optical estimate a-b ≈ 0.085(4) nm is not uniquely determined because the conversion from measured Δβ to geometry assumes that the linear birefringence is caused solely by a homogeneous elliptical silica core in vacuum. The manuscript itself reports a factor-of-two discrepancy with the mechanical value and about 50% variation of the beat length with pressure and probe power (Section d), and attributes this to adsorbates without a quantitative model. Unless the adsorbate or stress contribution is modeled or bounded, Δβ measures an effective birefringence and the inference a-b ≈ 0.085(4) nm is not quantitatively supported. The claim that the two methods yield 'comparable' semi-axis differences therefore needs either a quantitative adsorbate model or a weakened statement.
  2. [Appendix A, Eq. (A9)] The derivation of ζ from the normalized mode splitting assumes ζ(z) = const along the entire beam, including the exponential tapers (stated in the paragraph preceding Eq. (A9)). This assumption is not tested. If the asymmetry varies with radius along the taper, then the extracted ζ is an effective or weighted quantity, and the mechanical value a-b ≈ 0.180(2) nm should be recharacterized accordingly, with some estimate of the sensitivity to taper-region asymmetry.
minor comments (4)
  1. [Section c and Section d] Eq. (5) gives Δβ = 0.442(9) mm^-1 and L_beat = 14.2(3) mm using the mechanical ζ, while the polarization-imaging fit in Section d gives Δβ = 0.222(9) mm^-1 and L_beat = 28.2(12) mm. The text should state explicitly whether Eq. (5) is a prediction to be compared with the fit or a value extracted from the fit; as written, the two sets of numbers appear without a clear statement of connection, which obscures the factor-of-two comparison.
  2. [Figure 4 caption and main text] The camera angle for camera 2 is given as θc,2 = 57.9(4)° in the main text and as θc,2 = 53.9(9)° in the Figure 4 caption; these values should be reconciled.
  3. [Abstract and Section d] The word 'comparable' used for the two semi-axis differences (about 0.18 nm versus about 0.085 nm) is too strong for a factor of two; consider 'same order of magnitude' or a quantified statement.
  4. [Section b] The phrase 'is prior unknown' should read 'is not known a priori' or 'is unknown beforehand'.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the mechanical splitting relation and the optical birefringence prefactor are independently derived, and the factor-of-two discrepancy shows the two methods are not forced into agreement by construction.

full rationale

The derivation chain is self-contained and non-circular. Mechanical path: Eq. (A9) is derived from the Euler-Bernoulli beam equation for a slightly elliptical beam with constant asymmetry, yielding Ωn = s_n^2 c0(1±ζ), so that the normalized splitting (Ωb-Ωa)/(Ωa+Ωb) equals ζ to first order. The frequency-splitting data are then fit with Eq. (3), giving a-b ≈ 0.180(2) nm, and cross-checked with the parameter-independent Eq. (4), giving ζ ≈ 3.62(5)×10^-4; neither quantity is set by definition. Optical path: Eq. (5) uses the prefactor 0.176 computed in App. B by solving the elliptical-waveguide characteristic equations with the stated independent parameters (λ=852 nm, r0=257 nm, n=1.452), not by fitting the polarization-imaging data. The visibility model, Eq. (7) and App. C, is fit to the scattered-light images to extract Δβ = 0.222(9) mm^-1, and only then converted to a-b via Eq. (5). The two methods rely on different measured observables and agree only at the factor-of-two level, which the authors explicitly attribute to adsorbates; a forced equivalence would show much closer agreement. Self-citations to Refs. [27,29] identify measurement techniques and torsional-mode identification, but they do not carry the central derivation. The reported factor-of-two discrepancy is an honest limitation, not a circular step. Score 1 reflects only the minor method-citing self-citations, which are not load-bearing.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The paper's theoretical core is a parameter-free beam-theory relation and a perturbation calculation of elliptical-waveguide birefringence; the fitted parameters are experimental nuisance/target values. The main unverified postulates are the constant-ζ model, the Rayleigh-polarization assumption, and the geometry-only birefringence assumption.

free parameters (5)
  • n0, absolute mode number offset = 27.3(2)
    Fit to Eq. (1b) converts relative peak order into absolute mode numbers; needed for Eq. (3) splitting fit.
  • mean radius r0 = 255.6(9) nm
    Fit to mean resonance frequencies; used to compute mean radius and, with ζ, the semi-axis difference in the optical method.
  • semi-axis difference a-b (mechanical) = 0.180(2) nm
    Fit of Eq. (3) to mode-splitting data; this is the paper's headline quantitative claim.
  • linear birefringence Δβ (optical) = 0.222(9) mm^-1
    Joint fit of Eq. (7) to camera visibility data; converted to a-b via Eq. (5).
  • camera angles θc,1 and θc,2 = 129.9(4)°, 57.9(4)° (text) / 53.9(9)° (caption)
    Joint fit; used to extract Δβ and determine eigenaxis orientation.
assumptions (5)
  • domain assumption Euler-Bernoulli beam theory with fixed-fixed end conditions and effective length Leff = L + 8/α.
    Used to write resonance frequencies in Eq. (1) and to extract r0 and n0; ignores shear deformation, axial tension, and damping.
  • ad hoc to paper Elliptical cross-section with constant ζ along the waist and tapers.
    Needed for Eq. (A9) so that normalized splitting equals ζ; if ζ varies along z, the measured constant splitting is only a weighted average.
  • domain assumption Rayleigh scattering preserves the local polarization of the guided light.
    Justifies Eq. (C3); supported by Refs. [27,33] but not directly verified in this work.
  • domain assumption Elliptical dielectric waveguide characteristic equations from Ref. [50] with Mathieu functions accurately model the air-clad silica nanofiber.
    Used to compute the birefringence prefactor 0.176 in Eq. (5) and Fig. 5.
  • ad hoc to paper Birefringence is dominated by geometric ellipticity; stress and adsorbates are negligible.
    The factor-of-2 discrepancy between methods is attributed to adsorbates; if stress or adsorbates contribute, the optical a-b is not purely geometric.

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Pith. "Pith review of Measuring deviations from a perfectly circular cross-section of an optical nanofiber at the \r{A}ngstr\"om scale." pith.science (2026). https://pith.science/paper/WFESROQZ

@misc{pith2026250520476,
  author       = {Pith},
  title        = {Pith review of: Measuring deviations from a perfectly circular cross-section of an optical nanofiber at the \rAngstr\"om scale},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WFESROQZ}},
  note         = {Machine review of arXiv:2505.20476}
}
read the original abstract

Tapered optical fibers (TOFs) with sub-wavelength-diameter waists, known as optical nanofibers, are powerful tools for interfacing quantum emitters and nanophotonics. These applications demand stable polarization of the fiber-guided light field. However, the linear birefringence resulting from \r{A}ngstr\"om-scale deviations in the nanofiber's ideally circular cross-section can lead to significant polarization changes within millimeters of light propagation. Here, we experimentally investigate such deviations using two in-situ approaches. First, we measure the resonance frequencies of hundreds of flexural modes along the nanofiber, which exhibit splitting due to the non-circular cross section. By analyzing the mean resonance frequencies of each pair and the corresponding frequency splitting, we conclude that the nanofiber can be well described as having an elliptical cross-section with a mean radius of 255.6(9) nm, where the semi-axes differ by only about 2\r{A}. Second, we monitor the polarization of the guided light field by imaging the light scattered out of the nanofiber and observe a periodic polarization change along it. From the linear birefringence due to the elliptical cross-section, we infer a comparable difference in the semi-axes as the first method, and determine the orientation of the polarization eigenaxes. Our work is crucial for any fundamental or applied study that requires a well-controlled interaction between guided light and matter, in particular for quantum memories, frequency conversion, or lasing that require a large interaction length.

Figures

Figures reproduced from arXiv: 2505.20476 by the authors.

Figure 1
Figure 1. Schematic of the experimental setup. We launch linearly polarized laser light into the TOF, which is placed inside a [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Measurement and analysis of flexural modes, focusing on mode splitting. (a) Power spectral density (PSD), [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Polarization dependent scattering pattern of the [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Visibility and phase measurement for camera 1 [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: Differences in the effective refractive indices as [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

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Works this paper leans on

52 extracted references · 49 canonical work pages

  1. [1]

    asymmetry

    From the fit, we determine the absolute mode number asn=n rel +n 0, where n0 = 27.3(2)≈27is the fit parameter correspond- ing to the mode number of the first observed peak. We also extract the mean radius of the nanofiber as r0 = 255.6(9) nm, closely matching the nominal value of257 nm. Second, we calculate the mode splitting, Ωb−Ωa, and fit it using Eq. ...

    work page

  2. [2]

    L. Tong, F. Zi, X. Guo, and J. Lou, Opt. Commun.285, 4641 (2012)

    work page 2012

  3. [3]

    M. J. Morrissey, K. Deasy, M. Frawley, R. Kumar, E. Prel, L. Russell, V. G. Truong, and S. Nic Chormaic, Sensors13, 10449 (2013)

    work page 2013

  4. [4]

    Solano, J

    P. Solano, J. A. Grover, J. E. Hoffman, S. Ravets, F. K. Fatemi, L. A. Orozco, and S. L. Rolston, inAdv. At. Mol. Opt. Phys., Vol. 66 (Elsevier, 2017) pp. 439–505

    work page 2017

  5. [5]

    K. P. Nayak, M. Sadgrove, R. Yalla, F. Le Kien, and K. Hakuta, J. Opt.20, 073001 (2018)

    work page 2018

  6. [6]

    Le Kien, J

    F. Le Kien, J. Liang, K. Hakuta, and V. Balykin, Opt. Commun.242, 445 (2004)

    work page 2004

  7. [7]

    T. A. Birks, W. J. Wadsworth, and P. S. J. Russell, Opt. Lett.25, 1415 (2000)

    work page 2000

  8. [8]

    Spillane, G

    S. Spillane, G. Pati, K. Salit, M. Hall, P. Kumar, R. Beausoleil, and M. Shahriar, Phys. Rev. Lett.100, 233602 (2008)

    work page 2008

Show all 52 references
  1. [9]

    Wiedemann, K

    U. Wiedemann, K. Karapetyan, C. Dan, D. Pritzkau, W. Alt, S. Irsen, and D. Meschede, Opt. Express18, 7693 (2010)

    2010

  2. [10]

    Zhang, Y

    J. Zhang, Y. Kang, X. Guo, Y. Li, K. Liu, Y. Xie, H. Wu, D. Cai, J. Gong, Z. Shi,et al., Light Sci. Appl.12, 89 (2023)

    2023

  3. [11]

    Keiser,Fiber Optic Communications(Springer, 2021)

    G. Keiser,Fiber Optic Communications(Springer, 2021)

    2021

  4. [12]

    T. A. Birks, P. S. J. Russell, and D. Culverhouse, J. Lightwave Technol.14, 2519 (1996)

    1996

  5. [13]

    Blaha, A

    M. Blaha, A. Rauschenbeutel, and R. Pennetta, Phys. Rev. Appl.22, 054008 (2024)

    2024

  6. [14]

    Praveen Kamath, S

    P. Praveen Kamath, S. Sil, V. G. Truong, and S. Nic Chormaic, Biomed. Opt. Express14, 6172 (2023)

    2023

  7. [15]

    Nagai and T

    R. Nagai and T. Aoki, Opt. Express22, 28427 (2014)

    2014

  8. [16]

    Hoffman, S

    J. Hoffman, S. Ravets, J. Grover, P. Solano, P. Kordell, J. Wong-Campos, L. Orozco, and S. Rolston, AIP Adv. 4(2014)

    2014

  9. [17]

    M. C. Frawley, A. Petcu-Colan, V. G. Truong, and S. Nic Chormaic, Opt. Commun.285, 4648 (2012)

    2012

  10. [18]

    Ravets, J

    S. Ravets, J. Hoffman, L. Orozco, S. Rolston, G. Beadie, and F. Fatemi, Opt. Express21, 18325 (2013)

    2013

  11. [19]

    Warken and H

    F. Warken and H. Giessen, Opt. Lett.29, 1727 (2004)

    2004

  12. [20]

    Sumetsky, Y

    M. Sumetsky, Y. Dulashko, J. Fini, A. Hale, and J. Nicholson, Opt. Lett.31, 2393 (2006)

    2006

  13. [21]

    L. S. Madsen, C. Baker, H. Rubinsztein-Dunlop, and W. P. Bowen, Nano Lett.16, 7333 (2016). 9

    2016

  14. [22]

    F. K. Fatemi, J. E. Hoffman, P. Solano, E. F. Fenton, G. Beadie, S. L. Rolston, and L. A. Orozco, Optica4, 157 (2017)

    2017

  15. [23]

    Holleis, T

    S. Holleis, T. Hoinkes, C. Wuttke, P. Schneeweiss, and A. Rauschenbeutel, Appl. Phys. Lett.104, 163109 (2014)

    2014

  16. [24]

    Birks and Y

    T. Birks and Y. Li, J. Lightwave Technol.10, 432 (1992)

    1992

  17. [25]

    J. Ward, A. Maimaiti, V. H. Le, and S. Chormaic, Rev. Sci. Instrum.85(2014)

    2014

  18. [26]

    Goban, K

    A. Goban, K. Choi, D. Alton, D. Ding, C. Lacroûte, M. Pototschnig, T. Thiele, N. Stern, and H. Kimble, Phys. Rev. Lett.109, 033603 (2012)

    2012

  19. [27]

    C. Wang, L. Song, J. Wang, J. Zhou, K. Feng, Q. Zhang, C. L. Zou, G. Li, P. Zhang, and T. Zhang, Opt. Express 33, 14964 (2025)

    2025

  20. [28]

    Vetsch, S

    E. Vetsch, S. T. Dawkins, R. Mitsch, D. Reitz, P.Schneeweiss,andA.Rauschenbeutel,IEEEJ.Sel.Top. Quantum Electron.18, 1763 (2012)

    2012

  21. [29]

    Wuttke, G

    C. Wuttke, G. D. Cole, and A. Rauschenbeutel, Phys. Rev. A88, 061801 (2013)

    2013

  22. [30]

    Tebbenjohanns, J

    F. Tebbenjohanns, J. Jia, M. Antesberger, A. S. Prasad, S. Pucher, A. Rauschenbeutel, J. Volz, and P. Schneeweiss, Phys. Rev. A108, L031101 (2023)

    2023

  23. [31]

    D. Su, Y. Jiang, P. Solano, L. A. Orozco, J. Lawall, and Y. Zhao, Photon. Res.11, 2179 (2023)

    2023

  24. [32]

    L. Song, C. Wang, Y. Hu, J. Zhou, Q. Zhang, C.-L. Zou, G. Li, P. Zhang, and T. Zhang, Phys. Rev. Lett.132, 033801 (2024)

    2024

  25. [33]

    Rao,Mechanical Vibrations in SI Units, 6th ed

    S. Rao,Mechanical Vibrations in SI Units, 6th ed. (Addison-Wesley New York, 2017)

    2017

  26. [34]

    M. Joos, A. Bramati, and Q. Glorieux, Opt. Express27, 18818 (2019)

    2019

  27. [35]

    Delic,Cavity cooling by coherent scattering of a levi- tated nanosphere in vacuum, Ph.D

    U. Delic,Cavity cooling by coherent scattering of a levi- tated nanosphere in vacuum, Ph.D. thesis, University of Vienna (2019)

    2019

  28. [36]

    Ricci, M

    F. Ricci, M. T. Cuairan, A. W. Schell, E. Hebestreit, R. A. Rica, N. Meyer, and R. Quidant, ACS Nano16, 8677 (2022)

    2022

  29. [37]

    Y. Jung, G. Brambilla, K. Oh, and D. J. Richardson, Opt. Lett.35, 378 (2010)

    2010

  30. [38]

    H. Xuan, J. Ju, and W. Jin, Opt. Express18, 3828 (2010)

    2010

  31. [39]

    J. C. Beugnot, S. Lebrun, G. Pauliat, H. Maillotte, V. Laude, and T. Sylvestre, Nat. Commun.5, 5242 (2014)

    2014

  32. [40]

    Florez, P

    O. Florez, P. F. Jarschel, Y. A. Espinel, C. Cordeiro, T. Mayer Alegre, G. S. Wiederhecker, and P. Dainese, Nat. Commun.7, 11759 (2016)

    2016

  33. [41]

    Petersen, J

    J. Petersen, J. Volz, and A. Rauschenbeutel, Science346, 67 (2014)

    2014

  34. [42]

    J. Lee, J. Grover, J. Hoffman, L. Orozco, and S. Rolston, J. Phys. B48, 165004 (2015)

    2015

  35. [43]

    Ruddell, K

    S. Ruddell, K. Webb, I. Herrera, A. Parkins, and M. Hoogerland, Optica4, 576 (2017)

    2017

  36. [44]

    Østfeldt, J.-B

    C. Østfeldt, J.-B. S. Béguin, F. T. Pedersen, E. S. Polzik, J. H. Müller, and J. Appel, Opt. Lett.42, 4315 (2017)

    2017

  37. [45]

    N. V. Corzo, J. Raskop, A. Chandra, A. S. Sheremet, B. Gouraud, and J. Laurat, Nature566, 359 (2019)

    2019

  38. [46]

    R. K. Gupta, J. L. Everett, A. D. Tranter, R. Henke, V.Gokhroo, P.K.Lam,andS.NicChormaic,AVSQuan- tum Sci.4(2022)

    2022

  39. [47]

    Kestler, K

    G. Kestler, K. Ton, D. Filin, C. Cheung, P. Schneeweiss, T. Hoinkes, J. Volz, M. Safronova, A. Rauschenbeutel, and J. Barreiro, PRX Quantum4, 040308 (2023)

    2023

  40. [48]

    Pennetta, S

    R. Pennetta, S. Xie, R. Zeltner, J. Hammer, and P. S. J. Russell, Photon. Res.8, 844 (2020)

    2020

  41. [49]

    Aspelmeyer, T

    M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Rev. Mod. Phys.86, 1391 (2014)

    2014

  42. [50]

    Treutlein, C

    P. Treutlein, C. Genes, K. Hammerer, M. Poggio, and P. Rabl, Hybrid mechanical systems, inCavity Optome- chanics: Nano- and Micromechanical Resonators Inter- acting with Light, edited by M. Aspelmeyer, T. J. Kip- penberg, and F. Marquardt (Springer Berlin Heidelberg, Berlin, H...

    2014

  43. [51]

    Yeh and F

    C. Yeh and F. I. Shimabukuro,The essence of dielectric waveguides(Springer, 2008)

    2008

  44. [52]

    N. W. McLachlan,Theory and application of Mathieu functions(Clarendon Press, Oxford, 1947)

    1947

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