REVIEW 2 major objections 4 minor 74 references
Light propagation through an atomic vapor with non-orthogonal electric field modes
T0 review · 2 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash
Pith's one-line read Magnetized atomic vapors need non-orthogonal light modes: a corrected propagation formalism removes unphysical spectral features and matches Rb D2 transmission data.
desk verdict A genuinely useful correction to a widely used magneto-optics model, validated by careful experiments; the only real caveat is an unverified smallness assumption about longitudinal mode components. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The load-bearing object is the mode-overlap matrix $S$ with entries $S_{ij} = \langle \hat{\mathbf{m}}_i | \hat{\mathbf{m}}_j \rangle = \hat{\mathbf{m}}_i^\dagger \cdot \hat{\mathbf{m}}_j$, built from the two eigenmodes solved out of the wave equation with the magnetized vapor's dielectric tensor; its diagonal entries are 1 and its off-diagonal entry is the complex mode overlap. The argument runs through the coefficient formula $\mathbf{c} = S^{-1} M \boldsymbol{\epsilon}_{\mathrm{inc}}$: when the modes are orthogonal, $S$ is the identity and the old formalism is recovered, and the explicit $S^{-1}$ factor is precisely what re-weights the modes where the overlap is large. Each mode then accrues its own phase $\exp(\mathrm{i} n_i k_0 L)$, and the exit field is reassembled as $E_0[c_1 t(n_1)\hat{\mathbf{m}}_1 + c_2 t(n_2)\hat{\mathbf{m}}_2]$. The modes are visualized as frequency-dependent polarization ellipses whose tilt and handedness track the regions where the old and new predictions disagree.
What would settle it
Repeat the Regime I transmission measurement (natural Rb D2, cell length 2 mm, temperature near 120 C, B = 240 G, theta_B = 84 degrees, with incident linear polarization scanned over theta_E approximately 0-172 degrees) and look at the spectrum near $\Delta$ approximately 3 GHz: the old formalism predicts a sharp unphysical transmission feature with up to 55-57% disagreement, while the new formalism predicts a smooth, Voigt-like profile, and data matching the sharp feature would refute the central claim. A second check is to measure the longitudinal field component just after the cell exit, which the formalism assumes is negligible (m_i,z < $10^{-3}$).
Extended reading notes
Core claim
The central claim is that the two eigenmodes of the wave equation for a magnetized atomic vapor -- the polarization states that propagate without changing shape -- are generally non-orthogonal whenever the magnetic field is neither parallel nor perpendicular to the beam, with a frequency-dependent complex overlap $\langle \hat{\mathbf{m}}_1 | \hat{\mathbf{m}}_2 \rangle$ that vanishes only in the Faraday and Voigt geometries (or if the susceptibilities were real). The paper's corrected formalism computes the incident-field decomposition coefficients as the solution of the overlap matrix equation $\mathbf{c} = S^{-1} M \boldsymbol{\epsilon}_{\mathrm{inc}}$, where $S_{ij} = \langle \hat{\mathbf{m}}_i | \hat{\mathbf{m}}_j \rangle$, and propagates each mode with its own complex phase $t(n_i) = \exp(\mathrm{i} n_i k_0 L)$, so that $\mathbf{E}_{\mathrm{out}} = E_0[c_1 t(n_1)\hat{\mathbf{m}}_1 + c_2 t(n_2)\hat{\mathbf{m}}_2]$. The previous formalism implicitly set $S$ to the identity matrix, mis-weighting the modes wherever their overlap is significant; the paper shows this produces unphysical sharp transmission features, while the corrected formalism removes them and fits measured natural-abundance Rb D2 spectra in two regimes -- 240 G near the Voigt geometry and 2.5 kG at oblique angles between 100 and 130 degrees -- with residuals of 0.5-0.7% root-mean-square error.
Load-bearing premise
The whole calculation rests on the modes' beam-direction components being negligible: the paper assumes $m_{i,z} < 10^{-3}$ of each mode's norm so that the incident field is spanned by the transverse parts alone, and it assumes the small longitudinal component of the output field reflects off the exit interface and can be set to zero; if those components were significant at the conditions tested, the mode coefficients and the predicted transmission would be inaccurate.
Editorial extensions
If this is right
- Models that ignore mode non-orthogonality (the previous ElecSus formalism and its relatives) predict unphysical spectral features of up to 55-57% transmission in oblique-field geometries, and those predictions should not be used for design or parameter extraction there.
- With the corrected formalism, weak-probe transmission spectra can be fitted with shared global parameters for temperature, field magnitude, and field angle, achieving 0.5-0.7% root-mean-square error across both small-field and intermediate-field regimes.
- The frequency-dependent mode overlap, tunable through the incident polarization angle, becomes a control handle for atomic photonic devices; the paper names suppression of single-cell atomic-filter bandwidth as the concrete follow-on application.
- At the Faraday and Voigt geometries the overlap vanishes and the new model coincides with the old one -- a built-in consistency check that holds across the parameter-space heatmaps.
Reading between the lines
- The same $S^{-1}$ correction applies to any propagation model that expands fields in eigenmodes of an anisotropic medium -- lossy crystals, magnetized plasmas, structured waveguides -- because non-orthogonal eigenvectors are generic for non-Hermitian propagation operators; the thermal vapor is a clean, continuously tunable test bed for that broader class of problems.
- A direct test the paper does not perform: polarization tomography of the exit beam could independently reconstruct the complex mode overlap $\langle \hat{\mathbf{m}}_1 | \hat{\mathbf{m}}_2 \rangle$ and compare it with the model's prediction, upgrading the indirect transmission fit into a direct measurement of non-orthogonality.
- The boundary treatment (negligible $m_{i,z}$ inside the cell and $E_{\mathrm{out},z} = 0$ at the exit) sets a boundary on where the formalism applies; a variant with a full Fresnel boundary condition for the longitudinal component would make the prediction quantitative at larger fields or sharper angles where the z-component grows.
- Because the old and new formalisms differ by up to ±57% transmission near $\theta_E \approx 82^\circ$-$172^\circ$, re-analyzing previously published oblique-geometry filter spectra might reveal systematic residuals that the corrected formalism would remove -- a cheap retrospective test of the claim.
Signed reviews
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper addresses propagation of weak probe light through an alkali-metal vapor in an external magnetic field whose direction is oblique to the laser wavevector. The authors argue that the two eigenmodes of the wave equation are generally non-orthogonal and frequency dependent, and that existing propagation models (ElecSus 3) neglect this non-orthogonality, producing unphysical transmission features. They derive a revised formalism (ElecSus 4) in which the incident field is decomposed onto the two modes by inverting the overlap (Gram) matrix, each mode propagates with its own complex refractive index, and the transmitted intensity is computed from the reconstructed output field. The formalism is validated with weak-probe transmission spectroscopy of the Rb D2 line in two regimes: Regime I at B = 240 G and theta_B = 80 deg with varying input polarization, and Regime II at B = 2.5 kG with theta_B between 100 and 130 deg and two fixed polarizations. The reported fits give RMSE values of about 0.5-0.7%, and the old formalism is shown to disagree with the new one by up to 55-57% in transmission in regions of strongest mode overlap.
Significance. If the formalism is correct, it fills a genuine gap in the modeling of arbitrary-angle magneto-optics in thermal vapors: previous propagation models used orthogonal-mode assumptions that are exact only in the Faraday and Voigt geometries. The paper shows that the correction can be large, removes unphysical spectral features, and is compatible with careful weak-probe experiments. The correction introduces no new free parameters; it uses the same electric-susceptibility engine as ElecSus 3, and the experimental validation uses physically constrained simultaneous fits with global parameters. The open-source ElecSus implementation, the deposited dataset with a DOI, and the explicit comparison to ElecSus 3 fits under different constraints are additional strengths. The main caveat is that one boundary-condition approximation in Section 2.2 is asserted but not numerically quantified at the resonant detunings where the central quantitative claims are made.
major comments (2)
- [§2.2, Eqs. (8)-(11)] The derivation of the mode coefficients relies on the assertion that the z-components of the modes satisfy m_i,z < 10^-3 of the mode norm, and that the incident field can therefore be decomposed in the transverse plane. This assumption is load-bearing: Eq. (10) solves the normal equations with the full 3D overlap matrix S, while the incident field has only x and y components, so the system is overdetermined unless the z-components are exactly zero. The Euclidean solution used in Eq. (11) is then only an approximation to the physically required matching of the transverse electric-field components, and the error in the coefficients can be amplified by the condition number of S when the modes become nearly parallel. The text states the bound but does not demonstrate it at the detunings where |<m1|m2>| is largest and where ElecSus 3 and ElecSus 4 differ by ~50%. Please add a numerical evaluation of max_i |m_i,z| over the full detuning range and over the theta_B and theta_E values used in Figs. 3-6, together with the condition number of S and a comparison of c_i and the resulting transmission computed with and without including the z-components. This check is needed to confirm that the headline 55-57% disagreement is a consequence of mode non-orthogonality rather than an artifact of the approximate boundary treatment.
- [§2.2, Eq. (9) and §4] The same z-component approximation is used at the exit interface, where E_out,z = 0 is set by assuming that the longitudinal component reflects off the boundary. This is self-consistent only if the z-component is indeed negligible throughout the cell, including at resonance. Since the modes are frequency dependent and the disagreement between old and new models is largest at resonance, the numerical check requested above should also cover the exit boundary treatment. Without that check, the quantitative claim that the old formalism mispredicts transmission by 55-57% is not fully supported.
minor comments (4)
- [Eq. (4)] In the version of the manuscript supplied for review, the matrix in Eq. (4) is rendered with stray non-mathematical characters, making the equation difficult to verify. Please check the typeset file and ensure the matrix elements appear correctly.
- [Supplemental document, Section 1 and Fig. S3 caption] The supplemental document contains at least two unresolved citation placeholders shown as "[? ]" (in the first paragraph and in the Fig. S3 caption text). These should be replaced with proper references.
- [§4.1.2] The text says that "since the only variable changed during the experiment was theta_E, each spectrum should have the same atom parameters," but then notes that the vapor cell was not actively temperature stabilized and that temperature may vary. Please clarify whether T was fitted as a single global parameter or allowed to vary per spectrum; the description is slightly ambiguous.
- [Fig. 6 caption] The caption states that residuals quantify the deviation of data from the ElecSus 4 fit, but the residual panels are not clearly visible in the figure as rendered. Please ensure the residual traces are visible and labeled in the final figure.
Circularity Check
No significant circularity: the new propagation formalism is derived from the wave equation and boundary matching, with the ElecSus susceptibility engine used only as an externally validated input.
full rationale
The paper's central derivation chain is self-contained: the refractive indices and electric-field modes are obtained by solving the wave equation, Eq. (4)/(6); the incident field is expanded in those modes, Eq. (8); the expansion coefficients are determined from the overlap matrix S, Eqs. (10)-(11); the output field is constructed by assigning each mode its propagation phase, Eq. (9); and the transmission is computed from the output field, Eq. (12). No step in this chain reintroduces as a 'prediction' a quantity that was used as an input to the same step. The electric susceptibilities chi_q are taken from the ElecSus engine [23,24], but that engine is an independently developed and previously validated input; using it does not make the new propagation result circular. The comparison with 'ElecSus 3' [24] is a same-group baseline, but the new formalism is not derived from ElecSus 3; it is derived from the wave equation, and the old model is then contrasted with it. The experimental validation fits physical parameters (T, B, theta_B, Gamma_B and theta_E) to ElecSus 4 and reports residuals; this is standard model validation rather than the production of a prediction from the same fitted quantity, and the extracted parameters agree with laboratory calibrations to within about 1-2%. The stated approximations, notably m_i,z < 1e-3 and setting E_out,z = 0, are assumptions whose numerical verification near resonance is not shown; that is a correctness or robustness concern, not a circularity, because the assumptions do not encode the paper's conclusion. No equation in the paper reduces by construction to its own input, and the central claim does not rest on a self-citation chain. The result is therefore not circular.
Assumptions & free parameters
free parameters (5)
- Atom temperature T =
119.69 degC (Regime I); fitted in Regime II
- Magnetic field magnitude B =
239.0 G (Regime I); ~2.5 kG (Regime II)
- Lorentzian broadening Gamma_B =
7.9 MHz (Regime I), fixed in Regime II
- Incident polarization angle theta_E =
e.g., 90.9 deg, 49.1 deg, 19.8 deg, -48.1 deg (Regime I)
- Magnetic field angle theta_B =
80 deg (set, Regime I); 100-130 deg (fit with 10 deg steps, Regime II)
assumptions (5)
- domain assumption The weak-probe field is monochromatic, plane-wave, and low enough intensity that the susceptibility is linear (Eq. (1), Section 2.1).
- domain assumption The dielectric tensor in the basis aligned with B has only epsilon'_xx, epsilon'_xy, epsilon'_zz nonzero for an alkali vapor (Eq. (5), citing [53]).
- ad hoc to paper The z-components of the modes are negligible (<10^-3 of the norm), so the incident field decomposition can be restricted to the transverse plane (Section 2.2).
- domain assumption At the exit interface, the z-component of E reflects off and is neglected; the transmitted field is treated as transverse (Section 2.2).
- standard math The incident field has zero z-component (epsilon_inc,z = 0), which follows from the laser beam being a transverse free-space plane wave before entering the cell (Section 2.2).
Cite this review
Pith. "Pith review of Light propagation through an atomic vapor with non-orthogonal electric field modes." pith.science (2026). https://pith.science/paper/UDTEN2Y6
@misc{pith2026250504504,
author = {Pith},
title = {Pith review of: Light propagation through an atomic vapor with non-orthogonal electric field modes},
year = {2026},
howpublished = {\url{https://pith.science/paper/UDTEN2Y6}},
note = {Machine review of arXiv:2505.04504}
}
abstract
Alkali-metal atomic vapors are the foundation of an ever-growing range of applications, driven by a comprehensive understanding of their interaction with light. In particular, many models have been developed which characterize this interaction for low intensity laser fields. An atomic medium subject to an external magnetic field of arbitrary direction exhibits two electric field modes that, in general, are non-orthogonal. Mode non-orthogonality is currently neglected by the models used in this context. We derive a new light propagation formalism which takes into account the non-zero overlap of the two modes. We verify the theory using weak-probe spectroscopy of the Rb D$_{2}$ line, showing excellent agreement with experiment. The predictions of the new theory can be exploited, and optimized, to design better atomic photonic devices.
Figures
Figures from the paper (3 more)
Reference graph
Works this paper leans on
-
[1]
Atom based RF electric field sensing,
H. Fan, S. Kumar, J. Sedlacek,et al., “Atom based RF electric field sensing,” J. Phys. B: At. Mol. Opt. Phys.48, 202001 (2015)
work page 2015
-
[2]
G. Allinson, M. J. Jamieson, A. R. Mackellar,et al., “Simultaneous multi-band radio-frequency detection using high-orbital-angular-momentum states in a Rydberg-atom receiver,” Phys. Rev. Res.6, 023317 (2024)
work page 2024
-
[3]
Vapor-cell-based atomic electrometry for detection frequencies below 1 kHz,
Y.-Y. Jau and T. Carter, “Vapor-cell-based atomic electrometry for detection frequencies below 1 kHz,” Phys. Rev. Appl. 13, 054034 (2020)
work page 2020
-
[4]
Full-field terahertz imaging at kilohertz frame rates using atomic vapor,
L. A. Downes, A. R. MacKellar, D. J. Whiting,et al., “Full-field terahertz imaging at kilohertz frame rates using atomic vapor,” Phys. Rev. X10, 011027 (2020)
work page 2020
-
[5]
Microfabricated atomic clocks and magnetometers,
S. Knappe, P. Schwindt, V. Gerginov,et al., “Microfabricated atomic clocks and magnetometers,” J. Opt. A: Pure Appl. Opt.8, S318 (2006)
work page 2006
-
[6]
High performance vapour-cell frequency standards,
M. Gharavipour, C. Affolderbach, S. Kang,et al., “High performance vapour-cell frequency standards,” inJournal of Physics: Conference Series, vol. 723 (IOP Publishing, 2016), p. 012006
work page 2016
-
[7]
Optical quantum memory,
A. I. Lvovsky, B. C. Sanders, and W. Tittel, “Optical quantum memory,” Nat. Photonics3, 706–714 (2009)
2009
-
[8]
Optical memory in a microfabricated rubidium vapor cell,
R. Mottola, G. Buser, and P. Treutlein, “Optical memory in a microfabricated rubidium vapor cell,” Phys. Rev. Lett. 131, 260801 (2023)
work page 2023
Show all 74 references
-
[9]
Frequency-stabilized Faraday laser with 10−14 short-term instability for atomic clocks,
P. Chang, H. Shi, J. Miao,et al., “Frequency-stabilized Faraday laser with 10−14 short-term instability for atomic clocks,” Appl. Phys. Lett.120, 141102 (2022)
2022
-
[10]
Frequency stabilization of a Cesium Faraday laser with a double-layer vapor cell as frequency reference,
H. Shi, P. Chang, Z. Wang,et al., “Frequency stabilization of a Cesium Faraday laser with a double-layer vapor cell as frequency reference,” IEEE Photonics J.14, 1–6 (2022)
2022
-
[11]
Femtotesla atomic magnetometry in a microfabricated vapor cell,
W. C. Griffith, S. Knappe, and J. Kitching, “Femtotesla atomic magnetometry in a microfabricated vapor cell,” Opt. Express 18, 27167–27172 (2010)
2010
-
[12]
Recording the heart beat of cattle using a gradiometer system of optically pumped magnetometers,
J. U. Sutter, O. Lewis, C. Robinson,et al., “Recording the heart beat of cattle using a gradiometer system of optically pumped magnetometers,” Comput. Electron. Agric.177, 105651 (2020)
2020
-
[13]
High-field optical cesium magnetometer for magnetic resonance imaging,
H. Stærkind, K. Jensen, J. H. Müller,et al., “High-field optical cesium magnetometer for magnetic resonance imaging,” PRX Quantum5, 020320 (2024)
2024
-
[14]
Wide range linear magnetometer based on a sub-microsized K vapor cell,
M. Auzinsh, A. Sargsyan, A. Tonoyan,et al., “Wide range linear magnetometer based on a sub-microsized K vapor cell,” Appl. Opt.61, 5749–5754 (2022)
2022
-
[15]
Ultrahigh-noise rejection optical filter,
D. Dick and T. M. Shay, “Ultrahigh-noise rejection optical filter,” Opt. Lett.16, 867–869 (1991)
1991
-
[16]
Dispersive magnetooptic filters,
P. Yeh, “Dispersive magnetooptic filters,” Appl. Opt.21, 2069–2075 (1982)
1982
-
[17]
How to build an optical filter with an atomic vapor cell,
D. Uhland, H. Dillmann, Y. Wang, and I. Gerhardt, “How to build an optical filter with an atomic vapor cell,” New J. Phys. 25, 125001 (2023)
2023
-
[18]
Simple Python tools for modelling few-level atom-light interactions,
L. Downes, “Simple Python tools for modelling few-level atom-light interactions,” J. Phys. B: At. Mol. Opt. Phys.56, 223001 (2023)
2023
-
[19]
CoOMBE: A suite of open-source programs for the integration of the optical Bloch equations and Maxwell-Bloch equations,
R. M. Potvliege and S. A. Wrathmall, “CoOMBE: A suite of open-source programs for the integration of the optical Bloch equations and Maxwell-Bloch equations,” Comput. Phys. Commun.306, 109374 (2025)
2025
-
[20]
Atomic Density Matrix,
Simon Rochester, “Atomic Density Matrix,”https://www.rochesterscientific.com/ADM/ (2020). Accessed: 08-12-24
2020
-
[21]
A comprehensive model for Doppler spectra in thermal atomic vapour,
R. Bala, J. Ghosh, and V. Venkataraman, “A comprehensive model for Doppler spectra in thermal atomic vapour,” J. Phys. B: At. Mol. Opt. Phys.55, 165003 (2022)
2022
-
[22]
Measurement and modelling of intensity dependent absorption and transit relaxation on the cesium D1 line,
J. Sagle, R. K. Namiotka, and J. Huennekens, “Measurement and modelling of intensity dependent absorption and transit relaxation on the cesium D1 line,” J. Phys. B: At. Mol. Opt. Phys.29, 2629 (1996)
1996
-
[23]
ElecSus: A program to calculate the electric susceptibility of an atomic ensemble,
M. A. Zentile, J. Keaveney, L. Weller,et al., “ElecSus: A program to calculate the electric susceptibility of an atomic ensemble,” Comput. Phys. Commun.189, 162–174 (2015)
2015
-
[24]
ElecSus: Extension to arbitrary geometry magneto-optics,
J. Keaveney, C. S. Adams, and I. G. Hughes, “ElecSus: Extension to arbitrary geometry magneto-optics,” Comput. Phys. Commun.224, 311–324 (2018)
2018
-
[25]
C. S. Adams and I. G. Hughes,Optics f2f: from Fourier to Fresnel (Oxford University Press, 2018)
2018
-
[26]
Absolute absorption on rubidium D lines: comparison between theory and experiment,
P. Siddons, C. S. Adams, C. Ge, and I. G. Hughes, “Absolute absorption on rubidium D lines: comparison between theory and experiment,” J. Phys. B: At. Mol. Opt. Phys.41, 155004 (2008)
2008
-
[27]
Atomic Faraday filter with equivalent noise bandwidth less than 1 GHz,
M. A. Zentile, D. J. Whiting, J. Keaveney,et al., “Atomic Faraday filter with equivalent noise bandwidth less than 1 GHz,” Opt. Lett.40, 2000–2003 (2015)
2015
-
[28]
Optimization of atomic Faraday filters in the presence of homogeneous line broadening,
M. A. Zentile, J. Keaveney, R. S. Mathew,et al., “Optimization of atomic Faraday filters in the presence of homogeneous line broadening,” J. Phys. B: At. Mol. Opt. Phys.48, 185001 (2015)
2015
-
[29]
The hyperfine Paschen–Back Faraday effect,
M. A. Zentile, R. Andrews, L. Weller,et al., “The hyperfine Paschen–Back Faraday effect,” J. Phys. B: At. Mol. Opt. Phys. 47, 075005 (2014)
2014
-
[30]
Absolute absorption on the potassium D lines: theory and experiment,
R. K. Hanley, P. D. Gregory, I. G. Hughes, and S. L. Cornish, “Absolute absorption on the potassium D lines: theory and experiment,” J. Phys. B: At. Mol. Opt. Phys.48, 195004 (2015)
2015
-
[31]
Absorption spectroscopy and Stokes polarimetry in a87Rb vapour in the Voigt geometrywith a 1.5 T external magnetic field,
F. S. Ponciano-Ojeda, F. D. Logue, and I. G. Hughes, “Absorption spectroscopy and Stokes polarimetry in a87Rb vapour in the Voigt geometrywith a 1.5 T external magnetic field,” J. Phys.B: At. Mol.Opt. Phys.54, 015401 (2020)
2020
-
[32]
Voigttransmissionwindowsinopticallythickatomicvapours: amethod to create single-peaked line centre filters,
J.D.Briscoe,F.D.Logue,D.Pizzey, et al.,“Voigttransmissionwindowsinopticallythickatomicvapours: amethod to create single-peaked line centre filters,” J. Phys. B: At. Mol. Opt. Phys.56, 105403 (2023)
2023
-
[33]
Indirect measurement of atomic magneto-optical rotation via Hilbert transform,
J. D. Briscoe, D. Pizzey, S. A. Wrathmall, and I. G. Hughes, “Indirect measurement of atomic magneto-optical rotation via Hilbert transform,” J. Phys. B: At. Mol. Opt. Phys.57, 175401 (2024)
2024
-
[34]
Laser spectroscopy of hot atomic vapours: from’scope to theoretical fit,
D. Pizzey, J. Briscoe, F. Logue,et al., “Laser spectroscopy of hot atomic vapours: from’scope to theoretical fit,” New J. Phys.24, 125001 (2022)
2022
-
[35]
Low-drift Zeeman shifted atomic frequency reference,
D. Reed, N. Šibalić, D. Whiting,et al., “Low-drift Zeeman shifted atomic frequency reference,” OSA Continuum1, 4–12 (2018)
2018
-
[36]
Signal intensity influences on the atomic Faraday filter,
B. Luo, L. Yin, J. Xiong,et al., “Signal intensity influences on the atomic Faraday filter,” Opt. Lett.43, 2458–2461 (2018)
2018
-
[37]
The characteristics of Ar and Cs mixed Faraday optical filter under different signal powers,
J. Xiong, B. Luo, L. Yin,et al., “The characteristics of Ar and Cs mixed Faraday optical filter under different signal powers,” IEEE Photonics Technol. Lett.30, 716–719 (2018)
2018
-
[38]
Practical Doppler broadening thermometry,
N. Agnew, G. Machin, E. Riis, and A. S. Arnold, “Practical Doppler broadening thermometry,” inAIP Conference Proceedings,vol. 3230 (AIP Publishing, 2024)
2024
-
[39]
C. J. Foot,Atomic physics, vol. 7 (Oxford university press, 2005)
2005
-
[40]
Measuring the Stokes parameters for light transmitted by a high-density rubidium vapour in large magnetic fields,
L. Weller, T. Dalton, P. Siddons,et al., “Measuring the Stokes parameters for light transmitted by a high-density rubidium vapour in large magnetic fields,” J. Phys. B: At. Mol. Opt. Phys.45, 055001 (2012)
2012
-
[41]
I. Experimental researches in electricity.—Nineteenth series,
M. Faraday, “I. Experimental researches in electricity.—Nineteenth series,” Philos. Trans. Royal Soc. Lond.136, 1–20 (1846)
-
[42]
Resonant nonlinear magneto-optical effects in atoms,
D. Budker, W. Gawlik, D. Kimball,et al., “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74, 1153 (2002)
2002
-
[43]
A gigahertz-bandwidth atomic probe based on the slow-light Faraday effect,
P. Siddons, N. C. Bell, Y. Cai,et al., “A gigahertz-bandwidth atomic probe based on the slow-light Faraday effect,” Nat. Photonics3, 225–229 (2009)
2009
-
[44]
A Faraday effect optical isolator,
L. Aplet and J. W. Carson, “A Faraday effect optical isolator,” Appl. Opt.3, 544–545 (1964)
1964
-
[45]
Optical determination of alkali metal vapor number density using Faraday rotation,
Z. Wu, M. Kitano, W. Happer,et al., “Optical determination of alkali metal vapor number density using Faraday rotation,” Appl. Opt.25, 4483–4492 (1986)
1986
-
[46]
Simultaneous Faraday filtering of the Mollow triplet sidebands with the Cs-D1 clock transition,
S. L. Portalupi, M. Widmann, C. Nawrath,et al., “Simultaneous Faraday filtering of the Mollow triplet sidebands with the Cs-D1 clock transition,” Nat. Commun.7, 13632 (2016)
2016
-
[47]
Electromagnetically induced transparency and optical pumping in the hyperfine Paschen-Back regime,
R. Mottola, G. Buser, and P. Treutlein, “Electromagnetically induced transparency and optical pumping in the hyperfine Paschen-Back regime,” Phys. Rev. A108, 062820 (2023)
2023
-
[48]
Resonant Voigt-effect spectrum of the rubidium D2 transition,
K. Muroo, T. Matsunobe, Y. Shishido,et al., “Resonant Voigt-effect spectrum of the rubidium D2 transition,” JOSA B 11, 409–414 (1994)
1994
-
[49]
Dual-beam potassium Voigt filter for atomic line imaging,
M. W. Kudenov, B. Pantalone, and R. Yang, “Dual-beam potassium Voigt filter for atomic line imaging,” Appl. Opt. 59, 5282–5289 (2020)
2020
-
[50]
A Voigt laser lasing on Cs 852 nm transition,
Z. Ge, C. Zhu, Y. Wang,et al., “A Voigt laser lasing on Cs 852 nm transition,” IEEE Access12, 196171–196177 (2024)
2024
-
[51]
An atomic filter laser with a compact Voigt anomalous dispersion optical filter,
Z. Liu, X. Guan, X. Qin,et al., “An atomic filter laser with a compact Voigt anomalous dispersion optical filter,” Appl. Phys. Lett.123, 131103 (2023)
2023
-
[52]
Infrared and microwave magnetoplasma effects in semiconductors,
E. Palik and J. Furdyna, “Infrared and microwave magnetoplasma effects in semiconductors,” Reports on Prog. Phys. 33, 1193 (1970)
1970
-
[53]
Generalized treatment of magneto-optical transmission filters,
M. D. Rotondaro, B. V. Zhdanov, and R. J. Knize, “Generalized treatment of magneto-optical transmission filters,” JOSA B32, 2507–2513 (2015)
2015
-
[54]
Magneto-optic rotation for an arbitrary field direction,
N. Edwards, S. Phipp, and P. Baird, “Magneto-optic rotation for an arbitrary field direction,” J. Phys. B: At. Mol. Opt. Phys. 28, 4041 (1995)
1995
-
[55]
Magneto-optical effects of saturating light for arbitrary field direction,
G. Nienhuis and F. Schuller, “Magneto-optical effects of saturating light for arbitrary field direction,” Opt. Commun. 151, 40–45 (1998)
1998
-
[56]
Optimized ultra-narrow atomic bandpass filters via magneto-optic rotation in an unconstrained geometry,
J. Keaveney, S. A. Wrathmall, C. S. Adams, and I. G. Hughes, “Optimized ultra-narrow atomic bandpass filters via magneto-optic rotation in an unconstrained geometry,” Opt. Lett.43, 4272–4275 (2018)
2018
-
[57]
Atomic line versus lens cavity filters: a comparison of their merits,
C. R. Higgins, D. Pizzey, R. S. Mathew, and I. G. Hughes, “Atomic line versus lens cavity filters: a comparison of their merits,” OSA Continuum3, 961–970 (2020)
2020
-
[58]
A device for magnetic-field angle control in magneto-optical filters using a solenoid-permanent magnet pair,
S. A. Alqarni, J. D. Briscoe, C. R. Higgins,et al., “A device for magnetic-field angle control in magneto-optical filters using a solenoid-permanent magnet pair,” Rev. Sci. Instruments95, 035103 (2024)
2024
-
[59]
Improving Magneto-Optical Filter Performance: Cascading and Oblique B-fields
F. D. Logue, “Improving Magneto-Optical Filter Performance: Cascading and Oblique B-fields.” Ph.D. thesis, Durham University (2023)
2023
-
[60]
ElecSus,
Mark Zentile and James Keaveney, “ElecSus,”https://github.com/durham-qlm/ElecSus (2018). Accessed: 11-04-25
2018
-
[61]
AbsoluteAbsorptionandDispersioninaThermalRbVapouratHighDensitiesandHighMagneticField,
L.Weller,“AbsoluteAbsorptionandDispersioninaThermalRbVapouratHighDensitiesandHighMagneticField,” Ph.D. thesis, Durham University (2013)
2013
-
[62]
A New Calculus for the Treatment of Optical Systems I. Description and Discussion of the Calculus,
R. C. Jones, “A New Calculus for the Treatment of Optical Systems I. Description and Discussion of the Calculus,” J. Opt. Soc. Am.31, 488–493 (1941)
1941
-
[63]
D. J. Griffiths,Introduction to electrodynamics (Cambridge University Press, 2023)
2023
-
[64]
Automated translating beam profiler for in situ laser beam spot-size and focal position measurements,
J. Keaveney, “Automated translating beam profiler for in situ laser beam spot-size and focal position measurements,” Rev. Sci. Instruments89, 035114 (2018)
2018
-
[65]
How weak is a weak probe in laser spectroscopy?
B. E. Sherlock and I. G. Hughes, “How weak is a weak probe in laser spectroscopy?” Am. J. Phys.77, 111–115 (2009)
2009
-
[66]
Modelling spectra of hot alkali vapour in the saturation regime,
D. R. Häupl, C. R. Higgins, D. Pizzey,et al., “Modelling spectra of hot alkali vapour in the saturation regime,” New J. Phys.27, 033003 (2025)
2025
-
[67]
Hyperfine Paschen–Back regime realized in Rb nanocell,
A. Sargsyan, G. Hakhumyan, C. Leroy,et al., “Hyperfine Paschen–Back regime realized in Rb nanocell,” Opt. Lett. 37, 1379–1381 (2012)
2012
-
[68]
Optical spectroscopy of a microsized Rb vapor sample in magnetic fields up to 58 T,
D. Ciampini, R. Battesti, C. Rizzo, and E. Arimondo, “Optical spectroscopy of a microsized Rb vapor sample in magnetic fields up to 58 T,” Phys. Rev. A96, 052504 (2017)
2017
-
[69]
Precisionmeasurementoftheexcitedstatelandég-factoranddiamagnetic shift of the cesium D2 line,
H.Stærkind,K.Jensen,J.H.Müller, et al.,“Precisionmeasurementoftheexcitedstatelandég-factoranddiamagnetic shift of the cesium D2 line,” Phys. Rev. X13, 021036 (2023)
2023
-
[70]
Hughes and T
I. Hughes and T. Hase,Measurements and their uncertainties: a practical guide to modern error analysis (OUP Oxford, 2010)
2010
-
[71]
Collisional broadening and shift of the rubidium D1 and D2 lines (52S12→ 52P12, 52P32) by rare gases, H2, D2, N2, CH4 and CF4,
M. D. Rotondaro and G. P. Perram, “Collisional broadening and shift of the rubidium D1 and D2 lines (52S12→ 52P12, 52P32) by rare gases, H2, D2, N2, CH4 and CF4,” J. Quant. Spectrosc. Radiat. Transf.57, 497–507 (1997)
1997
-
[72]
Lightpropagationthroughanatomicvaporwithnon-orthogonalelectricfieldmodes[dataset].Durham University Collections
J.D.Briscoe,“Lightpropagationthroughanatomicvaporwithnon-orthogonalelectricfieldmodes[dataset].Durham University Collections.”http://doi.org/10.15128/r24m90dv58f (2025). Light propagation through an atomic vapor with non-orthogonal electric field modes: supplemental document T...
2025 doi
-
[73]
COMPARISON OF ELECSUS 3 AND ELECSUS 4 OVER A LARGER PARAMETER SPACE Paper Figs. 3 and 5 not only demonstrated the existence of non-orthogonal electric field modes in a simple atomic vapor system, but also highlighted two of many regimes where significant disagreement between o...
2025 arXiv
-
[74]
ElecSus 3 fits were omitted, primarily due to fitting to parameters which do not match those measured in the lab
FITTING WITH ELECSUS 3 (OLD LIGHT PROPAGATION FORMALISM) In the results section of the paper, we compare data taken in Regimes I and II with ElecSus 4 fits. ElecSus 3 fits were omitted, primarily due to fitting to parameters which do not match those measured in the lab. This i...
Reviewed August 15, 2026 · model on record in the stance chip above.
Discussion (0). Continue with ORCID to comment.