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Scattering of light with angular momentum from an array of particles

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Pith's one-line read The orbital angular momentum (OAM) spectrum of light scattered by a dilute particle distribution directly encodes the distribution's azimuthal Fourier harmonics, so ordered or chiral subsets can be detected even when they are a few…

desk verdict Clean new selection rule linking scattered OAM to azimuthal structure, but the numerics need a quantitative check on the single-scattering assumption. read the letter →

arxiv 1908.03439 v1 pith:2OXCVIGE submitted 2019-08-09 physics.optics

Duncan McArthur , Alison Yao , Francesco Papoff This is my paper · ORCID
classification physics.optics
keywords orbitalangularmomentumMiescatteringLaguerre-GaussianbeamsdiluteparticledistributionsazimuthalFourierharmonicsOAMmodesortingchiraldetectionnanoparticlearrays
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

This paper develops a generalized Mie theory for quasi-monochromatic structured light, specifically Laguerre-Gaussian beams carrying orbital angular momentum (OAM), scattered by dilute distributions of micro- and nanoparticles. The authors show that the far-field scattered light follows a selection rule: a beam with OAM $\ell$ scattering from a distribution whose density has azimuthal harmonic $u$ produces scattered field components with total angular momentum $j_z = m + u + \ell$, so the OAM spectrum measured in the far field directly reveals the spatial azimuthal harmonics of the particle distribution. In the forward direction only the $u = -\ell$ harmonic survives, meaning the incident OAM acts as a filter that selects one Fourier component of the particle arrangement. This turns scattering, usually a source of signal loss, into a probe that can expose symmetric, polygonal, or chiral subsets of particles inside a disordered medium at concentrations as low as a few percent of the total. The authors further find that the forward-scattered signal-to-noise ratio is the same for all Laguerre-Gaussian orders, supporting OAM-multiplexed communication through scattering media.

What carries the argument

The argument is carried by the density of multipole-multipole transitions, $D^{AB}_{j'm'jm}(\mathbf{r}')$, a distribution of how each particle converts incident multipoles into scattered multipoles, built from T-matrix elements and delta functions located at the particle centers. Expanding this density in azimuthal harmonics $\exp(iu\phi)$ and the incident beam's expansion coefficients in harmonics $\exp(iq\phi)$, the Jacobi-Anger identity turns the translation of scattered waves to the far field into a Bessel-function sum that enforces the selection rule $n = u + q$. This yields Eq. (18): the far-field scattered field is a coherent sum over multipoles with total angular momentum component $j_z = m + u + q$. For spherical particles the T-matrix collapses to the Mie coefficients, and for paraxial Laguerre-Gaussian beams $q = \ell$, which makes the forward/backward selection rule $u = -\ell$ fully analytical.

What would settle it

Use a known dilute suspension of 80 nm gold nanospheres with engineered azimuthal order, illuminate it with a circularly polarized Laguerre-Gaussian beam of order $\ell$, and sort the forward-scattered light by OAM: the central claim predicts a dominant peak at $l_z = \ell$ from the $u = -\ell$ harmonic, with strength tracking the distribution's measured azimuthal moment. If the spectrum instead shows comparable power across all $l_z$, or is insensitive to changes in the distribution's azimuthal moments, the selection rule is false.

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Extended reading notes

Core claim

The central discovery is that the orbital angular momentum content of scattered light is a readout of the spatial structure of the scattering ensemble. For a dilute distribution of identical particles illuminated along the $z$-axis by a paraxial Laguerre-Gaussian beam of order $\ell$, the far-field scattered field can be written as a coherent sum over multipolar waves, each carrying total angular momentum component $j_z = u + q + m$ along the beam axis, with $q = \ell$ for the LG beam. The index $u$ is the azimuthal Fourier harmonic of the particle distribution, equivalently of the density of multipole-multipole transitions. Because the spin component $s_z$ takes only the values $0$ or $\pm 1$, the measured OAM $l_z = j_z - s_z$ is tied one-to-one to $u$. In the forward and backward directions only the harmonic $u = -\ell$ and circular polarizations with $m = \pm 1$ contribute, so the forward OAM spectrum directly reveals the Fourier component of the particle arrangement selected by the incident beam. This is why a few percent of particles arranged with $N$-fold symmetry or chirality can be detected inside a random background: they contribute sharp features in the scattered OAM spectrum even when they are a small fraction of the total number.

Load-bearing premise

The load-bearing premise is that the particle distribution is dilute enough that multiple scattering can be neglected, so the total scattered field is simply the coherent sum of each particle's single-scattering response; if particles are closely spaced or the medium is dense, re-scattering between particles invalidates the sum and the OAM selection rules built on it.

Editorial extensions

If this is right

  • The azimuthal Fourier moments of a particle distribution can be read directly from the OAM spectrum of forward-scattered light: for incident OAM $\ell$, the $u = -\ell$ harmonic dominates, so scanning $\ell$ maps the distribution's harmonics.
  • Symmetric subsets, for example particles arranged on $N$-sided polygons or on two parallel lines, remain detectable through their even azimuthal harmonics even when they are only about 4% of the total particle number.
  • Backward scattering suppresses contributions from randomly distributed particles except at wavelengths where particles lying in planes orthogonal to the beam, or spaced periodically along it, scatter in phase; wavelength scanning therefore reveals ordered planar structures through interference fringes.
  • For particles distributed over volumes much larger than the wavelength, the forward-scattered signal-to-noise ratio is the same for all Laguerre-Gaussian orders $\ell$, so OAM multiplexing does not sacrifice SNR in relatively dense but still dilute media.
  • For small regular arrays, increasing the detection angle spreads scattered power over OAM states that mirror the array's azimuthal harmonics, and displacing the array from the beam axis produces strong $l_z = \pm 1$ peaks, locating the symmetry axis to about 1% of the beam waist.

Reading between the lines

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

  • Because the selection rule is kinematic, the same azimuthal-moment readout should transfer to non-paraxial structured beams once their azimuthal expansion coefficients are known; the mechanism does not depend on paraxiality.
  • Time-resolved OAM spectroscopy could reveal the onset of ordered clustering in flowing or self-assembling suspensions before the structure is visible in ordinary intensity imaging.
  • The theory implies a concrete threshold experiment: increase particle concentration until the $u = -\ell$ selection rule degrades; the density at which spurious $l_z$ states appear quantifies the breakdown of the dilute assumption.
  • The handedness discrimination for 3D helices suggests OAM scattering could serve as a chiral probe using linearly polarized light, complementing circular-dichroism measurements with a single-beam-axis geometry.
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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 / 6 minor

Summary. The paper develops a generalized Mie-theory formalism for the far-field scattering of quasi-monochromatic structured beams (paraxial Laguerre-Gaussian modes) by dilute distributions of micro- and nanoparticles. The central result is Eq. (18), which represents the scattered far field as a sum over azimuthal harmonics u of the particle distribution and harmonics q of the incident beam, with total angular momentum component j_z = m + u + q. For forward and backward directions the authors derive the selection rule u = -ℓ and m = ±1, implying that the OAM spectrum of the scattered light directly encodes the azimuthal Fourier components of the particle ensemble. Numerical examples with 80-nm gold spheres illustrate detection of ordered subsets, array displacement, and chiral structures. The paper explicitly restricts validity to distributions where multiple scattering can be neglected.

Significance. If the central claim holds, the paper offers a parameter-free, analytically derived mapping between a measurable far-field quantity (the scattered OAM spectrum) and the spatial structure of a scattering ensemble; this is a potentially novel tool for nanophotonics, environmental sensing, and optical communications. The derivation from Maxwell's equations through the T-matrix and Jacobi-Anger identity is coherent under the stated single-scattering assumption, and the forward/backward selection rule is clearly articulated. The paper produces falsifiable predictions, such as the l_z = ℓ peak for the u = 0 harmonic and backward interference fringes for z-periodic arrays. The main weakness is that the practical numerical regimes never verify the load-bearing dilute-condition assumption, and several key derivations are referenced only through broken cross-references to missing sections and appendices.

major comments (2)
  1. [Numerical Results (Eq. (8) and following)] The entire detection procedure rests on the coherent-sum ansatz of Eq. (8), which is stated to be valid for 'dilute' distributions, but no quantitative dilution criterion is provided. The simulated systems (80-nm gold spheres near the 670 nm plasmon resonance with 870 nm nearest-neighbor spacing in the 7×7 array, and the 'relatively dense' random/combined distributions) are not checked against multiple-scattering contributions. Because the selection rule j_z = m + u + q and the forward condition u = -ℓ are exact only when Eq. (8) holds, the authors should either state a quantitative condition (e.g., interparticle distance relative to scattering mean free path or to the scattering cross-section) or compare the coherent-sum prediction with a multiple-scattering calculation at the quoted parameters. This is a load-bearing point for the paper's central detection claims.
  2. [Throughout, especially Theory and Local Plane Wave Approximation] Several derivations that are essential to the main results are referenced to sections and appendices that do not appear in the manuscript: 'as discussed in Sec. .' (Numerical Results, first paragraph), 'as we show in Sec. .' (ibid.), 'defined as in Appendix .' (Theory, after Eq. (4)), 'see Eq. (55) in Appendix .' (Theory, before Eq. (14)), 'as shown in Appendix .' (Local Plane Wave Approximation), and 'Eqs. (4a-4b) in Appendix .' (Local Plane Wave Approximation). In particular, the reduction of the Laguerre-Gaussian beam to q = ℓ and m = ±1 in the local plane wave approximation is a key step for all numerical predictions and is currently only supported by a cross-reference to a missing appendix. Without these materials, the derivation is not self-contained and the selection rules cannot be independently verified.
minor comments (6)
  1. [Theory, Eq. (14)] In Eq. (14), the field is written for a single particle at position r_t, but the text introduces it as 'the field scattered by all the particles'; the total field presumably requires a sum over t, which should be shown explicitly to avoid ambiguity.
  2. [Abstract and Conclusions] The claim that 'the signal-to-noise ratio, in the forward direction, is equivalent for all orders of the Laguerre-Gaussian modes' is not accompanied by a definition of signal or noise. Please define the SNR used in this comparison (e.g., power in the l_z = ℓ peak versus total scattered power or mode-sorter dark counts) so the claim is falsifiable.
  3. [Regular arrays of particles] There are several typographical errors: 'partcles' instead of 'particles' in the first paragraph, 'scatted' instead of 'scattered' in the same paragraph, and 'permittivitty'/'permitivitty' instead of 'permittivity' in the Overview and Eq. (1).
  4. [Fig. 4(b)] The color axis in Fig. 4(b) is labeled only as 'Psca (arb. units)' with a color bar; please add a quantitative scale or at least state the normalization used, since the four scattering regimes are identified by relative power levels.
  5. [Chiral structures] The text in the Chiral structures section states that for helices 'the polarization of the incident beam is not as important,' but the caption of Fig. 7 says 'For helixes the polarization of the incident beam is important.' Please reconcile this apparent contradiction.
  6. [Theory, selection-rule bullets] The bullet 'For these terms lz=0, however the two conditions above are more restrictive than lz=0' is confusing: it should be clarified that lz=0 follows from the combination of m = ±1 and u = -ℓ, while the conditions on m and u are indeed stronger than merely requiring lz=0.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the OAM selection rules follow from a self-contained multipole derivation; self-citations are not load-bearing.

full rationale

The paper's central results (j_z = m + u + q, l_z = j_z - s_z, and the forward/backward condition u = -q) are obtained by a self-contained calculation from Maxwell's equations: the incident field is expanded in vector spherical waves (Eqs. 3-4), the single-particle T-matrix relates incident to scattered multipole coefficients (Eqs. 5-6), the total scattered field is the coherent sum over particles under the explicitly stated dilute/multiple-scattering-neglected condition (Eq. 8, with ref. [18]), and the Jacobi-Anger expansion together with a Fourier decomposition of the multipole-multipole transition density (Eqs. 15-17) leads directly to Eq. (18) with the azimuthal phase exp[i(u+q)phi] and hence to the OAM selection rules. No parameter is fitted to any subset of the data to produce the predicted OAM spectra; the numerical examples are consistency checks computed from the same distributions using standard Mie theory and the Lorentz-Drude dielectric function. The authors' own prior works [25-27] appear only for six-vector notation and for a proposed extension to multiple scattering via Green's functions; they are not the source of the selection rules. The only concerns are non-circular: the dilute condition is not quantified independently for the plasmon-resonant numerical cases, and several cross-references are missing (e.g., 'as discussed in Sec. .' and 'see Eq. (55) in Appendix .'), which are omissions rather than circular reductions. Therefore no circular step is present.

Assumptions & free parameters 0 free parameters · 6 assumptions · 1 invented entities

No free parameters are fitted to data in this paper. The theory is parameter-free given the incident beam, particle dielectric function, and spatial distribution; the numerical examples use fixed parameter values (e.g., 80 nm gold spheres, 870 nm spacing) from prior literature or chosen for illustration, not fitted to achieve the reported phenomena.

assumptions (6)
  • standard math Maxwell's equations with harmonic time dependence and linear constitutive relations.
    Starting point in Theory, Eq. (1).
  • domain assumption The scattering process for each particle is linear and described by a T-matrix.
    Eqs. (5) and (13) in Theory; assumes no nonlinear effects and single scattering.
  • domain assumption Multiple scattering between particles is negligible; total scattered field is the coherent sum of single-particle fields.
    Explicitly stated in Numerical Results, first paragraph, and used in Eq. (8).
  • domain assumption Incident LG beam is paraxial, and particle radius Rt << w0, zR, so transverse field seen by each particle is approximately a local plane wave and longitudinal components do not scatter (claimed, not fully shown).
    Local Plane Wave Approximation section; the longitudinal non-scattering claim is referenced to a missing appendix.
  • standard math Mie coefficients for spherical particles are known from prior literature.
    Used for spheres in Local Plane Wave Approximation; from Mie theory [35].
  • standard math Vector multipole expansions, translation addition theorems, and the Jacobi-Anger identity are valid in the far field.
    Used to derive Eqs. (14) and (18), with asymptotic forms in Appendix.
invented entities (1)
  • Density of multipole-multipole transitions D^AB_{j'm'jm}(r')
    purpose: To replace sums over discrete particles with integrals over a continuous density in the derivation of the far-field scattering amplitude (Eqs. 15-19).
    This is a mathematical bookkeeping device, not a new physical entity. It is exact (built from Dirac deltas at particle centers) and does not add degrees of freedom, so it should not be counted as a physical postulate.

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Cite this review

Pith. "Pith review of Scattering of light with angular momentum from an array of particles." pith.science (2026). https://pith.science/paper/2OXCVIGE

@misc{pith2026190803439,
  author       = {Pith},
  title        = {Pith review of: Scattering of light with angular momentum from an array of particles},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2OXCVIGE}},
  note         = {Machine review of arXiv:1908.03439}
}
read the original abstract

Understanding the scattering properties of various media is of critical importance in many applications, from secure, high-bandwidth communications to extracting information about biological and mineral particles dissolved in sea water. In this paper we demonstrate how beams carrying orbital angular momentum (OAM) can be used to detect the presence of symmetric or chiral subsets of particles in disordered media. Using a generalized Mie theory we calculate analytical expressions for quasi-monochromatic structured light scattered by dilute distributions of micro- and nanoparticles. These allow us to determine the angular momentum of the scattered field as a function of the angular momentum of the incident beam and of the spatial distributions of scattering particles. Our numerical results show that we can distinguish structured from random distributions of particles, even when the number density of ordered particles is a few percent of the total distribution. We also find that the signal-to-noise ratio, in the forward direction, is equivalent for all orders of the Laguerre-Gaussian modes in relatively dense (but still dilute) distributions, making them an ideal basis to encode and transmit multiplexed signals.

Figures

Figures reproduced from arXiv: 1908.03439 by the authors.

Figure 1
Figure 1. FIG. 1: Schematic of a basic experimental setup (a) where [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: From left to right [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Power of scattered light with defined OAM within a smal [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4: Effect of increasing the angle of detection, [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 7
Figure 7. Figure 7: FIG. 7: Power of scattered light with defined OAM for a left [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]

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Reference graph

Works this paper leans on

51 extracted references · 49 canonical work pages

  1. [18]

    we can derive the following properties that apply to distributions of particles with any shape and for any incident field, as long as multiple scattering can be neglected: • F or each spatial harmonic u of the multipole- multipole distributions and harmonic q of the beam expansion coefficient, the multipo- lar waves SH∞ jm and S E∞ jm , scattered by every pa...

    work page 2017

  2. [1]

    Nanoparticles randomly distributed within a cylin- drical volume, with radius of cross-section ∝ w0

    work page

  3. [2]

    Particles regularly distributed, on layers orthogo- nal to the z-axis, along lines with the symmetry of regular n-sided polygons

    work page

  4. [3]

    Information on the distribution of particles is most easily extracted from either backward or forward scattering, so we consider these simple cases first

    Combinations of the previous two types of distri- butions. Information on the distribution of particles is most easily extracted from either backward or forward scattering, so we consider these simple cases first. We use the index t to label the spheres and the azimuthal moments of the parti- cles’ distribution, defined as | ∑ t exp (iuϕt)|/N, to iden- tify...

    work page

  5. [4]

    Mobley, Radiative Transfer in Natural Waters (Aca- demic Press, 1994)

    C. Mobley, Radiative Transfer in Natural Waters (Aca- demic Press, 1994)

    work page 1994

  6. [5]

    Leach, J

    J. Leach, J. Courtial, K. Skeldon, S. M. Bar- nett, S. Franke-Arnold, and M. J. Padgett, Inter- ferometric methods to measure orbital and spin, or the total angular momentum of a single photon, Phys. Rev. Lett. 92, 013601 (2004)

    work page 2004

  7. [6]

    it is essential that the beam expansion coefficients are calculated with respect to the center of the scattering particle. If we now allow the particle to be centered at some arbitrary position rt we can write the scattered field as F s t (r) = [ aH,s jm SH jm(r − rt) + aE,s jm SE jm(r − rt) ] , (7) where j, m are associated with the angular momenta in the c...

    work page

  8. [7]

    with beam expan- sion coefficients calculated with respect to the center of each particle [21], F s(r) = ∑ t F s t (r) = [ aH,s jm (rt)SH jm(r − rt) +aE,s jm (rt)SE jm(r − rt) ] , (8) where aH,s jm (rt) and aE,s jm (rt) are the coefficients for the particle at rt. When the incident beam consists of an arbitrary super- position of plane waves, at the position ...

    work page

Show all 51 references
  1. [8]

    Mirhosseini, M

    M. Mirhosseini, M. Malik, Z. Shi, and R. W. Boyd, Effi- cient separation of the orbital angular momentum eigen- states of light, Nature Communications 4, 2781 (2013)

    2013

  2. [9]

    X. Gu, M. Krenn, M. Erhard, and A. Zeilinger, Gouy phase radial mode sorter for light: Concepts and experi- ments, Phys. Rev. Lett. 120, 103601 (2018)

    2018

  3. [10]

    N. K. Fontaine, R. Ryf, H. Chen, D. T. Neilson, K. Kim, and J. Carpenter, Laguerre-Gaussian mode sorter, Nature Communications 10, 1865 (2019)

    2019

  4. [11]

    T. A. Klar, S. Jakobs, M. Dyba, A. Egner, and S. W. Hell, Fluorescence microscopy with diffrac- tion resolution barrier broken by stimulated emission, PNAS 97, 8206 (2000)

    2000

  5. [12]

    This is done by applying the asymptotic form of the translation formu- lae and the Jacobi-Anger identity, which are valid in the far field region, see Eq

    in terms of products of func- tions that depend only on r or on rt. This is done by applying the asymptotic form of the translation formu- lae and the Jacobi-Anger identity, which are valid in the far field region, see Eq. (

  6. [13]

    H. He, M. E. J. Friese, N. R. Heckenberg, and H. Rubinsztein-Dunlop, Direct observation of trans- fer of angular momentum to absorptive parti- cles from a laser beam with a phase singularity, Phys. Rev. Lett. 75, 826 (1995)

    1995

  7. [14]

    G. A. Tyler and R. W. Boyd, Influence of atmo- spheric turbulence on the propagation of quantum states of light carrying orbital angular momentum, Opt. Lett. 34, 142 (2009)

    2009

  8. [15]

    Di Leonardo, S

    R. Di Leonardo, S. Keen, J. Leach, C. D. Saunter, G. D. Love, G. Ruocco, and M. J. Padgett, Eigenmodes of a hydrodynamically coupled micron-size multiple-particle ring, Phys. Rev. E 76, 061402 (2007)

    2007

  9. [16]

    G. C. G. Berkhout, M. P. J. Lavery, J. Courtial, M. W. Beijersbergen, and M. J. Padgett, Efficient sorting of or- bital angular momentum states of light, Phys. Rev. Lett. 105, 153601 (2010)

    2010

  10. [17]

    Dudley, T

    A. Dudley, T. Mhlanga, M. Lavery, A. McDonald, F. S. Roux, M. Padgett, and A. Forbes, Efficient sorting of bessel beams, Opt. Express 21, 165 (2013)

    2013

  11. [19]

    A. D. Raki´ c, A. B. Djuriˇ si´ c, J. M. Elazar, and M. L. Majewski, Optical properties of metal- lic films for vertical-cavity optoelectronic devices, Appl. Opt. 37, 5271 (1998)

    1998

  12. [20]

    Imura, K

    K. Imura, K. Ueno, H. Misawa, H. Okamoto, D. McArthur, B. Hourahine, and F. Papoff, Plasmon modes in single gold nanodiscs, Opt. Express 22, 12189 (2014)

    2014

  13. [21]

    Cochenour, L

    B. Cochenour, L. Rodgers, A. Laux, L. Mullen, K. Mor- gan, J. K. Miller, and E. G. Johnson, The detection of objects in a turbid underwater medium using orbital an- gular momentum (OAM), Proc. SPIE 10186, 1018603 (2017)

    2017

  14. [22]

    Balkovsky, G

    E. Balkovsky, G. Falkovich, and A. Fouxon, Intermit- tent distribution of inertial particles in turbulent flows, Phys. Rev. Lett. 86, 2790 (2001)

    2001

  15. [23]

    D. G. Grier, A revolution in optical manipulation, Nature 424, 810 (2003)

    2003

  16. [24]

    Polin, D

    M. Polin, D. G. Grier, and S. R. Quake, Anomalous vi- brational dispersion in holographically trapped colloida l arrays, Phys. Rev. Lett. 96, 088101 (2006)

    2006

  17. [25]

    Papoff and B

    F. Papoff and B. Hourahine, Geometrical Mie theory for resonances in nanoparticles of any shape, Opt. Express 19, 21432 (2011)

    2011

  18. [26]

    Curran, A

    A. Curran, A. Yao, G. Gibson, R. Bowman, J. Cooper, and M. Padgett, Real time characterization of hydrody- namics in optically trapped networks of micro-particles, Journal of Biophotonics 3, 244 (2010)

    2010

  19. [27]

    Biedenharn and J

    L. Biedenharn and J. Louck, Angular Momentum in Quantum Physics (Cambridge University Press, 1985)

    1985

  20. [28]

    M. Berg, C. Sorensen, and A. Chakrabarti, Extinction and the optical theorem. part ii. multiple particles, J. Opt. Soc. Am. A 25, 1514 (2008)

    2008

  21. [29]

    M.I.Mishchenko, J. H. Hovernier, and L. D. Travis, eds., Light scattering by nonspherical particles: Theory, Mea- surements and Applications (Academic Press, 2000)

    2000

  22. [30]

    M. I. Mishchenko, G. Videen, V. A. Babenko, N. G. Khlebtsov, and T. Wriedt, T-matrix theory of electro- magnetic scattering by particles and its applications: a comprehensive reference database, J. Quant. Spectrosc. Radiat. Transfer 88, 357 (2004)

    2004

  23. [31]

    Guti´ errez-Cuevas, N

    R. Guti´ errez-Cuevas, N. J. Moore, and M. A. Alonso, Lorenz-mie scattering of focused light via complex focus fields: An analytic treatment, Phys. Rev. A 97, 053848 (2018)

    2018

  24. [33]

    S. M. Barnett, L. Allen, R. P. Cameron, C. R. Gilson, M. J. Padgett, F. C. Speirits, and A. M. Yao, On the natures of the spin and orbital parts of optical angular momentum, Journal of Optics 18, 064004 (2016)

    2016

  25. [34]

    Jackson, Classical electrodynamics (Wiley, New York, 1999)

    J. Jackson, Classical electrodynamics (Wiley, New York, 1999)

    1999

  26. [35]

    Mie, Beitr¨ age zur optik tr¨ uber medien, speziell kol- loidaler metall¨ osungen, Leipzig, Ann

    G. Mie, Beitr¨ age zur optik tr¨ uber medien, speziell kol- loidaler metall¨ osungen, Leipzig, Ann. Phys. 330, 377 (1908)

    1908

  27. [36]

    McArthur, B

    D. McArthur, B. Hourahine, and F. Papoff, Enhancing ultraviolet spontaneous emission with a designed quan- tum vacuum, Opt. Express 25, 12189 (2017)

    2017

  28. [37]

    McArthur and F

    D. McArthur and F. Papoff, Gap enhanced fluorescence as a road map for the detection of very weakly fluorescent emitters from visible to ultraviolet, Sci. Rep. 7, 14191 (2017)

    2017

  29. [38]

    A. D. Kiselev and D. O. Plutenko, Mie scattering of Laguerre-Gaussian beams: Photonic nanojets and near- field optical vortices, Phys. Rev. A 89, 043803 (2014)

    2014

  30. [39]

    (6.58) of Ref

    We note that in Eq. (6.58) of Ref. [17], the authors use ˆψ+ = − ˆ e+ and that there is a factor of i between their definition of Njm and ours. 17

  31. [40]

    L. D. Barron, Molecular Light Scattering and Optical Ac- tivity, 2nd ed. (Cambridge University Press, Cambridge, United Kingdom, 2004)

    2004

  32. [41]

    M. I. Mishchenko, L. D. Travis, and D. W. Mackowski, T-matrix computations of light scat- tering by nonspherical particles: A review, J. Quant. Spectrosc. Radiat. Transfer 55, 535 (1996)

    1996

  33. [42]

    P. C. Waterman, Symmetry, Unitarity, and Geometry in Electromagnetic Scattering, Phys. Rev. D 3, 825 (1971)

    1971

  34. [43]

    As it should be finite everywhere J E,H j′m′ are written in terms of regular Bessel functions

    The incident field is the field that would exist without a scatterer and therefore includes both incoming and out- going parts. As it should be finite everywhere J E,H j′m′ are written in terms of regular Bessel functions. Note that the electric and magnetic multipoles are ex- ac...

  35. [44]

    Doicu, T

    A. Doicu, T. Wriedt, and Y. Eremin, Light Scattering by Systems of Particles (Springer, 2006)

    2006

  36. [45]

    P. C. Waterman, The T-matrix revisited, JOSA A 24, 2257 (2007)

    2007

  37. [46]

    A. E. Siegman, Lasers (University Science Books, Mill Valley, California, 1986)

    1986

  38. [47]

    Allen, M

    L. Allen, M. J. Padgett, and M. Babiker, IV The orbital angular momentum of light (Elsevier, 1999) pp. 291 – 372

    1999

  39. [48]

    H. A. Haus, Waves and Fields in Optoelectronics (Pren- tice Hall, Englewood Cliffs, New Jersey, 1984)

    1984

  40. [51]

    Although no two-dimensional structure can be truly chi- ral, they may still exhibit the properties associated with chiral structures [40]

  41. [52]

    (6.58) of Ref

    We note that in Eq. (6.58) of Ref. [17], the authors use ˆψ+ = − ˆ e+ and that there is a factor of i between their definition of Njm and ours

  42. [55]

    in Appendix . In the far field region, the field scattered by all the particles is F s∞(θ, ϕ) = exp ( −ikˆr · rt) [ AH,t jm (rt)SH∞ jm (θ, ϕ) + AE,t jm (rt)SE∞ jm (θ, ϕ) ] = exp ( −ik|rt| cos θ cos θt) ∞∑ n=−∞ (−i)n exp (−inϕt)Jn(k|rt| sin θ sin θt) × [ AH,t jm (rt)SH∞ jm (θ, ϕ)...

  43. [59]

    This ex- plains why the dominant peak, corresponding to largest harmonic with u = 0, is always observed at lz = ℓ

    that the dominant terms are those with u = lz − ℓ and the same polarization as the incident beam. This ex- plains why the dominant peak, corresponding to largest harmonic with u = 0, is always observed at lz = ℓ. We also remark that higher order incident beams have an equivale...

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Reviewed August 14, 2026 · model on record in the stance chip above.