Eigenmode beam optimisation for optical micro-manipulation

Michael Mazilu

REVIEW 4 major objections 7 minor 16 references

Eigenmode beam optimisation for optical micro-manipulation

T0 review · 4 major / 7 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper shows that the optimal optical trap is the largest-eigenvalue eigenvector of a Hermitian momentum-transfer matrix, and that this eigenmode delivers a ten-fold increase in trap stiffness over a Gaussian beam of equal power.

desk verdict The optimal-beam claim rests on an unproven and possibly mistyped momentum-transfer matrix, but the OEi extension to 3D Mie scattering is a genuinely useful idea that deserves a serious revision, not a desk rejection. read the letter →

arxiv 1908.01179 v1 pith:DT3DDMKQ submitted 2019-08-03 physics.optics

Michael Mazilu This is my paper · ORCID

classification physics.optics

keywords opticaleigenmodestrappingMiescatteringbeamshapecoefficientsmomentumtransfertrapstiffnessBesselbeamsHermitianmatrix

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 establishes a recipe for finding the best light beam to trap and manipulate a microscopic sphere. Using Mie scattering, it writes the optical force on the particle as a Hermitian quadratic form in the coefficients of the illuminating beam; the eigenvectors of this form are optical eigenmodes, each with a real eigenvalue equal to the force that beam exerts at fixed power. The eigenvector with the largest eigenvalue is therefore the optimal beam for momentum transfer. Restricting to cylindrically symmetric beams and displacing the particle gives the optimal transverse trap, which in the paper's example is ten times stiffer than a Gaussian beam of the same power. The same logic extends to longitudinal tractor beams, with a non-commutativity caveat between the two directions.

What carries the argument

The central object is the momentum-transfer matrix $M_j^k$, a Hermitian matrix—equal to its own conjugate transpose—defined by expressing the $z$-component of the optical force as the quadratic form $F_z = g_k M_j^k g_j$ in the beam-shape coefficients $g_j$. The beam-shape coefficients come from projecting vector Bessel beams onto vector spherical harmonics, and the Mie scattering coefficients enter through the combinations $b_k + b_j^* - 2b_k b_j^*$ and $a_k + a_j^* - 2a_k a_j^*$. The eigenvectors of $M$ are the optical eigenmodes: orthogonal field profiles that contribute independently to the force, with eigenvalues giving the force at constant incident power. Choosing the largest eigenvalue solves the beam-optimisation problem.

What would settle it

A direct check would be to evaluate $M_j^k$ for two indices with $n_j \neq n_k$ and verify conjugate symmetry $M_j^k = (M_k^j)^*$; the printed matrix elements are not obviously symmetric under $j \leftrightarrow k$, so this computation would settle whether the eigenmode optimisation is valid.

Watch

Extended reading notes

Core claim

The central discovery is a variational principle for optical trapping: among all incident fields of a given power, the one that maximises the force on a spherical particle is the optical eigenmode with the largest eigenvalue of the momentum-transfer matrix $M_j^k$ defined in Eq. (2). The matrix is built from beam-shape coefficients and Mie scattering coefficients, and its Hermiticity makes the eigenvalues real and the eigenvectors orthogonal. In the numerical example, a particle of diameter $1.5\$\lambda$$ and refractive index $1.5$ displaced in a cylindrically symmetric beam exhibits a transverse trap stiffness roughly ten times larger for the optimal eigenmode than for a Gaussian beam of the same power (Fig. 4). Because the transverse and longitudinal force matrices do not commute, simultaneous optimisation of both directions is impossible; the paper instead optimises the phase between the transverse eigenmode and the longitudinal tractor-beam eigenmode.

Load-bearing premise

The load-bearing premise is that the matrix $M$ defined in Eq. (2) is Hermitian—conjugate-symmetric, so its eigenvalues are real—as the paper asserts by construction without showing the derivation; if that symmetry fails, the eigenvector ranking that selects the optimal beam is not defined.

Editorial extensions

If this is right

Given a particle size, refractive index, and numerical aperture, the optimal trapping beam is computable by diagonalising a finite matrix rather than by scanning trial beams.
The largest-eigenvalue eigenmode provides a benchmark for trap stiffness: any other beam of the same power can be compared against it.
The eigenmode decomposition gives a reduced basis, so force calculations can keep only the modes with significant eigenvalues instead of the full Hilbert space.
Because the transverse and longitudinal force operators do not commute, no single beam can simultaneously be the optimal transverse trap and the optimal tractor beam; a phase-optimised superposition is needed.
The number of significant optical eigenmodes grows with particle size, so larger particles offer more optical degrees of freedom for trapping.

Reading between the lines

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

If the method is sound, the same Hermitian-eigenmode construction should also yield optimal beams for other quadratic measures such as angular momentum transfer or torque, extending beyond simple trapping.
The non-commutativity of transverse and longitudinal force matrices suggests a fundamental trade-off for single-sided optical traps; mapping this Pareto frontier for various particle sizes would be a natural test of the framework.
Because the eigenmode basis is complete as the Mie order grows, the approach could be transferred to non-spherical particles by replacing Mie coefficients with T-matrix coefficients.
The predicted ten-fold stiffness enhancement is directly testable: building the optimal eigenmode with a spatial light modulator and comparing its trap stiffness with a Gaussian beam of equal power would confirm or refute the whole chain.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The core idea is sound and worth pursuing: Mazilu extends his optical eigenmode framework to full 3D Mie scattering for spheres, deriving a momentum-transfer matrix in a vector Bessel basis and using its largest-eigenvalue eigenvector to design trapping beams. The numerical example reports a tenfold stiffness improvement over a Gaussian beam. If the matrix is right, this is a useful tool for the micromanipulation community.

What is actually new: the 3D spherical generalization, the Bessel basis beam-shape coefficients, and the observation that transverse and longitudinal trapping operators do not commute, so the optimization has to trade one against the other. That last point is honest and gives a real sense of the structure of the problem. The paper also connects the eigenmodes to whispering-gallery-like angular structures, which is a nice touch.

Now the soft spots. The central matrix M_j^k is asserted, not derived. The sentence “by construction Hermitian” appears in Section 2.3, but no construction is shown. Looking at the printed entries in Eq. (2), things do not line up: the polarization index p_k=1 is labeled TM yet multiplies the magnetic Mie coefficient b, while p_k=2 is TE but multiplies the electric coefficient a. The nearest-neighbor n-coupling radicands contain n_j^2 - m_k^2, which can be negative while the corresponding n_k^2 - m_k^2 is positive. That is at least a typographical risk, but the reader cannot check because the derivation is absent.

There is also a normalization problem. The claim that the largest eigenvalue gives the largest momentum transfer at constant incident power requires that the Euclidean norm of the coefficient vector corresponds to power. No Gram matrix or power normalization for the Bessel basis is given. Without that, “constant power” is undefined.

The numerical example is illustrative, not reproducible. Figure 4 gives no details on the Gaussian comparison, the particle parameters beyond diameter and index, or any error/robustness discussion. A tenfold claim needs more than a single curve.

So the verdict is conditional, as the reader said. The approach is plausible, the paper is honest about its limitations, but the central pillar — Eq. (2) — has to be fully derived and verified. I would send this to peer review, but with a major-revision requirement: full derivation, Hermiticity check, power normalization, and a reproducible numerical section.

For the reading group: maybe — good for a methodology discussion, not a finished result. I would not cite the 10x number until the derivation is out.

Recommendation: send to a serious referee and flag the missing derivation as the make-or-break issue.

Referee Report

4 major / 7 minor

Summary. The paper applies the optical eigenmode (OEi) method to optical trapping of spherical Mie particles. It represents the incident field as a superposition of vector Bessel beams, defines a momentum-transfer matrix M from the Maxwell stress tensor, and claims that the eigenvectors of this Hermitian matrix are orthogonal optical eigenmodes whose eigenvalues give the force in a chosen direction. The mode with the largest eigenvalue is asserted to be the beam delivering the largest momentum transfer at constant incident power. A numerical example reports a ten-fold enhancement of transverse trap stiffness relative to a Gaussian beam, and the paper also discusses longitudinal 'tractor-beam' trapping. The central conceptual idea is promising, but the derivation and numerical support are incomplete as written.

Significance. If the momentum-transfer matrix is correctly derived and the power-normalization issue is resolved, the approach would provide a systematic, basis-set method for beam optimization in optical micromanipulation, extending earlier OEi work to 3D Mie particles and offering potential advantages for high-NA systems and resonant particles. The eigenvalue decomposition is elegant and could enable dimensionality reduction in force calculations. The paper does not provide code, data, or machine-checked derivations, so the credibility rests entirely on the analytic derivation and the numerical example. The central claim is plausible and of interest to the optical trapping community, but the current manuscript does not yet establish it.

major comments (4)

[Section 2.2, Eq. (2)] The matrix M_j^k is stated to be Hermitian 'by construction,' but no derivation from Eq. (1) is supplied, and the printed expression is not manifestly Hermitian. The nearest-neighbor coupling contains terms such as δ_{n_j+1,n_k}√((1−n_k)^2(n_j^2−m_k^2)/(n_k^2(4n_k^2−1))) and δ_{n_j,n_k+1}√((1−n_j)^2(n_k^2−m_k^2)/(n_j^2(4n_j^2−1))); the first radicand can be negative when |m_k|>n_j, and the second radicand appears to require n_k^2−m_j^2 for conjugate symmetry. In addition, the polarization diagonal term pairs p_k=1 (TM) with the magnetic Mie coefficient b and p_k=2 (TE) with the electric coefficient a, which is the reverse of the usual association. Please derive M_j^k step by step from the Maxwell stress tensor, define all index ranges and summation conventions, and demonstrate explicitly that M_j^k = (M_k^j)^*.
[Section 2.3] The optimality claim that the optical eigenmode with the largest eigenvalue delivers the largest momentum transfer at constant incident power assumes that the Euclidean norm of the beam-shape coefficient vector g is proportional to the incident power. For vector Bessel beams this is not established: the time-averaged power is a separate quadratic functional of the coefficients, generically with a non-identity Gram matrix. If the Bessel basis is not orthonormal with respect to the power measure, then the eigenvectors of M_j^k need not maximize the force at fixed power. Please define the power normalization explicitly, state the inner product with respect to which M is Hermitian, and show how the eigenvalue ordering relates to the force at constant power (or formulate a generalized eigenvalue problem).
[Section 3.2, Figure 4] The claimed ten-fold enhancement of transverse trap stiffness is not reproducible from the information given. The manuscript does not specify the maximum multipole order (l_max and n_max) used in the Mie and Bessel expansions, the numerical aperture (cone angle γ), the medium refractive index, the particle displacement at which the transverse force is evaluated, or the normalization procedure applied to the Gaussian and eigenmode beams. Please provide these details and include a convergence check showing that the leading eigenvalue and eigenvector are stable with respect to basis size. Without this, the numerical result remains unverified.
[Abstract and Section 2.4] The abstract and parts of Section 2.4 state that the method defines 'the optimal trapping beam' without qualification, but the optimization is explicitly restricted to cylindrically symmetric beams. Section 3.2 correctly says 'Within this restricted Hilbert space,' yet the broader language elsewhere overstates the result. Please either qualify the conclusion as optimal only within the cylindrical-symmetric subclass, or provide a symmetry or averaging argument showing that the unrestricted optimum can always be chosen to be cylindrically symmetric.

minor comments (7)

[Abstract] The sentence 'This relationship defines also a set of orthogonal optical eigenmodes' appears twice in the abstract; the duplicate should be removed.
[Section 2.2, Eq. (2)] The phrase 'where g_k = g^*_k' is confusing; state explicitly that the quadratic form is F_z = g^† M g with a defined conjugation and index ordering.
[Section 2.1] In the definition B_l(k_t ρ) = (i)^l J_l(k_t ρ)e^{ilφ}, the missing space before 'with ρ = ...' makes the sentence hard to read, and the symbol J_l should be defined as the Bessel function of the first kind (which is only mentioned later in the text).
[References] Reference [9] appears to duplicate reference [5] (same title and journal); please combine or delete the duplicate.
[Figures 1–3] The figure captions do not specify the axes, the sorting order of the eigenvalues, or the color/phase mapping used in the angular intensity distributions; adding these details would improve interpretability.
[Section 3.2, Figure 4] The label 'arbitrary units' on the vertical axis of the force plot makes the ten-fold enhancement claim less transparent; normalize both curves to the same incident power and report the stiffness ratio with a statement of numerical uncertainty.
[Introduction] The phrase 'optical eigemodes' in the last paragraph of the Introduction is a typo and should read 'optical eigenmodes'.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the optimal beam is the dominant eigenvector of an independently defined momentum-transfer matrix, and the reported enhancement is a model output, not a fitted input.

full rationale

The derivation chain is a standard Rayleigh-quotient optimisation. Eq. (2) defines the z-force as the quadratic form g† M g, with M expressed in terms of Mie coefficients and Bessel beam-shape coefficients. The Hermitian matrix M is presented as following from the Maxwell stress tensor and Mie scattering, not as a quantity fitted to the target beam. The claim that the largest-eigenvalue eigenvector delivers maximum momentum transfer at fixed incident power is the textbook spectral theorem for Hermitian matrices; it is a mathematical consequence of the definition of eigenvalue, not an empirical prediction fitted to data. The numerical ten-fold stiffness comparison in Fig. 4 is a simulation output produced by the same model, so no fitted parameter is renamed as a prediction. The heavy self-citation of the OEi framework is noticeable, but the load-bearing object in this paper—the specific matrix M_j^k and its eigen-decomposition for Mie scattering—is not carried by those citations: the citations supply a general quadratic-form viewpoint, while the Hermitian character of M is asserted 'by construction' rather than derived. That omission, and the absence of an explicit power-normalisation Gram matrix, are correctness risks; they do not make the derivation circular because no equation of the paper is equivalent to its own output by construction.

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

The paper fits no data and introduces no new physical entities. Its central claim depends on the standard Mie scattering framework, the quadratic-form assumption for optical forces, the completeness of the Bessel beam basis, the cylindrical symmetry restriction, and the unproven Hermiticity of the force matrix.

assumptions (5)

domain assumption Mie scattering theory for spherical particles gives the exact scattered field as a function of the incident field.
Used in Section 2 to compute the momentum transfer matrix; assumes the particle is a homogeneous sphere with known refractive index.
domain assumption The optical force is a quadratic Hermitian form in the beam shape coefficients.
Section 2.2 states 'we remark that the optical force ... can be expressed in a quadratic form with respect to the beam shape coefficients.' This is the foundation of the OEi method and is not proven here.
domain assumption The set of vector Bessel beams provides a sufficient basis for the incident field in the optimization.
Section 2.1 defines the incident field as a superposition of Bessel beams; the paper does not prove the optimal trap lies in this basis.
ad hoc to paper Restriction to cylindrical symmetric beams is sufficient for optimal transverse trapping.
Section 2.4 imposes this restriction to eliminate transverse forces; it limits the optimizer to a subspace, but the abstract claims unrestricted optimal beams.
ad hoc to paper The matrix M_j^k is Hermitian, so its eigenvalues are real and eigenvectors are orthogonal.
Section 2.3 states 'by construction Hermitian' without demonstration; the printed matrix elements do not obviously satisfy M_j^k = (M_k^j)^*.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Eigenmode beam optimisation for optical micro-manipulation." pith.science (2026). https://pith.science/paper/DT3DDMKQ

@misc{pith2026190801179,
  author       = {Pith},
  title        = {Pith review of: Eigenmode beam optimisation for optical micro-manipulation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DT3DDMKQ}},
  note         = {Machine review of arXiv:1908.01179}
}

read the original abstract

Optical micro-manipulation and trapping of micro-particles delivers a mechanical system in direct interaction with a beam of light. In this interaction, the optical properties such as polarisation, beam profile and wavelength of the trapping beam are important. Different beams are associated with different momentum transfer, trap stiffness and stabilisation properties, for example. One method to determine the best beam profile is through the use of the optical eigenmode approach. To use this method, we employ Mie scattering theory which enables the exact determination of the scattered field as a function of the incident field. More precisely, this approach allows us to calculate the Hermitian relationship between the incident field and the optical forces acting on the scattering objects. This Hermitian relationship defines also a set of orthogonal optical eigenmodes which deliver a natural basis to describe momentum transfer in light-matter interactions. This relationship defines also a set of orthogonal optical eigenmodes. Using these modes it is possible to define, for each numerical aperture, particle size or geometry, the optimal trapping beam.

Figures

Figures reproduced from arXiv: 1908.01179 by the authors.

**Figure 2.** (a) Eigenvalue representation of the bound linear momentum, [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Angular intensity distribution of the optical eigenmodes for two particles of different [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: (left) Transverse trapping forces for a Gaussian beam in yellow and for the optical [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

**Figure 5.** Figure 5: (left) Longitudinal trapping forces for a Gaussian beam in black and for the optical [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

16 extracted references · 16 canonical work pages

[1]

Mie scattering eigenmodes for optical trapping

Michael Mazilu. Mie scattering eigenmodes for optical trapping. arXiv e-prints, page arXiv:1704.08779, 2017

work page Pith review arXiv 2017
[2]

Optimal trapping beam for spherical micro-particles (conference presen- tation)

Michael Mazilu. Optimal trapping beam for spherical micro-particles (conference presen- tation). Proc. SPIE 10347, Optical Trapping and Optical Micromanipulation XIV, page 103470M, 2017

work page 2017
[3]

Nanophotonics generated optimal beam for optical trapping in vacuum.SPIE Nanophotonics Australasia, 10456(143):10456–143, 2017

Michael Mazilu. Nanophotonics generated optimal beam for optical trapping in vacuum.SPIE Nanophotonics Australasia, 10456(143):10456–143, 2017

work page 2017
[4]

Optical eigenmode description of single-photon light-matter interactions

Kyle Ballantine and Michael Mazilu. Optical eigenmode description of single-photon light-matter interactions. Proc. SPIE 10935, Complex Light and Optical Forces XIII , 10935:109351B, 2019

work page 2019
[5]

Mazilu, J

M. Mazilu, J. Baumgartl, S. Kosmeier, and K. Dholakia. Optical eigenmodes; exploiting the quadratic nature of the energy ﬂux and of scattering interactions.Opt. Express, 19(2):933–945, 2011

work page 2011
[6]

Spin and angular momentum operators and their conservation.J

Michael Mazilu. Spin and angular momentum operators and their conservation.J. Opt. A, 11(9):094005, 2009. 7

work page 2009
[7]

Optical eigenmodes; spin and angular momentum

Michael Mazilu. Optical eigenmodes; spin and angular momentum. J. Opt., 13(6):064009, 2011

work page 2011
[8]

Coherent control of plasmonic nanoantennas using optical eigenmodes

Sebastian Kosmeier, Anna Chiara De Luca, Svetlana Zolotovskaya, Andrea Di Falco, Kishan Dholakia, and Michael Mazilu. Coherent control of plasmonic nanoantennas using optical eigenmodes. Scientiﬁc Reports, 3:1808 EP –, 2013. Article

work page 2013

Show all 16 references

[9]

Optical Eigenmodes; exploiting the quadratic nature of the energy ﬂux and of scattering interactions.Opt

Michael Mazilu, J Baumgartl, S Kosmeier, and K Dholakia. Optical Eigenmodes; exploiting the quadratic nature of the energy ﬂux and of scattering interactions.Opt. Express, 19(2):933– 945, 2011

2011
[10]

Joerg Baumgartl, Sebastian Kosmeier, Michael Mazilu, Edward T. F. Rogers, Nikolay I Zhe- ludev, and Kishan Dholakia. Far ﬁeld subwavelength focusing using optical eigenmodes.Appl. Phys. Lett., 98(18):181109, 2011

2011
[11]

Resonance enhanced optical manipulation: the push and pull of light.Proc

Michael Mazilu and Kishan Dholakia. Resonance enhanced optical manipulation: the push and pull of light.Proc. SPIE 8458, Optical Trapping and Optical Micromanipulation IX, page 845809, 2012

2012
[12]

Axial optical trapping eﬃciency through a dielectric interface

Antonio Alvaro Ranha Neves, Adriana Fontes, Carlos Lenz Cesar, Andrea Camposeo, Roberto Cingolani, and Dario Pisignano. Axial optical trapping eﬃciency through a dielectric interface. Phys. Rev. E, 76:061917, 2007

2007
[13]

Optical eigenmode imaging

Anna Chiara De Luca, Sebastian Kosmeier, Kishan Dholakia, and Michael Mazilu. Optical eigenmode imaging. Phys Rev A, 84(2):021803(R), 2011

2011
[14]

Enhanced Optical Manipulation of Cells Using Antireﬂection Coated Mi- croparticles

Derek Craig, Alison McDonald, Michael Mazilu, Helen Rendall, Frank Gunn-Moore, and Kishan Dholakia. Enhanced Optical Manipulation of Cells Using Antireﬂection Coated Mi- croparticles. ACS Photonics, 2(10):1403–1409, 2015

2015
[15]

Orbital-angular-momentum transfer to optically levitated microparticles in vacuum

Michael Mazilu, Yoshihiko Arita, Tom Vettenburg, Juan M Auñón, Ewan M Wright, and Kishan Dholakia. Orbital-angular-momentum transfer to optically levitated microparticles in vacuum. Physical Review A - Atomic, Molecular, and Optical Physics, 94(5):053821, 2016

2016
[16]

Is there an optimal basis to maximise optical information transfer?Sci

Mingzhou Chen, Kishan Dholakia, and Michael Mazilu. Is there an optimal basis to maximise optical information transfer?Sci. Rep., 6:22821, 2016. 8

2016

Pith tools

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

[1] [1]

Mie scattering eigenmodes for optical trapping

Michael Mazilu. Mie scattering eigenmodes for optical trapping. arXiv e-prints, page arXiv:1704.08779, 2017

work page Pith review arXiv 2017

[2] [2]

Optimal trapping beam for spherical micro-particles (conference presen- tation)

Michael Mazilu. Optimal trapping beam for spherical micro-particles (conference presen- tation). Proc. SPIE 10347, Optical Trapping and Optical Micromanipulation XIV, page 103470M, 2017

work page 2017

[3] [3]

Nanophotonics generated optimal beam for optical trapping in vacuum.SPIE Nanophotonics Australasia, 10456(143):10456–143, 2017

Michael Mazilu. Nanophotonics generated optimal beam for optical trapping in vacuum.SPIE Nanophotonics Australasia, 10456(143):10456–143, 2017

work page 2017

[4] [4]

Optical eigenmode description of single-photon light-matter interactions

Kyle Ballantine and Michael Mazilu. Optical eigenmode description of single-photon light-matter interactions. Proc. SPIE 10935, Complex Light and Optical Forces XIII , 10935:109351B, 2019

work page 2019

[5] [5]

Mazilu, J

M. Mazilu, J. Baumgartl, S. Kosmeier, and K. Dholakia. Optical eigenmodes; exploiting the quadratic nature of the energy ﬂux and of scattering interactions.Opt. Express, 19(2):933–945, 2011

work page 2011

[6] [6]

Spin and angular momentum operators and their conservation.J

Michael Mazilu. Spin and angular momentum operators and their conservation.J. Opt. A, 11(9):094005, 2009. 7

work page 2009

[7] [7]

Optical eigenmodes; spin and angular momentum

Michael Mazilu. Optical eigenmodes; spin and angular momentum. J. Opt., 13(6):064009, 2011

work page 2011

[8] [8]

Coherent control of plasmonic nanoantennas using optical eigenmodes

Sebastian Kosmeier, Anna Chiara De Luca, Svetlana Zolotovskaya, Andrea Di Falco, Kishan Dholakia, and Michael Mazilu. Coherent control of plasmonic nanoantennas using optical eigenmodes. Scientiﬁc Reports, 3:1808 EP –, 2013. Article

work page 2013